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From: <da...@us...> - 2008-09-30 10:45:33
|
Revision: 984
http://axiom.svn.sourceforge.net/axiom/?rev=984&view=rev
Author: daly
Date: 2008-09-30 10:45:19 +0000 (Tue, 30 Sep 2008)
Log Message:
-----------
20080928 tpd books/bookvol10.2 add trigcat categories
20080928 tpd books/ps/v102trigonometricfunctioncategory.ps
20080928 tpd books/ps/v102transcendentalfunctioncategory.ps
20080928 tpd books/ps/v102specialfunctioncategory.ps
20080928 tpd books/ps/v102primitivefunctioncategory.ps
20080928 tpd books/ps/v102liouvillianfunctioncategory.ps added
20080928 tpd books/ps/v102hyperbolicfunctioncategory.ps added
20080928 tpd books/ps/v102elementaryfunctioncategory.ps added
20080928 tpd books/ps/v102combinatorialfunctioncategory.ps added
20080928 tpd books/ps/v102arctrigonometricfunctioncategory.ps added
20080928 tpd books/ps/v102archyperbolicfunctioncategory.ps added
20080928 tpd src/algebra/Makefile remove trigcat
20080928 tpd src/algebra/trigcat.spad absorbed into bookvol10.2
Modified Paths:
--------------
trunk/axiom/books/bookvol10.2.pamphlet
trunk/axiom/changelog
trunk/axiom/src/algebra/Makefile.pamphlet
Added Paths:
-----------
trunk/axiom/books/ps/v102archyperbolicfunctioncategory.ps
trunk/axiom/books/ps/v102arctrigonometricfunctioncategory.ps
trunk/axiom/books/ps/v102combinatorialfunctioncategory.ps
trunk/axiom/books/ps/v102elementaryfunctioncategory.ps
trunk/axiom/books/ps/v102hyperbolicfunctioncategory.ps
trunk/axiom/books/ps/v102liouvillianfunctioncategory.ps
trunk/axiom/books/ps/v102primitivefunctioncategory.ps
trunk/axiom/books/ps/v102specialfunctioncategory.ps
trunk/axiom/books/ps/v102transcendentalfunctioncategory.ps
trunk/axiom/books/ps/v102trigonometricfunctioncategory.ps
Removed Paths:
-------------
trunk/axiom/src/algebra/trigcat.spad.pamphlet
Modified: trunk/axiom/books/bookvol10.2.pamphlet
===================================================================
--- trunk/axiom/books/bookvol10.2.pamphlet 2008-09-28 22:36:41 UTC (rev 983)
+++ trunk/axiom/books/bookvol10.2.pamphlet 2008-09-30 10:45:19 UTC (rev 984)
@@ -286,13 +286,21 @@
This is the root of the category hierarchy and is not represented by code.
{\bf See:}\\
+\pageto{ArcHyperbolicFunctionCategory}{AHYP}
+\pageto{ArcTrigonometricFunctionCategory}{ATRIG}
\pageto{BasicType}{BASTYPE}
\pageto{CoercibleTo}{KOERCE}
+\pageto{CombinatorialFunctionCategory}{CFCAT}
\pageto{ConvertibleTo}{KONVERT}
+\pageto{ElementaryFunctionCategory}{ELEMFUN}
\pageto{Eltable}{ELTAB}
+\pageto{HyperbolicFunctionCategory}{HYPCAT}
\pageto{InnerEvalable}{IEVALAB}
\pageto{Logic}{LOGIC}
+\pageto{PrimitiveFunctionCategory}{PRIMCAT}
\pageto{RetractableTo}{RETRACT}
+\pageto{SpecialFunctionCategory}{SPFCAT}
+\pageto{TrigonometricFunctionCategory}{TRIGCAT}
\pageto{Type}{TYPE}
<<CATEGORY.dotabb>>=
@@ -316,6 +324,160 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{ArcHyperbolicFunctionCategory}{AHYP}
+\pagepic{ps/v102archyperbolicfunctioncategory.ps}{AHYP}{1.00}
+
+{\bf See:}\\
+\pageto{TranscendentalFunctionCategory}{TRANFUN}
+\pagefrom{Category}{CATEGORY}
+
+{\bf Exports:}\\
+\begin{tabular}{llllll}
+\cross{AHYP}{acosh} &
+\cross{AHYP}{acoth} &
+\cross{AHYP}{acsch} &
+\cross{AHYP}{asech} &
+\cross{AHYP}{asinh} &
+\cross{AHYP}{atanh}
+\end{tabular}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ acosh : % -> %
+ acoth : % -> %
+ acsch : % -> %
+ asech : % -> %
+ asinh : % -> %
+ atanh : % -> %
+\end{verbatim}
+
+<<category AHYP ArcHyperbolicFunctionCategory>>=
+)abbrev category AHYP ArcHyperbolicFunctionCategory
+++ Category for the inverse hyperbolic trigonometric functions
+++ Author: ???
+++ Date Created: ???
+++ Date Last Updated: 14 May 1991
+++ Description:
+++ Category for the inverse hyperbolic trigonometric functions;
+ArcHyperbolicFunctionCategory(): Category == with
+ acosh: $ -> $ ++ acosh(x) returns the hyperbolic arc-cosine of x.
+ acoth: $ -> $ ++ acoth(x) returns the hyperbolic arc-cotangent of x.
+ acsch: $ -> $ ++ acsch(x) returns the hyperbolic arc-cosecant of x.
+ asech: $ -> $ ++ asech(x) returns the hyperbolic arc-secant of x.
+ asinh: $ -> $ ++ asinh(x) returns the hyperbolic arc-sine of x.
+ atanh: $ -> $ ++ atanh(x) returns the hyperbolic arc-tangent of x.
+
+@
+<<AHYP.dotabb>>=
+"AHYP"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=AHYP"];
+"AHYP" -> "CATEGORY"
+
+@
+<<AHYP.dotfull>>=
+"ArcHyperbolicFunctionCategory()"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=AHYP"];
+"ArcHyperbolicFunctionCategory()" -> "Category"
+
+@
+<<AHYP.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"ArcHyperbolicFunctionCategory()" [color=lightblue];
+"ArcHyperbolicFunctionCategory()" -> "Category"
+
+"Category" [color=lightblue];
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{ArcTrigonometricFunctionCategory}{ATRIG}
+\pagepic{ps/v102arctrigonometricfunctioncategory.ps}{ATRIG}{1.00}
+
+The {\tt asec} and {\tt acsc} functions were modified to include an
+intermediate test to check that the argument has a reciprocal values.
+
+{\bf See:}\\
+\pageto{TranscendentalFunctionCategory}{TRANFUN}
+\pagefrom{Category}{CATEGORY}
+
+{\bf Exports:}\\
+\begin{tabular}{llllll}
+\cross{ATRIG}{acos} &
+\cross{ATRIG}{acot} &
+\cross{ATRIG}{acsc} &
+\cross{ATRIG}{asec} &
+\cross{ATRIG}{asin} &
+\cross{ATRIG}{atan}
+\end{tabular}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ acos : % -> %
+ acot : % -> %
+ asin : % -> %
+ atan : % -> %
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ acsc : % -> %
+ asec : % -> %
+\end{verbatim}
+
+<<category ATRIG ArcTrigonometricFunctionCategory>>=
+)abbrev category ATRIG ArcTrigonometricFunctionCategory
+++ Category for the inverse trigonometric functions
+++ Author: ???
+++ Date Created: ???
+++ Date Last Updated: 14 May 1991
+++ Description: Category for the inverse trigonometric functions;
+ArcTrigonometricFunctionCategory(): Category == with
+ acos: $ -> $ ++ acos(x) returns the arc-cosine of x.
+ acot: $ -> $ ++ acot(x) returns the arc-cotangent of x.
+ acsc: $ -> $ ++ acsc(x) returns the arc-cosecant of x.
+ asec: $ -> $ ++ asec(x) returns the arc-secant of x.
+ asin: $ -> $ ++ asin(x) returns the arc-sine of x.
+ atan: $ -> $ ++ atan(x) returns the arc-tangent of x.
+ add
+ if $ has Ring then
+ asec(x) ==
+ (a := recip x) case "failed" => error "asec: no reciprocal"
+ acos(a::$)
+ acsc(x) ==
+ (a := recip x) case "failed" => error "acsc: no reciprocal"
+ asin(a::$)
+
+@
+<<ATRIG.dotabb>>=
+"ATRIG"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ATRIG"];
+"ATRIG" -> "CATEGORY"
+
+@
+<<ATRIG.dotfull>>=
+"ArcTrigonometricFunctionCategory()"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ATRIG"];
+"ArcTrigonometricFunctionCategory()" -> "Category"
+
+@
+<<ATRIG.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"ArcTrigonometricFunctionCategory()" [color=lightblue];
+"ArcTrigonometricFunctionCategory()" -> "Category"
+
+"Category" [color=lightblue];
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{AttributeRegistry}{ATTREG}
\pagepic{ps/v102attributeregistry.ps}{ATTREG}{1.00}
@@ -610,6 +772,74 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{CombinatorialFunctionCategory}{CFCAT}
+\pagepic{ps/v102combinatorialfunctioncategory.ps}{CFCAT}{1.00}
+
+{\bf See:}\\
+\pagefrom{Category}{CATEGORY}
+
+{\bf Exports:}\\
+\begin{tabular}{lll}
+\cross{CFCAT}{binomial} &
+\cross{CFCAT}{factorial} &
+\cross{CFCAT}{permutation}
+\end{tabular}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ binomial : (%,%) -> %
+ factorial : % -> %
+ permutation : (%,%) -> %
+\end{verbatim}
+
+<<category CFCAT CombinatorialFunctionCategory>>=
+)abbrev category CFCAT CombinatorialFunctionCategory
+++ Category for the usual combinatorial functions
+++ Author: Manuel Bronstein
+++ Date Created: ???
+++ Date Last Updated: 14 May 1991
+++ Description: Category for the usual combinatorial functions;
+CombinatorialFunctionCategory(): Category == with
+ binomial : ($, $) -> $
+ ++ binomial(n,r) returns the \spad{(n,r)} binomial coefficient
+ ++ (often denoted in the literature by \spad{C(n,r)}).
+ ++ Note: \spad{C(n,r) = n!/(r!(n-r)!)} where \spad{n >= r >= 0}.
+ factorial : $ -> $
+ ++ factorial(n) computes the factorial of n
+ ++ (denoted in the literature by \spad{n!})
+ ++ Note: \spad{n! = n (n-1)! when n > 0}; also, \spad{0! = 1}.
+ permutation: ($, $) -> $
+ ++ permutation(n, m) returns the number of
+ ++ permutations of n objects taken m at a time.
+ ++ Note: \spad{permutation(n,m) = n!/(n-m)!}.
+
+@
+<<CFCAT.dotabb>>=
+"CFCAT"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=CFCAT"];
+"CFCAT" -> "CATEGORY"
+
+@
+<<CFCAT.dotfull>>=
+"CombinatorialFunctionCategory()"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=CFCAT"];
+"CombinatorialFunctionCategory()" -> "Category"
+
+@
+<<CFCAT.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"CombinatorialFunctionCategory()" [color=lightblue];
+"CombinatorialFunctionCategory()" -> "Category"
+
+"Category" [color=lightblue];
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{ConvertibleTo}{KONVERT}
\pagepic{ps/v102konvert.ps}{KONVERT}{1.00}
@@ -728,6 +958,73 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{ElementaryFunctionCategory}{ELEMFUN}
+\pagepic{ps/v102elementaryfunctioncategory.ps}{ELEMFUN}{1.00}
+
+{\bf See:}\\
+\pageto{TranscendentalFunctionCategory}{TRANFUN}
+\pagefrom{Category}{CATEGORY}
+
+{\bf Exports:}\\
+\begin{tabular}{lll}
+\cross{ELEMFUN}{?**?} &
+\cross{ELEMFUN}{exp} &
+\cross{ELEMFUN}{log}
+\end{tabular}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ exp : % -> %
+ log : % -> %
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ ?**? : (%,%) -> %
+\end{verbatim}
+
+<<category ELEMFUN ElementaryFunctionCategory>>=
+)abbrev category ELEMFUN ElementaryFunctionCategory
+++ Category for the elementary functions
+++ Author: Manuel Bronstein
+++ Date Created: ???
+++ Date Last Updated: 14 May 1991
+++ Description: Category for the elementary functions;
+ElementaryFunctionCategory(): Category == with
+ log : $ -> $ ++ log(x) returns the natural logarithm of x.
+ exp : $ -> $ ++ exp(x) returns %e to the power x.
+ "**": ($, $) -> $ ++ x**y returns x to the power y.
+ add
+ if $ has Monoid then
+ x ** y == exp(y * log x)
+
+@
+<<ELEMFUN.dotabb>>=
+"ELEMFUN"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ELEMFUN"];
+"ELEMFUN" -> "CATEGORY"
+
+@
+<<ELEMFUN.dotfull>>=
+"ElementaryFunctionCategory()"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ELEMFUN"];
+"ElementaryFunctionCategory()" -> "Category"
+
+@
+<<ELEMFUN.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"ElementaryFunctionCategory()" [color=lightblue];
+"ElementaryFunctionCategory()" -> "Category"
+
+"Category" [color=lightblue];
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{Eltable}{ELTAB}
\pagepic{ps/v102eltab.ps}{ELTAB}{1.00}
@@ -793,6 +1090,95 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{HyperbolicFunctionCategory}{HYPCAT}
+\pagepic{ps/v102hyperbolicfunctioncategory.ps}{HYPCAT}{1.00}
+
+The {\tt csch} and {\tt sech} functions were modified to include an
+intermediate test to check that the argument has a reciprocal values.
+
+{\bf See:}\\
+\pageto{TranscendentalFunctionCategory}{TRANFUN}
+\pagefrom{Category}{CATEGORY}
+
+{\bf Exports:}\\
+\begin{tabular}{llllll}
+\cross{HYPCAT}{cosh} &
+\cross{HYPCAT}{coth} &
+\cross{HYPCAT}{csch} &
+\cross{HYPCAT}{sech} &
+\cross{HYPCAT}{sinh} &
+\cross{HYPCAT}{tanh}
+\end{tabular}
+
+These are implemented by this category:
+\begin{verbatim}
+ cosh : % -> %
+ coth : % -> %
+ csch : % -> %
+ sech : % -> %
+ sinh : % -> %
+ tanh : % -> %
+\end{verbatim}
+
+<<category HYPCAT HyperbolicFunctionCategory>>=
+)abbrev category HYPCAT HyperbolicFunctionCategory
+++ Category for the hyperbolic trigonometric functions
+++ Author: ???
+++ Date Created: ???
+++ Date Last Updated: 14 May 1991
+++ Description: Category for the hyperbolic trigonometric functions;
+HyperbolicFunctionCategory(): Category == with
+ cosh: $ -> $ ++ cosh(x) returns the hyperbolic cosine of x.
+ coth: $ -> $ ++ coth(x) returns the hyperbolic cotangent of x.
+ csch: $ -> $ ++ csch(x) returns the hyperbolic cosecant of x.
+ sech: $ -> $ ++ sech(x) returns the hyperbolic secant of x.
+ sinh: $ -> $ ++ sinh(x) returns the hyperbolic sine of x.
+ tanh: $ -> $ ++ tanh(x) returns the hyperbolic tangent of x.
+ add
+ if $ has Ring then
+ csch x ==
+ (a := recip(sinh x)) case "failed" => error "csch: no reciprocal"
+ a::$
+ sech x ==
+ (a := recip(cosh x)) case "failed" => error "sech: no reciprocal"
+ a::$
+ tanh x == sinh x * sech x
+ coth x == cosh x * csch x
+ if $ has ElementaryFunctionCategory then
+ cosh x ==
+ e := exp x
+ (e + recip(e)::$) * recip(2::$)::$
+ sinh(x):$ ==
+ e := exp x
+ (e - recip(e)::$) * recip(2::$)::$
+
+@
+<<HYPCAT.dotabb>>=
+"HYPCAT"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=HYPCAT"];
+"HYPCAT" -> "CATEGORY"
+
+@
+<<HYPCAT.dotfull>>=
+"HyperbolicFunctionCategory()"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=HYPCAT"];
+"HyperbolicFunctionCategory()" -> "Category"
+
+@
+<<HYPCAT.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"HyperbolicFunctionCategory()" [color=lightblue];
+"HyperbolicFunctionCategory()" -> "Category"
+
+"Category" [color=lightblue];
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{InnerEvalable}{IEVALAB}
\pagepic{ps/v102innerevalable.ps}{IEVALAB}{1.00}
@@ -884,6 +1270,65 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{PrimitiveFunctionCategory}{PRIMCAT}
+\pagepic{ps/v102primitivefunctioncategory.ps}{PRIMCAT}{1.00}
+
+{\bf See:}\\
+\pageto{LiouvillianFunctionCategory}{LFCAT}
+\pagefrom{Category}{CATEGORY}
+
+{\bf Exports:}\\
+\begin{tabular}{l}
+\cross{PRIMCAT}{integral}
+\end{tabular}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ integral : (%,Symbol) -> %
+ integral : (%,SegmentBinding %) -> %
+\end{verbatim}
+
+<<category PRIMCAT PrimitiveFunctionCategory>>=
+)abbrev category PRIMCAT PrimitiveFunctionCategory
+++ Category for the integral functions
+++ Author: Manuel Bronstein
+++ Date Created: ???
+++ Date Last Updated: 14 May 1991
+++ Description: Category for the functions defined by integrals;
+PrimitiveFunctionCategory(): Category == with
+ integral: ($, Symbol) -> $
+ ++ integral(f, x) returns the formal integral of f dx.
+ integral: ($, SegmentBinding $) -> $
+ ++ integral(f, x = a..b) returns the formal definite integral
+ ++ of f dx for x between \spad{a} and b.
+
+@
+<<PRIMCAT.dotabb>>=
+"PRIMCAT" -> "CATEGORY"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=PRIMCAT"];
+"PRIMCAT" -> "CATEGORY"
+
+@
+<<PRIMCAT.dotfull>>=
+"PrimitiveFunctionCategory()"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=PRIMCAT"];
+"PrimitiveFunctionCategory()" -> "Category"
+
+@
+<<PRIMCAT.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"PrimitiveFunctionCategory()" [color=lightblue];
+"PrimitiveFunctionCategory()" -> "Category"
+
+"Category" [color=lightblue];
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{RetractableTo}{RETRACT}
\pagepic{ps/v102retractableto.ps}{RETRACT}{1.00}
@@ -993,6 +1438,195 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{SpecialFunctionCategory}{SPFCAT}
+\pagepic{ps/v102specialfunctioncategory.ps}{SPFCAT}{1.00}
+
+{\bf See:}\\
+\pagefrom{Category}{CATEGORY}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+\cross{SPFCAT}{abs} &
+\cross{SPFCAT}{airyAi} &
+\cross{SPFCAT}{airyBi} &
+\cross{SPFCAT}{besselI} &
+\cross{SPFCAT}{besselJ} \\
+\cross{SPFCAT}{besselK} &
+\cross{SPFCAT}{besselY} &
+\cross{SPFCAT}{Beta} &
+\cross{SPFCAT}{digamma} &
+\cross{SPFCAT}{Gamma} \\
+\cross{SPFCAT}{polygamma} &
+\end{tabular}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ abs : % -> %
+ airyAi : % -> %
+ airyBi : % -> %
+ besselI : (%,%) -> %
+ besselJ : (%,%) -> %
+ besselK : (%,%) -> %
+ besselY : (%,%) -> %
+ Beta : (%,%) -> %
+ digamma : % -> %
+ Gamma : % -> %
+ Gamma : (%,%) -> %
+ polygamma : (%,%) -> %
+\end{verbatim}
+
+<<category SPFCAT SpecialFunctionCategory>>=
+)abbrev category SPFCAT SpecialFunctionCategory
+++ Category for the other special functions
+++ Author: Manuel Bronstein
+++ Date Created: ???
+++ Date Last Updated: 11 May 1993
+++ Description: Category for the other special functions;
+SpecialFunctionCategory(): Category == with
+ abs : $ -> $
+ ++ abs(x) returns the absolute value of x.
+ Gamma: $ -> $
+ ++ Gamma(x) is the Euler Gamma function.
+ Beta: ($,$)->$
+ ++ Beta(x,y) is \spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.
+ digamma: $ -> $
+ ++ digamma(x) is the logarithmic derivative of \spad{Gamma(x)}
+ ++ (often written \spad{psi(x)} in the literature).
+ polygamma: ($, $) -> $
+ ++ polygamma(k,x) is the \spad{k-th} derivative of \spad{digamma(x)},
+ ++ (often written \spad{psi(k,x)} in the literature).
+ Gamma: ($, $) -> $
+ ++ Gamma(a,x) is the incomplete Gamma function.
+ besselJ: ($,$) -> $
+ ++ besselJ(v,z) is the Bessel function of the first kind.
+ besselY: ($,$) -> $
+ ++ besselY(v,z) is the Bessel function of the second kind.
+ besselI: ($,$) -> $
+ ++ besselI(v,z) is the modified Bessel function of the first kind.
+ besselK: ($,$) -> $
+ ++ besselK(v,z) is the modified Bessel function of the second kind.
+ airyAi: $ -> $
+ ++ airyAi(x) is the Airy function \spad{Ai(x)}.
+ airyBi: $ -> $
+ ++ airyBi(x) is the Airy function \spad{Bi(x)}.
+
+@
+<<SPFCAT.dotabb>>=
+"SPFCAT"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=SPFCAT"];
+"SPFCAT" -> "CATEGORY"
+
+@
+<<SPFCAT.dotfull>>=
+"SpecialFunctionCategory()"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=SPFCAT"];
+"SpecialFunctionCategory()" -> "Category"
+
+@
+<<SPFCAT.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"SpecialFunctionCategory()" [color=lightblue];
+"SpecialFunctionCategory()" -> "Category"
+
+"Category" [color=lightblue];
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{TrigonometricFunctionCategory}{TRIGCAT}
+\pagepic{ps/v102trigonometricfunctioncategory.ps}{TRIGCAT}{1.00}
+
+The {\tt csc} and {\tt sec} functions were modified to include an
+intermediate test to check that the argument has a reciprocal values.
+
+{\bf See:}\\
+\pageto{TranscendentalFunctionCategory}{TRANFUN}
+\pagefrom{Category}{CATEGORY}
+
+{\bf Exports:}\\
+\begin{tabular}{llllll}
+\cross{TRIGCAT}{cos} &
+\cross{TRIGCAT}{cot} &
+\cross{TRIGCAT}{csc} &
+\cross{TRIGCAT}{sec} &
+\cross{TRIGCAT}{sin} &
+\cross{TRIGCAT}{tan}
+\end{tabular}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ cos : % -> %
+ sin : % -> %
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ cot : % -> %
+ csc : % -> %
+ sec : % -> %
+ tan : % -> %
+\end{verbatim}
+
+<<category TRIGCAT TrigonometricFunctionCategory>>=
+)abbrev category TRIGCAT TrigonometricFunctionCategory
+++ Category for the trigonometric functions
+++ Author: ???
+++ Date Created: ???
+++ Date Last Updated: 14 May 1991
+++ Description: Category for the trigonometric functions;
+TrigonometricFunctionCategory(): Category == with
+ cos: $ -> $ ++ cos(x) returns the cosine of x.
+ cot: $ -> $ ++ cot(x) returns the cotangent of x.
+ csc: $ -> $ ++ csc(x) returns the cosecant of x.
+ sec: $ -> $ ++ sec(x) returns the secant of x.
+ sin: $ -> $ ++ sin(x) returns the sine of x.
+ tan: $ -> $ ++ tan(x) returns the tangent of x.
+ add
+ if $ has Ring then
+ csc x ==
+ (a := recip(sin x)) case "failed" => error "csc: no reciprocal"
+ a::$
+ sec x ==
+ (a := recip(cos x)) case "failed" => error "sec: no reciprocal"
+ a::$
+ tan x == sin x * sec x
+ cot x == cos x * csc x
+
+@
+<<TRIGCAT.dotabb>>=
+"TRIGCAT"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=TRIGCAT"];
+"TRIGCAT" -> "CATEGORY"
+
+@
+<<TRIGCAT.dotfull>>=
+"TrigonometricFunctionCategory()"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=TRIGCAT"];
+"TrigonometricFunctionCategory()" -> "Category"
+
+@
+<<TRIGCAT.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"TrigonometricFunctionCategory()" [color=lightblue];
+"TrigonometricFunctionCategory()" -> "Category"
+
+"Category" [color=lightblue];
+}
+
+
+
+
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{Type}{TYPE}
\pagepic{ps/v102type.ps}{TYPE}{1.00}
@@ -1665,6 +2299,201 @@
}
@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{TranscendentalFunctionCategory}{TRANFUN}
+\pagepic{ps/v102transcendentalfunctioncategory.ps}{TRANFUN}{0.75}
+
+The {\tt acsch}, {\tt asech}, and {\tt acoth} functions were modified to
+include an intermediate test to check that the argument has a
+reciprocal values.
+
+{\bf See:}\\
+\pageto{LiouvillianFunctionCategory}{LFCAT}
+\pagefrom{ArcHyperbolicFunctionCategory}{AHYP}
+\pagefrom{ArcTrigonometricFunctionCategory}{ATRIG}
+\pagefrom{ElementaryFunctionCategory}{ELEMFUN}
+\pagefrom{HyperbolicFunctionCategory}{HYPCAT}
+\pagefrom{TrigonometricFunctionCategory}{TRIGCAT}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+\cross{TRANFUN}{?**?} &
+\cross{TRANFUN}{acos} &
+\cross{TRANFUN}{acosh} &
+\cross{TRANFUN}{acot} &
+\cross{TRANFUN}{acoth} \\
+\cross{TRANFUN}{acsc} &
+\cross{TRANFUN}{acsch} &
+\cross{TRANFUN}{asec} &
+\cross{TRANFUN}{asech} &
+\cross{TRANFUN}{asin} \\
+\cross{TRANFUN}{asinh} &
+\cross{TRANFUN}{atan} &
+\cross{TRANFUN}{atanh} &
+\cross{TRANFUN}{cos} &
+\cross{TRANFUN}{cosh} \\
+\cross{TRANFUN}{cot} &
+\cross{TRANFUN}{coth} &
+\cross{TRANFUN}{csc} &
+\cross{TRANFUN}{csch} &
+\cross{TRANFUN}{exp} \\
+\cross{TRANFUN}{log} &
+\cross{TRANFUN}{pi} &
+\cross{TRANFUN}{sec} &
+\cross{TRANFUN}{sech} &
+\cross{TRANFUN}{sin} \\
+\cross{TRANFUN}{sinh} &
+\cross{TRANFUN}{tan} &
+\cross{TRANFUN}{tanh} &&
+\end{tabular}
+
+These are implemented by this category:
+\begin{verbatim}
+ pi : () -> %
+\end{verbatim}
+
+These exports come from TrigonometricFunctionCategory():
+\begin{verbatim}
+ cos : % -> %
+ cot : % -> %
+ csc : % -> %
+ sec : % -> %
+ sin : % -> %
+ tan : % -> %
+\end{verbatim}
+
+These exports come from ArcTrigonometricFunctionCategory():
+\begin{verbatim}
+ acos : % -> %
+ acot : % -> %
+ acsc : % -> %
+ asec : % -> %
+ asin : % -> %
+ atan : % -> %
+\end{verbatim}
+
+These exports come from HyperbolicFunctionCategory():
+\begin{verbatim}
+ cosh : % -> %
+ coth : % -> %
+ csch : % -> %
+ sech : % -> %
+ sinh : % -> %
+ tanh : % -> %
+\end{verbatim}
+
+These exports come from ArcHyperbolicFunctionCategory():
+\begin{verbatim}
+ acosh : % -> %
+ acoth : % -> %
+ acsch : % -> %
+ asech : % -> %
+ asinh : % -> %
+ atanh : % -> %
+\end{verbatim}
+
+These exports come from ElementaryFunctionCategory():
+\begin{verbatim}
+ ?**? : (%,%) -> %
+ exp : % -> %
+ log : % -> %
+\end{verbatim}
+
+<<category TRANFUN TranscendentalFunctionCategory>>=
+)abbrev category TRANFUN TranscendentalFunctionCategory
+++ Category for the transcendental elementary functions
+++ Author: Manuel Bronstein
+++ Date Created: ???
+++ Date Last Updated: 14 May 1991
+++ Description: Category for the transcendental elementary functions;
+TranscendentalFunctionCategory(): Category ==
+ Join(TrigonometricFunctionCategory,ArcTrigonometricFunctionCategory,
+ HyperbolicFunctionCategory,ArcHyperbolicFunctionCategory,
+ ElementaryFunctionCategory) with
+ pi : () -> $ ++ pi() returns the constant pi.
+ add
+ if $ has Ring then
+ pi() == 2*asin(1)
+ acsch x ==
+ (a := recip x) case "failed" => error "acsch: no reciprocal"
+ asinh(a::$)
+ asech x ==
+ (a := recip x) case "failed" => error "asech: no reciprocal"
+ acosh(a::$)
+ acoth x ==
+ (a := recip x) case "failed" => error "acoth: no reciprocal"
+ atanh(a::$)
+ if $ has Field and $ has sqrt: $ -> $ then
+ asin x == atan(x/sqrt(1-x**2))
+ acos x == pi()/2::$ - asin x
+ acot x == pi()/2::$ - atan x
+ asinh x == log(x + sqrt(x**2 + 1))
+ acosh x == 2*log(sqrt((x+1)/2::$) + sqrt((x-1)/2::$))
+ atanh x == (log(1+x)-log(1-x))/2::$
+
+@
+<<TRANFUN.dotabb>>=
+"TRANFUN" -> "TRIGCAT"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=TRANFUN"];
+"TRANFUN" -> "TRIGCAT"
+"TRANFUN" -> "ATRIG"
+"TRANFUN" -> "HYPCAT"
+"TRANFUN" -> "AHYP"
+"TRANFUN" -> "ELEMFUN"
+
+@
+<<TRANFUN.dotfull>>=
+"TranscendentalFunctionCategory()"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=TRANFUN"];
+"TranscendentalFunctionCategory()" ->
+ "TrigonometricFunctionCategory()"
+"TranscendentalFunctionCategory()" ->
+ "ArcTrigonometricFunctionCategory()"
+"TranscendentalFunctionCategory()" ->
+ "HyperbolicFunctionCategory()"
+"TranscendentalFunctionCategory()" ->
+ "ArcHyperbolicFunctionCategory()"
+"TranscendentalFunctionCategory()" ->
+ "ElementaryFunctionCategory()"
+
+@
+<<TRANFUN.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"TranscendentalFunctionCategory()" [color=lightblue];
+"TranscendentalFunctionCategory()" ->
+ "TRIGCAT"
+"TranscendentalFunctionCategory()" ->
+ "ATRIG"
+"TranscendentalFunctionCategory()" ->
+ "HYPCAT"
+"TranscendentalFunctionCategory()" ->
+ "AHYP"
+"TranscendentalFunctionCategory()" ->
+ "ELEMFUN"
+
+"TRIGCAT" [color=lightblue];
+"TRIGCAT" -> "Category"
+
+"ATRIG" [color=lightblue];
+"ATRIG" -> "Category"
+
+"HYPCAT" [color=lightblue];
+"HYPCAT" -> "Category"
+
+"AHYP" [color=lightblue];
+"AHYP" -> "Category"
+
+"ELEMFUN" [color=lightblue];
+"ELEMFUN" -> "Category"
+
+"Category" [color=lightblue];
+}
+
+@
\chapter{Category Layer 3}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{AbelianSemiGroup}{ABELSG}
@@ -2264,6 +3093,189 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{LiouvillianFunctionCategory}{LFCAT}
+\pagepic{ps/v102liouvillianfunctioncategory.ps}{LFCAT}{0.60}
+
+{\bf See:}\\
+\pagefrom{PrimitiveFunctionCategory}{PRIMCAT}
+\pagefrom{TranscendentalFunctionCategory}{TRANFUN}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+\cross{LFCAT}{?**?} &
+\cross{LFCAT}{Ci} &
+\cross{LFCAT}{Ei} &
+\cross{LFCAT}{Si} &
+\cross{LFCAT}{acos} \\
+\cross{LFCAT}{acosh} &
+\cross{LFCAT}{acot} &
+\cross{LFCAT}{acoth} &
+\cross{LFCAT}{acsc} &
+\cross{LFCAT}{acsch} \\
+\cross{LFCAT}{asec} &
+\cross{LFCAT}{asech} &
+\cross{LFCAT}{asin} &
+\cross{LFCAT}{asinh} &
+\cross{LFCAT}{atan} \\
+\cross{LFCAT}{atanh} &
+\cross{LFCAT}{cos} &
+\cross{LFCAT}{cosh} &
+\cross{LFCAT}{cot} &
+\cross{LFCAT}{coth} \\
+\cross{LFCAT}{csc} &
+\cross{LFCAT}{csch} &
+\cross{LFCAT}{dilog} &
+\cross{LFCAT}{erf} &
+\cross{LFCAT}{exp} \\
+\cross{LFCAT}{integral} &
+\cross{LFCAT}{integral} &
+\cross{LFCAT}{li} &
+\cross{LFCAT}{log} &
+\cross{LFCAT}{pi} \\
+\cross{LFCAT}{sec} &
+\cross{LFCAT}{sech} &
+\cross{LFCAT}{sin} &
+\cross{LFCAT}{sinh} &
+\cross{LFCAT}{tan} \\
+\cross{LFCAT}{tanh} &&&&
+\end{tabular}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ Ci : % -> %
+ dilog : % -> %
+ Ei : % -> %
+ erf : % -> %
+ li : % -> %
+ Si : % -> %
+\end{verbatim}
+
+These exports come from PrimitiveFunctionCategory()
+\begin{verbatim}
+ integral : (%,Symbol) -> %
+ integral : (%,SegmentBinding %) -> %
+\end{verbatim}
+
+These exports come from TranscendentalFunctionCategory():
+\begin{verbatim}
+ ?**? : (%,%) -> %
+ acos : % -> %
+ acosh : % -> %
+ acot : % -> %
+ acoth : % -> %
+ acsc : % -> %
+ acsch : % -> %
+ asec : % -> %
+ asech : % -> %
+ asin : % -> %
+ asinh : % -> %
+ atan : % -> %
+ atanh : % -> %
+ cos : % -> %
+ cosh : % -> %
+ cot : % -> %
+ coth : % -> %
+ csc : % -> %
+ csch : % -> %
+ exp : % -> %
+ log : % -> %
+ pi : () -> %
+ sec : % -> %
+ sech : % -> %
+ sin : % -> %
+ sinh : % -> %
+ tan : % -> %
+ tanh : % -> %
+\end{verbatim}
+
+<<category LFCAT LiouvillianFunctionCategory>>=
+)abbrev category LFCAT LiouvillianFunctionCategory
+++ Category for the transcendental Liouvillian functions
+++ Author: Manuel Bronstein
+++ Date Created: ???
+++ Date Last Updated: 14 May 1991
+++ Description: Category for the transcendental Liouvillian functions;
+LiouvillianFunctionCategory(): Category ==
+ Join(PrimitiveFunctionCategory, TranscendentalFunctionCategory) with
+ Ei : $ -> $
+ ++ Ei(x) returns the exponential integral of x, i.e.
+ ++ the integral of \spad{exp(x)/x dx}.
+ Si : $ -> $
+ ++ Si(x) returns the sine integral of x, i.e.
+ ++ the integral of \spad{sin(x) / x dx}.
+ Ci : $ -> $
+ ++ Ci(x) returns the cosine integral of x, i.e.
+ ++ the integral of \spad{cos(x) / x dx}.
+ li : $ -> $
+ ++ li(x) returns the logarithmic integral of x, i.e.
+ ++ the integral of \spad{dx / log(x)}.
+ dilog : $ -> $
+ ++ dilog(x) returns the dilogarithm of x, i.e.
+ ++ the integral of \spad{log(x) / (1 - x) dx}.
+ erf : $ -> $
+ ++ erf(x) returns the error function of x, i.e.
+ ++ \spad{2 / sqrt(%pi)} times the integral of \spad{exp(-x**2) dx}.
+
+@
+<<LFCAT.dotabb>>=
+"LFCAT"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=LFCAT"];
+"LFCAT" -> "PRIMCAT"
+"LFCAT" -> "TRANFUN"
+
+@
+<<LFCAT.dotfull>>=
+"LiouvillianFunctionCategory()"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=LFCAT"];
+"LiouvillianFunctionCategory()" -> "PrimitiveFunctionCategory()"
+"LiouvillianFunctionCategory()" -> "TranscendentalFunctionCategory()"
+
+@
+<<LFCAT.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"LiouvillianFunctionCategory()" [color=lightblue];
+"LiouvillianFunctionCategory()" -> "PrimitiveFunctionCategory()"
+"LiouvillianFunctionCategory()" -> "TranscendentalFunctionCategory()"
+
+"PrimitiveFunctionCategory()" [color=lightblue];
+"PrimitiveFunctionCategory()" -> "Category"
+
+"TranscendentalFunctionCategory()" [color=lightblue];
+"TranscendentalFunctionCategory()" ->
+ "TRIGCAT"
+"TranscendentalFunctionCategory()" ->
+ "ATRIG"
+"TranscendentalFunctionCategory()" ->
+ "HYPCAT"
+"TranscendentalFunctionCategory()" ->
+ "AHYP"
+"TranscendentalFunctionCategory()" ->
+ "ELEMFUN"
+
+"TRIGCAT" [color=lightblue];
+"TRIGCAT" -> "Category"
+
+"ATRIG" [color=lightblue];
+"ATRIG" -> "Category"
+
+"HYPCAT" [color=lightblue];
+"HYPCAT" -> "Category"
+
+"AHYP" [color=lightblue];
+"AHYP" -> "Category"
+
+"ELEMFUN" [color=lightblue];
+"ELEMFUN" -> "Category"
+
+"Category" [color=lightblue];
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{Monad}{MONAD}
\pagepic{ps/v102monad.ps}{MONAD}{0.70}
@@ -28110,9 +29122,11 @@
<<category ABELMON AbelianMonoid>>
<<category ABELSG AbelianSemiGroup>>
<<category AGG Aggregate>>
+<<category AHYP ArcHyperbolicFunctionCategory>>
<<category ALAGG AssociationListAggregate>>
<<category ALGEBRA Algebra>>
<<category ARR2CAT TwoDimensionalArrayCategory>>
+<<category ATRIG ArcTrigonometricFunctionCategory>>
<<category ATTREG AttributeRegistry>>
<<category A1AGG OneDimensionalArrayAggregate>>
<<category BASTYPE BasicType>>
@@ -28121,6 +29135,7 @@
<<category BRAGG BinaryRecursiveAggregate>>
<<category BTAGG BitAggregate>>
<<category CABMON CancellationAbelianMonoid>>
+<<category CFCAT CombinatorialFunctionCategory>>
<<category CHARNZ CharacteristicNonZero>>
<<category CHARZ CharacteristicZero>>
<<category CLAGG Collection>>
@@ -28133,6 +29148,7 @@
<<category DLAGG DoublyLinkedAggregate>>
<<category DQAGG DequeueAggregate>>
<<category ELAGG ExtensibleLinearAggregate>>
+<<category ELEMFUN ElementaryFunctionCategory>>
<<category ELTAB Eltable>>
<<category ELTAGG EltableAggregate>>
<<category ENTIRER EntireRing>>
@@ -28154,12 +29170,14 @@
<<category GRMOD GradedModule>>
<<category GROUP Group>>
<<category HOAGG HomogeneousAggregate>>
+<<category HYPCAT HyperbolicFunctionCategory>>
<<category IEVALAB InnerEvalable>>
<<category INTDOM IntegralDomain>>
<<category IXAGG IndexedAggregate>>
<<category KDAGG KeyedDictionary>>
<<category KOERCE CoercibleTo>>
<<category KONVERT ConvertibleTo>>
+<<category LFCAT LiouvillianFunctionCategory>>
<<category LINEXP LinearlyExplicitRingOver>>
<<category LMODULE LeftModule>>
<<category LNAGG LinearAggregate>>
@@ -28189,6 +29207,7 @@
<<category PDRING PartialDifferentialRing>>
<<category PFECAT PolynomialFactorizationExplicit>>
<<category PID PrincipalIdealDomain>>
+<<category PRIMCAT PrimitiveFunctionCategory>>
<<category PRQAGG PriorityQueueAggregate>>
<<category QUAGG QueueAggregate>>
<<category RCAGG RecursiveAggregate>>
@@ -28200,9 +29219,12 @@
<<category SETCAT SetCategory>>
<<category SGROUP SemiGroup>>
<<category SKAGG StackAggregate>>
+<<category SPFCAT SpecialFunctionCategory>>
<<category SRAGG StringAggregate>>
<<category STAGG StreamAggregate>>
<<category STEP StepThrough>>
+<<category TRANFUN TranscendentalFunctionCategory>>
+<<category TRIGCAT TrigonometricFunctionCategory>>
<<category TYPE Type>>
<<category TBAGG TableAggregate>>
<<category UFD UniqueFactorizationDomain>>
@@ -28220,9 +29242,11 @@
<<ABELMON.dotabb>>
<<ABELSG.dotabb>>
<<AGG.dotabb>>
+<<AHYP.dotabb>>
<<ALAGG.dotabb>>
<<ALGEBRA.dotabb>>
<<ARR2CAT.dotabb>>
+<<ATRIG.dotabb>>
<<ATTREG.dotabb>>
<<A1AGG.dotabb>>
<<BASTYPE.dotabb>>
@@ -28231,6 +29255,7 @@
<<BRAGG.dotabb>>
<<BTAGG.dotabb>>
<<CABMON.dotabb>>
+<<CFCAT.dotabb>>
<<CHARNZ.dotabb>>
<<CHARZ.dotabb>>
<<CLAGG.dotabb>>
@@ -28242,6 +29267,7 @@
<<DLAGG.dotabb>>
<<DQAGG.dotabb>>
<<ELAGG.dotabb>>
+<<ELEMFUN.dotabb>>
<<ELTAB.dotabb>>
<<ELTAGG.dotabb>>
<<ENTIRER.dotabb>>
@@ -28262,12 +29288,14 @@
<<GRALG.dotabb>>
<<GRMOD.dotabb>>
<<HOAGG.dotabb>>
+<<HYPCAT.dotabb>>
<<IEVALAB.dotabb>>
<<INTDOM.dotabb>>
<<IXAGG.dotabb>>
<<KDAGG.dotabb>>
<<KOERCE.dotabb>>
<<KONVERT.dotabb>>
+<<LFCAT.dotabb>>
<<LINEXP.dotabb>>
<<LMODULE.dotabb>>
<<LNAGG.dotabb>>
@@ -28297,6 +29325,7 @@
<<PDRING.dotabb>>
<<PFECAT.dotabb>>
<<PID.dotabb>>
+<<PRIMCAT.dotabb>>
<<PRQAGG.dotabb>>
<<QUAGG.dotabb>>
<<RCAGG.dotabb>>
@@ -28308,9 +29337,12 @@
<<SETCAT.dotabb>>
<<SGROUP.dotabb>>
<<SKAGG.dotabb>>
+<<SPFCAT.dotabb>>
<<SRAGG.dotabb>>
<<STAGG.dotabb>>
<<STEP.dotabb>>
+<<TRANFUN.dotabb>>
+<<TRIGCAT.dotabb>>
<<TYPE.dotabb>>
<<TBAGG.dotabb>>
<<UFD.dotabb>>
@@ -28331,9 +29363,11 @@
<<ABELMON.dotfull>>
<<ABELSG.dotfull>>
<<AGG.dotfull>>
+<<AHYP.dotfull>>
<<ALAGG.dotfull>>
<<ALGEBRA.dotfull>>
<<ARR2CAT.dotfull>>
+<<ATRIG.dotfull>>
<<ATTREG.dotfull>>
<<A1AGG.dotfull>>
<<BASTYPE.dotfull>>
@@ -28342,6 +29376,7 @@
<<BRAGG.dotfull>>
<<BTAGG.dotfull>>
<<CABMON.dotfull>>
+<<CFCAT.dotfull>>
<<CHARNZ.dotfull>>
<<CHARZ.dotfull>>
<<CLAGG.dotfull>>
@@ -28353,6 +29388,7 @@
<<DLAGG.dotfull>>
<<DQAGG.dotfull>>
<<ELAGG.dotfull>>
+<<ELEMFUN.dotfull>>
<<ELTAB.dotfull>>
<<ELTAGG.dotfull>>
<<ENTIRER.dotfull>>
@@ -28373,12 +29409,14 @@
<<GRALG.dotfull>>
<<GRMOD.dotfull>>
<<HOAGG.dotfull>>
+<<HYPCAT.dotfull>>
<<IEVALAB.dotfull>>
<<INTDOM.dotfull>>
<<IXAGG.dotfull>>
<<KDAGG.dotfull>>
<<KOERCE.dotfull>>
<<KONVERT.dotfull>>
+<<LFCAT.dotfull>>
<<LINEXP.dotfull>>
<<LMODULE.dotfull>>
<<LNAGG.dotfull>>
@@ -28408,6 +29446,7 @@
<<PDRING.dotfull>>
<<PFECAT.dotfull>>
<<PID.dotfull>>
+<<PRIMCAT.dotfull>>
<<PRQAGG.dotfull>>
<<QUAGG.dotfull>>
<<RCAGG.dotfull>>
@@ -28419,9 +29458,12 @@
<<SETCAT.dotfull>>
<<SGROUP.dotfull>>
<<SKAGG.dotfull>>
+<<SPFCAT.dotfull>>
<<SRAGG.dotfull>>
<<STAGG.dotfull>>
<<STEP.dotfull>>
+<<TRANFUN.dotfull>>
+<<TRIGCAT.dotfull>>
<<TYPE.dotfull>>
<<TBAGG.dotfull>>
<<UFD.dotfull>>
Added: trunk/axiom/books/ps/v102archyperbolicfunctioncategory.ps
===================================================================
--- trunk/axiom/books/ps/v102archyperbolicfunctioncategory.ps (rev 0)
+++ trunk/axiom/books/ps/v102archyperbolicfunctioncategory.ps 2008-09-30 10:45:19 UTC (rev 984)
@@ -0,0 +1,289 @@
+%!PS-Adobe-2.0
+%%Creator: dot version 2.8 (Thu Sep 14 20:34:11 UTC 2006)
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+%%EndComments
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+
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+/coord-font-family /Times-Roman def
+/default-font-family /Times-Roman def
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+
+/InvScaleFactor 1.0 def
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+ dup 1 exch div /InvScaleFactor exch def
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+
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+/solid { [] 0 setdash } bind def
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+/bold { 2 setlinewidth } bind def
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+
+% hooks for setting color
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+
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+ npages 1 gt {
+ gsave
+ coordfont setfont
+ 0 0 moveto
+ (\() show i str cvs show (,) show j str cvs show (\)) show
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[truncated message content] |
|
From: <gi...@ax...> - 2008-09-30 10:43:21
|
books/bookvol10.2.pamphlet | 1042 ++++++++++++++++++++++
books/ps/v102archyperbolicfunctioncategory.ps | 289 ++++++
books/ps/v102arctrigonometricfunctioncategory.ps | 289 ++++++
books/ps/v102combinatorialfunctioncategory.ps | 289 ++++++
books/ps/v102elementaryfunctioncategory.ps | 289 ++++++
books/ps/v102hyperbolicfunctioncategory.ps | 289 ++++++
books/ps/v102liouvillianfunctioncategory.ps | 713 +++++++++++++++
books/ps/v102primitivefunctioncategory.ps | 289 ++++++
books/ps/v102specialfunctioncategory.ps | 289 ++++++
books/ps/v102transcendentalfunctioncategory.ps | 599 +++++++++++++
books/ps/v102trigonometricfunctioncategory.ps | 289 ++++++
changelog | 23 +
src/algebra/Makefile.pamphlet | 6 +-
src/algebra/trigcat.spad.pamphlet | 388 --------
14 files changed, 4691 insertions(+), 392 deletions(-)
New commits:
commit 5ad7e4f55770bd413d0ff05645fa30358142f701
Author: Tim Daly <da...@ax...>
Date: Sat Aug 2 19:29:49 2008 -0400
20080928 tpd books/bookvol10.2 add trigcat categories
20080928 tpd books/ps/v102trigonometricfunctioncategory.ps
20080928 tpd books/ps/v102transcendentalfunctioncategory.ps
20080928 tpd books/ps/v102specialfunctioncategory.ps
20080928 tpd books/ps/v102primitivefunctioncategory.ps
20080928 tpd books/ps/v102liouvillianfunctioncategory.ps added
20080928 tpd books/ps/v102hyperbolicfunctioncategory.ps added
20080928 tpd books/ps/v102elementaryfunctioncategory.ps added
20080928 tpd books/ps/v102combinatorialfunctioncategory.ps added
20080928 tpd books/ps/v102arctrigonometricfunctioncategory.ps added
20080928 tpd books/ps/v102archyperbolicfunctioncategory.ps added
20080928 tpd src/algebra/Makefile remove trigcat
20080928 tpd src/algebra/trigcat.spad absorbed into bookvol10.2
|
|
From: <da...@us...> - 2008-09-28 22:36:52
|
Revision: 983
http://axiom.svn.sourceforge.net/axiom/?rev=983&view=rev
Author: daly
Date: 2008-09-28 22:36:41 +0000 (Sun, 28 Sep 2008)
Log Message:
-----------
20080927 tpd books/ps/v102nonassociativerng.ps added
20080927 tpd books/ps/v102nonassociativering.ps added
20080927 tpd books/ps/v102nonassociativealgebra.ps added
20080927 tpd books/ps/v102monadwithunit.ps added
20080927 tpd books/ps/v102monad.ps added
20080927 tpd books/ps/v102gradedmodule.ps added
20080927 tpd books/ps/v102gradedalgebra.ps added
20080927 tpd books/ps/v102functionfieldcategory.ps added
20080927 tpd books/ps/v102framednonassociativealgebra.ps added
20080927 tpd books/ps/v102finiteranknonassociativealgebra.ps added
20080927 tpd src/algebra/Makefile remove naalgc
20080927 tpd books/bookvol10.2 add categories
20080927 tpd src/algebra/naalgc.spad absorbed into bookvol10.2
20080927 tpd src/algebra/curve.spad move categories to bookvol10.2
20080927 tpd src/algebra/carten.spad move categories to bookvol10.2
Modified Paths:
--------------
trunk/axiom/books/bookvol10.2.pamphlet
trunk/axiom/changelog
trunk/axiom/src/algebra/Makefile.pamphlet
trunk/axiom/src/algebra/carten.spad.pamphlet
trunk/axiom/src/algebra/curve.spad.pamphlet
Added Paths:
-----------
trunk/axiom/books/ps/v102finiteranknonassociativealgebra.ps
trunk/axiom/books/ps/v102framednonassociativealgebra.ps
trunk/axiom/books/ps/v102functionfieldcategory.ps
trunk/axiom/books/ps/v102gradedalgebra.ps
trunk/axiom/books/ps/v102gradedmodule.ps
trunk/axiom/books/ps/v102monad.ps
trunk/axiom/books/ps/v102monadwithunit.ps
trunk/axiom/books/ps/v102nonassociativealgebra.ps
trunk/axiom/books/ps/v102nonassociativering.ps
trunk/axiom/books/ps/v102nonassociativerng.ps
Removed Paths:
-------------
trunk/axiom/src/algebra/naalgc.spad.pamphlet
Modified: trunk/axiom/books/bookvol10.2.pamphlet
===================================================================
--- trunk/axiom/books/bookvol10.2.pamphlet 2008-09-27 16:25:03 UTC (rev 982)
+++ trunk/axiom/books/bookvol10.2.pamphlet 2008-09-28 22:36:41 UTC (rev 983)
@@ -889,6 +889,7 @@
{\bf See:}\\
\pageto{FullyRetractableTo}{FRETRCT}
+\pageto{GradedAlgebra}{GRALG}
\pagefrom{Category}{CATEGORY}
{\bf Exports:}\\
@@ -976,6 +977,7 @@
"RetractableTo(CommutativeRing)"
[color=seagreen,href="bookvol10.2.pdf#nameddest=RETRACT"];
"RetractableTo(CommutativeRing)" -> "RetractableTo(a:Type)"
+
@
<<RETRACT.dotpic>>=
digraph pic {
@@ -1562,6 +1564,7 @@
{\bf See:}\\
\pageto{AbelianSemiGroup}{ABELSG}
\pageto{Finite}{FINITE}
+\pageto{GradedModule}{GRMOD}
\pageto{HomogeneousAggregate}{HOAGG}
\pageto{OrderedSet}{ORDSET}
\pageto{SemiGroup}{SGROUP}
@@ -1894,6 +1897,142 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{GradedModule}{GRMOD}
+\pagepic{ps/v102gradedmodule.ps}{GRMOD}{1.00}
+
+{\bf See:}\\
+\pageto{GradedAlgebra}{GRALG}
+\pagefrom{SetCategory}{SETCAT}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+\cross{GRMOD}{0} &
+\cross{GRMOD}{coerce} &
+\cross{GRMOD}{degree} &
+\cross{GRMOD}{hash} &
+\cross{GRMOD}{latex} \\
+\cross{GRMOD}{?\~{}=?} &
+\cross{GRMOD}{?*?} &
+\cross{GRMOD}{?+?} &
+\cross{GRMOD}{?-?} &
+\cross{GRMOD}{-?} \\
+\cross{GRMOD}{?=?} &&&&
+\end{tabular}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ 0 : () -> %
+ degree : % -> E
+ ?*? : (%,R) -> %
+ ?*? : (R,%) -> %
+ -? : % -> %
+ ?+? : (%,%) -> %
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ ?-? : (%,%) -> %
+\end{verbatim}
+
+These exports come from SetCategory():
+\begin{verbatim}
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ ?~=? : (%,%) -> Boolean
+ ?=? : (%,%) -> Boolean
+\end{verbatim}
+
+<<category GRMOD GradedModule>>=
+)abbrev category GRMOD GradedModule
+++ Author: Stephen M. Watt
+++ Date Created: May 20, 1991
+++ Date Last Updated: May 20, 1991
+++ Basic Operations: +, *, degree
+++ Related Domains: CartesianTensor(n,dim,R)
+++ Also See:
+++ AMS Classifications:
+++ Keywords: graded module, tensor, multi-linear algebra
+++ Examples:
+++ References: Algebra 2d Edition, MacLane and Birkhoff, MacMillan 1979
+++ Description:
+++ GradedModule(R,E) denotes ``E-graded R-module'', i.e. collection of
+++ R-modules indexed by an abelian monoid E.
+++ An element \spad{g} of \spad{G[s]} for some specific \spad{s} in \spad{E}
+++ is said to be an element of \spad{G} with {\em degree} \spad{s}.
+++ Sums are defined in each module \spad{G[s]} so two elements of \spad{G}
+++ have a sum if they have the same degree.
+++
+++ Morphisms can be defined and composed by degree to give the
+++ mathematical category of graded modules.
+
+GradedModule(R: CommutativeRing, E: AbelianMonoid): Category ==
+ SetCategory with
+ degree: % -> E
+ ++ degree(g) names the degree of g. The set of all elements
+ ++ of a given degree form an R-module.
+ 0: constant -> %
+ ++ 0 denotes the zero of degree 0.
+ _*: (R, %) -> %
+ ++ r*g is left module multiplication.
+ _*: (%, R) -> %
+ ++ g*r is right module multiplication.
+
+ _-: % -> %
+ ++ -g is the additive inverse of g in the module of elements
+ ++ of the same grade as g.
+ _+: (%, %) -> %
+ ++ g+h is the sum of g and h in the module of elements of
+ ++ the same degree as g and h. Error: if g and h
+ ++ have different degrees.
+ _-: (%, %) -> %
+ ++ g-h is the difference of g and h in the module of elements of
+ ++ the same degree as g and h. Error: if g and h
+ ++ have different degrees.
+ add
+ (x: %) - (y: %) == x+(-y)
+
+@
+<<GRMOD.dotabb>>=
+"GRMOD"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=GRMOD"];
+"GRMOD" -> "SETCAT"
+
+@
+<<GRMOD.dotfull>>=
+"GradedModule(a:CommutativeRing,b:AbelianMonoid)"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=GRMOD"];
+"GradedModule(a:CommutativeRing,b:AbelianMonoid)" -> "SetCategory()"
+
+@
+<<GRMOD.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"GradedModule(a:CommutativeRing,b:AbelianMonoid)" [color=lightblue];
+"GradedModule(a:CommutativeRing,b:AbelianMonoid)" -> "SetCategory()"
+
+"SetCategory()" [color=lightblue];
+"SetCategory()" -> "BasicType()"
+"SetCategory()" -> "CoercibleTo(OutputForm)"
+
+"BasicType()" [color=lightblue];
+"BasicType()" -> "Category"
+
+"CoercibleTo(OutputForm)" [color=seagreen];
+"CoercibleTo(OutputForm)" -> "CoercibleTo(a:Type)"
+
+"CoercibleTo(a:Type)" [color=lightblue];
+"CoercibleTo(a:Type)" -> "Category"
+
+"Category" [color=lightblue];
+
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{HomogeneousAggregate}{HOAGG}
\pagepic{ps/v102homogeneousaggregate.ps}{HOAGG}{1.00}
@@ -2125,6 +2264,145 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{Monad}{MONAD}
+\pagepic{ps/v102monad.ps}{MONAD}{0.70}
+
+{\bf See:}\\
+\pageto{MonadWithUnit}{MONADWU}
+\pageto{NonAssociativeRng}{NARNG}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+\cross{MONAD}{coerce} &
+\cross{MONAD}{hash} &
+\cross{MONAD}{latex} &
+\cross{MONAD}{leftPower} &
+\cross{MONAD}{rightPower} \\
+\cross{MONAD}{?**?} &
+\cross{MONAD}{?*?} &
+\cross{MONAD}{?=?} &
+\cross{MONAD}{?\~{}=?} &
+\end{tabular}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ ?*? : (%,%) -> %
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ leftPower : (%,PositiveInteger) -> %
+ rightPower : (%,PositiveInteger) -> %
+ ?**? : (%,PositiveInteger) -> %
+\end{verbatim}
+
+These exports come from SetCategory():
+\begin{verbatim}
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ ?=? : (%,%) -> Boolean
+ ?~=? : (%,%) -> Boolean
+\end{verbatim}
+
+<<category MONAD Monad>>=
+)abbrev category MONAD Monad
+++ Authors: J. Grabmeier, R. Wisbauer
+++ Date Created: 01 March 1991
+++ Date Last Updated: 11 June 1991
+++ Basic Operations: *, **
+++ Related Constructors: SemiGroup, Monoid, MonadWithUnit
+++ Also See:
+++ AMS Classifications:
+++ Keywords: Monad, binary operation
+++ Reference:
+++ N. Jacobson: Structure and Representations of Jordan Algebras
+++ AMS, Providence, 1968
+++ Description:
+++ Monad is the class of all multiplicative monads, i.e. sets
+++ with a binary operation.
+Monad(): Category == SetCategory with
+ "*": (%,%) -> %
+ ++ a*b is the product of \spad{a} and b in a set with
+ ++ a binary operation.
+ rightPower: (%,PositiveInteger) -> %
+ ++ rightPower(a,n) returns the \spad{n}-th right power of \spad{a},
+ ++ i.e. \spad{rightPower(a,n) := rightPower(a,n-1) * a} and
+ ++ \spad{rightPower(a,1) := a}.
+ leftPower: (%,PositiveInteger) -> %
+ ++ leftPower(a,n) returns the \spad{n}-th left power of \spad{a},
+ ++ i.e. \spad{leftPower(a,n) := a * leftPower(a,n-1)} and
+ ++ \spad{leftPower(a,1) := a}.
+ "**": (%,PositiveInteger) -> %
+ ++ a**n returns the \spad{n}-th power of \spad{a},
+ ++ defined by repeated squaring.
+ add
+ import RepeatedSquaring(%)
+ x:% ** n:PositiveInteger == expt(x,n)
+ rightPower(a,n) ==
+-- one? n => a
+ (n = 1) => a
+ res := a
+ for i in 1..(n-1) repeat res := res * a
+ res
+ leftPower(a,n) ==
+-- one? n => a
+ (n = 1) => a
+ res := a
+ for i in 1..(n-1) repeat res := a * res
+ res
+
+@
+<<MONAD.dotabb>>=
+"MONAD"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=MONAD"];
+"MONAD" -> "SETCAT"
+
+@
+<<MONAD.dotfull>>=
+"Monad()"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=MONAD"];
+"Monad()" -> "SetCategory()"
+"Monad()" -> "RepeatedSquaring(Monad)"
+
+@
+<<MONAD.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"Monad()" [color=lightblue];
+"Monad()" -> "SetCategory()"
+"Monad()" -> "RepeatedSquaring(Monad)"
+
+"RepeatedSquaring(Monad)" [color="#00EE00"];
+"RepeatedSquaring(Monad)" -> "RepeatedSquaring(a:SetCategory)"
+
+"RepeatedSquaring(a:SetCategory)" [color="#00EE00"];
+"RepeatedSquaring(a:SetCategory)" -> "Package"
+
+"Package" [color="#00EE00"];
+
+"SetCategory()" [color=lightblue];
+"SetCategory()" -> "BasicType()"
+"SetCategory()" -> "CoercibleTo(OutputForm)"
+
+"BasicType()" [color=lightblue];
+"BasicType()" -> "Category"
+
+"CoercibleTo(OutputForm)" [color=seagreen];
+"CoercibleTo(OutputForm)" -> "CoercibleTo(a:Type)"
+
+"CoercibleTo(a:Type)" [color=lightblue];
+"CoercibleTo(a:Type)" -> "Category"
+
+"Category" [color=lightblue];
+
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{OrderedSet}{ORDSET}
\pagepic{ps/v102orderedset.ps}{ORDSET}{1.00}
@@ -2626,552 +2904,6 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\pagehead{TwoDimensionalArrayCategory}{ARR2CAT}
-\pagepic{ps/v102twodimensionalarraycategory.ps}{ARR2CAT}{0.60}
-
-TwoDimensionalArrayCategory is a general array category which
-allows different representations and indexing schemes.
-Rows and columns may be extracted with rows returned as objects
-of type Row and columns returned as objects of type Col.
-The index of the 'first' row may be obtained by calling the
-function 'minRowIndex'. The index of the 'first' column may
-be obtained by calling the function 'minColIndex'. The index of
-the first element of a 'Row' is the same as the index of the
-first column in an array and vice versa.
-
-{\bf See:}\\
-\pagefrom{HomogeneousAggregate}{HOAGG}
-
-{\bf Exports:}\\
-\begin{tabular}{lllll}
-\cross{ARR2CAT}{any?} &
-\cross{ARR2CAT}{column} &
-\cross{ARR2CAT}{coerce} &
-\cross{ARR2CAT}{copy} &
-\cross{ARR2CAT}{count} \\
-\cross{ARR2CAT}{elt} &
-\cross{ARR2CAT}{empty} &
-\cross{ARR2CAT}{empty?} &
-\cross{ARR2CAT}{eq?} &
-\cross{ARR2CAT}{eval} \\
-\cross{ARR2CAT}{every?} &
-\cross{ARR2CAT}{fill!} &
-\cross{ARR2CAT}{hash} &
-\cross{ARR2CAT}{latex} &
-\cross{ARR2CAT}{less?} \\
-\cross{ARR2CAT}{map} &
-\cross{ARR2CAT}{map!} &
-\cross{ARR2CAT}{maxColIndex} &
-\cross{ARR2CAT}{maxRowIndex} &
-\cross{ARR2CAT}{member?} \\
-\cross{ARR2CAT}{members} &
-\cross{ARR2CAT}{minColIndex} &
-\cross{ARR2CAT}{minRowIndex} &
-\cross{ARR2CAT}{more?} &
-\cross{ARR2CAT}{ncols} \\
-\cross{ARR2CAT}{new} &
-\cross{ARR2CAT}{nrows} &
-\cross{ARR2CAT}{parts} &
-\cross{ARR2CAT}{qelt} &
-\cross{ARR2CAT}{qsetelt!} \\
-\cross{ARR2CAT}{row} &
-\cross{ARR2CAT}{sample} &
-\cross{ARR2CAT}{setColumn!} &
-\cross{ARR2CAT}{setRow!} &
-\cross{ARR2CAT}{setelt} \\
-\cross{ARR2CAT}{size?} &
-\cross{ARR2CAT}{\#?} &
-\cross{ARR2CAT}{?=?} &
-\cross{ARR2CAT}{?\~{}=?} &
-\end{tabular}
-
-{\bf Attributes Exported:}
-\begin{itemize}
-\item {\bf \cross{ARR2CAT}{finiteAggregate}}
-is true if it is an aggregate with a finite number of elements.
-\item {\bf \cross{ARR2CAT}{shallowlyMutable}}
-is true if its values have immediate components that are
-updateable (mutable). Note: the properties of any component
-domain are irrevelant to the shallowlyMutable proper.
-\end{itemize}
-
-{\bf Attributes Used:}
-\begin{itemize}
-\item {\bf \cross{ARR2CAT}{shallowlyMutable}}
-is true if its values have immediate components that are
-updateable (mutable). Note: the properties of any component
-domain are irrevelant to the shallowlyMutable proper.
-\end{itemize}
-
-These are directly exported but not implemented:
-\begin{verbatim}
- elt : (%,Integer,Integer) -> R
- maxColIndex : % -> Integer
- maxRowIndex : % -> Integer
- minColIndex : % -> Integer
- minRowIndex : % -> Integer
- new : (NonNegativeInteger,NonNegativeInteger,R) -> %
- ncols : % -> NonNegativeInteger
- nrows : % -> NonNegativeInteger
- qelt : (%,Integer,Integer) -> R
- qsetelt! : (%,Integer,Integer,R) -> R
- setelt : (%,Integer,Integer,R) -> R
-\end{verbatim}
-
-These are implemented by this category:
-\begin{verbatim}
- any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
- copy : % -> %
- coerce : % -> OutputForm if R has SETCAT
- column : (%,Integer) -> Col
- count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
- count : (R,%) -> NonNegativeInteger if R has SETCAT and $ has finiteAggregate
- elt : (%,Integer,Integer,R) -> R
- every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
- fill! : (%,R) -> %
- less? : (%,NonNegativeInteger) -> Boolean
- map : ((R -> R),%) -> %
- map : (((R,R) -> R),%,%) -> %
- map : (((R,R) -> R),%,%,R) -> %
- map! : ((R -> R),%) -> %
- member? : (R,%) -> Boolean if R has SETCAT and $ has finiteAggregate
- more? : (%,NonNegativeInteger) -> Boolean
- parts : % -> List R
- row : (%,Integer) -> Row
- setColumn! : (%,Integer,Col) -> %
- setRow! : (%,Integer,Row) -> %
- size? : (%,NonNegativeInteger) -> Boolean
- #? : % -> NonNegativeInteger if $ has finiteAggregate
- ?=? : (%,%) -> Boolean if R has SETCAT
-\end{verbatim}
-
-These exports come from HomogeneousAggregate(R:Type)
-\begin{verbatim}
- empty : () -> %
- empty? : % -> Boolean
- eq? : (%,%) -> Boolean
- eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT
- eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT
- eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT
- eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT
- hash : % -> SingleInteger if R has SETCAT
- latex : % -> String if R has SETCAT
- members : % -> List R if $ has finiteAggregate
- sample : () -> %
- ?~=? : (%,%) -> Boolean if R has SETCAT
-\end{verbatim}
-
-<<category ARR2CAT TwoDimensionalArrayCategory>>=
-)abbrev category ARR2CAT TwoDimensionalArrayCategory
-++ Two dimensional array categories and domains
-++ Author:
-++ Date Created: 27 October 1989
-++ Date Last Updated: 27 June 1990
-++ Keywords: array, data structure
-++ Examples:
-++ References:
-TwoDimensionalArrayCategory(R,Row,Col): Category == Definition where
- R : Type
- Row : FiniteLinearAggregate R
- Col : FiniteLinearAggregate R
-
- Definition == HomogeneousAggregate(R) with
-
- shallowlyMutable
- ++ one may destructively alter arrays
-
- finiteAggregate
- ++ two-dimensional arrays are finite
-
---% Array creation
-
- new: (NonNegativeInteger,NonNegativeInteger,R) -> %
- ++ new(m,n,r) is an m-by-n array all of whose entries are r
- ++
- ++X arr : ARRAY2 INT := new(5,4,0)
-
- fill_!: (%,R) -> %
- ++ fill!(m,r) fills m with r's
- ++
- ++X arr : ARRAY2 INT := new(5,4,0)
- ++X fill!(arr,10)
-
---% Size inquiries
-
- minRowIndex : % -> Integer
- ++ minRowIndex(m) returns the index of the 'first' row of the array m
- ++
- ++X arr : ARRAY2 INT := new(5,4,10)
- ++X minRowIndex(arr)
-
- maxRowIndex : % -> Integer
- ++ maxRowIndex(m) returns the index of the 'last' row of the array m
- ++
- ++X arr : ARRAY2 INT := new(5,4,10)
- ++X maxRowIndex(arr)
-
- minColIndex : % -> Integer
- ++ minColIndex(m) returns the index of the 'first' column of the array m
- ++
- ++X arr : ARRAY2 INT := new(5,4,10)
- ++X minColIndex(arr)
-
- maxColIndex : % -> Integer
- ++ maxColIndex(m) returns the index of the 'last' column of the array m
- ++
- ++X arr : ARRAY2 INT := new(5,4,10)
- ++X maxColIndex(arr)
-
- nrows : % -> NonNegativeInteger
- ++ nrows(m) returns the number of rows in the array m
- ++
- ++X arr : ARRAY2 INT := new(5,4,10)
- ++X nrows(arr)
-
- ncols : % -> NonNegativeInteger
- ++ ncols(m) returns the number of columns in the array m
- ++
- ++X arr : ARRAY2 INT := new(5,4,10)
- ++X ncols(arr)
-
---% Part extractions
-
- elt: (%,Integer,Integer) -> R
- ++ elt(m,i,j) returns the element in the ith row and jth
- ++ column of the array m
- ++ error check to determine if indices are in proper ranges
- ++
- ++X arr : ARRAY2 INT := new(5,4,10)
- ++X elt(arr,1,1)
-
- qelt: (%,Integer,Integer) -> R
- ++ qelt(m,i,j) returns the element in the ith row and jth
- ++ column of the array m
- ++ NO error check to determine if indices are in proper ranges
- ++
- ++X arr : ARRAY2 INT := new(5,4,10)
- ++X qelt(arr,1,1)
-
- elt: (%,Integer,Integer,R) -> R
- ++ elt(m,i,j,r) returns the element in the ith row and jth
- ++ column of the array m, if m has an ith row and a jth column,
- ++ and returns r otherwise
- ++
- ++X arr : ARRAY2 INT := new(5,4,10)
- ++X elt(arr,1,1,6)
- ++X elt(arr,1,10,6)
-
- row: (%,Integer) -> Row
- ++ row(m,i) returns the ith row of m
- ++ error check to determine if index is in proper ranges
- ++
- ++X arr : ARRAY2 INT := new(5,4,10)
- ++X row(arr,1)
-
- column: (%,Integer) -> Col
- ++ column(m,j) returns the jth column of m
- ++ error check to determine if index is in proper ranges
- ++
- ++X arr : ARRAY2 INT := new(5,4,10)
- ++X column(arr,1)
-
- parts: % -> List R
- ++ parts(m) returns a list of the elements of m in row major order
- ++
- ++X arr : ARRAY2 INT := new(5,4,10)
- ++X parts(arr)
-
---% Part assignments
-
- setelt: (%,Integer,Integer,R) -> R
- -- will become setelt_!
- ++ setelt(m,i,j,r) sets the element in the ith row and jth
- ++ column of m to r
- ++ error check to determine if indices are in proper ranges
- ++
- ++X arr : ARRAY2 INT := new(5,4,0)
- ++X setelt(arr,1,1,17)
-
- qsetelt_!: (%,Integer,Integer,R) -> R
- ++ qsetelt!(m,i,j,r) sets the element in the ith row and jth
- ++ column of m to r
- ++ NO error check to determine if indices are in proper ranges
- ++
- ++X arr : ARRAY2 INT := new(5,4,0)
- ++X qsetelt!(arr,1,1,17)
-
- setRow_!: (%,Integer,Row) -> %
- ++ setRow!(m,i,v) sets to ith row of m to v
- ++
- ++X T1:=TwoDimensionalArray Integer
- ++X arr:T1:= new(5,4,0)
- ++X T2:=OneDimensionalArray Integer
- ++X arow:=construct([1,2,3,4]::List(INT))$T2
- ++X setRow!(arr,1,arow)$T1
-
- setColumn_!: (%,Integer,Col) -> %
- ++ setColumn!(m,j,v) sets to jth column of m to v
- ++
- ++X T1:=TwoDimensionalArray Integer
- ++X arr:T1:= new(5,4,0)
- ++X T2:=OneDimensionalArray Integer
- ++X acol:=construct([1,2,3,4,5]::List(INT))$T2
- ++X setColumn!(arr,1,acol)$T1
-
---% Map and Zip
-
- map: (R -> R,%) -> %
- ++ map(f,a) returns \spad{b}, where \spad{b(i,j) = f(a(i,j))}
- ++ for all \spad{i, j}
- ++
- ++X arr : ARRAY2 INT := new(5,4,10)
- ++X map(-,arr)
- ++X map((x +-> x + x),arr)
-
- map_!: (R -> R,%) -> %
- ++ map!(f,a) assign \spad{a(i,j)} to \spad{f(a(i,j))}
- ++ for all \spad{i, j}
- ++X arr : ARRAY2 INT := new(5,4,10)
- ++X map!(-,arr)
-
- map:((R,R) -> R,%,%) -> %
- ++ map(f,a,b) returns \spad{c}, where \spad{c(i,j) = f(a(i,j),b(i,j))}
- ++ for all \spad{i, j}
- ++
- ++X adder(a:Integer,b:Integer):Integer == a+b
- ++X arr : ARRAY2 INT := new(5,4,10)
- ++X map(adder,arr,arr)
-
- map:((R,R) -> R,%,%,R) -> %
- ++ map(f,a,b,r) returns \spad{c}, where \spad{c(i,j) = f(a(i,j),b(i,j))}
- ++ when both \spad{a(i,j)} and \spad{b(i,j)} exist;
- ++ else \spad{c(i,j) = f(r, b(i,j))} when \spad{a(i,j)} does not exist;
- ++ else \spad{c(i,j) = f(a(i,j),r)} when \spad{b(i,j)} does not exist;
- ++ otherwise \spad{c(i,j) = f(r,r)}.
- ++
- ++X adder(a:Integer,b:Integer):Integer == a+b
- ++X arr1 : ARRAY2 INT := new(5,4,10)
- ++X arr2 : ARRAY2 INT := new(3,3,10)
- ++X map(adder,arr1,arr2,17)
-
- add
-
---% Predicates
-
- any?(f,m) ==
- for i in minRowIndex(m)..maxRowIndex(m) repeat
- for j in minColIndex(m)..maxColIndex(m) repeat
- f(qelt(m,i,j)) => return true
- false
-
- every?(f,m) ==
- for i in minRowIndex(m)..maxRowIndex(m) repeat
- for j in minColIndex(m)..maxColIndex(m) repeat
- not f(qelt(m,i,j)) => return false
- true
-
- size?(m,n) == nrows(m) * ncols(m) = n
- less?(m,n) == nrows(m) * ncols(m) < n
- more?(m,n) == nrows(m) * ncols(m) > n
-
---% Size inquiries
-
- # m == nrows(m) * ncols(m)
-
---% Part extractions
-
- elt(m,i,j,r) ==
- i < minRowIndex(m) or i > maxRowIndex(m) => r
- j < minColIndex(m) or j > maxColIndex(m) => r
- qelt(m,i,j)
-
- count(f:R -> Boolean,m:%) ==
- num : NonNegativeInteger := 0
- for i in minRowIndex(m)..maxRowIndex(m) repeat
- for j in minColIndex(m)..maxColIndex(m) repeat
- if f(qelt(m,i,j)) then num := num + 1
- num
-
- parts m ==
- entryList : List R := nil()
- for i in maxRowIndex(m)..minRowIndex(m) by -1 repeat
- for j in maxColIndex(m)..minColIndex(m) by -1 repeat
- entryList := concat(qelt(m,i,j),entryList)
- entryList
-
---% Creation
-
- copy m ==
- ans := new(nrows m,ncols m,NIL$Lisp)
- for i in minRowIndex(m)..maxRowIndex(m) repeat
- for j in minColIndex(m)..maxColIndex(m) repeat
- qsetelt_!(ans,i,j,qelt(m,i,j))
- ans
-
- fill_!(m,r) ==
- for i in minRowIndex(m)..maxRowIndex(m) repeat
- for j in minColIndex(m)..maxColIndex(m) repeat
- qsetelt_!(m,i,j,r)
- m
-
- map(f,m) ==
- ans := new(nrows m,ncols m,NIL$Lisp)
- for i in minRowIndex(m)..maxRowIndex(m) repeat
- for j in minColIndex(m)..maxColIndex(m) repeat
- qsetelt_!(ans,i,j,f(qelt(m,i,j)))
- ans
-
- map_!(f,m) ==
- for i in minRowIndex(m)..maxRowIndex(m) repeat
- for j in minColIndex(m)..maxColIndex(m) repeat
- qsetelt_!(m,i,j,f(qelt(m,i,j)))
- m
-
- map(f,m,n) ==
- (nrows(m) ^= nrows(n)) or (ncols(m) ^= ncols(n)) =>
- error "map: arguments must have same dimensions"
- ans := new(nrows m,ncols m,NIL$Lisp)
- for i in minRowIndex(m)..maxRowIndex(m) repeat
- for j in minColIndex(m)..maxColIndex(m) repeat
- qsetelt_!(ans,i,j,f(qelt(m,i,j),qelt(n,i,j)))
- ans
-
- map(f,m,n,r) ==
- maxRow := max(maxRowIndex m,maxRowIndex n)
- maxCol := max(maxColIndex m,maxColIndex n)
- ans := new(max(nrows m,nrows n),max(ncols m,ncols n),NIL$Lisp)
- for i in minRowIndex(m)..maxRow repeat
- for j in minColIndex(m)..maxCol repeat
- qsetelt_!(ans,i,j,f(elt(m,i,j,r),elt(n,i,j,r)))
- ans
-
- setRow_!(m,i,v) ==
- i < minRowIndex(m) or i > maxRowIndex(m) =>
- error "setRow!: index out of range"
- for j in minColIndex(m)..maxColIndex(m) _
- for k in minIndex(v)..maxIndex(v) repeat
- qsetelt_!(m,i,j,v.k)
- m
-
- setColumn_!(m,j,v) ==
- j < minColIndex(m) or j > maxColIndex(m) =>
- error "setColumn!: index out of range"
- for i in minRowIndex(m)..maxRowIndex(m) _
- for k in minIndex(v)..maxIndex(v) repeat
- qsetelt_!(m,i,j,v.k)
- m
-
- if R has _= : (R,R) -> Boolean then
-
- m = n ==
- eq?(m,n) => true
- (nrows(m) ^= nrows(n)) or (ncols(m) ^= ncols(n)) => false
- for i in minRowIndex(m)..maxRowIndex(m) repeat
- for j in minColIndex(m)..maxColIndex(m) repeat
- not (qelt(m,i,j) = qelt(n,i,j)) => return false
- true
-
- member?(r,m) ==
- for i in minRowIndex(m)..maxRowIndex(m) repeat
- for j in minColIndex(m)..maxColIndex(m) repeat
- qelt(m,i,j) = r => return true
- false
-
- count(r:R,m:%) == count(#1 = r,m)
-
- if Row has shallowlyMutable then
-
- row(m,i) ==
- i < minRowIndex(m) or i > maxRowIndex(m) =>
- error "row: index out of range"
- v : Row := new(ncols m,NIL$Lisp)
- for j in minColIndex(m)..maxColIndex(m) _
- for k in minIndex(v)..maxIndex(v) repeat
- qsetelt_!(v,k,qelt(m,i,j))
- v
-
- if Col has shallowlyMutable then
-
- column(m,j) ==
- j < minColIndex(m) or j > maxColIndex(m) =>
- error "column: index out of range"
- v : Col := new(nrows m,NIL$Lisp)
- for i in minRowIndex(m)..maxRowIndex(m) _
- for k in minIndex(v)..maxIndex(v) repeat
- qsetelt_!(v,k,qelt(m,i,j))
- v
-
- if R has CoercibleTo(OutputForm) then
-
- coerce(m:%) ==
- l : List List OutputForm
- l := [[qelt(m,i,j) :: OutputForm _
- for j in minColIndex(m)..maxColIndex(m)] _
- for i in minRowIndex(m)..maxRowIndex(m)]
- matrix l
-
-@
-<<ARR2CAT.dotabb>>=
-"ARR2CAT"
- [color=lightblue,href="bookvol10.2.pdf#nameddest=ARR2CAT"];
-"ARR2CAT" -> "HOAGG"
-
-@
-<<ARR2CAT.dotfull>>=
-"TwoDimensionalArrayCategory(a:Type,b:FiniteLinearAggregate(a),c:FiniteLinearAggregate(a))"
- [color=lightblue,href="bookvol10.2.pdf#nameddest=ARR2CAT"];
-"TwoDimensionalArrayCategory(a:Type,b:FiniteLinearAggregate(a),c:FiniteLinearAggregate(a))"
- -> "HomogeneousAggregate(a:Type)"
-
-"TwoDimensionalArrayCategory(a:Type,d:IndexedOneDimensionalArray(a,b),e:IndexedOneDimensionalArray(a,c))"
- [color=seagreen,href="bookvol10.2.pdf#nameddest=ARR2CAT"];
-"TwoDimensionalArrayCategory(a:Type,d:IndexedOneDimensionalArray(a,b),e:IndexedOneDimensionalArray(a,c))"
--> "TwoDimensionalArrayCategory(a:Type,b:FiniteLinearAggregate(a),c:FiniteLinearAggregate(a))"
-
-@
-<<ARR2CAT.dotpic>>=
-digraph pic {
- fontsize=10;
- bgcolor="#FFFF66";
- node [shape=box, color=white, style=filled];
-
-"TwoDimensionalArrayCategory(a:Type,b:FiniteLinearAggregate(a),c:FiniteLinearAggregate(a))"
- [color=lightblue];
-"TwoDimensionalArrayCategory(a:Type,b:FiniteLinearAggregate(a),c:FiniteLinearAggregate(a))"
- -> "HomogeneousAggregate(a:Type)"
-
-"HomogeneousAggregate(a:Type)" [color=lightblue];
-"HomogeneousAggregate(a:Type)" -> "Aggregate()"
-"HomogeneousAggregate(a:Type)" -> "Evalable(a:Type)"
-"HomogeneousAggregate(a:Type)" -> "SetCategory()"
-
-"Evalable(a:Type)" [color="#00EE00"];
-
-"SetCategory()" [color=lightblue];
-"SetCategory()" -> "BasicType()"
-"SetCategory()" -> "CoercibleTo(OutputForm)"
-
-"BasicType()" [color=lightblue];
-"BasicType()" -> "Category"
-
-"CoercibleTo(OutputForm)" [color=seagreen];
-"CoercibleTo(OutputForm)" -> "CoercibleTo(a:Type)"
-
-"CoercibleTo(a:Type)" [color=lightblue];
-"CoercibleTo(a:Type)" -> "Category"
-
-"Aggregate()" [color=lightblue];
-"Aggregate()" -> "Type()"
-
-"Type()" [color=lightblue];
-"Type()" -> "Category"
-
-"Category" [color=lightblue];
-
-}
-
-@
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{BagAggregate}{BGAGG}
\pagepic{ps/v102bagaggregate.ps}{BGAGG}{1.00}
@@ -3594,6 +3326,161 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{GradedAlgebra}{GRALG}
+\pagepic{ps/v102gradedalgebra.ps}{GRALG}{0.75}
+
+{\bf See:}\\
+\pagefrom{GradedModule}{GRMOD}
+\pagefrom{RetractableTo}{RETRACT}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+\cross{GRALG}{0} &
+\cross{GRALG}{1} &
+\cross{GRALG}{coerce} &
+\cross{GRALG}{degree} &
+\cross{GRALG}{hash} \\
+\cross{GRALG}{latex} &
+\cross{GRALG}{product} &
+\cross{GRALG}{retract} &
+\cross{GRALG}{retractIfCan} &
+\cross{GRALG}{?\~{}=?} \\
+\cross{GRALG}{?*?} &
+\cross{GRALG}{?+?} &
+\cross{GRALG}{?-?} &
+\cross{GRALG}{-?} &
+\cross{GRALG}{?=?} \\
+\end{tabular}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ product : (%,%) -> %
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ 0 : () -> %
+ 1 : () -> %
+ ?*? : (%,R) -> %
+ ?*? : (R,%) -> %
+\end{verbatim}
+
+These exports come from GradedModule(R, E)\\
+where R:CommutativeRing and E:AbelianMonoid:
+\begin{verbatim}
+ coerce : % -> OutputForm
+ degree : % -> E
+ hash : % -> SingleInteger
+ latex : % -> String
+ ?~=? : (%,%) -> Boolean
+ ?=? : (%,%) -> Boolean
+ ?-? : (%,%) -> %
+ -? : % -> %
+ ?+? : (%,%) -> %
+\end{verbatim}
+
+These exports come from ,RetractableTo(R:CommutativeRing):
+\begin{verbatim}
+ coerce : R -> %
+ retract : % -> R
+ retractIfCan : % -> Union(R,"failed")
+\end{verbatim}
+
+<<category GRALG GradedAlgebra>>=
+)abbrev category GRALG GradedAlgebra
+++ Author: Stephen M. Watt
+++ Date Created: May 20, 1991
+++ Date Last Updated: May 20, 1991
+++ Basic Operations: +, *, degree
+++ Related Domains: CartesianTensor(n,dim,R)
+++ Also See:
+++ AMS Classifications:
+++ Keywords: graded module, tensor, multi-linear algebra
+++ Examples:
+++ References: Encyclopedic Dictionary of Mathematics, MIT Press, 1977
+++ Description:
+++ GradedAlgebra(R,E) denotes ``E-graded R-algebra''.
+++ A graded algebra is a graded module together with a degree preserving
+++ R-linear map, called the {\em product}.
+++
+++ The name ``product'' is written out in full so inner and outer products
+++ with the same mapping type can be distinguished by name.
+
+GradedAlgebra(R: CommutativeRing, E: AbelianMonoid): Category ==
+ Join(GradedModule(R, E),RetractableTo(R)) with
+ 1: constant -> %
+ ++ 1 is the identity for \spad{product}.
+ product: (%, %) -> %
+ ++ product(a,b) is the degree-preserving R-linear product:
+ ++
+ ++ \spad{degree product(a,b) = degree a + degree b}
+ ++ \spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}
+ ++ \spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}
+ ++ \spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}
+ ++ \spad{product(a,product(b,c)) = product(product(a,b),c)}
+ add
+ if not (R is %) then
+ 0: % == (0$R)::%
+ 1: % == 1$R::%
+ (r: R)*(x: %) == product(r::%, x)
+ (x: %)*(r: R) == product(x, r::%)
+
+@
+<<GRALG.dotabb>>=
+"GRALG"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=GRALG"];
+"GRALG" -> "GRMOD"
+"GRALG" -> "RETRACT"
+
+@
+<<GRALG.dotfull>>=
+"GradedAlgebra(a:CommutativeRing,b:AbelianMonoid)"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=GRALG"];
+"GradedAlgebra(a:CommutativeRing,b:AbelianMonoid)" ->
+ "GradedModule(a:CommutativeRing,b:AbelianMonoid)"
+"GradedAlgebra(a:CommutativeRing,b:AbelianMonoid)" ->
+ "RetractableTo(CommutativeRing)"
+@
+<<GRALG.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"GradedAlgebra(a:CommutativeRing,b:AbelianMonoid)" [color=lightblue];
+"GradedAlgebra(a:CommutativeRing,b:AbelianMonoid)" ->
+ "GradedModule(a:CommutativeRing,b:AbelianMonoid)"
+"GradedAlgebra(a:CommutativeRing,b:AbelianMonoid)" ->
+ "RetractableTo(CommutativeRing)"
+
+"RetractableTo(CommutativeRing)" [color=seagreen];
+"RetractableTo(CommutativeRing)" -> "RetractableTo(a:Type)"
+
+"RetractableTo(a:Type)" [color=lightblue];
+"RetractableTo(a:Type)" -> "Category"
+
+"GradedModule(a:CommutativeRing,b:AbelianMonoid)" [color=lightblue];
+"GradedModule(a:CommutativeRing,b:AbelianMonoid)" -> "SetCategory()"
+
+"SetCategory()" [color=lightblue];
+"SetCategory()" -> "BasicType()"
+"SetCategory()" -> "CoercibleTo(OutputForm)"
+
+"BasicType()" [color=lightblue];
+"BasicType()" -> "Category"
+
+"CoercibleTo(OutputForm)" [color=seagreen];
+"CoercibleTo(OutputForm)" -> "CoercibleTo(a:Type)"
+
+"CoercibleTo(a:Type)" [color=lightblue];
+"CoercibleTo(a:Type)" -> "Category"
+
+"Category" [color=lightblue];
+
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{IndexedAggregate}{IXAGG}
\pagepic{ps/v102indexedaggregate.ps}{IXAGG}{1.00}
@@ -3867,6 +3754,181 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{MonadWithUnit}{MONADWU}
+\pagepic{ps/v102monadwithunit.ps}{MONADWU}{0.75}
+
+{\bf See:}\\
+\pageto{NonAssociativeRing}{NASRING}
+\pagefrom{Monad}{MONAD}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+\cross{MONADWU}{1} &
+\cross{MONADWU}{coerce} &
+\cross{MONADWU}{hash} &
+\cross{MONADWU}{latex} &
+\cross{MONADWU}{one?} \\
+\cross{MONADWU}{recip} &
+\cross{MONADWU}{leftPower} &
+\cross{MONADWU}{leftRecip} &
+\cross{MONADWU}{rightPower} &
+\cross{MONADWU}{rightRecip} \\
+\cross{MONADWU}{?*?} &
+\cross{MONADWU}{?\~{}=?} &
+\cross{MONADWU}{?**?} &
+\cross{MONADWU}{?=?} &
+\end{tabular}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ 1 : () -> %
+ leftRecip : % -> Union(%,"failed")
+ recip : % -> Union(%,"failed")
+ rightRecip : % -> Union(%,"failed")
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ leftPower : (%,NonNegativeInteger) -> %
+ one? : % -> Boolean
+ rightPower : (%,NonNegativeInteger) -> %
+ ?**? : (%,NonNegativeInteger) -> %
+\end{verbatim}
+
+These exports come from Monad():
+\begin{verbatim}
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ leftPower : (%,PositiveInteger) -> %
+ rightPower : (%,PositiveInteger) -> %
+ ?**? : (%,PositiveInteger) -> %
+ ?*? : (%,%) -> %
+ ?~=? : (%,%) -> Boolean
+ ?=? : (%,%) -> Boolean
+\end{verbatim}
+
+<<category MONADWU MonadWithUnit>>=
+)abbrev category MONADWU MonadWithUnit
+++ Authors: J. Grabmeier, R. Wisbauer
+++ Date Created: 01 March 1991
+++ Date Last Updated: 11 June 1991
+++ Basic Operations: *, **, 1
+++ Related Constructors: SemiGroup, Monoid, Monad
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ Keywords: Monad with unit, binary operation
+++ Reference:
+++ N. Jacobson: Structure and Representations of Jordan Algebras
+++ AMS, Providence, 1968
+++ Description:
+++ MonadWithUnit is the class of multiplicative monads with unit,
+++ i.e. sets with a binary operation and a unit element.
+++ Axioms
+++ leftIdentity("*":(%,%)->%,1) \tab{30} 1*x=x
+++ rightIdentity("*":(%,%)->%,1) \tab{30} x*1=x
+++ Common Additional Axioms
+++ unitsKnown---if "recip" says "failed", that PROVES input wasn't a unit
+MonadWithUnit(): Category == Monad with
+ 1: constant -> %
+ ++ 1 returns the unit element, denoted by 1.
+ one?: % -> Boolean
+ ++ one?(a) tests whether \spad{a} is the unit 1.
+ rightPower: (%,NonNegativeInteger) -> %
+ ++ rightPower(a,n) returns the \spad{n}-th right power of \spad{a},
+ ++ i.e. \spad{rightPower(a,n) := rightPower(a,n-1) * a} and
+ ++ \spad{rightPower(a,0) := 1}.
+ leftPower: (%,NonNegativeInteger) -> %
+ ++ leftPower(a,n) returns the \spad{n}-th left power of \spad{a},
+ ++ i.e. \spad{leftPower(a,n) := a * leftPower(a,n-1)} and
+ ++ \spad{leftPower(a,0) := 1}.
+ "**": (%,NonNegativeInteger) -> %
+ ++ \spad{a**n} returns the \spad{n}-th power of \spad{a},
+ ++ defined by repeated squaring.
+ recip: % -> Union(%,"failed")
+ ++ recip(a) returns an element, which is both a left and a right
+ ++ inverse of \spad{a},
+ ++ or \spad{"failed"} if such an element doesn't exist or cannot
+ ++ be determined (see unitsKnown).
+ leftRecip: % -> Union(%,"failed")
+ ++ leftRecip(a) returns an element, which is a left inverse of
+ ++ \spad{a}, or \spad{"failed"} if such an element doesn't exist
+ ++ or cannot be determined (see unitsKnown).
+ rightRecip: % -> Union(%,"failed")
+ ++ rightRecip(a) returns an element, which is a right inverse of
+ ++ \spad{a}, or \spad{"failed"} if such an element doesn't exist
+ ++ or cannot be determined (see unitsKnown).
+ add
+ import RepeatedSquaring(%)
+ one? x == x = 1
+ x:% ** n:NonNegativeInteger ==
+ zero? n => 1
+ expt(x,n pretend PositiveInteger)
+ rightPower(a,n) ==
+ zero? n => 1
+ res := 1
+ for i in 1..n repeat res := res * a
+ res
+ leftPower(a,n) ==
+ zero? n => 1
+ res := 1
+ for i in 1..n repeat res := a * res
+ res
+
+@
+<<MONADWU.dotabb>>=
+"MONADWU"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=MONADWU"];
+"MONADWU" -> "MONAD"
+
+@
+<<MONADWU.dotfull>>=
+"MonadWithUnit()"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=MONADWU"];
+"MonadWithUnit()" -> "Monad()"
+
+@
+<<MONADWU.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"MonadWithUnit()" [color=lightblue];
+"MonadWithUnit()" -> "Monad()"
+
+"Monad()" [color=lightblue];
+"Monad()" -> "SetCategory()"
+"Monad()" -> "RepeatedSquaring(Monad)"
+
+"RepeatedSquaring(Monad)" [color="#00EE00"];
+"RepeatedSquaring(Monad)" -> "RepeatedSquaring(a:SetCategory)"
+
+"RepeatedSquaring(a:SetCategory)" [color="#00EE00"];
+"RepeatedSquaring(a:SetCategory)" -> "Package"
+
+"Package" [color="#00EE00"];
+
+"SetCategory()" [color=lightblue];
+"SetCategory()" -> "BasicType()"
+"SetCategory()" -> "CoercibleTo(OutputForm)"
+
+"BasicType()" [color=lightblue];
+"BasicType()" -> "Category"
+
+"CoercibleTo(OutputForm)" [color=seagreen];
+"CoercibleTo(OutputForm)" -> "CoercibleTo(a:Type)"
+
+"CoercibleTo(a:Type)" [color=lightblue];
+"CoercibleTo(a:Type)" -> "Category"
+
+"Category" [color=lightblue];
+
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{Monoid}{MONOID}
\pagepic{ps/v102monoid.ps}{MONOID}{0.75}
@@ -4349,6 +4411,552 @@
}
@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{TwoDimensionalArrayCategory}{ARR2CAT}
+\pagepic{ps/v102twodimensionalarraycategory.ps}{ARR2CAT}{0.60}
+
+TwoDimensionalArrayCategory is a general array category which
+allows different representations and indexing schemes.
+Rows and columns may be extracted with rows returned as objects
+of type Row and columns returned as objects of type Col.
+The index of the 'first' row may be obtained by calling the
+function 'minRowIndex'. The index of the 'first' column may
+be obtained by calling the function 'minColIndex'. The index of
+the first element of a 'Row' is the same as the index of the
+first column in an array and vice versa.
+
+{\bf See:}\\
+\pagefrom{HomogeneousAggregate}{HOAGG}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+\cross{ARR2CAT}{any?} &
+\cross{ARR2CAT}{column} &
+\cross{ARR2CAT}{coerce} &
+\cross{ARR2CAT}{copy} &
+\cross{ARR2CAT}{count} \\
+\cross{ARR2CAT}{elt} &
+\cross{ARR2CAT}{empty} &
+\cross{ARR2CAT}{empty?} &
+\cross{ARR2CAT}{eq?} &
+\cross{ARR2CAT}{eval} \\
+\cross{ARR2CAT}{every?} &
+\cross{ARR2CAT}{fill!} &
+\cross{ARR2CAT}{hash} &
+\cross{ARR2CAT}{latex} &
+\cross{ARR2CAT}{less?} \\
+\cross{ARR2CAT}{map} &
+\cross{ARR2CAT}{map!} &
+\cross{ARR2CAT}{maxColIndex} &
+\cross{ARR2CAT}{maxRowIndex} &
+\cross{ARR2CAT}{member?} \\
+\cross{ARR2CAT}{members} &
+\cross{ARR2CAT}{minColIndex} &
+\cross{ARR2CAT}{minRowIndex} &
+\cross{ARR2CAT}{more?} &
+\cross{ARR2CAT}{ncols} \\
+\cross{ARR2CAT}{new} &
+\cross{ARR2CAT}{nrows} &
+\cross{ARR2CAT}{parts} &
+\cross{ARR2CAT}{qelt} &
+\cross{ARR2CAT}{qsetelt!} \\
+\cross{ARR2CAT}{row} &
+\cross{ARR2CAT}{sample} &
+\cross{ARR2CAT}{setColumn!} &
+\cross{ARR2CAT}{setRow!} &
+\cross{ARR2CAT}{setelt} \\
+\cross{ARR2CAT}{size?} &
+\cross{ARR2CAT}{\#?} &
+\cross{ARR2CAT}{?=?} &
+\cross{ARR2CAT}{?\~{}=?} &
+\end{tabular}
+
+{\bf Attributes Exported:}
+\begin{itemize}
+\item {\bf \cross{ARR2CAT}{finiteAggregate}}
+is true if it is an aggregate with a finite number of elements.
+\item {\bf \cross{ARR2CAT}{shallowlyMutable}}
+is true if its values have immediate components that are
+updateable (mutable). Note: the properties of any component
+domain are irrevelant to the shallowlyMutable proper.
+\end{itemize}
+
+{\bf Attributes Used:}
+\begin{itemize}
+\item {\bf \cross{ARR2CAT}{shallowlyMutable}}
+is true if its values have immediate components that are
+updateable (mutable). Note: the properties of any component
+domain are irrevelant to the shallowlyMutable proper.
+\end{itemize}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ elt : (%,Integer,Integer) -> R
+ maxColIndex : % -> Integer
+ maxRowIndex : % -> Integer
+ minColIndex : % -> Integer
+ minRowIndex : % -> Integer
+ new : (NonNegativeInteger,NonNegativeInteger,R) -> %
+ ncols : % -> NonNegativeInteger
+ nrows : % -> NonNegativeInteger
+ qelt : (%,Integer,Integer) -> R
+ qsetelt! : (%,Integer,Integer,R) -> R
+ setelt : (%,Integer,Integer,R) -> R
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
+ copy : % -> %
+ coerce : % -> OutputForm if R has SETCAT
+ column : (%,Integer) -> Col
+ count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
+ count : (R,%) -> NonNegativeInteger if R has SETCAT and $ has finiteAggregate
+ elt : (%,Integer,Integer,R) -> R
+ every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
+ fill! : (%,R) -> %
+ less? : (%,NonNegativeInteger) -> Boolean
+ map : ((R -> R),%) -> %
+ map : (((R,R) -> R),%,%) -> %
+ map : (((R,R) -> R),%,%,R) -> %
+ map! : ((R -> R),%) -> %
+ member? : (R,%) -> Boolean if R has SETCAT and $ has finiteAggregate
+ more? : (%,NonNegativeInteger) -> Boolean
+ parts : % -> List R
+ row : (%,Integer) -> Row
+ setColumn! : (%,Integer,Col) -> %
+ setRow! : (%,Integer,Row) -> %
+ size? : (%,NonNegativeInteger) -> Boolean
+ #? : % -> NonNegativeInteger if $ has finiteAggregate
+ ?=? : (%,%) -> Boolean if R has SETCAT
+\end{verbatim}
+
+These exports come from HomogeneousAggregate(R:Type)
+\begin{verbatim}
+ empty : () -> %
+ empty? : % -> Boolean
+ eq? : (%,%) -> Boolean
+ eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT
+ eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT
+ eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT
+ eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT
+ hash : % -> SingleInteger if R has SETCAT
+ latex : % -> String if R has SETCAT
+ members : % -> List R if $ has finiteAggregate
+ sample : () -> %
+ ?~=? : (%,%) -> Boolean if R has SETCAT
+\end{verbatim}
+
+<<category ARR2CAT TwoDimensionalArrayCategory>>=
+)abbrev category ARR2CAT TwoDimensionalArrayCategory
+++ Two dimensional array categories and domains
+++ Author:
+++ Date Created: 27 October 1989
+++ Date Last Updated: 27 June 1990
+++ Keywords: array, data structure
+++ Examples:
+++ References:
+TwoDimensionalArrayCategory(R,Row,Col): Category == Definition where
+ R : Type
+ Row : FiniteLinearAggregate R
+ Col : FiniteLinearAggregate R
+
+ Definition == HomogeneousAggregate(R) with
+
+ shallowlyMutable
+ ++ one may destructively alter arrays
+
+ finiteAggregate
+ ++ two-dimensional arrays are finite
+
+--% Array creation
+
+ new: (NonNegativeInteger,NonNegativeInteger,R) -> %
+ ++ new(m,n,r) is an m-by-n array all of whose entries are r
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,0)
+
+ fill_!: (%,R) -> %
+ ++ fill!(m,r) fills m with r's
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,0)
+ ++X fill!(arr,10)
+
+--% Size inquiries
+
+ minRowIndex : % -> Integer
+ ++ minRowIndex(m) returns the index of the 'first' row of the array m
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X minRowIndex(arr)
+
+ maxRowIndex : % -> Integer
+ ++ maxRowIndex(m) returns the index of the 'last' row of the array m
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X maxRowIndex(arr)
+
+ minColIndex : % -> Integer
+ ++ minColIndex(m) returns the index of the 'first' column of the array m
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X minColIndex(arr)
+
+ maxColIndex : % -> Integer
+ ++ maxColIndex(m) returns the index of the 'last' column of the array m
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X maxColIndex(arr)
+
+ nrows : % -> NonNegativeInteger
+ ++ nrows(m) returns the number of rows in the array m
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X nrows(arr)
+
+ ncols : % -> NonNegativeInteger
+ ++ ncols(m) returns the number of columns in the array m
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X ncols(arr)
+
+--% Part extractions
+
+ elt: (%,Integer,Integer) -> R
+ ++ elt(m,i,j) returns the element in the ith row and jth
+ ++ column of the array m
+ ++ error check to determine if indices are in proper ranges
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X elt(arr,1,1)
+
+ qelt: (%,Integer,Integer) -> R
+ ++ qelt(m,i,j) returns the element in the ith row and jth
+ ++ column of the array m
+ ++ NO error check to determine if indices are in proper ranges
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X qelt(arr,1,1)
+
+ elt: (%,Integer,Integer,R) -> R
+ ++ elt(m,i,j,r) returns the element in the ith row and jth
+ ++ column of the array m, if m has an ith row and a jth column,
+ ++ and returns r otherwise
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X elt(arr,1,1,6)
+ ++X elt(arr,1,10,6)
+
+ row: (%,Integer) -> Row
+ ++ row(m,i) returns the ith row of m
+ ++ error check to determine if index is in proper ranges
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X row(arr,1)
+
+ column: (%,Integer) -> Col
+ ++ column(m,j) returns the jth column of m
+ ++ error check to determine if index is in proper ranges
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X column(arr,1)
+
+ parts: % -> List R
+ ++ parts(m) returns a list of the elements of m in row major order
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X parts(arr)
+
+--% Part assignments
+
+ setelt: (%,Integer,Integer,R) -> R
+ -- will become setelt_!
+ ++ setelt(m,i,j,r) sets the element in the ith row and jth
+ ++ column of m to r
+ ++ error check to determine if indices are in proper ranges
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,0)
+ ++X setelt(arr,1,1,17)
+
+ qsetelt_!: (%,Integer,Integer,R) -> R
+ ++ qsetelt!(m,i,j,r) sets the element in the ith row and jth
+ ++ column of m to r
+ ++ NO error check to determine if indices are in proper ranges
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,0)
+ ++X qsetelt!(arr,1,1,17)
+
+ setRow_!: (%,Integer,Row) -> %
+ ++ setRow!(m,i,v) sets to ith row of m to v
+ ++
+ ++X T1:=TwoDimensionalArray Integer
+ ++X arr:T1:= new(5,4,0)
+ ++X T2:=OneDimensionalArray Integer
+ ++X arow:=construct([1,2,3,4]::List(INT))$T2
+ ++X setRow!(arr,1,arow)$T1
+
+ setColumn_!: (%,Integer,Col) -> %
+ ++ setColumn!(m,j,v) sets to jth column of m to v
+ ++
+ ++X T1:=TwoDimensionalArray Integer
+ ++X arr:T1:= new(5,4,0)
+ ++X T2:=OneDimensionalArray Integer
+ ++X acol:=construct([1,2,3,4,5]::List(INT))$T2
+ ++X setColumn!(arr,1,acol)$T1
+
+--% Map and Zip
+
+ map: (R -> R,%) -> %
+ ++ map(f,a) returns \spad{b}, where \spad{b(i,j) = f(a(i,j))}
+ ++ for all \spad{i, j}
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X map(-,arr)
+ ++X map((x +-> x + x),arr)
+
+ map_!: (R -> R,%) -> %
+ ++ map!(f,a) assign \spad{a(i,j)} to \spad{f(a(i,j))}
+ ++ for all \spad{i, j}
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X map!(-,arr)
+
+ map:((R,R) -> R,%,%) -> %
+ ++ map(f,a,b) returns \spad{c}, where \spad{c(i,j) = f(a(i,j),b(i,j))}
+ ++ for all \spad{i, j}
+ ++
+ ++X adder(a:Integer,b:Integer):Integer == a+b
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X map(adder,arr,arr)
+
+ map:((R,R) -> R,%,%,R) -> %
+ ++ map(f,a,b,r) returns \spad{c}, where \spad{c(i,j) = f(a(i,j),b(i,j))}
+ ++ when both \spad{a(i,j)} and \spad{b(i,j)} exist;
+ ++ else \spad{c(i,j) = f(r, b(i,j))} when \spad{a(i,j)} does not exist;
+ ++ else \spad{c(i,j) = f(a(i,j),r)} when \spad{b(i,j)} does not exist;
+ ++ otherwise \spad{c(i,j) = f(r,r)}.
+ ++
+ ++X adder(a:Integer,b:Integer):Integer == a+b
+ ++X arr1 : ARRAY2 INT := new(5,4,10)
+ ++X arr2 : ARRAY2 INT := new(3,3,10)
+ ++X map(adder,arr1,arr2,17)
+
+ add
+
+--% Predicates
+
+ any?(f,m) ==
+ for i in minRowIndex(m)..maxRowIndex(m) repeat
+ for j in minColIndex(m)..maxColIndex(m) repeat
+ f(qelt(m,i,j)) => return true
+ false
+
+ every?(f,m) ==
+ for i in minRowIndex(m)..maxRowIndex(m) repeat
+ for j in minColIndex(m)..maxColIndex(m) repeat
+ not f(qelt(m,i,j)) => return false
+ true
+
+ size?(m,n) == nrows(m) * ncols(m) = n
+ less?(m,n) == nrows(m) * ncols(m) < n
+ more?(m,n) == nrows(m) * ncols(m) > n
+
+--% Size inquiries
+
+ # m == nrows(m) * ncols(m)
+
+--% Part extractions
+
+ elt(m,i,j,r) ==
+ i < minRowIndex(m) or i > maxRowIndex(m) => r
+ j < minColIndex(m) or j > maxColIndex(m) => r
+ qelt(m,i,j)
+
+ count(f:R -> Boolean,m:%) ==
+ num : NonNegativeInteger := 0
+ for i in minRowIndex(m)..maxRowIndex(m) repeat
+ for j in minColIndex(m)..maxColIndex(m) repeat
+ if f(qelt(m,i,j)) then num := num + 1
+ num
+
+ parts m ==
+ entryList : List R := nil()
+ for i in maxRowIndex(m)..minRowIndex(m) by -1 repeat
+ for j in maxColIndex(m)..minColIndex(m) by -1 repeat
+ entryList := concat(qelt(m,i,j),entryList)
+ entryList
+
+--% Creation
+
+ copy m ==
+ ans := new(nrows m,ncols m,NIL$Lisp)
+ for i in minRowIndex(m)..maxRowIndex(m) repeat
+ for j in minColIndex(m)..maxColIndex(m) repeat
+ qsetelt_!(ans,i,j,qelt(m,i,j))
+ ans
+
+ fill_!(m,r) ==
+ for i in minRowIndex(m)..maxRowIndex(m) repeat
+ for j in minColIndex(m)..maxColIndex(m) repeat
+ qsetelt_!(m,i,j,r)
+ m
+
+ map(f,m) ==
+ ans := new(nrows m,ncols m,NIL$Lisp)
+ for i in minRowIndex(m)..maxRowIndex(m) repeat
+ for j in minColIndex(m)..maxColIndex(m) repeat
+ qsetelt_!(ans,i,j,f(qelt(m,i,j)))
+ ans
+
+ map_!(f,m) ==
+ for i in minRowIndex(m)..maxRowIndex(m) repeat
+ for j in minColIndex(m)..maxColIndex(m) repeat
+ qsetelt_!(m,i,j,f(qelt(m,i,j)))
+ m
+
+ map(f,m,n) ==
+ (nrows(m) ^= nrows(n)) or (ncols(m) ^= ncols(n)) =>
+ error "map: arguments must have same dimensions"
+ ans := new(nrows m,ncols m,NIL$Lisp)
+ for i in minRowIndex(m)..maxRowIndex(m) repeat
+ for j in minColIndex(m)..maxColIndex(m) repeat
+ qsetelt_!(ans,i,j,f(qelt(m,i,j),qelt(n,i,j)))
+ ans
+
+ map(f,m,n,r) ==
+ maxRow := max(maxRowIndex m,maxRowIndex n)
+ maxCol := max(maxColIndex m,maxColIndex n)
+ ans := new(max(nrows m,nrows n),max(ncols m,ncols n),NIL$Lisp)
+ for i in minRowIndex(m)..maxRow repeat
+ for j in minColIndex(m)..maxCol repeat
+ qsetelt_!(ans,i,j,f(elt(m,i,j,r),elt(n,i,j,r)))
+ ans
+
+ setRow_!(m,i,v) ==
+ i < minRowIndex(m) or i > maxRowIndex(m) =>
+ error "setRow!: index out of range"
+ for j in minColIndex(m)..maxColIndex(m) _
+ for k in minIndex(v)..maxIndex(v) repeat
+ qsetelt_!(m,i,j,v.k)
+ m
+
+ setColumn_!(m,j,v) ==
+ j < minColIndex(m) or j > maxColIndex(m) =>
+ error "setColumn!: index out of range"
+ for i in minRowIndex(m)..maxRowIndex(m) _
+ for k in minIndex(v)..maxIndex(v) repeat
+ qsetelt_!(m,i,j,v.k)
+ m
+
+ if R has _= : (R,R) -> Boolean then
+
+ m = n ==
+ eq?(m,n) => true
+ (nrows(m) ^= nrows(n)) or (ncols(m) ^= ncols(n)) => false
+ for i in minRowIndex(m)..maxRowIndex(m) repeat
+ for j in minColIndex(m)..maxColIndex(m) repeat
+ not (qelt(m,i,j) = qelt(n,i,j)) => return false
+ true
+
+ member?(r,m) ==
+ for i in minRowIndex(m)..maxRowIndex(m) repeat
+ for j in minColIndex(m)..maxColIndex(m) repeat
+ qelt(m,i,j) = r => return true
+ false
+
+ count(r:R,m:%) == count(#1 = r,m)
+
+ if Row has shallowlyMutable then
+
+ row(m,i) ==
+ i < minRowIndex(m) or i > maxRowIndex(m) =>
+ error "row: index out of range"
+ v : Row := new(ncols m,NIL$Lisp)
+ for j in minColIndex(m)..maxColIndex(m) _
+ for k in minIndex(v)..maxIndex(v) repeat
+ qsetelt_!(v,k,qelt(m,i,j))
+ v
+
+ if Col has shallowlyMutable then
+
+ column(m,j) ==
+ j < minColIndex(m) or j > maxColIndex(m) =>
+ error "column: index out of range"
+ v : Col := new(nrows m,NIL$Lisp)
+ for i in minRowIndex(m)..maxRowIndex(m) _
+ for k in minIndex(v)..maxIndex(v) repeat
+ qsetelt_!(v,k,qelt(m,i,j))
+ v
+
+ if R has CoercibleTo(OutputForm) then
+
+ coerce(m:%) ==
+ l : List List OutputForm
+ l := [[qelt(m,i,j) :: OutputForm _
+ for j in minColIndex(m)..maxColIndex(m)] _
+ for i in minRowIndex(m)..maxRowIndex(m)]
+ matrix l
+
+@
+<<ARR2CAT.dotabb>>=
+"ARR2CAT"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ARR2CAT"];
+"ARR2CAT" -> "HOAGG"
+
+@
+<<ARR2CAT.dotfull>>=
+"TwoDimensionalArrayCategory(a:Type,b:FiniteLinearAggregate(a),c:FiniteLinearAggregate(a))"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ARR2CAT"];
+"TwoDimensionalArrayCategory(a:Type,b:FiniteLinearAggregate(a),c:FiniteLinearAggregate(a))"
+ -> "HomogeneousAggregate(a:Type)"
+
+"TwoDimensionalArrayCategory(a:Type,d:IndexedOneDimensionalArray(a,b),e:IndexedOneDimensionalArray(a,c))"
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=ARR2CAT"];
+"TwoDimensionalArrayCategory(a:Type,d:IndexedOneDimensionalArray(a,b),e:IndexedOneDimensionalArray(a,c))"
+-> "TwoDimensionalArrayCategory(a:Type,b:FiniteLinearAggregate(a),c:FiniteLinearAggregate(a))"
+
+@
+<<ARR2CAT.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"TwoDimensionalArrayCategory(a:Type,b:FiniteLinearAggregate(a),c:FiniteLinearAggregate(a))"
+ [color=lightblue];
+"TwoDimensionalArrayCategory(a:Type,b:FiniteLinearAggregate(a),c:FiniteLinearAggregate(a))"
+ -> "HomogeneousAggregate(a:Type)"
+
+"HomogeneousAggregate(a:Type)" [color=lightblue];
+"HomogeneousAggregate(a:Type)" -> "Aggregate()"
+"HomogeneousAggregate(a:Type)" -> "Evalable(a:Type)"
+"HomogeneousAggregate(a:Type)" -> "SetCategory()"
+
+"Evalable(a:Type)" [color="#00EE00"];
+
+"SetCategory()" [color=lightblue];
+"SetCategory()" -> "BasicType()"
+"SetCategory()" -> "CoercibleTo(OutputForm)"
+
+"BasicType()" [color=lightblue];
+"BasicType()" -> "Category"
+
+"CoercibleTo(OutputForm)" [color=seagreen];
+"CoercibleTo(OutputForm)" -> "CoercibleTo(a:Type)"
+
+"CoercibleTo(a:Type)" [color=lightblue];
+"CoercibleTo(a:Type)" -> "Category"
+
+"Aggregate()" [color=lightblue];
+"Aggregate()" -> "Type()"
+
+"Type()" [color=lightblue];
+"Type()" -> "Category"
+
+"Category" [color=lightblue];
+
+}
+
+@
\chapter{Category Layer 5}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{BinaryRecursiveAggregate}{BRAGG}
@@ -7232,6 +7840,7 @@
{\bf See:}\\
\pageto{LeftModule}{LMODULE}
+\pageto{NonAssociativeRng}{NARNG}
\pageto{OrderedAbelianGroup}{OAGROUP}
\pageto{RightModule}{RMODULE}
\pageto{Rng}{RNG}
@@ -7339,6 +7948,22 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
+"NonAssociativeRng()" [color=lightblue];
+"NonAssociativeRng()" -> "AbelianGroup()"
+"NonAssociativeRng()" -> "Monad()"
+
+"Monad()" [color=lightblue];
+"Monad()" -> "SETCAT..."
+"Monad()" -> "RepeatedSquaring(Monad)"
+
+"RepeatedSquaring(Monad)" [color="#00EE00"];
+"RepeatedSquaring(Monad)" -> "RepeatedSquaring(a:SetCategory)"
+
+"RepeatedSquaring(a:SetCategory)" [color="#00EE00"];
+"RepeatedSquaring(a:SetCategory)" -> "Package"
+
+"Package" [color="#00EE00"];
+
"AbelianGroup()" [color=lightblue];
"AbelianGroup()" -> "CancellationAbelianMonoid()"
"AbelianGroup()" -> "RepeatedDoubling(AbelianGroup)"
@@ -9143,6 +9768,155 @@
@
\chapter{Category Layer 7}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{NonAssociativeRng}{NARNG}
+\pagepic{ps/v102nonassociativerng.ps}{NARNG}{1.00}
+
+{\bf See:}\\
+\pageto{NonAssociativeAlgebra}{NAALG}
+\pageto{NonAssociativeRing}{NASRING}
+\pagefrom{AbelianGroup}{ABELGRP}
+\pagefrom{Monad}{MONAD}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+\cross{NARNG}{0} &
+\cross{NARNG}{antiCommutator} &
+\cross{NARNG}{associator} &
+\cross{NARNG}{coerce} &
+\cross{NARNG}{commutator} \\
+\cross{NARNG}{hash} &
+\cross{NARNG}{latex} &
+\cross{NARNG}{leftPower} &
+\cross{NARNG}{rightPower} &
+\cross{NARNG}{sample} \\
+\cross{NARNG}{subtractIfCan} &
+\cross{NARNG}{zero?} &
+\cross{NARNG}{?*?} &
+\cross{NARNG}{?**?} &
+\cross{NARNG}{?+?} \\
+\cross{NARNG}{?-?} &
+\cross{NARNG}{-?} &
+\cross{NARNG}{?=?} &
+\cross{NARNG}{?~=?} &
+\end{tabular}
+
+These are implemented by this category:
+\begin{verbatim}
+ antiCommutator : (%,%) -> %
+ associator : (%,%,%) -> %
+ commutator : (%,%) -> %
+\end{verbatim}
+
+These exports come from AbelianGroup():
+\begin{verbatim}
+ 0 : () -> %
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ sample : () -> %
+ subtractIfCan : (%,%) -> Union(%,"failed")
+ zero? : % -> Boolean
+ ?~=? : (%,%) -> Boolean
+ ?*? : (PositiveInteger,%) -> %
+ ?+? : (%,%) -> %
+ ?=? : (%,%) -> Boolean
+ ?*? : (Integer,%) -> %
+ ?*? : (NonNegativeInteger,%) -> %
+ ?-? : (%,%) -> %
+ -? : % -> %
+\end{verbatim}
+
+These exports come from Monad():
+\begin{verbatim}
+ leftPower : (%,PositiveInteger) -> %
+ rightPower : (%,PositiveInteger) -> %
+ ?*? : (%,%) -> %
+ ?**? : (%,PositiveInteger) -> %
+\end{verbatim}
+
+<<category NARNG NonAssociativeRng>>=
+)abbrev category NARNG NonAssociativeRng
+++ Author: J. Grabmeier, R. Wisbauer
+++ Date Created: 01 March 1991
+++ Date Last Updated: 03 July 1991
+++ Basic Operations: +, *, -, **
+++ Related Constructors: Rng, Ring, NonAssociativeRing
+++ Also See:
+++ AMS Classifications:
+++ Keywords: not associative ring
+++ Reference:
+++ R.D. Schafer: An Introduction to Nonassociative Algebras
+++ Academic Pr...
[truncated message content] |
|
From: <gi...@ax...> - 2008-09-28 22:34:56
|
books/bookvol10.2.pamphlet | 4687 ++++++++++++++++++++---
books/ps/v102finiteranknonassociativealgebra.ps | 884 +++++
books/ps/v102framednonassociativealgebra.ps | 930 +++++
books/ps/v102functionfieldcategory.ps | 575 +++
books/ps/v102gradedalgebra.ps | 654 ++++
books/ps/v102gradedmodule.ps | 494 +++
books/ps/v102monad.ps | 632 +++
books/ps/v102monadwithunit.ps | 678 ++++
books/ps/v102nonassociativealgebra.ps | 838 ++++
books/ps/v102nonassociativering.ps | 771 ++++
books/ps/v102nonassociativerng.ps | 653 ++++
changelog | 5 +
src/algebra/Makefile.pamphlet | 5 +-
src/algebra/carten.spad.pamphlet | 106 -
src/algebra/curve.spad.pamphlet | 441 +--
src/algebra/naalgc.spad.pamphlet | 1260 ------
16 files changed, 11275 insertions(+), 2338 deletions(-)
New commits:
commit 18be64be3f9d817475f519a66faa50bc8c0af35b
Author: Tim Daly <da...@ax...>
Date: Fri Aug 1 20:19:37 2008 -0400
20080927 tpd books/ps/v102nonassociativerng.ps added
20080927 tpd books/ps/v102nonassociativering.ps added
20080927 tpd books/ps/v102nonassociativealgebra.ps added
20080927 tpd books/ps/v102monadwithunit.ps added
20080927 tpd books/ps/v102monad.ps added
20080927 tpd books/ps/v102gradedmodule.ps added
20080927 tpd books/ps/v102gradedalgebra.ps added
20080927 tpd books/ps/v102functionfieldcategory.ps added
20080927 tpd books/ps/v102framednonassociativealgebra.ps added
20080927 tpd books/ps/v102finiteranknonassociativealgebra.ps added
20080927 tpd src/algebra/Makefile remove naalgc
20080927 tpd books/bookvol10.2 add categories
20080927 tpd src/algebra/naalgc.spad absorbed into bookvol10.2
20080927 tpd src/algebra/curve.spad move categories to bookvol10.2
20080927 tpd src/algebra/carten.spad move categories to bookvol10.2
|
|
From: <da...@us...> - 2008-09-27 16:25:11
|
Revision: 982
http://axiom.svn.sourceforge.net/axiom/?rev=982&view=rev
Author: daly
Date: 2008-09-27 16:25:03 +0000 (Sat, 27 Sep 2008)
Log Message:
-----------
20080926 tpd books/bookvol10.2 add attributes
20080926 tpd src/algebra/Makefile remove attreg
20080926 tpd books/ps/v102twodimensionalarraycategory.ps added
20080926 tpd books/ps/v102monogenicalgebra.ps added
20080926 tpd books/ps/v102fullyretractableto.ps added
20080926 tpd books/ps/v102framedalgebra.ps added
20080926 tpd books/ps/v102finiterankalgebra.ps added
20080926 tpd books/ps/v102category.ps added
20080926 tpd books/ps/v102attributeregistry.ps added
20080926 tpd books/bookvol10.2 add categories
20080926 tpd src/algebra/attreg.spad deleted, absorbed by bookvol10.2
20080926 tpd src/algebra/array2.spad move ARR2CAT to bookvol10.2
20080926 tpd src/algebra/retract.spad move FRETRCT to bookvol10.2
20080926 tpd src/algebra/algcat.spad move categories to bookvol10.2
Modified Paths:
--------------
trunk/axiom/books/bookvol10.2.pamphlet
trunk/axiom/changelog
trunk/axiom/src/algebra/Makefile.pamphlet
trunk/axiom/src/algebra/array2.spad.pamphlet
trunk/axiom/src/algebra/retract.spad.pamphlet
Added Paths:
-----------
trunk/axiom/books/ps/v102attributeregistry.ps
trunk/axiom/books/ps/v102category.ps
trunk/axiom/books/ps/v102finiterankalgebra.ps
trunk/axiom/books/ps/v102framedalgebra.ps
trunk/axiom/books/ps/v102fullyretractableto.ps
trunk/axiom/books/ps/v102monogenicalgebra.ps
trunk/axiom/books/ps/v102twodimensionalarraycategory.ps
Removed Paths:
-------------
trunk/axiom/src/algebra/attreg.spad.pamphlet
Modified: trunk/axiom/books/bookvol10.2.pamphlet
===================================================================
--- trunk/axiom/books/bookvol10.2.pamphlet 2008-09-26 06:32:53 UTC (rev 981)
+++ trunk/axiom/books/bookvol10.2.pamphlet 2008-09-27 16:25:03 UTC (rev 982)
@@ -279,7 +279,10 @@
can infer that this ``subsumption node'' matches the category.
A ``yellow'' color indicates a domain.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{Category}{CATEGORY}
+\pagepic{ps/v102category.ps}{CATEGORY}{1.00}
+
This is the root of the category hierarchy and is not represented by code.
{\bf See:}\\
@@ -292,7 +295,190 @@
\pageto{RetractableTo}{RETRACT}
\pageto{Type}{TYPE}
+<<CATEGORY.dotabb>>=
+"CATEGORY"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=CATEGORY"];
+
+@
+<<CATEGORY.dotfull>>=
+"Category"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=CATEGORY"];
+
+@
+<<CATEGORY.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"Category" [color=lightblue];
+}
+
+@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{AttributeRegistry}{ATTREG}
+\pagepic{ps/v102attributeregistry.ps}{ATTREG}{1.00}
+
+{\bf See:}\\
+\pagefrom{Category}{CATEGORY}
+
+{\bf Exports:} Nothing
+
+{\bf Attributes Exported:}
+\begin{itemize}
+\item {\bf \cross{ATTREG}{finiteAggregate}}
+is true if it is an aggregate with a finite number of elements.
+\item {\bf \cross{ATTREG}{commutative("*")}}
+is true if it has an operation $"*": (D,D) -> D$
+which is commutative.
+\item {\bf \cross{ATTREG}{shallowlyMutable}}
+is true if its values have immediate components that are
+updateable (mutable). Note: the properties of any component
+domain are irrevelant to the shallowlyMutable proper.
+\item {\bf \cross{ATTREG}{unitsKnown}}
+is true if a monoid (a multiplicative semigroup with a 1) has
+unitsKnown means that the operation {\tt recip} can only return
+``failed'' if its argument is not a unit.
+\item {\bf \cross{ATTREG}{leftUnitary}}
+is true if $1 * x = x$ for all x.
+\item {\bf \cross{ATTREG}{rightUnitary}}
+is true if $x * 1 = x$ for all x.
+\item {\bf \cross{ATTREG}{noZeroDivisors}}
+is true if $x * y ~= 0$ implies both x and y are non-zero.
+\item {\bf \cross{ATTREG}{canonicalUnitNormal}}
+is true if we can choose a canonical representative for each class
+of associate elements, that is {\tt associates?(a,b)} returns true
+if and only if {\tt unitCanonical(a) = unitCanonical(b)}.
+\item {\bf \cross{ATTREG}{canonicalsClosed}}
+is true if\\
+{\tt unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.
+\item {\bf \cross{ATTREG}{arbitraryPrecision}}
+means the user can set the precision for subsequent calculations.
+\item {\bf \cross{ATTREG}{partiallyOrderedSet}}
+is true if a set with $<$ which is transitive, but
+not($a < b$ or $a = b$) does not necessarily imply $b<a$.
+\item {\bf \cross{ATTREG}{central}}
+is true if, given an algebra over a ring R, the image of R is the center
+of the algebra, i.e. the set of members of the algebra which commute
+with all others is precisely the image of R in the algebra.
+\item {\bf \cross{ATTREG}{noetherian}}
+is true if all of its ideals are finitely generated.
+\item {\bf \cross{ATTREG}{additiveValuation}}
+implies\\
+{\tt euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.
+\item {\bf \cross{ATTREG}{multiplicativeValuation}}
+implies\\
+{\tt euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.
+\item {\bf \cross{ATTREG}{NullSquare}}
+means that $[x,x] = 0$ holds. See {\tt LieAlgebra}.
+\item {\bf \cross{ATTREG}{JacobiIdentity}}
+means that $[x,[y,z]]+[y,[z,x]]+[z,[x,y]] = 0$ holds.
+See {\tt LieAlgebra}.
+\item {\bf \cross{ATTREG}{canonical}}
+is true if and only if distinct elements have distinct data structures.
+For example, a domain of mathematical objects which has the
+{\tt canonical} attribute means that two objects are mathematically
+equal if and only if their data structures are equal.
+\end{itemize}
+
+<<category ATTREG AttributeRegistry>>=
+)abbrev category ATTREG AttributeRegistry
+
+++ This category exports the attributes in the AXIOM Library
+AttributeRegistry(): Category == with
+ finiteAggregate
+ ++ \spad{finiteAggregate} is true if it is an aggregate with a
+ ++ finite number of elements.
+ commutative("*")
+ ++ \spad{commutative("*")} is true if it has an operation
+ ++ \spad{"*": (D,D) -> D} which is commutative.
+ shallowlyMutable
+ ++ \spad{shallowlyMutable} is true if its values
+ ++ have immediate components that are updateable (mutable).
+ ++ Note: the properties of any component domain are irrevelant to the
+ ++ \spad{shallowlyMutable} proper.
+ unitsKnown
+ ++ \spad{unitsKnown} is true if a monoid (a multiplicative semigroup
+ ++ with a 1) has \spad{unitsKnown} means that
+ ++ the operation \spadfun{recip} can only return "failed"
+ ++ if its argument is not a unit.
+ leftUnitary
+ ++ \spad{leftUnitary} is true if \spad{1 * x = x} for all x.
+ rightUnitary
+ ++ \spad{rightUnitary} is true if \spad{x * 1 = x} for all x.
+ noZeroDivisors
+ ++ \spad{noZeroDivisors} is true if \spad{x * y \~~= 0} implies
+ ++ both x and y are non-zero.
+ canonicalUnitNormal
+ ++ \spad{canonicalUnitNormal} is true if we can choose a canonical
+ ++ representative for each class of associate elements, that is
+ ++ \spad{associates?(a,b)} returns true if and only if
+ ++ \spad{unitCanonical(a) = unitCanonical(b)}.
+ canonicalsClosed
+ ++ \spad{canonicalsClosed} is true if
+ ++ \spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.
+ arbitraryPrecision
+ ++ \spad{arbitraryPrecision} means the user can set the
+ ++ precision for subsequent calculations.
+ partiallyOrderedSet
+ ++ \spad{partiallyOrderedSet} is true if
+ ++ a set with \spadop{<} which is transitive,
+ ++ but \spad{not(a < b or a = b)}
+ ++ does not necessarily imply \spad{b<a}.
+ central
+ ++ \spad{central} is true if, given an algebra over a ring R,
+ ++ the image of R is the center
+ ++ of the algebra, i.e. the set of members of the algebra which commute
+ ++ with all others is precisely the image of R in the algebra.
+ noetherian
+ ++ \spad{noetherian} is true if all of its ideals are finitely generated.
+ additiveValuation
+ ++ \spad{additiveValuation} implies
+ ++ \spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.
+ multiplicativeValuation
+ ++ \spad{multiplicativeValuation} implies
+ ++ \spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.
+ NullSquare
+ ++ \axiom{NullSquare} means that \axiom{[x,x] = 0} holds.
+ ++ See \axiomType{LieAlgebra}.
+ JacobiIdentity
+ ++ \axiom{JacobiIdentity} means that
+ ++ \axiom{[x,[y,z]]+[y,[z,x]]+[z,[x,y]] = 0} holds.
+ ++ See \axiomType{LieAlgebra}.
+ canonical
+ ++ \spad{canonical} is true if and only if distinct elements have
+ ++ distinct data structures. For example, a domain of mathematical
+ ++ objects which has the \spad{canonical} attribute means that two
+ ++ objects are mathematically equal if and only if their data
+ ++ structures are equal.
+
+@
+<<ATTREG.dotabb>>=
+"ATTREG"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ATTREG"];
+"ATTREG" -> "CATEGORY"
+
+@
+<<ATTREG.dotabb>>=
+"AttributeRegistry()"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ATTREG"];
+"AttributeRegistry()" -> "Category"
+
+@
+<<ATTREG.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"AttributeRegistry()" [color=lightblue];
+"AttributeRegistry()" -> "Category"
+
+"Category" [color=lightblue];
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{BasicType}{BASTYPE}
\pagepic{ps/v102basictype.ps}{BASTYPE}{1.00}
@@ -429,6 +615,7 @@
{\bf See:}\\
\pageto{Collection}{CLAGG}
+\pageto{MonogenicAlgebra}{MONOGEN}
\pagefrom{Category}{CATEGORY}
{\bf Exports:}\\
@@ -525,6 +712,7 @@
[color=seagreen,href="bookvol10.2.pdf#nameddest=KONVERT"];
"ConvertibleTo(UnivariatePolynomialCategory(CommutativeRing))" ->
"ConvertibleTo(a:Type)"
+
@
<<KONVERT.dotpic>>=
digraph pic {
@@ -700,6 +888,7 @@
\pagepic{ps/v102retractableto.ps}{RETRACT}{1.00}
{\bf See:}\\
+\pageto{FullyRetractableTo}{FRETRCT}
\pagefrom{Category}{CATEGORY}
{\bf Exports:}\\
@@ -860,6 +1049,12 @@
\cross{AGG}{size?}
\end{tabular}
+{\bf Attributes Used:}
+\begin{itemize}
+\item {\bf \cross{AGG}{finiteAggregate}}
+is true if it is an aggregate with a finite number of elements.
+\end{itemize}
+
These are implemented by this category:
\begin{verbatim}
empty? : % -> Boolean
@@ -969,6 +1164,14 @@
\cross{ELTAGG}{?.?}
\end{tabular}
+{\bf Attributes Used:}
+\begin{itemize}
+\item {\bf \cross{ELTAGG}{shallowlyMutable}}
+is true if its values have immediate components that are
+updateable (mutable). Note: the properties of any component
+domain are irrevelant to the shallowlyMutable proper.
+\end{itemize}
+
These are part of this category's direct exports:
\begin{verbatim}
elt : (%,Dom,Im) -> Im
@@ -1159,6 +1362,116 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{FullyRetractableTo}{FRETRCT}
+\pagepic{ps/v102fullyretractableto.ps}{FRETRCT}{1.00}
+
+{\bf See:}\\
+\pageto{MonogenicAlgebra}{MONOGEN}
+\pagefrom{RetractableTo}{RETRACT}
+
+{\bf Exports:}\\
+\begin{tabular}{lll}
+\cross{FRETRCT}{coerce} &
+\cross{FRETRCT}{retract} &
+\cross{FRETRCT}{retractIfCan}
+\end{tabular}
+
+These are implemented by this category:
+\begin{verbatim}
+ coerce : Integer -> %
+ if S has RETRACT INT
+ coerce : Fraction Integer -> %
+ if S has RETRACT FRAC INT
+ retract : % -> Integer
+ if S has RETRACT INT
+ retract : % -> Fraction Integer
+ if S has RETRACT FRAC INT
+ retractIfCan : % -> Union(Integer,"failed")
+ if S has RETRACT INT
+ retractIfCan : % -> Union(Fraction Integer,"failed")
+ if S has RETRACT FRAC INT
+\end{verbatim}
+
+These exports come from RetractableTo(S:Type):
+\begin{verbatim}
+ coerce : S -> %
+ retract : % -> S
+ retractIfCan : % -> Union(S,"failed")
+\end{verbatim}
+
+<<category FRETRCT FullyRetractableTo>>=
+)abbrev category FRETRCT FullyRetractableTo
+++ Author: Manuel Bronstein
+++ Description:
+++ A is fully retractable to B means that A is retractable to B, and,
+++ in addition, if B is retractable to the integers or rational
+++ numbers then so is A.
+++ In particular, what we are asserting is that there are no integers
+++ (rationals) in A which don't retract into B.
+++ Date Created: March 1990
+++ Date Last Updated: 9 April 1991
+FullyRetractableTo(S: Type): Category == RetractableTo(S) with
+ if (S has RetractableTo Integer) then RetractableTo Integer
+ if (S has RetractableTo Fraction Integer) then
+ RetractableTo Fraction Integer
+ add
+ if not(S is Integer) then
+ if (S has RetractableTo Integer) then -- induction
+ coerce(n:Integer):% == n::S::%
+ retract(r:%):Integer == retract(retract(r)@S)
+
+ retractIfCan(r:%):Union(Integer, "failed") ==
+ (u:= retractIfCan(r)@Union(S,"failed")) case "failed"=> "failed"
+ retractIfCan(u::S)
+
+ if not(S is Fraction Integer) then
+ if (S has RetractableTo Fraction Integer) then -- induction
+ coerce(n:Fraction Integer):% == n::S::%
+ retract(r:%):Fraction(Integer) == retract(retract(r)@S)
+
+ retractIfCan(r:%):Union(Fraction Integer, "failed") ==
+ (u:=retractIfCan(r)@Union(S,"failed")) case "failed"=>"failed"
+ retractIfCan(u::S)
+
+@
+<<FRETRCT.dotabb>>=
+"FRETRCT"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=FRETRCT"];
+"FRETRCT" -> "RETRACT"
+
+@
+<<FRETRCT.dotfull>>=
+"FullyRetractableTo(a:Type)"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=FRETRCT"];
+"FullyRetractableTo(a:Type)" -> "RetractableTo(a:Type)"
+
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=FRETRCT"];
+"FullyRetractableTo(a:Ring)" -> "FullyRetractableTo(a:Type)"
+
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=FRETRCT"];
+"FullyRetractableTo(a:CommutativeRing)" -> "FullyRetractableTo(a:Type)"
+
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=FRETRCT"];
+"FullyRetractableTo(a:SetCategory)" -> "FullyRetractableTo(a:Type)"
+
+@
+<<FRETRCT.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"FullyRetractableTo(a:Type)" [color=lightblue];
+"FullyRetractableTo(a:Type)" -> "RetractableTo(a:Type)"
+
+"RetractableTo(a:Type)" [color=lightblue];
+"RetractableTo(a:Type)" -> "Category"
+
+"Category" [color=lightblue];
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{Logic}{LOGIC}
\pagepic{ps/v102logic.ps}{LOGIC}{1.00}
@@ -1303,7 +1616,6 @@
++ Conditional Attributes:
++ canonical\tab{15}data structure equality is the same as \spadop{=}
SetCategory(): Category == Join(BasicType,CoercibleTo OutputForm) with
- --operations
hash: % -> SingleInteger ++ hash(s) calculates a hash code for s.
latex: % -> String ++ latex(s) returns a LaTeX-printable output
++ representation of s.
@@ -1408,7 +1720,6 @@
++ \spad{associative("+":(%,%)->%)}\tab{30}\spad{ (x+y)+z = x+(y+z) }
++ \spad{commutative("+":(%,%)->%)}\tab{30}\spad{ x+y = y+x }
AbelianSemiGroup(): Category == SetCategory with
- --operations
"+": (%,%) -> % ++ x+y computes the sum of x and y.
"*": (PositiveInteger,%) -> %
++ n*x computes the left-multiplication of x by the positive
@@ -1430,7 +1741,7 @@
"AbelianSemiGroup()"
[color=lightblue,href="bookvol10.2.pdf#nameddest=ABELSG"];
"AbelianSemiGroup()" -> "SetCategory()"
-"AbelianSemiGroup()" -> "RepeatedDoubling(SetCategory)"
+"AbelianSemiGroup()" -> "RepeatedDoubling(a:SetCategory)"
<<ABELSG.dotpic>>=
digraph pic {
@@ -1528,7 +1839,6 @@
++ \spad{index(lookup(s)) = s}
Finite(): Category == SetCategory with
- --operations
size: () -> NonNegativeInteger
++ size() returns the number of elements in the set.
index: PositiveInteger -> %
@@ -1592,6 +1902,7 @@
\pageto{Collection}{CLAGG}
\pageto{IndexedAggregate}{IXAGG}
\pageto{RecursiveAggregate}{RCAGG}
+\pageto{TwoDimensionalArrayCategory}{ARR2CAT}
\pagefrom{Aggregate}{AGG}
\pagefrom{Evalable}{EVALAB}
\pagefrom{SetCategory}{SETCAT}
@@ -1623,6 +1934,16 @@
\cross{HOAGG}{?\~{}=?} &&
\end{tabular}
+{\bf Attributes Used:}
+\begin{itemize}
+\item {\bf \cross{HOAGG}{finiteAggregate}}
+is true if it is an aggregate with a finite number of elements.
+\item {\bf \cross{HOAGG}{shallowlyMutable}}
+is true if its values have immediate components that are
+updateable (mutable). Note: the properties of any component
+domain are irrevelant to the shallowlyMutable proper.
+\end{itemize}
+
These are directly exported but not implemented:
\begin{verbatim}
map : ((S -> S),%) -> %
@@ -1869,7 +2190,6 @@
++ exactly one of the following relations holds \spad{a<b or a=b or b<a}
++ and the relation is transitive, i.e. \spad{a<b and b<c => a<c}.
OrderedSet(): Category == SetCategory with
- --operations
"<": (%,%) -> Boolean
++ x < y is a strict total ordering on the elements of the set.
">": (%, %) -> Boolean
@@ -1878,15 +2198,12 @@
++ x >= y is a greater than or equal test.
"<=": (%, %) -> Boolean
++ x <= y is a less than or equal test.
-
max: (%,%) -> %
++ max(x,y) returns the maximum of x and y relative to "<".
min: (%,%) -> %
++ min(x,y) returns the minimum of x and y relative to "<".
add
- --declarations
x,y: %
- --definitions
-- These really ought to become some sort of macro
max(x,y) ==
x > y => x
@@ -2007,7 +2324,6 @@
++ Conditional attributes:
++ \spad{commutative("*":(%,%)->%)}\tab{30}\spad{ x*y = y*x }
SemiGroup(): Category == SetCategory with
- --operations
"*": (%,%) -> % ++ x*y returns the product of x and y.
"**": (%,PositiveInteger) -> % ++ x**n returns the repeated product
++ of x n times, i.e. exponentiation.
@@ -2029,7 +2345,7 @@
"SemiGroup()"
[color=lightblue,href="bookvol10.2.pdf#nameddest=SGROUP"];
"SemiGroup()" -> "SetCategory()"
-"SemiGroup()" -> "RepeatedSquaring(SemiGroup)"
+"SemiGroup()" -> "RepeatedSquaring(a:SemiGroup)"
@
<<SGROUP.dotpic>>=
@@ -2040,7 +2356,7 @@
"SemiGroup()" [color=lightblue];
"SemiGroup()" -> "SetCategory()"
-"SemiGroup()" -> "RepeatedSquaring(SemiGroup)"
+"SemiGroup()" -> "RepeatedSquaring(a:SemiGroup)"
"SetCategory()" [color=lightblue];
"SetCategory()" -> "BasicType()"
@@ -2055,8 +2371,8 @@
"CoercibleTo(a:Type)" [color=lightblue];
"CoercibleTo(a:Type)" -> "Category"
-"RepeatedSquaring(SemiGroup)" [color="#00EE00"];
-"RepeatedSquaring(SemiGroup)" -> "RepeatedSquaring(a:SetCategory)"
+"RepeatedSquaring(a:SemiGroup)" [color="#00EE00"];
+"RepeatedSquaring(a:SemiGroup)" -> "RepeatedSquaring(a:SetCategory)"
"RepeatedSquaring(a:SetCategory)" [color="#00EE00"];
"RepeatedSquaring(a:SetCategory)" -> "Package"
@@ -2125,11 +2441,11 @@
++ Conditional attributes:
++ infinite\tab{15}repeated \spad{nextItem}'s are never "failed".
StepThrough(): Category == SetCategory with
- --operations
init: constant -> %
++ init() chooses an initial object for stepping.
nextItem: % -> Union(%,"failed")
- ++ nextItem(x) returns the next item, or "failed" if domain is exhausted.
+ ++ nextItem(x) returns the next item, or "failed"
+ ++ if domain is exhausted.
@
<<STEP.dotabb>>=
@@ -2239,7 +2555,6 @@
-- following domain must be compiled with subsumption disabled
-- define SourceLevelSubset to be EQUAL
AbelianMonoid(): Category == AbelianSemiGroup with
- --operations
0: constant -> %
++ 0 is the additive identity element.
sample: constant -> %
@@ -2311,6 +2626,552 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{TwoDimensionalArrayCategory}{ARR2CAT}
+\pagepic{ps/v102twodimensionalarraycategory.ps}{ARR2CAT}{0.60}
+
+TwoDimensionalArrayCategory is a general array category which
+allows different representations and indexing schemes.
+Rows and columns may be extracted with rows returned as objects
+of type Row and columns returned as objects of type Col.
+The index of the 'first' row may be obtained by calling the
+function 'minRowIndex'. The index of the 'first' column may
+be obtained by calling the function 'minColIndex'. The index of
+the first element of a 'Row' is the same as the index of the
+first column in an array and vice versa.
+
+{\bf See:}\\
+\pagefrom{HomogeneousAggregate}{HOAGG}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+\cross{ARR2CAT}{any?} &
+\cross{ARR2CAT}{column} &
+\cross{ARR2CAT}{coerce} &
+\cross{ARR2CAT}{copy} &
+\cross{ARR2CAT}{count} \\
+\cross{ARR2CAT}{elt} &
+\cross{ARR2CAT}{empty} &
+\cross{ARR2CAT}{empty?} &
+\cross{ARR2CAT}{eq?} &
+\cross{ARR2CAT}{eval} \\
+\cross{ARR2CAT}{every?} &
+\cross{ARR2CAT}{fill!} &
+\cross{ARR2CAT}{hash} &
+\cross{ARR2CAT}{latex} &
+\cross{ARR2CAT}{less?} \\
+\cross{ARR2CAT}{map} &
+\cross{ARR2CAT}{map!} &
+\cross{ARR2CAT}{maxColIndex} &
+\cross{ARR2CAT}{maxRowIndex} &
+\cross{ARR2CAT}{member?} \\
+\cross{ARR2CAT}{members} &
+\cross{ARR2CAT}{minColIndex} &
+\cross{ARR2CAT}{minRowIndex} &
+\cross{ARR2CAT}{more?} &
+\cross{ARR2CAT}{ncols} \\
+\cross{ARR2CAT}{new} &
+\cross{ARR2CAT}{nrows} &
+\cross{ARR2CAT}{parts} &
+\cross{ARR2CAT}{qelt} &
+\cross{ARR2CAT}{qsetelt!} \\
+\cross{ARR2CAT}{row} &
+\cross{ARR2CAT}{sample} &
+\cross{ARR2CAT}{setColumn!} &
+\cross{ARR2CAT}{setRow!} &
+\cross{ARR2CAT}{setelt} \\
+\cross{ARR2CAT}{size?} &
+\cross{ARR2CAT}{\#?} &
+\cross{ARR2CAT}{?=?} &
+\cross{ARR2CAT}{?\~{}=?} &
+\end{tabular}
+
+{\bf Attributes Exported:}
+\begin{itemize}
+\item {\bf \cross{ARR2CAT}{finiteAggregate}}
+is true if it is an aggregate with a finite number of elements.
+\item {\bf \cross{ARR2CAT}{shallowlyMutable}}
+is true if its values have immediate components that are
+updateable (mutable). Note: the properties of any component
+domain are irrevelant to the shallowlyMutable proper.
+\end{itemize}
+
+{\bf Attributes Used:}
+\begin{itemize}
+\item {\bf \cross{ARR2CAT}{shallowlyMutable}}
+is true if its values have immediate components that are
+updateable (mutable). Note: the properties of any component
+domain are irrevelant to the shallowlyMutable proper.
+\end{itemize}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ elt : (%,Integer,Integer) -> R
+ maxColIndex : % -> Integer
+ maxRowIndex : % -> Integer
+ minColIndex : % -> Integer
+ minRowIndex : % -> Integer
+ new : (NonNegativeInteger,NonNegativeInteger,R) -> %
+ ncols : % -> NonNegativeInteger
+ nrows : % -> NonNegativeInteger
+ qelt : (%,Integer,Integer) -> R
+ qsetelt! : (%,Integer,Integer,R) -> R
+ setelt : (%,Integer,Integer,R) -> R
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
+ copy : % -> %
+ coerce : % -> OutputForm if R has SETCAT
+ column : (%,Integer) -> Col
+ count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
+ count : (R,%) -> NonNegativeInteger if R has SETCAT and $ has finiteAggregate
+ elt : (%,Integer,Integer,R) -> R
+ every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
+ fill! : (%,R) -> %
+ less? : (%,NonNegativeInteger) -> Boolean
+ map : ((R -> R),%) -> %
+ map : (((R,R) -> R),%,%) -> %
+ map : (((R,R) -> R),%,%,R) -> %
+ map! : ((R -> R),%) -> %
+ member? : (R,%) -> Boolean if R has SETCAT and $ has finiteAggregate
+ more? : (%,NonNegativeInteger) -> Boolean
+ parts : % -> List R
+ row : (%,Integer) -> Row
+ setColumn! : (%,Integer,Col) -> %
+ setRow! : (%,Integer,Row) -> %
+ size? : (%,NonNegativeInteger) -> Boolean
+ #? : % -> NonNegativeInteger if $ has finiteAggregate
+ ?=? : (%,%) -> Boolean if R has SETCAT
+\end{verbatim}
+
+These exports come from HomogeneousAggregate(R:Type)
+\begin{verbatim}
+ empty : () -> %
+ empty? : % -> Boolean
+ eq? : (%,%) -> Boolean
+ eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT
+ eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT
+ eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT
+ eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT
+ hash : % -> SingleInteger if R has SETCAT
+ latex : % -> String if R has SETCAT
+ members : % -> List R if $ has finiteAggregate
+ sample : () -> %
+ ?~=? : (%,%) -> Boolean if R has SETCAT
+\end{verbatim}
+
+<<category ARR2CAT TwoDimensionalArrayCategory>>=
+)abbrev category ARR2CAT TwoDimensionalArrayCategory
+++ Two dimensional array categories and domains
+++ Author:
+++ Date Created: 27 October 1989
+++ Date Last Updated: 27 June 1990
+++ Keywords: array, data structure
+++ Examples:
+++ References:
+TwoDimensionalArrayCategory(R,Row,Col): Category == Definition where
+ R : Type
+ Row : FiniteLinearAggregate R
+ Col : FiniteLinearAggregate R
+
+ Definition == HomogeneousAggregate(R) with
+
+ shallowlyMutable
+ ++ one may destructively alter arrays
+
+ finiteAggregate
+ ++ two-dimensional arrays are finite
+
+--% Array creation
+
+ new: (NonNegativeInteger,NonNegativeInteger,R) -> %
+ ++ new(m,n,r) is an m-by-n array all of whose entries are r
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,0)
+
+ fill_!: (%,R) -> %
+ ++ fill!(m,r) fills m with r's
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,0)
+ ++X fill!(arr,10)
+
+--% Size inquiries
+
+ minRowIndex : % -> Integer
+ ++ minRowIndex(m) returns the index of the 'first' row of the array m
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X minRowIndex(arr)
+
+ maxRowIndex : % -> Integer
+ ++ maxRowIndex(m) returns the index of the 'last' row of the array m
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X maxRowIndex(arr)
+
+ minColIndex : % -> Integer
+ ++ minColIndex(m) returns the index of the 'first' column of the array m
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X minColIndex(arr)
+
+ maxColIndex : % -> Integer
+ ++ maxColIndex(m) returns the index of the 'last' column of the array m
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X maxColIndex(arr)
+
+ nrows : % -> NonNegativeInteger
+ ++ nrows(m) returns the number of rows in the array m
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X nrows(arr)
+
+ ncols : % -> NonNegativeInteger
+ ++ ncols(m) returns the number of columns in the array m
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X ncols(arr)
+
+--% Part extractions
+
+ elt: (%,Integer,Integer) -> R
+ ++ elt(m,i,j) returns the element in the ith row and jth
+ ++ column of the array m
+ ++ error check to determine if indices are in proper ranges
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X elt(arr,1,1)
+
+ qelt: (%,Integer,Integer) -> R
+ ++ qelt(m,i,j) returns the element in the ith row and jth
+ ++ column of the array m
+ ++ NO error check to determine if indices are in proper ranges
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X qelt(arr,1,1)
+
+ elt: (%,Integer,Integer,R) -> R
+ ++ elt(m,i,j,r) returns the element in the ith row and jth
+ ++ column of the array m, if m has an ith row and a jth column,
+ ++ and returns r otherwise
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X elt(arr,1,1,6)
+ ++X elt(arr,1,10,6)
+
+ row: (%,Integer) -> Row
+ ++ row(m,i) returns the ith row of m
+ ++ error check to determine if index is in proper ranges
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X row(arr,1)
+
+ column: (%,Integer) -> Col
+ ++ column(m,j) returns the jth column of m
+ ++ error check to determine if index is in proper ranges
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X column(arr,1)
+
+ parts: % -> List R
+ ++ parts(m) returns a list of the elements of m in row major order
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X parts(arr)
+
+--% Part assignments
+
+ setelt: (%,Integer,Integer,R) -> R
+ -- will become setelt_!
+ ++ setelt(m,i,j,r) sets the element in the ith row and jth
+ ++ column of m to r
+ ++ error check to determine if indices are in proper ranges
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,0)
+ ++X setelt(arr,1,1,17)
+
+ qsetelt_!: (%,Integer,Integer,R) -> R
+ ++ qsetelt!(m,i,j,r) sets the element in the ith row and jth
+ ++ column of m to r
+ ++ NO error check to determine if indices are in proper ranges
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,0)
+ ++X qsetelt!(arr,1,1,17)
+
+ setRow_!: (%,Integer,Row) -> %
+ ++ setRow!(m,i,v) sets to ith row of m to v
+ ++
+ ++X T1:=TwoDimensionalArray Integer
+ ++X arr:T1:= new(5,4,0)
+ ++X T2:=OneDimensionalArray Integer
+ ++X arow:=construct([1,2,3,4]::List(INT))$T2
+ ++X setRow!(arr,1,arow)$T1
+
+ setColumn_!: (%,Integer,Col) -> %
+ ++ setColumn!(m,j,v) sets to jth column of m to v
+ ++
+ ++X T1:=TwoDimensionalArray Integer
+ ++X arr:T1:= new(5,4,0)
+ ++X T2:=OneDimensionalArray Integer
+ ++X acol:=construct([1,2,3,4,5]::List(INT))$T2
+ ++X setColumn!(arr,1,acol)$T1
+
+--% Map and Zip
+
+ map: (R -> R,%) -> %
+ ++ map(f,a) returns \spad{b}, where \spad{b(i,j) = f(a(i,j))}
+ ++ for all \spad{i, j}
+ ++
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X map(-,arr)
+ ++X map((x +-> x + x),arr)
+
+ map_!: (R -> R,%) -> %
+ ++ map!(f,a) assign \spad{a(i,j)} to \spad{f(a(i,j))}
+ ++ for all \spad{i, j}
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X map!(-,arr)
+
+ map:((R,R) -> R,%,%) -> %
+ ++ map(f,a,b) returns \spad{c}, where \spad{c(i,j) = f(a(i,j),b(i,j))}
+ ++ for all \spad{i, j}
+ ++
+ ++X adder(a:Integer,b:Integer):Integer == a+b
+ ++X arr : ARRAY2 INT := new(5,4,10)
+ ++X map(adder,arr,arr)
+
+ map:((R,R) -> R,%,%,R) -> %
+ ++ map(f,a,b,r) returns \spad{c}, where \spad{c(i,j) = f(a(i,j),b(i,j))}
+ ++ when both \spad{a(i,j)} and \spad{b(i,j)} exist;
+ ++ else \spad{c(i,j) = f(r, b(i,j))} when \spad{a(i,j)} does not exist;
+ ++ else \spad{c(i,j) = f(a(i,j),r)} when \spad{b(i,j)} does not exist;
+ ++ otherwise \spad{c(i,j) = f(r,r)}.
+ ++
+ ++X adder(a:Integer,b:Integer):Integer == a+b
+ ++X arr1 : ARRAY2 INT := new(5,4,10)
+ ++X arr2 : ARRAY2 INT := new(3,3,10)
+ ++X map(adder,arr1,arr2,17)
+
+ add
+
+--% Predicates
+
+ any?(f,m) ==
+ for i in minRowIndex(m)..maxRowIndex(m) repeat
+ for j in minColIndex(m)..maxColIndex(m) repeat
+ f(qelt(m,i,j)) => return true
+ false
+
+ every?(f,m) ==
+ for i in minRowIndex(m)..maxRowIndex(m) repeat
+ for j in minColIndex(m)..maxColIndex(m) repeat
+ not f(qelt(m,i,j)) => return false
+ true
+
+ size?(m,n) == nrows(m) * ncols(m) = n
+ less?(m,n) == nrows(m) * ncols(m) < n
+ more?(m,n) == nrows(m) * ncols(m) > n
+
+--% Size inquiries
+
+ # m == nrows(m) * ncols(m)
+
+--% Part extractions
+
+ elt(m,i,j,r) ==
+ i < minRowIndex(m) or i > maxRowIndex(m) => r
+ j < minColIndex(m) or j > maxColIndex(m) => r
+ qelt(m,i,j)
+
+ count(f:R -> Boolean,m:%) ==
+ num : NonNegativeInteger := 0
+ for i in minRowIndex(m)..maxRowIndex(m) repeat
+ for j in minColIndex(m)..maxColIndex(m) repeat
+ if f(qelt(m,i,j)) then num := num + 1
+ num
+
+ parts m ==
+ entryList : List R := nil()
+ for i in maxRowIndex(m)..minRowIndex(m) by -1 repeat
+ for j in maxColIndex(m)..minColIndex(m) by -1 repeat
+ entryList := concat(qelt(m,i,j),entryList)
+ entryList
+
+--% Creation
+
+ copy m ==
+ ans := new(nrows m,ncols m,NIL$Lisp)
+ for i in minRowIndex(m)..maxRowIndex(m) repeat
+ for j in minColIndex(m)..maxColIndex(m) repeat
+ qsetelt_!(ans,i,j,qelt(m,i,j))
+ ans
+
+ fill_!(m,r) ==
+ for i in minRowIndex(m)..maxRowIndex(m) repeat
+ for j in minColIndex(m)..maxColIndex(m) repeat
+ qsetelt_!(m,i,j,r)
+ m
+
+ map(f,m) ==
+ ans := new(nrows m,ncols m,NIL$Lisp)
+ for i in minRowIndex(m)..maxRowIndex(m) repeat
+ for j in minColIndex(m)..maxColIndex(m) repeat
+ qsetelt_!(ans,i,j,f(qelt(m,i,j)))
+ ans
+
+ map_!(f,m) ==
+ for i in minRowIndex(m)..maxRowIndex(m) repeat
+ for j in minColIndex(m)..maxColIndex(m) repeat
+ qsetelt_!(m,i,j,f(qelt(m,i,j)))
+ m
+
+ map(f,m,n) ==
+ (nrows(m) ^= nrows(n)) or (ncols(m) ^= ncols(n)) =>
+ error "map: arguments must have same dimensions"
+ ans := new(nrows m,ncols m,NIL$Lisp)
+ for i in minRowIndex(m)..maxRowIndex(m) repeat
+ for j in minColIndex(m)..maxColIndex(m) repeat
+ qsetelt_!(ans,i,j,f(qelt(m,i,j),qelt(n,i,j)))
+ ans
+
+ map(f,m,n,r) ==
+ maxRow := max(maxRowIndex m,maxRowIndex n)
+ maxCol := max(maxColIndex m,maxColIndex n)
+ ans := new(max(nrows m,nrows n),max(ncols m,ncols n),NIL$Lisp)
+ for i in minRowIndex(m)..maxRow repeat
+ for j in minColIndex(m)..maxCol repeat
+ qsetelt_!(ans,i,j,f(elt(m,i,j,r),elt(n,i,j,r)))
+ ans
+
+ setRow_!(m,i,v) ==
+ i < minRowIndex(m) or i > maxRowIndex(m) =>
+ error "setRow!: index out of range"
+ for j in minColIndex(m)..maxColIndex(m) _
+ for k in minIndex(v)..maxIndex(v) repeat
+ qsetelt_!(m,i,j,v.k)
+ m
+
+ setColumn_!(m,j,v) ==
+ j < minColIndex(m) or j > maxColIndex(m) =>
+ error "setColumn!: index out of range"
+ for i in minRowIndex(m)..maxRowIndex(m) _
+ for k in minIndex(v)..maxIndex(v) repeat
+ qsetelt_!(m,i,j,v.k)
+ m
+
+ if R has _= : (R,R) -> Boolean then
+
+ m = n ==
+ eq?(m,n) => true
+ (nrows(m) ^= nrows(n)) or (ncols(m) ^= ncols(n)) => false
+ for i in minRowIndex(m)..maxRowIndex(m) repeat
+ for j in minColIndex(m)..maxColIndex(m) repeat
+ not (qelt(m,i,j) = qelt(n,i,j)) => return false
+ true
+
+ member?(r,m) ==
+ for i in minRowIndex(m)..maxRowIndex(m) repeat
+ for j in minColIndex(m)..maxColIndex(m) repeat
+ qelt(m,i,j) = r => return true
+ false
+
+ count(r:R,m:%) == count(#1 = r,m)
+
+ if Row has shallowlyMutable then
+
+ row(m,i) ==
+ i < minRowIndex(m) or i > maxRowIndex(m) =>
+ error "row: index out of range"
+ v : Row := new(ncols m,NIL$Lisp)
+ for j in minColIndex(m)..maxColIndex(m) _
+ for k in minIndex(v)..maxIndex(v) repeat
+ qsetelt_!(v,k,qelt(m,i,j))
+ v
+
+ if Col has shallowlyMutable then
+
+ column(m,j) ==
+ j < minColIndex(m) or j > maxColIndex(m) =>
+ error "column: index out of range"
+ v : Col := new(nrows m,NIL$Lisp)
+ for i in minRowIndex(m)..maxRowIndex(m) _
+ for k in minIndex(v)..maxIndex(v) repeat
+ qsetelt_!(v,k,qelt(m,i,j))
+ v
+
+ if R has CoercibleTo(OutputForm) then
+
+ coerce(m:%) ==
+ l : List List OutputForm
+ l := [[qelt(m,i,j) :: OutputForm _
+ for j in minColIndex(m)..maxColIndex(m)] _
+ for i in minRowIndex(m)..maxRowIndex(m)]
+ matrix l
+
+@
+<<ARR2CAT.dotabb>>=
+"ARR2CAT"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ARR2CAT"];
+"ARR2CAT" -> "HOAGG"
+
+@
+<<ARR2CAT.dotfull>>=
+"TwoDimensionalArrayCategory(a:Type,b:FiniteLinearAggregate(a),c:FiniteLinearAggregate(a))"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ARR2CAT"];
+"TwoDimensionalArrayCategory(a:Type,b:FiniteLinearAggregate(a),c:FiniteLinearAggregate(a))"
+ -> "HomogeneousAggregate(a:Type)"
+
+"TwoDimensionalArrayCategory(a:Type,d:IndexedOneDimensionalArray(a,b),e:IndexedOneDimensionalArray(a,c))"
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=ARR2CAT"];
+"TwoDimensionalArrayCategory(a:Type,d:IndexedOneDimensionalArray(a,b),e:IndexedOneDimensionalArray(a,c))"
+-> "TwoDimensionalArrayCategory(a:Type,b:FiniteLinearAggregate(a),c:FiniteLinearAggregate(a))"
+
+@
+<<ARR2CAT.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"TwoDimensionalArrayCategory(a:Type,b:FiniteLinearAggregate(a),c:FiniteLinearAggregate(a))"
+ [color=lightblue];
+"TwoDimensionalArrayCategory(a:Type,b:FiniteLinearAggregate(a),c:FiniteLinearAggregate(a))"
+ -> "HomogeneousAggregate(a:Type)"
+
+"HomogeneousAggregate(a:Type)" [color=lightblue];
+"HomogeneousAggregate(a:Type)" -> "Aggregate()"
+"HomogeneousAggregate(a:Type)" -> "Evalable(a:Type)"
+"HomogeneousAggregate(a:Type)" -> "SetCategory()"
+
+"Evalable(a:Type)" [color="#00EE00"];
+
+"SetCategory()" [color=lightblue];
+"SetCategory()" -> "BasicType()"
+"SetCategory()" -> "CoercibleTo(OutputForm)"
+
+"BasicType()" [color=lightblue];
+"BasicType()" -> "Category"
+
+"CoercibleTo(OutputForm)" [color=seagreen];
+"CoercibleTo(OutputForm)" -> "CoercibleTo(a:Type)"
+
+"CoercibleTo(a:Type)" [color=lightblue];
+"CoercibleTo(a:Type)" -> "Category"
+
+"Aggregate()" [color=lightblue];
+"Aggregate()" -> "Type()"
+
+"Type()" [color=lightblue];
+"Type()" -> "Category"
+
+"Category" [color=lightblue];
+
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{BagAggregate}{BGAGG}
\pagepic{ps/v102bagaggregate.ps}{BGAGG}{1.00}
@@ -2352,6 +3213,14 @@
\cross{BGAGG}{?\~{}=?} &&&
\end{tabular}
+{\bf Attributes Exported:}
+\begin{itemize}
+\item {\bf \cross{BGAGG}{shallowlyMutable}}
+is true if its values have immediate components that are
+updateable (mutable). Note: the properties of any component
+domain are irrevelant to the shallowlyMutable proper.
+\end{itemize}
+
These are directly exported but not implemented:
\begin{verbatim}
extract! : % -> S
@@ -2520,6 +3389,12 @@
\cross{CLAGG}{?\~{}=?} \\
\end{tabular}
+{\bf Attributes Used:}
+\begin{itemize}
+\item {\bf \cross{CLAGG}{finiteAggregate}}
+is true if it is an aggregate with a finite number of elements.
+\end{itemize}
+
These are directly exported but not implemented:
\begin{verbatim}
construct: List S -> %
@@ -2769,6 +3644,16 @@
\cross{IXAGG}{?=?} &&&
\end{tabular}
+{\bf Attributes Used:}
+\begin{itemize}
+\item {\bf \cross{IXAGG}{finiteAggregate}}
+is true if it is an aggregate with a finite number of elements.
+\item {\bf \cross{IXAGG}{shallowlyMutable}}
+is true if its values have immediate components that are
+updateable (mutable). Note: the properties of any component
+domain are irrevelant to the shallowlyMutable proper.
+\end{itemize}
+
These are directly exported but not implemented:
\begin{verbatim}
index? : (Index,%) -> Boolean
@@ -3107,7 +3992,7 @@
"SemiGroup()" [color=lightblue];
"SemiGroup()" -> "SetCategory()"
-"SemiGroup()" -> "RepeatedSquaring(SemiGroup)"
+"SemiGroup()" -> "RepeatedSquaring(a:SemiGroup)"
"SetCategory()" [color=lightblue];
"SetCategory()" -> "BasicType()"
@@ -3122,8 +4007,8 @@
"CoercibleTo(a:Type)" [color=lightblue];
"CoercibleTo(a:Type)" -> "Category"
-"RepeatedSquaring(SemiGroup)" [color="#00EE00"];
-"RepeatedSquaring(SemiGroup)" -> "RepeatedSquaring(a:SetCategory)"
+"RepeatedSquaring(a:SemiGroup)" [color="#00EE00"];
+"RepeatedSquaring(a:SemiGroup)" -> "RepeatedSquaring(a:SetCategory)"
"RepeatedSquaring(a:SetCategory)" [color="#00EE00"];
"RepeatedSquaring(a:SetCategory)" -> "Package"
@@ -3299,6 +4184,14 @@
\cross{RCAGG}{?=?} &&&&
\end{tabular}
+{\bf Attributes Used:}
+\begin{itemize}
+\item {\bf \cross{RCAGG}{shallowlyMutable}}
+is true if its values have immediate components that are
+updateable (mutable). Note: the properties of any component
+domain are irrevelant to the shallowlyMutable proper.
+\end{itemize}
+
These are directly exported but not implemented:
\begin{verbatim}
children : % -> List %
@@ -3510,6 +4403,16 @@
\cross{BRAGG}{?.value} &&&
\end{tabular}
+{\bf Attributes Used:}
+\begin{itemize}
+\item {\bf \cross{BRAGG}{finiteAggregate}}
+is true if it is an aggregate with a finite number of elements.
+\item {\bf \cross{BRAGG}{shallowlyMutable}}
+is true if its values have immediate components that are
+updateable (mutable). Note: the properties of any component
+domain are irrevelant to the shallowlyMutable proper.
+\end{itemize}
+
These are directly exported but not implemented:
\begin{verbatim}
left : % -> %
@@ -3902,6 +4805,12 @@
\cross{DIOPS}{?\~{}=?} &&&
\end{tabular}
+{\bf Attributes Used:}
+\begin{itemize}
+\item {\bf \cross{DIOPS}{finiteAggregate}}
+is true if it is an aggregate with a finite number of elements.
+\end{itemize}
+
These are directly exported but not implemented:
\begin{verbatim}
dictionary : List S -> %
@@ -4130,6 +5039,14 @@
\cross{DLAGG}{?.value} &&
\end{tabular}
+{\bf Attributes Used:}
+\begin{itemize}
+\item {\bf \cross{DLAGG}{shallowlyMutable}}
+is true if its values have immediate components that are
+updateable (mutable). Note: the properties of any component
+domain are irrevelant to the shallowlyMutable proper.
+\end{itemize}
+
These are directly exported but not implemented:
\begin{verbatim}
concat! : (%,%) -> % if $ has shallowlyMutable
@@ -4305,6 +5222,14 @@
\cross{GROUP}{?\^{}?} &&&&
\end{tabular}
+{\bf Attributes Exported:}
+\begin{itemize}
+\item {\bf \cross{GROUP}{unitsKnown}}
+is true if a monoid (a multiplicative semigroup with a 1) has
+unitsKnown means that the operation {\tt recip} can only return
+``failed'' if its argument is not a unit.
+\end{itemize}
+
These are directly exported but not implemented:
\begin{verbatim}
inv : % -> %
@@ -4515,6 +5440,16 @@
\cross{LNAGG}{?.?} &&&
\end{tabular}
+{\bf Attributes Used:}
+\begin{itemize}
+\item {\bf \cross{LNAGG}{finiteAggregate}}
+is true if it is an aggregate with a finite number of elements.
+\item {\bf \cross{LNAGG}{shallowlyMutable}}
+is true if its values have immediate components that are
+updateable (mutable). Note: the properties of any component
+domain are irrevelant to the shallowlyMutable proper.
+\end{itemize}
+
These are directly exported but not implemented:
\begin{verbatim}
concat : (%,%) -> %
@@ -5057,6 +5992,12 @@
\cross{PRQAGG}{?\~{}=?} \\
\end{tabular}
+{\bf Attributes Exported:}
+\begin{itemize}
+\item {\bf \cross{PRQAGG}{finiteAggregate}}
+is true if it is an aggregate with a finite number of elements.
+\end{itemize}
+
These are directly exported but not implemented:
\begin{verbatim}
max : % -> S
@@ -5224,6 +6165,12 @@
\cross{QUAGG}{?\~{}=?} &&
\end{tabular}
+{\bf Attributes Exported:}
+\begin{itemize}
+\item {\bf \cross{QUAGG}{finiteAggregate}}
+is true if it is an aggregate with a finite number of elements.
+\end{itemize}
+
These are implemented by this category:
\begin{verbatim}
back : % -> S
@@ -5408,6 +6355,13 @@
\cross{SETAGG}{?\~{}=?} &&
\end{tabular}
+{\bf Attributes Exported:}
+\begin{itemize}
+\item {\bf \cross{SETAGG}{partiallyOrderedSet}}
+is true if a set with $<$ which is transitive, but
+not($a < b$ or $a = b$) does not necessarily imply $b<a$.
+\end{itemize}
+
These are directly exported but not implemented:
\begin{verbatim}
brace : List S -> %
@@ -5678,6 +6632,12 @@
\cross{SKAGG}{?\~{}=?} &&&&
\end{tabular}
+{\bf Attributes Exported:}
+\begin{itemize}
+\item {\bf \cross{SKAGG}{finiteAggregate}}
+is true if it is an aggregate with a finite number of elements.
+\end{itemize}
+
These are directly exported but not implemented:
\begin{verbatim}
depth : % -> NonNegativeInteger
@@ -5868,6 +6828,16 @@
\cross{URAGG}{?\~{}=?} \\
\end{tabular}
+{\bf Attributes Used:}
+\begin{itemize}
+\item {\bf \cross{URAGG}{finiteAggregate}}
+is true if it is an aggregate with a finite number of elements.
+\item {\bf \cross{URAGG}{shallowlyMutable}}
+is true if its values have immediate components that are
+updateable (mutable). Note: the properties of any component
+domain are irrevelant to the shallowlyMutable proper.
+\end{itemize}
+
These are directly exported but not implemented:
\begin{verbatim}
concat : (S,%) -> %
@@ -6448,6 +7418,12 @@
\cross{DIAGG}{?=?} &&&
\end{tabular}
+{\bf Attributes Used:}
+\begin{itemize}
+\item {\bf \cross{DIAGG}{finiteAggregate}}
+is true if it is an aggregate with a finite number of elements.
+\end{itemize}
+
These are implemented by this category:
\begin{verbatim}
dictionary : List S -> %
@@ -6899,6 +7875,14 @@
\cross{ELAGG}{?\~{}=? } \\
\end{tabular}
+{\bf Attributes Exported:}
+\begin{itemize}
+\item {\bf \cross{ELAGG}{shallowlyMutable}}
+is true if its values have immediate components that are
+updateable (mutable). Note: the properties of any component
+domain are irrevelant to the shallowlyMutable proper.
+\end{itemize}
+
These are directly exported but not implemented:
\begin{verbatim}
concat! : (%,S) -> %
@@ -7195,6 +8179,20 @@
\cross{FLAGG}{?\~{}=?} &&
\end{tabular}
+{\bf Attributes Exported:}
+\begin{itemize}
+\item {\bf \cross{FLAGG}{finiteAggregate}}
+is true if it is an aggregate with a finite number of elements.
+\end{itemize}
+
+{\bf Attributes Used:}
+\begin{itemize}
+\item {\bf \cross{FLAGG}{shallowlyMutable}}
+is true if its values have immediate components that are
+updateable (mutable). Note: the properties of any component
+domain are irrevelant to the shallowlyMutable proper.
+\end{itemize}
+
These are directly exported but not implemented:
\begin{verbatim}
copyInto! : (%,%,Integer) -> %
@@ -7846,6 +8844,14 @@
\cross{STAGG}{?\~{}=?} &
\end{tabular}
+{\bf Attributes Used:}
+\begin{itemize}
+\item {\bf \cross{STAGG}{shallowlyMutable}}
+is true if its values have immediate components that are
+updateable (mutable). Note: the properties of any component
+domain are irrevelant to the shallowlyMutable proper.
+\end{itemize}
+
These are implemented by this category:
\begin{verbatim}
concat : (%,%) -> %
@@ -8211,6 +9217,14 @@
\cross{A1AGG}{?$>=$?} &&&
\end{tabular}
+{\bf Attributes Exported:}
+\begin{itemize}
+\item {\bf \cross{A1AGG}{shallowlyMutable}}
+is true if its values have immediate components that are
+updateable (mutable). Note: the properties of any component
+domain are irrevelant to the shallowlyMutable proper.
+\end{itemize}
+
These are implemented by this category:
\begin{verbatim}
any? : ((S -> Boolean),%) -> Boolean
@@ -8686,6 +9700,12 @@
\cross{FSAGG}{?\~{}=?} \\
\end{tabular}
+{\bf Attributes Exported:}
+\begin{itemize}
+\item {\bf \cross{FSAGG}{finiteAggregate}}
+is true if it is an aggregate with a finite number of elements.
+\end{itemize}
+
These are implemented by this category:
\begin{verbatim}
brace : List S -> %
@@ -8984,6 +10004,12 @@
\cross{KDAGG}{?\~{}=?} \\
\end{tabular}
+{\bf Attributes Used:}
+\begin{itemize}
+\item {\bf \cross{KDAGG}{finiteAggregate}}
+is true if it is an aggregate with a finite number of elements.
+\end{itemize}
+
These are directly exported but not implemented:
\begin{verbatim}
remove! : (Key,%) -> Union(Entry,"failed")
@@ -10712,20 +11738,18 @@
++ replace(s,i..j,t) replaces the substring \axiom{s(i..j)}
++ of s by string t.
position : (%, %, Integer) -> Integer
- ++ position(s,t,i) returns the position j of the substring s in string t,
- ++ where \axiom{j >= i} is required.
+ ++ position(s,t,i) returns the position j of the substring s in
+ ++ string t, where \axiom{j >= i} is required.
position : (CharacterClass, %, Integer) -> Integer
++ position(cc,t,i) returns the position \axiom{j >= i} in t of
++ the first character belonging to cc.
coerce : Character -> %
++ coerce(c) returns c as a string s with the character c.
-
split: (%, Character) -> List %
++ split(s,c) returns a list of substrings delimited by character c.
split: (%, CharacterClass) -> List %
++ split(s,cc) returns a list of substrings delimited by
++ characters in cc.
-
trim: (%, Character) -> %
++ trim(s,c) returns s with all characters c deleted from right
++ and left ends.
@@ -10759,7 +11783,6 @@
add
trim(s: %, c: Character) == leftTrim(rightTrim(s, c), c)
trim(s: %, cc: CharacterClass) == leftTrim(rightTrim(s, cc), cc)
-
lowerCase s == lowerCase_! copy s
upperCase s == upperCase_! copy s
prefix?(s, t) == substring?(s, t, minIndex t)
@@ -10877,6 +11900,12 @@
\cross{TBAGG}{?\~{}=?} \\
\end{tabular}
+{\bf Attributes Used:}
+\begin{itemize}
+\item {\bf \cross{TBAGG}{finiteAggregate}}
+is true if it is an aggregate with a finite number of elements.
+\end{itemize}
+
These are directly exported but not implemented:
\begin{verbatim}
setelt : (%,Key,Entry) -> Entry
@@ -11068,7 +12097,6 @@
++E Data:=Record(age:Integer,gender:String)
++E a1:AssociationList(String,Data):=table()
++E a1."tim":=[55,"male"]$Data
-
table: List Record(key:Key,entry:Entry) -> %
++ table([x,y,...,z]) creates a table consisting of entries
++ \axiom{x,y,...,z}.
@@ -11776,6 +12804,14 @@
\cross{BMODULE}{?=?} &&
\end{tabular}
+{\bf Attributes Exported:}
+\begin{itemize}
+\item {\bf \cross{BMODULE}{leftUnitary}}
+is true if $1 * x = x$ for all x.
+\item {\bf \cross{BMODULE}{rightUnitary}}
+is true if $x * 1 = x$ for all x.
+\end{itemize}
+
These exports come from LeftModule(R:Ring):
\begin{verbatim}
0 : () -> %
@@ -12756,6 +13792,14 @@
\cross{RING}{?=?} &&&&
\end{tabular}
+{\bf Attributes Exported:}
+\begin{itemize}
+\item {\bf \cross{RING}{unitsKnown}}
+is true if a monoid (a multiplicative semigroup with a 1) has
+unitsKnown means that the operation {\tt recip} can only return
+``failed'' if its argument is not a unit.
+\end{itemize}
+
These are directly exported but not implemented:
\begin{verbatim}
characteristic : () -> NonNegativeInteger
@@ -12894,6 +13938,7 @@
\pagepic{ps/v102characteristicnonzero.ps}{CHARNZ}{0.90}
{\bf See:}\\
+\pageto{FiniteRankAlgebra}{FINRALG}
\pagefrom{Ring}{RING}
{\bf Exports:}\\
@@ -13032,6 +14077,7 @@
\pagepic{ps/v102characteristiczero.ps}{CHARZ}{0.90}
{\bf See:}\\
+\pageto{FiniteRankAlgebra}{FINRALG}
\pagefrom{Ring}{RING}
{\bf Exports:}\\
@@ -13109,9 +14155,9 @@
@
<<CHARZ.dotfull>>=
-"CharacteristicNonZero()"
+"CharacteristicZero()"
[color=lightblue,href="bookvol10.2.pdf#nameddest=CHARZ"];
-"CharacteristicNonZero()" -> "Ring()"
+"CharacteristicZero()" -> "Ring()"
@
<<CHARZ.dotpic>>=
@@ -13162,6 +14208,7 @@
{\bf See:}\\
\pageto{IntegralDomain}{INTDOM}
+\pageto{MonogenicAlgebra}{MONOGEN}
\pagefrom{BiModule}{BMODULE}
\pagefrom{Ring}{RING}
@@ -13188,7 +14235,14 @@
\cross{COMRING}{?=?} &
\end{tabular}
+{\bf Attributes:}
+\begin{itemize}
+\item {\bf \cross{COMRING}{commutative("*")}}
+is true if it has an operation $"*": (D,D) -> D$
+which is commutative.
+\end{itemize}
+
These exports come from Ring():
\begin{verbatim}
0 : () -> %
@@ -13509,6 +14563,12 @@
\cross{ENTIRER}{?=?} \\
\end{tabular}
+{\bf Attributes Exported:}
+\begin{itemize}
+\item {\bf \cross{ENTIRER}{noZeroDivisors}}
+is true if $x * y ~= 0$ implies both x and y are non-zero.
+\end{itemize}
+
These exports come from Ring():
\begin{verbatim}
0 : () -> %
@@ -13633,6 +14693,7 @@
{\bf See:}\\
\pageto{FullyLinearlyExplicitRingOver}{FLINEXP}
+\pageto{MonogenicAlgebra}{MONOGEN}
\pagefrom{Ring}{RING}
{\bf Exports:}\\
@@ -14700,6 +15761,7 @@
{\bf See:}\\
\pageto{DivisionRing}{DIVRING}
+\pageto{FiniteRankAlgebra}{FINRALG}
\pageto{IntegralDomain}{INTDOM}
\pagefrom{Module}{MODULE}
\pagefrom{Ring}{RING}
@@ -15230,6 +16292,14 @@
\cross{INTDOM}{?=?} &
\end{tabular}
+{\bf Attributes Used:}
+\begin{itemize}
+\item {\bf \cross{INTDOM}{canonicalUnitNormal}}
+is true if we can choose a canonical representative for each class
+of associate elements, that is {\tt associates?(a,b)} returns true
+if and only if {\tt unitCanonical(a) = unitCanonical(b)}.
+\end{itemize}
+
These are directly exported but not implemented:
\begin{verbatim}
exquo : (%,%) -> Union(%,"failed")
@@ -16708,6 +17778,7 @@
\pagepic{ps/v102field.ps}{FIELD}{1.00}
{\bf See:}\\
+\pageto{FiniteRankAlgebra}{FINRALG}
\pagefrom{DivisionRing}{DIVRING}
\pagefrom{EuclideanDomain}{EUCDOM}
\pagefrom{UniqueFactorizationDomain}{UFD}
@@ -16758,6 +17829,17 @@
\cross{FIELD}{?\~{}=?} &&&
\end{tabular}
+{\bf Attributes Exported:}
+\begin{itemize}
+\item {\bf \cross{FIELD}{canonicalUnitNormal}}
+is true if we can choose a canonical representative for each class
+of associate elements, that is {\tt associates?(a,b)} returns true
+if and only if {\tt unitCanonical(a) = unitCanonical(b)}.
+\item {\bf \cross{FIELD}{canonicalsClosed}}
+is true if\\
+{\tt unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.
+\end{itemize}
+
These are implemented by this category:
\begin{verbatim}
associates? : (%,%) -> Boolean
@@ -16920,14 +18002,652 @@
}
@
-\chapter{Temporary Placeholders}
-\pagehead{Evalable}{EVALAB}
-\pageto{HomogeneousAggregate}{HOAGG}
-<<EVALAB.dotfull>>=
-"Evalable(a:Type)"
- [color="#00EE00",href="bookvol10.2.pdf#nameddest=EVALAB"];
+\chapter{Category Layer 17}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{FiniteRankAlgebra}{FINRALG}
+\pagepic{ps/v102finiterankalgebra.ps}{FINRALG}{0.45}
+
+{\bf See:}\\
+\pageto{FramedAlgebra}{FRAMALG}
+\pagefrom{Algebra}{ALGEBRA}
+\pagefrom{CharacteristicNonZero}{CHARNZ}
+\pagefrom{CharacteristicZero}{CHARZ}
+\pagefrom{Field}{FIELD}
+
+{\bf Exports:}\\
+\begin{tabular}{lll}
+\cross{FINRALG}{0} &
+\cross{FINRALG}{1} &
+\cross{FINRALG}{characteristic} \\
+\cross{FINRALG}{characteristicPolynomial} &
+\cross{FINRALG}{charthRoot} &
+\cross{FINRALG}{coerce} \\
+\cross{FINRALG}{coordinates} &
+\cross{FINRALG}{discriminant} &
+\cross{FINRALG}{hash} \\
+\cross{FINRALG}{latex} &
+\cross{FINRALG}{minimalPolynomial} &
+\cross{FINRALG}{norm} \\
+\cross{FINRALG}{one?} &
+\cross{FINRALG}{rank} &
+\cross{FINRALG}{recip} \\
+\cross{FINRALG}{regularRepresentation} &
+\cross{FINRALG}{represents} &
+\cross{FINRALG}{sample} \\
+\cross{FINRALG}{subtractIfCan} &
+\cross{FINRALG}{trace} &
+\cross{FINRALG}{traceMatrix} \\
+\cross{FINRALG}{zero?} &
+\cross{FINRALG}{?*?} &
+\cross{FINRALG}{?**?} \\
+\cross{FINRALG}{?+?} &
+\cross{FINRALG}{?-?} &
+\cross{FINRALG}{-?} \\
+\cross{FINRALG}{?=?} &
+\cross{FINRALG}{?\^{}?} &
+\cross{FINRALG}{?\~{}=?} \\
+\end{tabular}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ characteristicPolynomial : % -> UP
+ coordinates : (%,Vector %) -> Vector R
+ minimalPolynomial : % -> UP if R has FIELD
+ norm : % -> R
+ rank : () -> PositiveInteger
+ trace : % -> R
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ coordinates : (Vector %,Vector %) -> Matrix R
+ discriminant : Vector % -> R
+ regularRepresentation : (%,Vector %) -> Matrix R
+ represents : (Vector R,Vector %) -> %
+ traceMatrix : Vector % -> Matrix R
+\end{verbatim}
+
+These exports come from Algebra(R:CommutativeRing):
+\begin{verbatim}
+ 0 : () -> %
+ 1 : () -> %
+ characteristic : () -> NonNegativeInteger
+ coerce : Integer -> %
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ one? : % -> Boolean
+ recip : % -> Union(%,"failed")
+ sample : () -> %
+ subtractIfCan : (%,%) -> Union(%,"failed")
+ zero? : % -> Boolean
+ ?+? : (%,%) -> %
+ ?=? : (%,%) -> Boolean
+ ?~=? : (%,%) -> Boolean
+ ?*? : (%,%) -> %
+ ?*? : (Integer,%) -> %
+ ?*? : (PositiveInteger,%) -> %
+ ?*? : (NonNegativeInteger,%) -> %
+ ?-? : (%,%) -> %
+ -? : % -> %
+ ?**? : (%,PositiveInteger) -> %
+ ?**? : (%,NonNegativeInteger) -> %
+ ?^? : (%,PositiveInteger) -> %
+ ?^? : (%,NonNegativeInteger) -> %
+\end{verbatim}
+
+These exports come from Field():
+\begin{verbatim}
+ ?*? : (R,%) -> %
+ ?*? : (%,R) -> %
+ coerce : R -> %
+\end{verbatim}
+
+These exports come from CharacteristicNonZero():
+\begin{verbatim}
+ charthRoot : % -> Union(%,"failed") if R has CHARNZ
+\end{verbatim}
+
+These exports come from CharacteristicZero():
+\begin{verbatim}
+\end{verbatim}
+
+<<category FINRALG FiniteRankAlgebra>>=
+)abbrev category FINRALG FiniteRankAlgebra
+++ Author: Barry Trager
+++ Date Created:
+++ Date Last Updated:
+++ Basic Functions:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++ A FiniteRankAlgebra is an algebra over a commutative ring R which
+++ is a free R-module of finite rank.
+
+FiniteRankAlgebra(R:CommutativeRing, UP:UnivariatePolynomialCategory R):
+ Category == Algebra R with
+ rank : () -> PositiveInteger
+ ++ rank() returns the rank of the algebra.
+ regularRepresentation : (% , Vector %) -> Matrix R
+ ++ regularRepresentation(a,basis) returns the matrix of the
+ ++ linear map defined by left multiplication by \spad{a} with respect
+ ++ to the basis \spad{basis}.
+ trace : % -> R
+ ++ trace(a) returns the trace of the regular representation
+ ++ of \spad{a} with respect to any basis.
+ norm : % -> R
+ ++ norm(a) returns the determinant of the regular representation
+ ++ of \spad{a} with respect to any basis.
+ coordinates : (%, Vector %) -> Vector R
+ ++ coordinates(a,basis) returns the coordinates of \spad{a} with
+ ++ respect to the basis \spad{basis}.
+ coordinates : (Vector %, Vector %) -> Matrix R
+ ++ coordinates([v1,...,vm], basis) returns the coordinates of the
+ ++ vi's with to the basis \spad{basis}. The coordinates of vi are
+ ++ contained in the ith row of the matrix returned by this
+ ++ function.
+ represents : (Vector R, Vector %) -> %
+ ++ represents([a1,..,an],[v1,..,vn]) returns \spad{a1*v1+...+an*vn}.
+ discriminant : Vector % -> R
+ ++ discriminant([v1,..,vn]) returns
+ ++ \spad{determinant(traceMatrix([v1,..,vn]))}.
+ traceMatrix : Vector % -> Matrix R
+ ++ traceMatrix([v1,..,vn]) is the n-by-n matrix ( Tr(vi * vj) )
+ characteristicPolynomial: % -> UP
+ ++ characteristicPolynomial(a) returns the characteristic
+ ++ polynomial of the regular representation of \spad{a} with respect
+ ++ to any basis.
+ if R has Field then minimalPolynomial : % -> UP
+ ++ minimalPolynomial(a) returns the minimal polynomial of \spad{a}.
+ if R has CharacteristicZero then CharacteristicZero
+ if R has CharacteristicNonZero then CharacteristicNonZero
+
+ add
+
+ discriminant v == determinant traceMatrix v
+
+ coordinates(v:Vector %, b:Vector %) ==
+ m := new(#v, #b, 0)$Matrix(R)
+ for i in minIndex v .. maxIndex v for j in minRowIndex m .. repeat
+ setRow_!(m, j, coordinates(qelt(v, i), b))
+ m
+
+ represents(v, b) ==
+ m := minIndex v - 1
+ _+/[v(i+m) * b(i+m) for i in 1..rank()]
+
+ traceMatrix v ==
+ matrix [[trace(v.i*v.j) for j in minIndex v..maxIndex v]$List(R)
+ for i in minIndex v .. maxIndex v]$List(List R)
+
+ regularRepresentation(x, b) ==
+ m := minIndex b - 1
+ matrix
+ [parts coordinates(x*b(i+m),b) for i in 1..rank()]$List(List R)
+
@
+<<FINRALG.dotabb>>=
+"FINRALG"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=FINRALG"];
+"FINRALG" -> "ALGEBRA"
+"FINRALG" -> "FIELD"
+"FINRALG" -> "CHARNZ"
+"FINRALG" -> "CHARZ"
+@
+<<FINRALG.dotfull>>=
+"FiniteRankAlgebra(a:CommutativeRing,b:UnivariatePolynomialCategory(a))"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=FINRALG"];
+"FiniteRankAlgebra(a:CommutativeRing,b:UnivariatePolynomialCategory(a))" ->
+ "Algebra(a:CommutativeRing)"
+"FiniteRankAlgebra(a:CommutativeRing,b:UnivariatePolynomialCategory(a))" ->
+ "Field()"
+"FiniteRankAlgebra(a:CommutativeRing,b:UnivariatePolynomialCategory(a))" ->
+ "CharacteristicNonZero()"
+"FiniteRankAlgebra(a:CommutativeRing,b:UnivariatePolynomialCategory(a))" ->
+ "CharacteristicZero()"
+
+@
+<<FINRALG.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"Finite...
[truncated message content] |
|
From: <gi...@ax...> - 2008-09-27 16:18:16
|
books/bookvol10.2.pamphlet | 1812 ++++++++++++++++++++++++++-
books/ps/v102attributeregistry.ps | 289 +++++
books/ps/v102category.ps | 243 ++++
books/ps/v102finiterankalgebra.ps | 702 +++++++++++
books/ps/v102framedalgebra.ps | 748 +++++++++++
books/ps/v102fullyretractableto.ps | 335 +++++
books/ps/v102monogenicalgebra.ps | 473 +++++++
books/ps/v102twodimensionalarraycategory.ps | 697 ++++++++++
changelog | 14 +
src/algebra/Makefile.pamphlet | 5 +-
src/algebra/array2.spad.pamphlet | 368 ------
src/algebra/attreg.spad.pamphlet | 131 --
src/algebra/retract.spad.pamphlet | 43 -
13 files changed, 5276 insertions(+), 584 deletions(-)
New commits:
commit e3f70d83d57a11785734965f8e36bfb961f87c51
Author: Tim Daly <da...@ax...>
Date: Fri Aug 1 02:30:49 2008 -0400
20080926 tpd books/bookvol10.2 add attributes
20080926 tpd src/algebra/Makefile remove attreg
20080926 tpd books/ps/v102twodimensionalarraycategory.ps added
20080926 tpd books/ps/v102monogenicalgebra.ps added
20080926 tpd books/ps/v102fullyretractableto.ps added
20080926 tpd books/ps/v102framedalgebra.ps added
20080926 tpd books/ps/v102finiterankalgebra.ps added
20080926 tpd books/ps/v102category.ps added
20080926 tpd books/ps/v102attributeregistry.ps added
20080926 tpd books/bookvol10.2 add categories
20080926 tpd src/algebra/attreg.spad deleted, absorbed by bookvol10.2
20080926 tpd src/algebra/array2.spad move ARR2CAT to bookvol10.2
20080926 tpd src/algebra/retract.spad move FRETRCT to bookvol10.2
20080926 tpd src/algebra/algcat.spad move categories to bookvol10.2
|
|
From: <da...@us...> - 2008-09-26 06:33:06
|
Revision: 981
http://axiom.svn.sourceforge.net/axiom/?rev=981&view=rev
Author: daly
Date: 2008-09-26 06:32:53 +0000 (Fri, 26 Sep 2008)
Log Message:
-----------
20080925 tpd books/ps/v102vectorspace.ps added
20080925 tpd books/ps/v102uniquefactorizationdomain.ps added
20080925 tpd books/ps/v102principalidealdomain.ps added
20080925 tpd books/ps/v102polynomialfactorizationexplicit.ps added
20080925 tpd books/ps/v102partialdifferentialring.ps added
20080925 tpd books/ps/v102orderedintegraldomain.ps added
20080925 tpd books/ps/v102module.ps added
20080925 tpd books/ps/v102logic.ps added
20080925 tpd books/ps/v102linearlyexplicitringover.ps added
20080925 tpd books/ps/v102integraldomain.ps added
20080925 tpd books/ps/v102innerevalable.ps added
20080925 tpd books/ps/v102gcddomain.ps added
20080925 tpd books/ps/v102fullylinearlyexplicitringover.ps added
20080925 tpd books/ps/v102field.ps added
20080925 tpd books/ps/v102evalable.ps added
20080925 tpd books/ps/v102euclideandomain.ps added
20080925 tpd books/ps/v102divisionring.ps added
20080925 tpd books/ps/v102differentialring.ps added
20080925 tpd books/ps/v102differentialextension.ps added
20080925 tpd books/ps/v102commutativering.ps added
20080925 tpd books/ps/v102characteristiczero.ps added
20080925 tpd books/ps/v102characteristicnonzero.ps added
20080925 tpd books/ps/v102bitaggregate.ps added
20080925 tpd books/ps/v102algebra.ps added
20080925 tpd books/ps/v102EntireRing.ps added
20080925 tpd books/ps/v102retractableto.ps added
20080925 tpd books/bookvol10.2 absorb equation1.spad
20080925 tpd src/algebra/Makefile remove equation1
20080925 tpd src/algebra/boolean.spad move LOGIC into bookvol10.2
20080925 tpd src/algebra/equation1.spad remove. merged into bookvol10.2
20080925 tpd src/algebra/Makefile remove catdef.spad
20080925 tpd books/bookvol10.2 absorb catdef.spad
20080925 tpd src/algebra/catdef.spad removed, moved to bookvol10.2
Modified Paths:
--------------
trunk/axiom/books/bookvol10.2.pamphlet
trunk/axiom/books/ps/v102retractableto.ps
trunk/axiom/changelog
trunk/axiom/src/algebra/Makefile.pamphlet
trunk/axiom/src/algebra/boolean.spad.pamphlet
Added Paths:
-----------
trunk/axiom/books/ps/v102EntireRing.ps
trunk/axiom/books/ps/v102algebra.ps
trunk/axiom/books/ps/v102bitaggregate.ps
trunk/axiom/books/ps/v102characteristicnonzero.ps
trunk/axiom/books/ps/v102characteristiczero.ps
trunk/axiom/books/ps/v102commutativering.ps
trunk/axiom/books/ps/v102differentialextension.ps
trunk/axiom/books/ps/v102differentialring.ps
trunk/axiom/books/ps/v102divisionring.ps
trunk/axiom/books/ps/v102euclideandomain.ps
trunk/axiom/books/ps/v102evalable.ps
trunk/axiom/books/ps/v102field.ps
trunk/axiom/books/ps/v102fullylinearlyexplicitringover.ps
trunk/axiom/books/ps/v102gcddomain.ps
trunk/axiom/books/ps/v102innerevalable.ps
trunk/axiom/books/ps/v102integraldomain.ps
trunk/axiom/books/ps/v102linearlyexplicitringover.ps
trunk/axiom/books/ps/v102logic.ps
trunk/axiom/books/ps/v102module.ps
trunk/axiom/books/ps/v102orderedintegraldomain.ps
trunk/axiom/books/ps/v102partialdifferentialring.ps
trunk/axiom/books/ps/v102polynomialfactorizationexplicit.ps
trunk/axiom/books/ps/v102principalidealdomain.ps
trunk/axiom/books/ps/v102uniquefactorizationdomain.ps
trunk/axiom/books/ps/v102vectorspace.ps
Removed Paths:
-------------
trunk/axiom/src/algebra/catdef.spad.pamphlet
trunk/axiom/src/algebra/equation1.spad.pamphlet
Modified: trunk/axiom/books/bookvol10.2.pamphlet
===================================================================
--- trunk/axiom/books/bookvol10.2.pamphlet 2008-09-22 05:30:00 UTC (rev 980)
+++ trunk/axiom/books/bookvol10.2.pamphlet 2008-09-26 06:32:53 UTC (rev 981)
@@ -284,9 +284,11 @@
{\bf See:}\\
\pageto{BasicType}{BASTYPE}
-\pageto{Eltable}{ELTAB}
\pageto{CoercibleTo}{KOERCE}
\pageto{ConvertibleTo}{KONVERT}
+\pageto{Eltable}{ELTAB}
+\pageto{InnerEvalable}{IEVALAB}
+\pageto{Logic}{LOGIC}
\pageto{RetractableTo}{RETRACT}
\pageto{Type}{TYPE}
@@ -603,6 +605,97 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{InnerEvalable}{IEVALAB}
+\pagepic{ps/v102innerevalable.ps}{IEVALAB}{1.00}
+
+{\bf See:}\\
+\pageto{Evalable}{EVALAB}
+\pagefrom{Category}{CATEGORY}
+
+{\bf Exports:}\\
+\begin{tabular}{l}
+\cross{IEVALAB}{eval}
+\end{tabular}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ eval : (%,A,B) -> %
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ eval : (%,List A,List B) -> %
+\end{verbatim}
+
+<<category IEVALAB InnerEvalable>>=
+)abbrev category IEVALAB InnerEvalable
+-- FOR THE BENEFIT OF LIBAX0 GENERATION
+++ Author:
+++ Date Created:
+++ Date Last Updated: June 3, 1991
+++ Basic Operations:
+++ Related Domains:
+++ Also See: Evalable
+++ AMS Classifications:
+++ Keywords: equation
+++ Examples:
+++ References:
+++ Description:
+++ This category provides \spadfun{eval} operations.
+++ A domain may belong to this category if it is possible to make
+++ ``evaluation'' substitutions. The difference between this
+++ and \spadtype{Evalable} is that the operations in this category
+++ specify the substitution as a pair of arguments rather than as
+++ an equation.
+InnerEvalable(A:SetCategory, B:Type): Category == with
+ eval: ($, A, B) -> $
+ ++ eval(f, x, v) replaces x by v in f.
+ eval: ($, List A, List B) -> $
+ ++ eval(f, [x1,...,xn], [v1,...,vn]) replaces xi by vi in f.
+ add
+ eval(f:$, x:A, v:B) == eval(f, [x], [v])
+
+@
+<<IEVALAB.dotabb>>=
+"IEVALAB"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=IEVALAB"];
+"IEVALAB" -> "CATEGORY"
+
+@
+<<IEVALAB.dotfull>>=
+"InnerEvalable(a:SetCategory,b:Type)"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=IEVALAB"];
+"InnerEvalable(a:SetCategory,b:Type)" -> "Category"
+
+"InnerEvalable(a:SetCategory,b:SetCategory)"
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=IEVALAB"];
+"InnerEvalable(a:SetCategory,b:SetCategory)" ->
+ "InnerEvalable(a:SetCategory,b:Type)"
+
+"InnerEvalable(a:Ring,MultivariateTaylorSeriesCategory(a:Ring,b:OrderedSet))"
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=IEVALAB"];
+"InnerEvalable(a:Ring,MultivariateTaylorSeriesCategory(a:Ring,b:OrderedSet))"
+ -> "InnerEvalable(a:SetCategory,b:Type)"
+
+"InnerEvalable(Kernal(ExpressionSpace),ExpressionSpace)"
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=IEVALAB"];
+"InnerEvalable(Kernal(ExpressionSpace),ExpressionSpace)" ->
+ "InnerEvalable(a:SetCategory,b:Type)"
+@
+<<IEVALAB.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"InnerEvalable(a:SetCategory,b:Type)" [color=lightblue];
+"InnerEvalable(a:SetCategory,b:Type)" -> "Category"
+
+"Category" [color=lightblue];
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{RetractableTo}{RETRACT}
\pagepic{ps/v102retractableto.ps}{RETRACT}{1.00}
@@ -972,6 +1065,184 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{Evalable}{EVALAB}
+\pagepic{ps/v102evalable.ps}{EVALAB}{1.00}
+
+{\bf See:}\\
+\pagefrom{InnerEvalable}{IEVALAB}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+\end{tabular}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ eval : (%,List Equation R) -> %
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+eval : (%,Equation R) -> %
+eval : (%,List R,List R) -> %
+\end{verbatim}
+
+These exports come from InnerEvalable(R:SetCategory,R:SetCategory):
+\begin{verbatim}
+ eval : (%,R,R) -> %
+\end{verbatim}
+
+<<category EVALAB Evalable>>=
+)abbrev category EVALAB Evalable
+++ Author:
+++ Date Created:
+++ Date Last Updated: June 3, 1991
+++ Basic Operations:
+++ Related Domains:
+++ Also See: FullyEvalable
+++ AMS Classifications:
+++ Keywords: equation
+++ Examples:
+++ References:
+++ Description:
+++ This category provides \spadfun{eval} operations.
+++ A domain may belong to this category if it is possible to make
+++ ``evaluation'' substitutions.
+Evalable(R:SetCategory): Category == InnerEvalable(R,R) with
+ eval: ($, Equation R) -> $
+ ++ eval(f,x = v) replaces x by v in f.
+ eval: ($, List Equation R) -> $
+ ++ eval(f, [x1 = v1,...,xn = vn]) replaces xi by vi in f.
+ add
+ eval(f:$, eq:Equation R) == eval(f, [eq])
+ eval(f:$, xs:List R,vs:List R) == eval(f,[x=v for x in xs for v in vs])
+
+@
+<<EVALAB.dotabb>>=
+"EVALAB"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=EVALAB"];
+"EVALAB" -> "IEVALAB"
+
+@
+<<EVALAB.dotfull>>=
+"Evalable(a:SetCategory)"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=EVALAB"];
+"Evalable(a:SetCategory)" -> "InnerEvalable(a:SetCategory,b:SetCategory)"
+
+"Evalable(MultivariateTaylorSeriesCategory(a:Ring,b:OrderedSet))"
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=EVALAB"];
+"Evalable(MultivariateTaylorSeriesCategory(a:Ring,b:OrderedSet))" ->
+ "Evalable(a:SetCategory)"
+
+"Evalable(ExpressionSpace)"
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=EVALAB"];
+"Evalable(ExpressionSpace)" -> "Evalable(a:SetCategory)"
+
+@
+<<EVALAB.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"Evalable(a:SetCategory)" [color=lightblue];
+"Evalable(a:SetCategory)" -> "InnerEvalable(a:SetCategory,b:SetCategory)"
+
+"InnerEvalable(a:SetCategory,b:SetCategory)" [color=seagreen];
+"InnerEvalable(a:SetCategory,b:SetCategory)" ->
+ "InnerEvalable(a:SetCategory,b:Type)"
+
+"InnerEvalable(a:SetCategory,b:Type)" [color=lightblue];
+"InnerEvalable(a:SetCategory,b:Type)" -> "Category"
+
+"Category" [color=lightblue];
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{Logic}{LOGIC}
+\pagepic{ps/v102logic.ps}{LOGIC}{1.00}
+
+{\bf See:}\\
+\pageto{BitAggregate}{BTAGG}
+\pagefrom{BasicType}{BASTYPE}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+\cross{LOGIC}{?$/\backslash{}$?}
+\cross{LOGIC}{?=?}
+\cross{LOGIC}{?$\backslash{}/$?}
+\cross{LOGIC}{\~{}?}
+\cross{LOGIC}{?\~{}=?}
+\end{tabular}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ ~? : % -> %
+ ?/\? : (%,%) -> %
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ ?\/? : (%,%) -> %
+\end{verbatim}
+
+These exports come from BasicType():
+\begin{verbatim}
+ ?=? : (%,%) -> Boolean
+ ?~=? : (%,%) -> Boolean
+\end{verbatim}
+
+<<category LOGIC Logic>>=
+)abbrev category LOGIC Logic
+++ Author:
+++ Date Created:
+++ Change History:
+++ Basic Operations: ~, /\, \/
+++ Related Constructors:
+++ Keywords: boolean
+++ Description:
+++ `Logic' provides the basic operations for lattices,
+++ e.g., boolean algebra.
+Logic: Category == BasicType with
+ _~: % -> %
+ ++ ~(x) returns the logical complement of x.
+ _/_\: (%, %) -> %
+ ++ \spadignore { /\ }returns the logical `meet', e.g. `and'.
+ _\_/: (%, %) -> %
+ ++ \spadignore{ \/ } returns the logical `join', e.g. `or'.
+ add
+ _\_/(x: %,y: %) == _~( _/_\(_~(x), _~(y)))
+
+@
+<<LOGIC.dotabb>>=
+"LOGIC"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=LOGIC"];
+"LOGIC" -> "BASTYPE"
+
+@
+<<LOGIC.dotfull>>=
+"Logic()"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=LOGIC"];
+"Logic()" -> "BasicType()"
+
+@
+<<LOGIC.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"Logic()" [color=lightblue];
+"Logic()" -> "BasicType()"
+
+"BasicType()" [color=lightblue];
+"BasicType()" -> "Category"
+
+"Category" [color=lightblue];
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{SetCategory}{SETCAT}
\pagepic{ps/v102setcategory.ps}{SETCAT}{1.00}
@@ -1082,7 +1353,7 @@
\chapter{Category Layer 3}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{AbelianSemiGroup}{ABELSG}
-\pagepic{ps/v102abeliansemigroup.ps}{ABELSG}{1.00}
+\pagepic{ps/v102abeliansemigroup.ps}{ABELSG}{0.75}
{\bf See:}\\
\pageto{AbelianMonoid}{ABELMON}
@@ -1537,6 +1808,7 @@
\pagepic{ps/v102orderedset.ps}{ORDSET}{1.00}
{\bf See:}\\
+\pageto{BitAggregate}{BTAGG}
\pageto{OrderedAbelianSemiGroup}{OASGP}
\pageto{OrderedFinite}{ORDFIN}
\pageto{OrderedMonoid}{ORDMON}
@@ -7869,6 +8141,7 @@
\pagepic{ps/v102onedimensionalarrayaggregate.ps}{A1AGG}{1.00}
{\bf See:}\\
+\pageto{BitAggregate}{BTAGG}
\pageto{StringAggregate}{SRAGG}
\pagefrom{FiniteLinearAggregate}{FLAGG}
@@ -8344,6 +8617,7 @@
"CLAGG..." [color=lightblue];
"IXAGG..." [color=lightblue];
}
+
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{FiniteSetAggregate}{FSAGG}
@@ -9639,11 +9913,14 @@
construct : List S -> %
convert : % -> InputForm if S has KONVERT INFORM
copy : % -> %
- count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
- count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
+ count : (S,%) -> NonNegativeInteger
+ if S has SETCAT and $ has finiteAggregate
+ count : ((S -> Boolean),%) -> NonNegativeInteger
+ if $ has finiteAggregate
dictionary : List S -> %
dictionary : () -> %
- duplicates : % -> List Record(entry: S,count: NonNegativeInteger)
+ duplicates : % ->
+ List Record(entry: S,count: NonNegativeInteger)
empty : () -> %
empty? : % -> Boolean
eq? : (%,%) -> Boolean
@@ -9662,21 +9939,31 @@
less? : (%,NonNegativeInteger) -> Boolean
map : ((S -> S),%) -> %
map! : ((S -> S),%) -> % if $ has shallowlyMutable
- member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
+ member? : (S,%) -> Boolean
+ if S has SETCAT and $ has finiteAggregate
members : % -> List S if $ has finiteAggregate
more? : (%,NonNegativeInteger) -> Boolean
parts : % -> List S if $ has finiteAggregate
- reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate
- reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate
- reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate
- remove : ((S -> Boolean),%) -> % if $ has finiteAggregate
- remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate
- removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate
+ reduce : (((S,S) -> S),%) -> S
+ if $ has finiteAggregate
+ reduce : (((S,S) -> S),%,S) -> S
+ if $ has finiteAggregate
+ reduce : (((S,S) -> S),%,S,S) -> S
+ if S has SETCAT and $ has finiteAggregate
+ remove : ((S -> Boolean),%) -> %
+ if $ has finiteAggregate
+ remove : (S,%) -> %
+ if S has SETCAT and $ has finiteAggregate
+ removeDuplicates : % -> %
+ if S has SETCAT and $ has finiteAggregate
removeDuplicates! : % -> %
- remove! : ((S -> Boolean),%) -> % if $ has finiteAggregate
+ remove! : ((S -> Boolean),%) -> %
+ if $ has finiteAggregate
remove! : (S,%) -> % if $ has finiteAggregate
- select : ((S -> Boolean),%) -> % if $ has finiteAggregate
- select! : ((S -> Boolean),%) -> % if $ has finiteAggregate
+ select : ((S -> Boolean),%) -> %
+ if $ has finiteAggregate
+ select! : ((S -> Boolean),%) -> %
+ if $ has finiteAggregate
size? : (%,NonNegativeInteger) -> Boolean
#? : % -> NonNegativeInteger if $ has finiteAggregate
?~=? : (%,%) -> Boolean
@@ -10957,7 +11244,7 @@
\chapter{Category Layer 8}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{AssociationListAggregate}{ALAGG}
-\pagepic{ps/v102associationlistaggregate.ps}{ALAGG}{0.50}
+\pagepic{ps/v102associationlistaggregate.ps}{ALAGG}{0.45}
{\bf See:}\\
\pagefrom{ListAggregate}{LSAGG}
@@ -11466,6 +11753,9 @@
\pagepic{ps/v102bimodule.ps}{BMODULE}{1.00}
{\bf See:}\\
+\pageto{CommutativeRing}{COMRING}
+\pageto{EntireRing}{ENTIRER}
+\pageto{Module}{MODULE}
\pagefrom{LeftModule}{LMODULE}
\pagefrom{RightModule}{RMODULE}
@@ -11564,8 +11854,7 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"BiModule(a:Ring,b:Ring)"
- [color=lightblue,href="bookvol10.2.pdf#nameddest=BMODULE"];
+"BiModule(a:Ring,b:Ring)" [color=lightblue];
"BiModule(a:Ring,b:Ring)" -> "LeftModule(a:Ring)"
"BiModule(a:Ring,b:Ring)" -> "RightModule(a:Ring)"
@@ -11592,16 +11881,349 @@
"REPDB..." [color="#00EE00"];
}
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{BitAggregate}{BTAGG}
+\pagepic{ps/v102bitaggregate.ps}{BTAGG}{0.65}
+{\bf See:}\\
+\pagefrom{Logic}{LOGIC}
+\pagefrom{OneDimensionalArrayAggregate}{A1AGG}
+\pagefrom{OrderedSet}{ORDSET}
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+\cross{BTAGG}{any?} &
+\cross{BTAGG}{coerce} &
+\cross{BTAGG}{concat} &
+\cross{BTAGG}{construct} &
+\cross{BTAGG}{convert} \\
+\cross{BTAGG}{copy} &
+\cross{BTAGG}{copyInto!} &
+\cross{BTAGG}{count} &
+\cross{BTAGG}{delete} &
+\cross{BTAGG}{elt} \\
+\cross{BTAGG}{empty} &
+\cross{BTAGG}{empty?} &
+\cross{BTAGG}{entry?} &
+\cross{BTAGG}{entries} &
+\cross{BTAGG}{eq?} \\
+\cross{BTAGG}{eval} &
+\cross{BTAGG}{every?} &
+\cross{BTAGG}{fill!} &
+\cross{BTAGG}{find} &
+\cross{BTAGG}{first} \\
+\cross{BTAGG}{hash} &
+\cross{BTAGG}{index?} &
+\cross{BTAGG}{indices} &
+\cross{BTAGG}{insert} &
+\cross{BTAGG}{latex} \\
+\cross{BTAGG}{less?} &
+\cross{BTAGG}{map} &
+\cross{BTAGG}{map!} &
+\cross{BTAGG}{max} &
+\cross{BTAGG}{maxIndex} \\
+\cross{BTAGG}{member?} &
+\cross{BTAGG}{members} &
+\cross{BTAGG}{merge} &
+\cross{BTAGG}{min} &
+\cross{BTAGG}{minIndex} \\
+\cross{BTAGG}{more?} &
+\cross{BTAGG}{nand} &
+\cross{BTAGG}{new} &
+\cross{BTAGG}{nor} &
+\cross{BTAGG}{not?} \\
+\cross{BTAGG}{parts} &
+\cross{BTAGG}{position} &
+\cross{BTAGG}{qelt} &
+\cross{BTAGG}{qsetelt!} &
+\cross{BTAGG}{reduce} \\
+\cross{BTAGG}{remove} &
+\cross{BTAGG}{removeDuplicates} &
+\cross{BTAGG}{reverse} &
+\cross{BTAGG}{reverse!} &
+\cross{BTAGG}{sample} \\
+\cross{BTAGG}{select} &
+\cross{BTAGG}{setelt} &
+\cross{BTAGG}{size?} &
+\cross{BTAGG}{sort} &
+\cross{BTAGG}{sort!} \\
+\cross{BTAGG}{sorted?} &
+\cross{BTAGG}{swap!} &
+\cross{BTAGG}{xor} &
+\cross{BTAGG}{\#?} &
+\cross{BTAGG}{?$/\backslash{}$?} \\
+\cross{BTAGG}{?$<$?} &
+\cross{BTAGG}{?$<=$?} &
+\cross{BTAGG}{?=?} &
+\cross{BTAGG}{?$>$?} &
+\cross{BTAGG}{?$>=$?} \\
+\cross{BTAGG}{?$\backslash{}/$?} &
+\cross{BTAGG}{\^{}?} &
+\cross{BTAGG}{?and?} &
+\cross{BTAGG}{?.?} &
+\cross{BTAGG}{?or?} \\
+\cross{BTAGG}{\~{}?} &
+\cross{BTAGG}{?\~{}=?} &&&
+\end{tabular}
+These are directly exported but not implemented:
+\begin{verbatim}
+ ?and? : (%,%) -> %
+ ?or? : (%,%) -> %
+ xor : (%,%) -> %
+\end{verbatim}
+These are implemented by this category:
+\begin{verbatim}
+ not? : % -> %
+ ^? : % -> %
+ ~? : % -> %
+ ?/\? : (%,%) -> %
+ ?\/? : (%,%) -> %
+ nand : (%,%) -> %
+ nor : (%,%) -> %
+\end{verbatim}
+These exports come from OrderedSet():
+\begin{verbatim}
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ max : (%,%) -> %
+ min : (%,%) -> %
+ ?=? : (%,%) -> Boolean
+ ?~=? : (%,%) -> Boolean
+ ?<? : (%,%) -> Boolean
+ ?>? : (%,%) -> Boolean
+ ?<=? : (%,%) -> Boolean
+ ?>=? : (%,%) -> Boolean
+\end{verbatim}
+TPDHERE: Note that none of the exports of Logic are needed.
+Perhaps this can be eliminated.
+These exports come from OneDimensionalArrayAggregate(Boolean):
+\begin{verbatim}
+ any? : ((Boolean -> Boolean),%) -> Boolean
+ if $ has finiteAggregate
+ concat : (%,%) -> %
+ concat : List % -> %
+ concat : (%,Boolean) -> %
+ concat : (Boolean,%) -> %
+ construct : List Boolean -> %
+ convert : % -> InputForm
+ if Boolean has KONVERT INFORM
+ copy : % -> %
+ copyInto! : (%,%,Integer) -> %
+ if $ has shallowlyMutable
+ count : (Boolean,%) -> NonNegativeInteger
+ if Boolean has SETCAT and $ has finiteAggregate
+ count : ((Boolean -> Boolean),%) -> NonNegativeInteger
+ if $ has finiteAggregate
+ delete : (%,UniversalSegment Integer) -> %
+ delete : (%,Integer) -> %
+ elt : (%,Integer,Boolean) -> Boolean
+ empty : () -> %
+ empty? : % -> Boolean
+ entry? : (Boolean,%) -> Boolean
+ if $ has finiteAggregate and Boolean has SETCAT
+ entries : % -> List Boolean
+ eq? : (%,%) -> Boolean
+ eval : (%,List Equation Boolean) -> %
+ if Boolean has EVALAB BOOLEAN and Boolean has SETCAT
+ eval : (%,Equation Boolean) -> %
+ if Boolean has EVALAB BOOLEAN and Boolean has SETCAT
+ eval : (%,Boolean,Boolean) -> %
+ if Boolean has EVALAB BOOLEAN and Boolean has SETCAT
+ eval : (%,List Boolean,List Boolean) -> %
+ if Boolean has EVALAB BOOLEAN and Boolean has SETCAT
+ every? : ((Boolean -> Boolean),%) -> Boolean
+ if $ has finiteAggregate
+ fill! : (%,Boolean) -> %
+ if $ has shallowlyMutable
+ find : ((Boolean -> Boolean),%) -> Union(Boolean,"failed")
+ first : % -> Boolean if Integer has ORDSET
+ index? : (Integer,%) -> Boolean
+ indices : % -> List Integer
+ insert : (Boolean,%,Integer) -> %
+ insert : (%,%,Integer) -> %
+ less? : (%,NonNegativeInteger) -> Boolean
+ map : ((Boolean -> Boolean),%) -> %
+ map : (((Boolean,Boolean) -> Boolean),%,%) -> %
+ map! : ((Boolean -> Boolean),%) -> %
+ if $ has shallowlyMutable
+ maxIndex : % -> Integer if Integer has ORDSET
+ member? : (Boolean,%) -> Boolean
+ if Boolean has SETCAT and $ has finiteAggregate
+ members : % -> List Boolean if $ has finiteAggregate
+ merge : (%,%) -> % if Boolean has ORDSET
+ minIndex : % -> Integer if Integer has ORDSET
+ more? : (%,NonNegativeInteger) -> Boolean
+ new : (NonNegativeInteger,Boolean) -> %
+ merge : (((Boolean,Boolean) -> Boolean),%,%) -> %
+ parts : % -> List Boolean if $ has finiteAggregate
+ position : ((Boolean -> Boolean),%) -> Integer
+ position : (Boolean,%,Integer) -> Integer
+ if Boolean has SETCAT
+ position : (Boolean,%) -> Integer
+ if Boolean has SETCAT
+ qelt : (%,Integer) -> Boolean
+ qsetelt! : (%,Integer,Boolean) -> Boolean
+ if $ has shallowlyMutable
+ reverse : % -> %
+ reduce : (((Boolean,Boolean) -> Boolean),%) -> Boolean
+ if $ has finiteAggregate
+ reduce : (((Boolean,Boolean) -> Boolean),%,Boolean) -> Boolean
+ if $ has finiteAggregate
+ reduce :
+ (((Boolean,Boolean) -> Boolean),%,Boolean,Boolean) -> Boolean
+ if Boolean has SETCAT and $ has finiteAggregate
+ remove : (Boolean,%) -> %
+ if Boolean has SETCAT and $ has finiteAggregate
+ remove : ((Boolean -> Boolean),%) -> %
+ if $ has finiteAggregate
+ removeDuplicates : % -> %
+ if Boolean has SETCAT and $ has finiteAggregate
+ reverse! : % -> % if $ has shallowlyMutable
+ sample : () -> %
+ setelt : (%,UniversalSegment Integer,Boolean) -> Boolean
+ if $ has shallowlyMutable
+ select : ((Boolean -> Boolean),%) -> %
+ if $ has finiteAggregate
+ setelt : (%,Integer,Boolean) -> Boolean
+ if $ has shallowlyMutable
+ size? : (%,NonNegativeInteger) -> Boolean
+ sort : (((Boolean,Boolean) -> Boolean),%) -> %
+ sort : % -> % if Boolean has ORDSET
+ sort! : % -> %
+ if Boolean has ORDSET and $ has shallowlyMutable
+ sort! : (((Boolean,Boolean) -> Boolean),%) -> %
+ if $ has shallowlyMutable
+ sorted? : % -> Boolean if Boolean has ORDSET
+ sorted? : (((Boolean,Boolean) -> Boolean),%) -> Boolean
+ swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable
+ ?.? : (%,UniversalSegment Integer) -> %
+ #? : % -> NonNegativeInteger if $ has finiteAggregate
+ ?.? : (%,Integer) -> Boolean
+\end{verbatim}
+<<category BTAGG BitAggregate>>=
+)abbrev category BTAGG BitAggregate
+++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
+++ Date Created: August 87 through August 88
+++ Date Last Updated: April 1991
+++ Basic Operations:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++ The bit aggregate category models aggregates representing large
+++ quantities of Boolean data.
+BitAggregate(): Category ==
+ Join(OrderedSet, Logic, OneDimensionalArrayAggregate Boolean) with
+ "not": % -> %
+ ++ not(b) returns the logical {\em not} of bit aggregate
+ ++ \axiom{b}.
+ "^" : % -> %
+ ++ ^ b returns the logical {\em not} of bit aggregate
+ ++ \axiom{b}.
+ nand : (%, %) -> %
+ ++ nand(a,b) returns the logical {\em nand} of bit aggregates
+ ++ \axiom{a} and \axiom{b}.
+ nor : (%, %) -> %
+ ++ nor(a,b) returns the logical {\em nor} of bit aggregates
+ ++ \axiom{a} and \axiom{b}.
+ _and : (%, %) -> %
+ ++ a and b returns the logical {\em and} of bit aggregates
+ ++ \axiom{a} and \axiom{b}.
+ _or : (%, %) -> %
+ ++ a or b returns the logical {\em or} of bit aggregates
+ ++ \axiom{a} and \axiom{b}.
+ xor : (%, %) -> %
+ ++ xor(a,b) returns the logical {\em exclusive-or} of bit aggregates
+ ++ \axiom{a} and \axiom{b}.
+ add
+ not v == map(_not, v)
+ _^ v == map(_not, v)
+ _~(v) == map(_~, v)
+ _/_\(v, u) == map(_/_\, v, u)
+ _\_/(v, u) == map(_\_/, v, u)
+ nand(v, u) == map(nand, v, u)
+ nor(v, u) == map(nor, v, u)
+
@
+<<BTAGG.dotabb>>=
+"BTAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=BTAGG"];
+"BTAGG" -> "ORDSET"
+"BTAGG" -> "LOGIC"
+"BTAGG" -> "A1AGG"
+
+@
+<<BTAGG.dotfull>>=
+"BitAggregate()"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=BTAGG"];
+"BitAggregate()" -> "OrderedSet()"
+"BitAggregate()" -> "Logic()"
+"BitAggregate()" -> "OneDimensionalArrayAggregate(Boolean)"
+
+@
+<<BTAGG.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"BitAggregate()" [color=lightblue];
+"BitAggregate()" -> "OrderedSet()"
+"BitAggregate()" -> "Logic()"
+"BitAggregate()" -> "OneDimensionalArrayAggregate(Boolean)"
+
+"OneDimensionalArrayAggregate(Boolean)"
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=A1AGG"];
+"OneDimensionalArrayAggregate(Boolean)" ->
+ "OneDimensionalArrayAggregate(a:Type)"
+
+"OneDimensionalArrayAggregate(a:Type)" [color=lightblue];
+"OneDimensionalArrayAggregate(a:Type)" ->
+ "FiniteLinearAggregate(a:Type)"
+
+"FiniteLinearAggregate(a:Type)" [color=lightblue];
+"FiniteLinearAggregate(a:Type)" -> "LinearAggregate(a:Type)"
+
+"LinearAggregate(a:Type)" [color=lightblue];
+"LinearAggregate(a:Type)" -> "IXAGG..."
+"LinearAggregate(a:Type)" -> "CLAGG..."
+
+"OrderedSet()" [color=lightblue];
+"OrderedSet()" -> "SetCategory()"
+
+"SetCategory()" [color=lightblue];
+"SetCategory()" -> "BasicType()"
+"SetCategory()" -> "CoercibleTo(OutputForm)"
+
+"CoercibleTo(OutputForm)" [color=seagreen];
+"CoercibleTo(OutputForm)" -> "CoercibleTo(a:Type)"
+
+"CoercibleTo(a:Type)" [color=lightblue];
+"CoercibleTo(a:Type)" -> "Category"
+
+"Logic()" [color=lightblue];
+"Logic()" -> "BasicType()"
+
+"BasicType()" [color=lightblue];
+"BasicType()" -> "Category"
+
+"Category" [color=lightblue];
+
+"CLAGG..." [color=lightblue];
+"IXAGG..." [color=lightblue];
+}
+
+@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{OrderedAbelianGroup}{OAGROUP}
\pagepic{ps/v102orderedabeliangroup.ps}{OAGROUP}{1.00}
@@ -11938,7 +12560,8 @@
dictionary : () -> %
difference : (%,S) -> %
difference : (%,%) -> %
- duplicates : % -> List Record(entry: S,count: NonNegativeInteger)
+ duplicates : % ->
+ List Record(entry: S,count: NonNegativeInteger)
empty : () -> %
empty? : % -> Boolean
eq? : (%,%) -> Boolean
@@ -12094,7 +12717,16 @@
\pagepic{ps/v102ring.ps}{RING}{1.00}
{\bf See:}\\
+\pageto{Algebra}{ALGEBRA}
+\pageto{CharacteristicNonZero}{CHARNZ}
+\pageto{CharacteristicZero}{CHARZ}
+\pageto{CommutativeRing}{COMRING}
+\pageto{DifferentialExtension}{DIFEXT}
+\pageto{DifferentialRing}{DIFRING}
+\pageto{EntireRing}{ENTIRER}
+\pageto{LinearlyExplicitRingOver}{LINEXP}
\pageto{OrderedRing}{ORDRING}
+\pageto{PartialDifferentialRing}{PDRING}
\pagefrom{LeftModule}{LMODULE}
\pagefrom{Monoid}{MONOID}
\pagefrom{Rng}{RNG}
@@ -12168,10 +12800,6 @@
TPDHERE: Note that none of the exports of LeftModule are needed.
Perhaps this can be eliminated.
-These exports come from LeftModule(Ring):
-\begin{verbatim}
-\end{verbatim}
-
<<category RING Ring>>=
)abbrev category RING Ring
++ Author:
@@ -12262,10 +12890,902 @@
@
\chapter{Category Layer 9}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{CharacteristicNonZero}{CHARNZ}
+\pagepic{ps/v102characteristicnonzero.ps}{CHARNZ}{0.90}
+
+{\bf See:}\\
+\pagefrom{Ring}{RING}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+\cross{CHARNZ}{1} &
+\cross{CHARNZ}{0} &
+\cross{CHARNZ}{coerce} &
+\cross{CHARNZ}{hash} &
+\cross{CHARNZ}{latex} \\
+\cross{CHARNZ}{one?} &
+\cross{CHARNZ}{recip} &
+\cross{CHARNZ}{sample} &
+\cross{CHARNZ}{zero?} &
+\cross{CHARNZ}{characteristic} \\
+\cross{CHARNZ}{charthRoot} &
+\cross{CHARNZ}{subtractIfCan} &
+\cross{CHARNZ}{?\~{}=?} &
+\cross{CHARNZ}{?\^{}?} &
+\cross{CHARNZ}{?*?} \\
+\cross{CHARNZ}{?**?} &
+\cross{CHARNZ}{?+?} &
+\cross{CHARNZ}{?-?} &
+\cross{CHARNZ}{-?} &
+\cross{CHARNZ}{?=?} \\
+\end{tabular}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ charthRoot : % -> Union(%,"failed")
+\end{verbatim}
+
+These exports come from Ring():
+\begin{verbatim}
+ 1 : () -> %
+ 0 : () -> %
+ coerce : Integer -> %
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ one? : % -> Boolean
+ recip : % -> Union(%,"failed")
+ sample : () -> %
+ zero? : % -> Boolean
+ characteristic : () -> NonNegativeInteger
+ subtractIfCan : (%,%) -> Union(%,"failed")
+ ?~=? : (%,%) -> Boolean
+ ?^? : (%,NonNegativeInteger) -> %
+ ?^? : (%,PositiveInteger) -> %
+ ?*? : (%,%) -> %
+ ?*? : (NonNegativeInteger,%) -> %
+ ?*? : (Integer,%) -> %
+ ?*? : (PositiveInteger,%) -> %
+ ?**? : (%,NonNegativeInteger) -> %
+ ?**? : (%,PositiveInteger) -> %
+ ?+? : (%,%) -> %
+ ?-? : (%,%) -> %
+ -? : % -> %
+ ?=? : (%,%) -> Boolean
+\end{verbatim}
+
+<<category CHARNZ CharacteristicNonZero>>=
+)abbrev category CHARNZ CharacteristicNonZero
+++ Author:
+++ Date Created:
+++ Date Last Updated:
+++ Basic Functions:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++ Rings of Characteristic Non Zero
+CharacteristicNonZero():Category == Ring with
+ charthRoot: % -> Union(%,"failed")
+ ++ charthRoot(x) returns the pth root of x
+ ++ where p is the characteristic of the ring.
+
+@
+<<CHARNZ.dotabb>>=
+"CHARNZ"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=CHARNZ"];
+"CHARNZ" -> "RING"
+
+@
+<<CHARNZ.dotfull>>=
+"CharacteristicNonZero()"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=CHARNZ"];
+"CharacteristicNonZero()" -> "Ring()"
+
+@
+<<CHARNZ.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"CharacteristicNonZero()" [color=lightblue];
+"CharacteristicNonZero()" -> "Ring()"
+
+"Ring()" [color=lightblue];
+"Ring()" -> "Rng()"
+"Ring()" -> "Monoid()"
+"Ring()" -> "LeftModule(a:Ring)"
+
+"Rng()" [color=lightblue];
+"Rng()" -> "AbelianGroup()"
+"Rng()" -> "SemiGroup()"
+
+"Monoid()" [color=lightblue];
+"Monoid()" -> "SemiGroup()"
+
+"LeftModule(a:Ring)" [color=seagreen];
+"LeftModule(a:Ring)" -> "LeftModule(a:Rng)"
+
+"LeftModule(a:Rng)" [color=lightblue];
+"LeftModule(a:Rng)" -> "AbelianGroup()"
+
+"AbelianGroup()" [color=lightblue];
+"AbelianGroup()" -> "CABMON..."
+"AbelianGroup()" -> "REPDB..."
+
+"SemiGroup()" [color=lightblue];
+"SemiGroup()" -> "SETCAT..."
+"SemiGroup()" -> "REPSQ..."
+
+"REPDB..." [color="#00EE00"];
+"REPSQ..." [color="#00EE00"];
+"SETCAT..." [color=lightblue];
+"CABMON..." [color=lightblue];
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{CharacteristicZero}{CHARZ}
+\pagepic{ps/v102characteristiczero.ps}{CHARZ}{0.90}
+
+{\bf See:}\\
+\pagefrom{Ring}{RING}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+\cross{CHARZ}{1} &
+\cross{CHARZ}{0} &
+\cross{CHARZ}{coerce} &
+\cross{CHARZ}{hash} &
+\cross{CHARZ}{latex} \\
+\cross{CHARZ}{one?} &
+\cross{CHARZ}{recip} &
+\cross{CHARZ}{sample} &
+\cross{CHARZ}{zero?} &
+\cross{CHARZ}{characteristic} \\
+\cross{CHARZ}{subtractIfCan} &
+\cross{CHARZ}{?\~{}=?} &
+\cross{CHARZ}{?\^{}?} &
+\cross{CHARZ}{?*?} \\
+\cross{CHARZ}{?**?} &
+\cross{CHARZ}{?+?} &
+\cross{CHARZ}{?-?} &
+\cross{CHARZ}{-?} &
+\cross{CHARZ}{?=?} \\
+\end{tabular}
+
+These exports come from Ring():
+\begin{verbatim}
+ 1 : () -> %
+ 0 : () -> %
+ coerce : Integer -> %
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ one? : % -> Boolean
+ recip : % -> Union(%,"failed")
+ sample : () -> %
+ zero? : % -> Boolean
+ characteristic : () -> NonNegativeInteger
+ subtractIfCan : (%,%) -> Union(%,"failed")
+ ?~=? : (%,%) -> Boolean
+ ?^? : (%,NonNegativeInteger) -> %
+ ?^? : (%,PositiveInteger) -> %
+ ?*? : (%,%) -> %
+ ?*? : (NonNegativeInteger,%) -> %
+ ?*? : (Integer,%) -> %
+ ?*? : (PositiveInteger,%) -> %
+ ?**? : (%,NonNegativeInteger) -> %
+ ?**? : (%,PositiveInteger) -> %
+ ?+? : (%,%) -> %
+ ?-? : (%,%) -> %
+ -? : % -> %
+ ?=? : (%,%) -> Boolean
+\end{verbatim}
+
+<<category CHARZ CharacteristicZero>>=
+)abbrev category CHARZ CharacteristicZero
+++ Author:
+++ Date Created:
+++ Date Last Updated:
+++ Basic Functions:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++ Rings of Characteristic Zero.
+CharacteristicZero():Category == Ring
+
+@
+<<CHARZ.dotabb>>=
+"CHARZ"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=CHARZ"];
+"CHARZ" -> "RING"
+
+@
+<<CHARZ.dotfull>>=
+"CharacteristicNonZero()"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=CHARZ"];
+"CharacteristicNonZero()" -> "Ring()"
+
+@
+<<CHARZ.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"CharacteristicZero()" [color=lightblue];
+"CharacteristicZero()" -> "Ring()"
+
+"Ring()" [color=lightblue];
+"Ring()" -> "Rng()"
+"Ring()" -> "Monoid()"
+"Ring()" -> "LeftModule(a:Ring)"
+
+"Rng()" [color=lightblue];
+"Rng()" -> "AbelianGroup()"
+"Rng()" -> "SemiGroup()"
+
+"Monoid()" [color=lightblue];
+"Monoid()" -> "SemiGroup()"
+
+"LeftModule(a:Ring)" [color=seagreen];
+"LeftModule(a:Ring)" -> "LeftModule(a:Rng)"
+
+"LeftModule(a:Rng)" [color=lightblue];
+"LeftModule(a:Rng)" -> "AbelianGroup()"
+
+"AbelianGroup()" [color=lightblue];
+"AbelianGroup()" -> "CABMON..."
+"AbelianGroup()" -> "REPDB..."
+
+"SemiGroup()" [color=lightblue];
+"SemiGroup()" -> "SETCAT..."
+"SemiGroup()" -> "REPSQ..."
+
+"REPDB..." [color="#00EE00"];
+"REPSQ..." [color="#00EE00"];
+"SETCAT..." [color=lightblue];
+"CABMON..." [color=lightblue];
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{CommutativeRing}{COMRING}
+\pagepic{ps/v102commutativering.ps}{COMRING}{0.65}
+
+{\bf See:}\\
+\pageto{IntegralDomain}{INTDOM}
+\pagefrom{BiModule}{BMODULE}
+\pagefrom{Ring}{RING}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+\cross{COMRING}{1} &
+\cross{COMRING}{0} &
+\cross{COMRING}{coerce} &
+\cross{COMRING}{hash} &
+\cross{COMRING}{latex} \\
+\cross{COMRING}{one?} &
+\cross{COMRING}{recip} &
+\cross{COMRING}{sample} &
+\cross{COMRING}{zero?} &
+\cross{COMRING}{characteristic} \\
+\cross{COMRING}{subtractIfCan} &
+\cross{COMRING}{?\~{}=?} &
+\cross{COMRING}{?\^{}?} &
+\cross{COMRING}{?*?} &
+\cross{COMRING}{?**?} \\
+\cross{COMRING}{?+?} &
+\cross{COMRING}{?-?} &
+\cross{COMRING}{-?} &
+\cross{COMRING}{?=?} &
+\end{tabular}
+
+
+These exports come from Ring():
+\begin{verbatim}
+ 0 : () -> %
+ 1 : () -> %
+ characteristic : () -> NonNegativeInteger
+ coerce : Integer -> %
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ one? : % -> Boolean
+ recip : % -> Union(%,"failed")
+ sample : () -> %
+ subtractIfCan : (%,%) -> Union(%,"failed")
+ zero? : % -> Boolean
+ ?+? : (%,%) -> %
+ ?=? : (%,%) -> Boolean
+ ?~=? : (%,%) -> Boolean
+ ?*? : (%,%) -> %
+ ?*? : (Integer,%) -> %
+ ?*? : (NonNegativeInteger,%) -> %
+ ?*? : (PositiveInteger,%) -> %
+ ?-? : (%,%) -> %
+ -? : % -> %
+ ?^? : (%,PositiveInteger) -> %
+ ?^? : (%,NonNegativeInteger) -> %
+ ?**? : (%,NonNegativeInteger) -> %
+ ?**? : (%,PositiveInteger) -> %
+\end{verbatim}
+
+TPDHERE: Note that none of the exports of BiModule(a:Ring,b:Ring)
+are needed. Perhaps this can be eliminated.
+
+<<category COMRING CommutativeRing>>=
+)abbrev category COMRING CommutativeRing
+++ Author:
+++ Date Created:
+++ Date Last Updated:
+++ Basic Functions:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++ The category of commutative rings with unity, i.e. rings where
+++ \spadop{*} is commutative, and which have a multiplicative identity.
+++ element.
+--CommutativeRing():Category == Join(Ring,BiModule(%:Ring,%:Ring)) with
+CommutativeRing():Category == Join(Ring,BiModule(%,%)) with
+ commutative("*") ++ multiplication is commutative.
+
+@
+<<COMRING.dotabb>>=
+"COMRING"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=COMRING"];
+"COMRING" -> "RING"
+"COMRING" -> "BMODULE"
+
+@
+<<COMRING.dotfull>>=
+"CommutativeRing()"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=COMRING"];
+"CommutativeRing()" -> "Ring()"
+"CommutativeRing()" -> "BiModule(a:Ring,b:Ring)"
+
+@
+<<COMRING.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"CommutativeRing()" [color=lightblue];
+"CommutativeRing()" -> "Ring()"
+"CommutativeRing()" -> "BiModule(a:Ring,b:Ring)"
+
+"Ring()" [color=lightblue];
+"Ring()" -> "Rng()"
+"Ring()" -> "Monoid()"
+"Ring()" -> "LeftModule(a:Ring)"
+
+"BiModule(a:Ring,b:Ring)" [color=lightblue];
+"BiModule(a:Ring,b:Ring)" -> "LeftModule(a:Ring)"
+"BiModule(a:Ring,b:Ring)" -> "RightModule(a:Ring)"
+
+"RightModule(a:Ring)" [color=seagreen];
+"RightModule(a:Ring)" -> "RightModule(a:Rng)"
+
+"RightModule(a:Rng)" [color=lightblue];
+"RightModule(a:Rng)" -> "AbelianGroup()"
+
+"Rng()" [color=lightblue];
+"Rng()" -> "AbelianGroup()"
+"Rng()" -> "SemiGroup()"
+
+"Monoid()" [color=lightblue];
+"Monoid()" -> "SemiGroup()"
+
+"LeftModule(a:Ring)" [color=seagreen];
+"LeftModule(a:Ring)" -> "LeftModule(a:Rng)"
+
+"LeftModule(a:Rng)" [color=lightblue];
+"LeftModule(a:Rng)" -> "AbelianGroup()"
+
+"AbelianGroup()" [color=lightblue];
+"AbelianGroup()" -> "CABMON..."
+"AbelianGroup()" -> "REPDB..."
+
+"SemiGroup()" [color=lightblue];
+"SemiGroup()" -> "SETCAT..."
+"SemiGroup()" -> "REPSQ..."
+
+"REPDB..." [color="#00EE00"];
+"REPSQ..." [color="#00EE00"];
+"SETCAT..." [color=lightblue];
+"CABMON..." [color=lightblue];
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{DifferentialRing}{DIFRING}
+\pagepic{ps/v102differentialring.ps}{DIFRING}{0.90}
+
+{\bf See:}\\
+\pagefrom{Ring}{RING}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+\cross{DIFRING}{1} &
+\cross{DIFRING}{0} &
+\cross{DIFRING}{characteristic} &
+\cross{DIFRING}{coerce} &
+\cross{DIFRING}{D} \\
+\cross{DIFRING}{differentiate} &
+\cross{DIFRING}{hash} &
+\cross{DIFRING}{latex} &
+\cross{DIFRING}{one?} &
+\cross{DIFRING}{recip} \\
+\cross{DIFRING}{sample} &
+\cross{DIFRING}{subtractIfCan} &
+\cross{DIFRING}{zero?} &
+\cross{DIFRING}{?\~{}=?} &
+\cross{DIFRING}{?**?} \\
+\cross{DIFRING}{?\^{}?} &
+\cross{DIFRING}{?*?} &
+\cross{DIFRING}{?+?} &
+\cross{DIFRING}{?-?} &
+\cross{DIFRING}{-?} \\
+\cross{DIFRING}{?=?} &
+\end{tabular}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ differentiate : % -> %
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ D : % -> %
+ D : (%,NonNegativeInteger) -> %
+ differentiate : (%,NonNegativeInteger) -> %
+\end{verbatim}
+
+These exports come from Ring():
+\begin{verbatim}
+ 1 : () -> %
+ 0 : () -> %
+ characteristic : () -> NonNegativeInteger
+ coerce : Integer -> %
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ one? : % -> Boolean
+ recip : % -> Union(%,"failed")
+ sample : () -> %
+ subtractIfCan : (%,%) -> Union(%,"failed")
+ zero? : % -> Boolean
+ ?~=? : (%,%) -> Boolean
+ ?**? : (%,NonNegativeInteger) -> %
+ ?**? : (%,PositiveInteger) -> %
+ ?^? : (%,NonNegativeInteger) -> %
+ ?^? : (%,PositiveInteger) -> %
+ ?*? : (%,%) -> %
+ ?*? : (NonNegativeInteger,%) -> %
+ ?*? : (Integer,%) -> %
+ ?*? : (PositiveInteger,%) -> %
+ ?+? : (%,%) -> %
+ ?-? : (%,%) -> %
+ -? : % -> %
+ ?=? : (%,%) -> Boolean
+\end{verbatim}
+
+<<category DIFRING DifferentialRing>>=
+)abbrev category DIFRING DifferentialRing
+++ Author:
+++ Date Created:
+++ Date Last Updated:
+++ Basic Functions:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++ An ordinary differential ring, that is, a ring with an operation
+++ \spadfun{differentiate}.
+++
+++ Axioms:
+++ \spad{differentiate(x+y) = differentiate(x)+differentiate(y)}
+++ \spad{differentiate(x*y) = x*differentiate(y) + differentiate(x)*y}
+
+DifferentialRing(): Category == Ring with
+ differentiate: % -> %
+ ++ differentiate(x) returns the derivative of x.
+ ++ This function is a simple differential operator
+ ++ where no variable needs to be specified.
+ D: % -> %
+ ++ D(x) returns the derivative of x.
+ ++ This function is a simple differential operator
+ ++ where no variable needs to be specified.
+ differentiate: (%, NonNegativeInteger) -> %
+ ++ differentiate(x, n) returns the n-th derivative of x.
+ D: (%, NonNegativeInteger) -> %
+ ++ D(x, n) returns the n-th derivative of x.
+ add
+ D r == differentiate r
+ differentiate(r, n) ==
+ for i in 1..n repeat r := differentiate r
+ r
+ D(r,n) == differentiate(r,n)
+
+@
+<<DIFRING.dotabb>>=
+"DIFRING"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=DIFRING"];
+"DIFRING" -> "RING"
+
+@
+<<DIFRING.dotfull>>=
+"DifferentialRing()"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=DIFRING"];
+"DifferentialRing()" -> "Ring()"
+
+@
+<<DIFRING.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"DifferentialRing()" [color=lightblue];
+"DifferentialRing()" -> "Ring()"
+
+"Ring()" [color=lightblue];
+"Ring()" -> "Rng()"
+"Ring()" -> "Monoid()"
+"Ring()" -> "LeftModule(a:Ring)"
+
+"Rng()" [color=lightblue];
+"Rng()" -> "AbelianGroup()"
+"Rng()" -> "SemiGroup()"
+
+"Monoid()" [color=lightblue];
+"Monoid()" -> "SemiGroup()"
+
+"LeftModule(a:Ring)" [color=seagreen];
+"LeftModule(a:Ring)" -> "LeftModule(a:Rng)"
+
+"LeftModule(a:Rng)" [color=lightblue];
+"LeftModule(a:Rng)" -> "AbelianGroup()"
+
+"AbelianGroup()" [color=lightblue];
+"AbelianGroup()" -> "CABMON..."
+"AbelianGroup()" -> "REPDB..."
+
+"SemiGroup()" [color=lightblue];
+"SemiGroup()" -> "SETCAT..."
+"SemiGroup()" -> "REPSQ..."
+
+"REPDB..." [color="#00EE00"];
+"REPSQ..." [color="#00EE00"];
+"SETCAT..." [color=lightblue];
+"CABMON..." [color=lightblue];
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{EntireRing}{ENTIRER}
+\pagepic{ps/v102EntireRing.ps}{ENTIRER}{0.65}
+
+{\bf See:}\\
+\pageto{DivisionRing}{DIVRING}
+\pageto{IntegralDomain}{INTDOM}
+\pagefrom{BiModule}{BMODULE}
+\pagefrom{Ring}{RING}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+\cross{ENTIRER}{1} &
+\cross{ENTIRER}{0} &
+\cross{ENTIRER}{characteristic} &
+\cross{ENTIRER}{coerce} &
+\cross{ENTIRER}{hash} \\
+\cross{ENTIRER}{latex} &
+\cross{ENTIRER}{one?} &
+\cross{ENTIRER}{recip} &
+\cross{ENTIRER}{sample} &
+\cross{ENTIRER}{subtractIfCan} \\
+\cross{ENTIRER}{zero?} &
+\cross{ENTIRER}{?\^{}?} &
+\cross{ENTIRER}{?\~{}=?} &
+\cross{ENTIRER}{?*?} &
+\cross{ENTIRER}{?**?} \\
+\cross{ENTIRER}{?*?} &
+\cross{ENTIRER}{?+?} &
+\cross{ENTIRER}{?-?} &
+\cross{ENTIRER}{-?} &
+\cross{ENTIRER}{?=?} \\
+\end{tabular}
+
+These exports come from Ring():
+\begin{verbatim}
+ 0 : () -> %
+ 1 : () -> %
+ characteristic : () -> NonNegativeInteger
+ coerce : Integer -> %
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ one? : % -> Boolean
+ recip : % -> Union(%,"failed")
+ sample : () -> %
+ subtractIfCan : (%,%) -> Union(%,"failed")
+ zero? : % -> Boolean
+ ?+? : (%,%) -> %
+ ?=? : (%,%) -> Boolean
+ ?~=? : (%,%) -> Boolean
+ ?*? : (%,%) -> %
+ ?*? : (Integer,%) -> %
+ ?*? : (PositiveInteger,%) -> %
+ ?*? : (NonNegativeInteger,%) -> %
+ ?-? : (%,%) -> %
+ -? : % -> %
+ ?^? : (%,PositiveInteger) -> %
+ ?^? : (%,NonNegativeInteger) -> %
+ ?**? : (%,NonNegativeInteger) -> %
+ ?**? : (%,PositiveInteger) -> %
+\end{verbatim}
+
+TPDHERE: Note that none of the exports of BiModule(a:Ring,b:Ring)
+are needed. Perhaps this can be eliminated.
+
+<<category ENTIRER EntireRing>>=
+)abbrev category ENTIRER EntireRing
+++ Author:
+++ Date Created:
+++ Date Last Updated:
+++ Basic Functions:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++ Entire Rings (non-commutative Integral Domains), i.e. a ring
+++ not necessarily commutative which has no zero divisors.
+++
+++ Axioms:
+++ \spad{ab=0 => a=0 or b=0} -- known as noZeroDivisors
+++ \spad{not(1=0)}
+--EntireRing():Category == Join(Ring,BiModule(%:Ring,%:Ring)) with
+EntireRing():Category == Join(Ring,BiModule(%,%)) with
+ noZeroDivisors ++ if a product is zero then one of the factors
+ ++ must be zero.
+
+@
+<<ENTIRER.dotabb>>=
+"ENTIRER"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ENTIRER"];
+"ENTIRER" -> "RING"
+"ENTIRER" -> "BMODULE"
+
+@
+<<ENTIRER.dotfull>>=
+"EntireRing()"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ENTIRER"];
+"EntireRing()" -> "Ring()"
+"EntireRing()" -> "BiModule(a:Ring,b:Ring)"
+
+@
+<<ENTIRER.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"EntireRing()" [color=lightblue];
+"EntireRing()" -> "Ring()"
+"EntireRing()" -> "BiModule(a:Ring,b:Ring)"
+
+"Ring()" [color=lightblue];
+"Ring()" -> "Rng()"
+"Ring()" -> "Monoid()"
+"Ring()" -> "LeftModule(a:Ring)"
+
+"Rng()" [color=lightblue];
+"Rng()" -> "ABELGRP..."
+"Rng()" -> "SemiGroup()"
+
+"Monoid()" [color=lightblue];
+"Monoid()" -> "SemiGroup()"
+
+"BiModule(a:Ring,b:Ring)" [color=lightblue];
+"BiModule(a:Ring,b:Ring)" -> "LeftModule(a:Ring)"
+"BiModule(a:Ring,b:Ring)" -> "RightModule(a:Ring)"
+
+"RightModule(a:Ring)" [color=seagreen];
+"RightModule(a:Ring)" -> "RightModule(a:Rng)"
+
+"RightModule(a:Rng)" [color=lightblue];
+"RightModule(a:Rng)" -> "ABELGRP..."
+
+"LeftModule(a:Ring)" [color=seagreen];
+"LeftModule(a:Ring)" -> "LeftModule(a:Rng)"
+
+"LeftModule(a:Rng)" [color=lightblue];
+"LeftModule(a:Rng)" -> "ABELGRP..."
+
+"SemiGroup()" [color=lightblue];
+"SemiGroup()" -> "SETCAT..."
+"SemiGroup()" -> "REPSQ..."
+
+"REPSQ..." [color="#00EE00"];
+"SETCAT..." [color=lightblue];
+"ABELGRP..." [color=lightblue];
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{LinearlyExplicitRingOver}{LINEXP}
+\pagepic{ps/v102linearlyexplicitringover.ps}{LINEXP}{0.90}
+
+{\bf See:}\\
+\pageto{FullyLinearlyExplicitRingOver}{FLINEXP}
+\pagefrom{Ring}{RING}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+\cross{LINEXP}{0} &
+\cross{LINEXP}{1} &
+\cross{LINEXP}{characteristic} &
+\cross{LINEXP}{coerce} &
+\cross{LINEXP}{hash} \\
+\cross{LINEXP}{latex} &
+\cross{LINEXP}{one?} &
+\cross{LINEXP}{recip} &
+\cross{LINEXP}{reducedSystem} &
+\cross{LINEXP}{subtractIfCan} \\
+\cross{LINEXP}{sample} &
+\cross{LINEXP}{zero?} &
+\cross{LINEXP}{?*?} &
+\cross{LINEXP}{?**?} &
+\cross{LINEXP}{?+?} \\
+\cross{LINEXP}{?-?} &
+\cross{LINEXP}{-?} &
+\cross{LINEXP}{?=?} &
+\cross{LINEXP}{?\^{}?} &
+\cross{LINEXP}{?\~{}=?} \\
+\end{tabular}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ reducedSystem : (Matrix %,Vector %) ->
+ Record(mat: Matrix R,vec: Vector R)
+ reducedSystem : Matrix % -> Matrix R
+\end{verbatim}
+
+These exports come from Ring():
+\begin{verbatim}
+ 0 : () -> %
+ 1 : () -> %
+ characteristic : () -> NonNegativeInteger
+ coerce : Integer -> %
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ one? : % -> Boolean
+ recip : % -> Union(%,"failed")
+ sample : () -> %
+ subtractIfCan : (%,%) -> Union(%,"failed")
+ zero? : % -> Boolean
+ ?+? : (%,%) -> %
+ ?=? : (%,%) -> Boolean
+ ?~=? : (%,%) -> Boolean
+ ?*? : (NonNegativeInteger,%) -> %
+ ?*? : (PositiveInteger,%) -> %
+ ?*? : (Integer,%) -> %
+ ?*? : (%,%) -> %
+ ?-? : (%,%) -> %
+ -? : % -> %
+ ?**? : (%,PositiveInteger) -> %
+ ?**? : (%,NonNegativeInteger) -> %
+ ?^? : (%,PositiveInteger) -> %
+ ?^? : (%,NonNegativeInteger) -> %
+\end{verbatim}
+
+<<category LINEXP LinearlyExplicitRingOver>>=
+)abbrev category LINEXP LinearlyExplicitRingOver
+++ Author:
+++ Date Created:
+++ Date Last Updated:
+++ Basic Functions:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++ An extension ring with an explicit linear dependence test.
+LinearlyExplicitRingOver(R:Ring): Category == Ring with
+ reducedSystem: Matrix % -> Matrix R
+ ++ reducedSystem(A) returns a matrix B such that \spad{A x = 0}
+ ++ and \spad{B x = 0} have the same solutions in R.
+ reducedSystem: (Matrix %,Vector %) -> Record(mat:Matrix R,vec:Vector R)
+ ++ reducedSystem(A, v) returns a matrix B and a vector w such that
+ ++ \spad{A x = v} and \spad{B x = w} have the same solutions in R.
+
+@
+<<LINEXP.dotabb>>=
+"LINEXP"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=LINEXP"];
+"LINEXP" -> "RING"
+
+@
+<<LINEXP.dotfull>>=
+"LinearlyExplicitRingOver(a:Ring)"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=LINEXP"];
+"LinearlyExplicitRingOver(a:Ring)" -> "Ring()"
+
+"LinearlyExplicitRingOver(Integer)"
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=LINEXP"];
+"LinearlyExplicitRingOver(Integer)" -> "LinearlyExplicitRingOver(a:Ring)"
+
+"LinearlyExplicitRingOver(Fraction(Integer))"
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=LINEXP"];
+"LinearlyExplicitRingOver(Fraction(Integer))" ->
+ "LinearlyExplicitRingOver(a:Ring)"
+
+@
+<<LINEXP.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"LinearlyExplicitRingOver(a:Ring)" [color=lightblue];
+"LinearlyExplicitRingOver(a:Ring)" -> "Ring()"
+
+"Ring()" [color=lightblue];
+"Ring()" -> "Rng()"
+"Ring()" -> "Monoid()"
+"Ring()" -> "LeftModule(a:Ring)"
+
+"Rng()" [color=lightblue];
+"Rng()" -> "AbelianGroup()"
+"Rng()" -> "SemiGroup()"
+
+"Monoid()" [color=lightblue];
+"Monoid()" -> "SemiGroup()"
+
+"LeftModule(a:Ring)" [color=seagreen];
+"LeftModule(a:Ring)" -> "LeftModule(a:Rng)"
+
+"LeftModule(a:Rng)" [color=lightblue];
+"LeftModule(a:Rng)" -> "AbelianGroup()"
+
+"AbelianGroup()" [color=lightblue];
+"AbelianGroup()" -> "CABMON..."
+"AbelianGroup()" -> "REPDB..."
+
+"SemiGroup()" [color=lightblue];
+"SemiGroup()" -> "SETCAT..."
+"SemiGroup()" -> "REPSQ..."
+
+"REPDB..." [color="#00EE00"];
+"REPSQ..." [color="#00EE00"];
+"SETCAT..." [color=lightblue];
+"CABMON..." [color=lightblue];
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{OrderedRing}{ORDRING}
\pagepic{ps/v102orderedring.ps}{ORDRING}{0.65}
{\bf See:}\\
+\pageto{OrderedIntegralDomain}{OINTDOM}
\pagefrom{Monoid}{MONOID}
\pagefrom{OrderedAbelianGroup}{OAGROUP}
\pagefrom{Ring}{RING}
@@ -12460,71 +13980,2946 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\chapter{Category Layers}
-\section{category BTAGG BitAggregate}
-<<category BTAGG BitAggregate>>=
-)abbrev category BTAGG BitAggregate
-++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
-++ Date Created: August 87 through August 88
-++ Date Last Updated: April 1991
-++ Basic Operations:
+\pagehead{PartialDifferentialRing}{PDRING}
+\pagepic{ps/v102partialdifferentialring.ps}{PDRING}{1.00}
+
+{\bf See:}\\
+\pageto{DifferentialExtension}{DIFEXT}
+\pagefrom{Ring}{RING}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+\cross{PDRING}{1} &
+\cross{PDRING}{0} &
+\cross{PDRING}{characteristic} &
+\cross{PDRING}{coerce} &
+\cross{PDRING}{D} \\
+\cross{PDRING}{differentiate} &
+\cross{PDRING}{hash} &
+\cross{PDRING}{latex} &
+\cross{PDRING}{one?} &
+\cross{PDRING}{recip} \\
+\cross{PDRING}{sample} &
+\cross{PDRING}{subtractIfCan} &
+\cross{PDRING}{zero?} &
+\cross{PDRING}{?\^{}?} &
+\cross{PDRING}{?*?} \\
+\cross{PDRING}{?\~{}=?} &
+\cross{PDRING}{?**?} &
+\cross{PDRING}{?+?} &
+\cross{PDRING}{?-?} &
+\cross{PDRING}{-?} \\
+\cross{PDRING}{?=?} &
+\end{tabular}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ differentiate : (%,S) -> %
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ differentiate : (%,List S) -> %
+ differentiate : (%,S,NonNegativeInteger) -> %
+ differentiate : (%,List S,List NonNegativeInteger) -> %
+ D : (%,S) -> %
+ D : (%,List S) -> %
+ D : (%,S,NonNegativeInteger) -> %
+ D : (%,List S,List NonNegativeInteger) -> %
+\end{verbatim}
+
+These exports come from Ring():
+\begin{verbatim}
+ characteristic : () -> NonNegativeInteger
+ 0 : () -> %
+ 1 : () -> %
+ coerce : Integer -> %
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ one? : % -> Boolean
+ recip : % -> Union(%,"failed")
+ sample : () -> %
+ subtractIfCan : (%,%) -> Union(%,"failed")
+ zero? : % -> Boolean
+ ?+? : (%,%) -> %
+ ?=? : (%,%) -> Boolean
+ ?~=? : (%,%) -> Boolean
+ ?*? : (%,%) -> %
+ ?*? : (Integer,%) -> %
+ ?*? : (PositiveInteger,%) -> %
+ ?*? : (NonNegativeInteger,%) -> %
+ ?-? : (%,%) -> %
+ -? : % -> %
+ ?^? : (%,PositiveInteger) -> %
+ ?^? : (%,NonNegativeInteger) -> %
+ ?**? : (%,NonNegativeInteger) -> %
+ ?**? : (%,PositiveInteger) -> %
+\end{verbatim}
+
+These exports come from Evalable(a:Type):
+\begin{verbatim}
+\end{verbatim}
+
+These exports come from SetCategory:
+\begin{verbatim}
+\end{verbatim}
+
+<<category PDRING PartialDifferentialRing>>=
+)abbrev category PDRING PartialDifferentialRing
+++ Author:
+++ Date Created:
+++ Date Last Updated:
+++ Basic Functions:
++ Related Constructors:
++ Also See:
++ AMS Classifications:
++ Keywords:
++ References:
++ Description:
-++ The bit aggregate category models aggregates representing large
-++ quantities of Boolean data.
-BitAggregate(): Category ==
- Join(OrderedSet, Logic, OneDimensionalArrayAggregate Boolean) with
- "not": % -> %
- ++ not(b) returns the logical {\em not} of bit aggregate
- ++ \axiom{b}.
- "^" : % -> %
- ++ ^ b returns the logical {\em not} of bit aggregate
- ++ \axiom{b}.
- nand : (%, %) -> %
- ++ nand(a,b) returns the logical {\em nand} of bit aggregates
- ++ \axiom{a} and \axiom{b}.
- nor : (%, %) -> %
- ++ nor(a,b) returns the logical {\em nor} of bit aggregates
- ++ \axiom{a} and \axiom{b}.
- _and : (%, %) -> %
- ++ a and b returns the logical {\em and} of bit aggregates
- ++ \axiom{a} and \axiom{b}.
- _or : (%, %) -> %
- ++ a or b returns the logical {\em or} of bit aggregates
- ++ \axiom{a} and \axiom{b}.
- xor : (%, %) -> %
- ++ xor(a,b) returns the logical {\em exclusive-or} of bit aggregates
- ++ \axiom{a} and \axiom{b}.
+++ A partial differential ring with differentiations indexed by a
+++ parameter type S.
+++
+++ Axioms:
+++ \spad{differentiate(x+y,e) = differentiate(x,e)+differentiate(y,e)}
+++ \spad{differentiate(x*y,e) = x*differentiate(y,e)+differentiate(x,e)*y}
+PartialDifferentialRing(S:SetCategory): Category == Ring with
+ differentiate: (%, S) -> %
+ ++ differentiate(x,v) computes the partial derivative of x
+ ++ with respect to v.
+ differentiate: (%, List S) -> %
+ ++ differentiate(x,[s1,...sn]) computes successive partial
+ ++ derivatives,
+ ++ i.e. \spad{differentiate(...differentiate(x, s1)..., sn)}.
+ differentiate: (%, S, NonNegativeInteger) -> %
+ ++ differentiate(x, s, n) computes multiple partial derivatives, i.e.
+ ++ n-th derivative of x with respect to s.
+ differentiate: (%, List S, List NonNegativeInteger) -> %
+ ++ differentiate(x, [s1,...,sn], [n1,...,nn]) computes
+ ++ multiple partial derivatives, i.e.
+ D: (%, S) -> %
+ ++ D(x,v) computes the partial derivative of x
+ ++ with respect to v.
+ D: (%, List S) -> %
+ ++ D(x,[s1,...sn]) computes successive partial derivatives,
+ ++ i.e. \spad{D(...D(x, s1)..., sn)}.
+ D: (%, S, NonNegativeInteger) -> %
+ ++ D(x, s, n) computes multiple partial derivatives, i.e.
+ ++ n-th derivative of x with respect to s.
+ D: (%, List S, List NonNegativeInteger) -> %
+ ++ D(x, [s1,...,sn], [n1,...,nn]) computes
+ ++ multiple partial derivatives, i.e.
+ ++ \spad{D(...D(x, s1, n1)..., sn, nn)}.
+ add
+ differentiate(r:%, l:List S) ==
+ for s in l repeat r := differentiate(r, s)
+ r
+
+ differentiate(r:%, s:S, n:NonNegativeInteger) ==
+ for i in 1..n repeat r := differentiate(r, s)
+ r
+
+ differentiate(r:%, ls:List S, ln:List NonNegativeInteger) ==
+ for s in ls for n in ln repeat r := differentiate(r, s, n)
+ r
+
+ D(r:%, v:S) == differentiate(r,v)
+ D(r:%, lv:List S) == differentiate(r,lv)
+ D(r:%, v:S, n:NonNegativeInteger) == differentiate(r,v,n)
+ D(r:%, lv:List S, ln:List NonNegativeInteger) == differentiate(r, lv, ln)
+
+@
+<<PDRING.dotabb>>=
+"PDRING"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=PDRING"];
+"PDRING" -> "RING"
+
+@
+<<PDRING.dotfull>>=
+"PartialDifferentialRing(a:SetCategory)"
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=PDRING"];
+"PartialDifferentialRing(a:SetCategory)" -> "Ring()"
+
+"PartialDifferentialRing(a:OrderedSet)"
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=PDRING"];
+"PartialDifferentialRing(a:OrderedSet)" ->
+ "PartialDifferentialRing(a:SetCategory)"
+
+"PartialDifferentialRing(Symbol)"
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=PDRING"];
+"PartialDifferentialRing(Symbol)" ->
+ "PartialDifferentialRing(a:SetCategory)"
+
+@
+<<PDRING.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"PartialDifferentialRing(a:SetCategory)" [color=lightblue];
+"PartialDifferentialRing(a:SetCategory)" -> "Ring()"
+
+"Ring()" [color=lightblue];
+"Ring()" -> "Rng()"
+"Ring()" -> "Monoid()"
+"Ring()" -> "LeftModule(a:Ring)"
+
+"Rng()" [color=lightblue];
+"Rng()" -> "AbelianGroup()"
+"Rng()" -> "SemiGroup()"
+
+"Monoid()" [color=lightblue];
+"Monoid()" -> "SemiGroup()"
+
+"LeftModule(a:Ring)" [color=seagreen];
+"LeftModule(a:Ring)" -> "LeftModule(a:Rng)"
+
+"LeftModule(a:Rng)" [color=lightblue];
+"LeftModule(a:Rng)" -> "AbelianGroup()"
+
+"AbelianGroup()" [colo...
[truncated message content] |
|
From: <gi...@ax...> - 2008-09-26 06:29:29
|
books/bookvol10.2.pamphlet | 6332 ++++++++++++++++++++++-
books/ps/v102EntireRing.ps | 876 ++++
books/ps/v102algebra.ps | 969 ++++
books/ps/v102bitaggregate.ps | 886 ++++
books/ps/v102characteristicnonzero.ps | 790 +++
books/ps/v102characteristiczero.ps | 790 +++
books/ps/v102commutativering.ps | 968 ++++
books/ps/v102differentialextension.ps | 775 +++
books/ps/v102differentialring.ps | 790 +++
books/ps/v102divisionring.ps | 745 +++
books/ps/v102euclideandomain.ps | 738 +++
books/ps/v102evalable.ps | 381 ++
books/ps/v102field.ps | 493 ++
books/ps/v102fullylinearlyexplicitringover.ps | 836 +++
books/ps/v102gcddomain.ps | 692 +++
books/ps/v102innerevalable.ps | 289 ++
books/ps/v102integraldomain.ps | 646 +++
books/ps/v102linearlyexplicitringover.ps | 790 +++
books/ps/v102logic.ps | 335 ++
books/ps/v102module.ps | 585 +++
books/ps/v102orderedintegraldomain.ps | 856 +++
books/ps/v102partialdifferentialring.ps | 790 +++
books/ps/v102polynomialfactorizationexplicit.ps | 738 +++
books/ps/v102principalidealdomain.ps | 738 +++
books/ps/v102retractableto.ps | 10 -
books/ps/v102uniquefactorizationdomain.ps | 738 +++
books/ps/v102vectorspace.ps | 677 +++
changelog | 50 +
src/algebra/Makefile.pamphlet | 17 +-
src/algebra/boolean.spad.pamphlet | 28 -
src/algebra/catdef.spad.pamphlet | 2818 ----------
src/algebra/equation1.spad.pamphlet | 129 -
32 files changed, 24222 insertions(+), 3073 deletions(-)
New commits:
commit cee2c100dbcff19e0071969f443b35d0bc5c5f1e
Author: Tim Daly <da...@ax...>
Date: Thu Jul 31 04:21:07 2008 -0400
20080925 tpd books/ps/v102vectorspace.ps added
20080925 tpd books/ps/v102uniquefactorizationdomain.ps added
20080925 tpd books/ps/v102principalidealdomain.ps added
20080925 tpd books/ps/v102polynomialfactorizationexplicit.ps added
20080925 tpd books/ps/v102partialdifferentialring.ps added
20080925 tpd books/ps/v102orderedintegraldomain.ps added
20080925 tpd books/ps/v102module.ps added
20080925 tpd books/ps/v102logic.ps added
20080925 tpd books/ps/v102linearlyexplicitringover.ps added
20080925 tpd books/ps/v102integraldomain.ps added
20080925 tpd books/ps/v102innerevalable.ps added
20080925 tpd books/ps/v102gcddomain.ps added
20080925 tpd books/ps/v102fullylinearlyexplicitringover.ps added
20080925 tpd books/ps/v102field.ps added
20080925 tpd books/ps/v102evalable.ps added
20080925 tpd books/ps/v102euclideandomain.ps added
20080925 tpd books/ps/v102divisionring.ps added
20080925 tpd books/ps/v102differentialring.ps added
20080925 tpd books/ps/v102differentialextension.ps added
20080925 tpd books/ps/v102commutativering.ps added
20080925 tpd books/ps/v102characteristiczero.ps added
20080925 tpd books/ps/v102characteristicnonzero.ps added
20080925 tpd books/ps/v102bitaggregate.ps added
20080925 tpd books/ps/v102algebra.ps added
20080925 tpd books/ps/v102EntireRing.ps added
20080925 tpd books/ps/v102retractableto.ps added
20080925 tpd books/bookvol10.2 absorb equation1.spad
20080925 tpd src/algebra/Makefile remove equation1
20080925 tpd src/algebra/boolean.spad move LOGIC into bookvol10.2
20080925 tpd src/algebra/equation1.spad remove. merged into bookvol10.2
20080925 tpd src/algebra/Makefile remove catdef.spad
20080925 tpd books/bookvol10.2 absorb catdef.spad
20080925 tpd src/algebra/catdef.spad removed, moved to bookvol10.2
|
|
From: <da...@us...> - 2008-09-22 05:30:24
|
Revision: 980
http://axiom.svn.sourceforge.net/axiom/?rev=980&view=rev
Author: daly
Date: 2008-09-22 05:30:00 +0000 (Mon, 22 Sep 2008)
Log Message:
-----------
20080921 tpd books/bookvol10.2 use .pdf rather than .pamphlet in URL
20080921 tpd books/ps/v71sept2008.eps add new image for sept 2008
20080921 tpd books/ps/v71releasenotes.eps update image to include sept2008
20080921 tpd books/bookvol7.1 add september release notes
20080921 tpd Makefile.pamphlet September 2008 release number
20080921 tpd Makefile September 2008 release number
Modified Paths:
--------------
trunk/axiom/Makefile
trunk/axiom/Makefile.pamphlet
trunk/axiom/books/bookvol10.2.pamphlet
trunk/axiom/books/bookvol7.1.pamphlet
trunk/axiom/books/ps/v71releasenotes.eps
Added Paths:
-----------
trunk/axiom/books/ps/v71sept2008.eps
Modified: trunk/axiom/Makefile
===================================================================
--- trunk/axiom/Makefile 2008-09-21 16:15:34 UTC (rev 979)
+++ trunk/axiom/Makefile 2008-09-22 05:30:00 UTC (rev 980)
@@ -1,4 +1,4 @@
-VERSION="Axiom (July 2008)"
+VERSION="Axiom (September 2008)"
SPD=$(shell pwd)
SYS=$(notdir $(AXIOM))
SPAD=${SPD}/mnt/${SYS}
Modified: trunk/axiom/Makefile.pamphlet
===================================================================
--- trunk/axiom/Makefile.pamphlet 2008-09-21 16:15:34 UTC (rev 979)
+++ trunk/axiom/Makefile.pamphlet 2008-09-22 05:30:00 UTC (rev 980)
@@ -292,7 +292,7 @@
to the document command. This will allow it to be
changed on the command line.
<<environment>>=
-VERSION="Axiom (July 2008)"
+VERSION="Axiom (September 2008)"
SPD=$(shell pwd)
SYS=$(notdir $(AXIOM))
SPAD=${SPD}/mnt/${SYS}
Modified: trunk/axiom/books/bookvol10.2.pamphlet
===================================================================
--- trunk/axiom/books/bookvol10.2.pamphlet 2008-09-21 16:15:34 UTC (rev 979)
+++ trunk/axiom/books/bookvol10.2.pamphlet 2008-09-22 05:30:00 UTC (rev 980)
@@ -338,13 +338,13 @@
@
<<BASTYPE.dotabb>>=
"BASTYPE"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=BASTYPE"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=BASTYPE"];
"BASTYPE" -> "CATEGORY"
@
<<BASTYPE.dotfull>>=
"BasicType()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=BASTYPE"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=BASTYPE"];
"BasicType()" -> "Category"
@
@@ -393,17 +393,17 @@
@
<<KOERCE.dotabb>>=
"KOERCE"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=KOERCE"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=KOERCE"];
"KOERCE" -> "CATEGORY"
@
<<KOERCE.dotfull>>=
"CoercibleTo(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=KOERCE"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=KOERCE"];
"CoercibleTo(a:Type)" -> "Category"
"CoercibleTo(OutputForm)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KOERCE"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=KOERCE"];
"CoercibleTo(OutputForm)" ->
"CoercibleTo(a:Type)"
@@ -454,73 +454,73 @@
@
<<KONVERT.dotabb>>=
"KONVERT"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=KONVERT"];
"KONVERT" -> "CATEGORY"
@
<<KONVERT.dotfull>>=
"ConvertibleTo(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=KONVERT"];
"ConvertibleTo(a:Type)" -> "Category"
"ConvertibleTo(DoubleFloat)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=KONVERT"];
"ConvertibleTo(DoubleFloat)" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(Float)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=KONVERT"];
"ConvertibleTo(Float)" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(InputForm)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=KONVERT"];
"ConvertibleTo(InputForm)" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(Integer)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=KONVERT"];
"ConvertibleTo(Integer)" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(Pattern(Integer))"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=KONVERT"];
"ConvertibleTo(Pattern(Integer))" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(Pattern(Float))"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=KONVERT"];
"ConvertibleTo(Pattern(Float))" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(Complex(Float))"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=KONVERT"];
"ConvertibleTo(Complex(Float))" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(Complex(DoubleFloat))"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=KONVERT"];
"ConvertibleTo(Complex(DoubleFloat))" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(String)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=KONVERT"];
"ConvertibleTo(String)" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(Symbol)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=KONVERT"];
"ConvertibleTo(Symbol)" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(SExpression)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=KONVERT"];
"ConvertibleTo(SExpression)" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(Pattern(Base))"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=KONVERT"];
"ConvertibleTo(Pattern(Base))" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(List(Integer))"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=KONVERT"];
"ConvertibleTo(List(Integer))" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(List(Character))"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=KONVERT"];
"ConvertibleTo(List(Character))" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(UnivariatePolynomialCategory(CommutativeRing))"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=KONVERT"];
"ConvertibleTo(UnivariatePolynomialCategory(CommutativeRing))" ->
"ConvertibleTo(a:Type)"
@
@@ -579,13 +579,13 @@
@
<<ELTAB.dotabb>>=
-"ELTAB" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ELTAB"];
+"ELTAB" [color=lightblue,href="bookvol10.2.pdf#nameddest=ELTAB"];
"ELTAB" -> "CATEGORY"
@
<<ELTAB.dotfull>>=
"Eltable(a:SetCategory,b:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ELTAB"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ELTAB"];
"Eltable(a:SetCategory,b:Type)" -> "Category"
@
@@ -654,45 +654,45 @@
@
<<RETRACT.dotabb>>=
"RETRACT"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=RETRACT"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=RETRACT"];
"RETRACT" -> "CATEGORY"
@
<<RETRACT.dotfull>>=
"RetractableTo(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=RETRACT"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=RETRACT"];
"RetractableTo(a:Type)" -> "Category"
"RetractableTo(SetCategory)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=RETRACT"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=RETRACT"];
"RetractableTo(SetCategory)" -> "RetractableTo(a:Type)"
"RetractableTo(Symbol)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=RETRACT"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=RETRACT"];
"RetractableTo(Symbol)" -> "RetractableTo(a:Type)"
"RetractableTo(Integer)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=RETRACT"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=RETRACT"];
"RetractableTo(Integer)" -> "RetractableTo(a:Type)"
"RetractableTo(NonNegativeInteger)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=RETRACT"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=RETRACT"];
"RetractableTo(NonNegativeInteger)" -> "RetractableTo(a:Type)"
"RetractableTo(Fraction(Integer))"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=RETRACT"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=RETRACT"];
"RetractableTo(Fraction(Integer))" -> "RetractableTo(a:Type)"
"RetractableTo(Float)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=RETRACT"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=RETRACT"];
"RetractableTo(Float)" -> "RetractableTo(a:Type)"
"RetractableTo(Kernel(ExpressionSpace))"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=RETRACT"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=RETRACT"];
"RetractableTo(Kernel(ExpressionSpace))" -> "RetractableTo(a:Type)"
"RetractableTo(CommutativeRing)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=RETRACT"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=RETRACT"];
"RetractableTo(CommutativeRing)" -> "RetractableTo(a:Type)"
@
<<RETRACT.dotpic>>=
@@ -726,12 +726,12 @@
@
<<TYPE.dotabb>>=
-"TYPE" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=TYPE"];
+"TYPE" [color=lightblue,href="bookvol10.2.pdf#nameddest=TYPE"];
"TYPE" -> "CATEGORY"
@
<<TYPE.dotfull>>=
-"Type()" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=TYPE"];
+"Type()" [color=lightblue,href="bookvol10.2.pdf#nameddest=TYPE"];
"Type()" -> "Category"
@
@@ -833,13 +833,13 @@
@
<<AGG.dotabb>>=
-"AGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=AGG"];
+"AGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=AGG"];
"AGG" -> "TYPE"
@
<<AGG.dotfull>>=
"Aggregate()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=AGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=AGG"];
"Aggregate()" -> "Type()"
@
@@ -945,13 +945,13 @@
@
<<ELTAGG.dotabb>>=
"ELTAGG"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ELTAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ELTAGG"];
"ELTAGG" -> "ELTAB"
@
<<ELTAGG.dotfull>>=
"EltableAggregate(a:SetCategory,b:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ELTAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ELTAGG"];
"EltableAggregate(a:SetCategory,b:Type)" -> "Eltable(a:SetCategory,b:Type)"
@
@@ -1043,14 +1043,14 @@
@
<<SETCAT.dotabb>>=
"SETCAT"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=SETCAT"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=SETCAT"];
"SETCAT" -> "BASTYPE"
"SETCAT" -> "KOERCE"
@
<<SETCAT.dotfull>>=
"SetCategory()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=SETCAT"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=SETCAT"];
"SetCategory()" -> "BasicType()"
"SetCategory()" -> "CoercibleTo(OutputForm)"
@@ -1150,14 +1150,14 @@
@
<<ABELSG.dotabb>>=
"ABELSG"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ABELSG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ABELSG"];
"ABELSG" -> "SETCAT"
"ABELSG" -> "REPDB"
@
<<ABELSG.dotfull>>=
"AbelianSemiGroup()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ABELSG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ABELSG"];
"AbelianSemiGroup()" -> "SetCategory()"
"AbelianSemiGroup()" -> "RepeatedDoubling(SetCategory)"
@@ -1275,13 +1275,13 @@
@
<<FINITE.dotabb>>=
"FINITE"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=FINITE"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=FINITE"];
"FINITE" -> "SETCAT"
@
<<FINITE.dotfull>>=
"Finite()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=FINITE"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=FINITE"];
"Finite()" -> "SetCategory()"
@
@@ -1485,13 +1485,13 @@
@
<<HOAGG.dotabb>>=
-"HOAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=HOAGG"];
+"HOAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=HOAGG"];
"HOAGG" -> "AGG"
@
<<HOAGG.dotfull>>=
"HomogeneousAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=HOAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=HOAGG"];
"HomogeneousAggregate(a:Type)" -> "Aggregate()"
@
@@ -1629,13 +1629,13 @@
@
<<ORDSET.dotabb>>=
"ORDSET"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ORDSET"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ORDSET"];
"ORDSET" -> "SETCAT"
@
<<ORDSET.dotfull>>=
"OrderedSet()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ORDSET"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ORDSET"];
"OrderedSet()" -> "SetCategory()"
@
@@ -1749,13 +1749,13 @@
@
<<SGROUP.dotabb>>=
"SGROUP"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=SGROUP"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=SGROUP"];
"SGROUP" -> "SETCAT"
@
<<SGROUP.dotfull>>=
"SemiGroup()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=SGROUP"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=SGROUP"];
"SemiGroup()" -> "SetCategory()"
"SemiGroup()" -> "RepeatedSquaring(SemiGroup)"
@@ -1861,13 +1861,13 @@
@
<<STEP.dotabb>>=
-"STEP" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=STEP"];
+"STEP" [color=lightblue,href="bookvol10.2.pdf#nameddest=STEP"];
"STEP" -> "SETCAT"
@
<<STEP.dotfull>>=
"StepThrough()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=STEP"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=STEP"];
"StepThrough()" -> "SetCategory()"
@
@@ -1989,13 +1989,13 @@
@
<<ABELMON.dotabb>>=
"ABELMON"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ABELMON"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ABELMON"];
"ABELMON" -> "ABELSG"
@
<<ABELMON.dotfull>>=
"AbelianMonoid()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ABELMON"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ABELMON"];
"AbelianMonoid()" -> "AbelianSemiGroup()"
@
@@ -2167,17 +2167,17 @@
@
<<BGAGG.dotabb>>=
-"BGAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=BGAGG"];
+"BGAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=BGAGG"];
"BGAGG" -> "HOAGG"
@
<<BGAGG.dotfull>>=
"BagAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=BGAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=BGAGG"];
"BagAggregate(a:Type)" -> "HomogeneousAggregate(a:Type)"
"BagAggregate(a:SetCategory)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=BGAGG"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=BGAGG"];
"BagAggregate(a:SetCategory)" -> "BagAggregate(a:Type)"
@
@@ -2403,17 +2403,17 @@
@
<<CLAGG.dotabb>>=
-"CLAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=CLAGG"];
+"CLAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=CLAGG"];
"CLAGG" -> "HOAGG"
@
<<CLAGG.dotfull>>=
"Collection(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=CLAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=CLAGG"];
"Collection(a:Type)" -> "HomogeneousAggregate(a:Type)"
"Collection(a:SetCategory)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=CLAGG"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=CLAGG"];
"Collection(a:SetCategory)" -> "Collection(a:Type)"
@
@@ -2654,26 +2654,26 @@
@
<<IXAGG.dotabb>>=
-"IXAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=IXAGG"];
+"IXAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=IXAGG"];
"IXAGG" -> "HOAGG"
"IXAGG" -> "ELTAGG"
@
<<IXAGG.dotfull>>=
"IndexedAggregate(a:SetCategory,b:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=IXAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=IXAGG"];
"IndexedAggregate(a:SetCategory,b:Type)" ->
"HomogeneousAggregate(a:Type)"
"IndexedAggregate(a:SetCategory,b:Type)" ->
"EltableAggregate(a:SetCategory,b:Type)"
"IndexedAggregate(a:SetCategory,b:SetCategory)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=IXAGG"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=IXAGG"];
"IndexedAggregate(a:SetCategory,b:SetCategory)" ->
"IndexedAggregate(a:SetCategory,b:Type)"
"IndexedAggregate(b:Integer,a:Type)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=IXAGG"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=IXAGG"];
"IndexedAggregate(b:Integer,a:Type)" ->
"IndexedAggregate(a:SetCategory,b:Type)"
@@ -2814,13 +2814,13 @@
@
<<MONOID.dotabb>>=
"MONOID"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=MONOID"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=MONOID"];
"MONOID" -> "SGROUP"
@
<<MONOID.dotfull>>=
"Monoid()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=MONOID"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=MONOID"];
"Monoid()" -> "SemiGroup()"
@
@@ -2932,14 +2932,14 @@
@
<<ORDFIN.dotabb>>=
"ORDFIN"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ORDFIN"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ORDFIN"];
"ORDFIN" -> "ORDSET"
"ORDFIN" -> "FINITE"
@
<<ORDFIN.dotfull>>=
"OrderedFinite()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ORDFIN"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ORDFIN"];
"OrderedFinite()" -> "OrderedSet()"
"OrderedFinite()" -> "Finite()"
@@ -3152,13 +3152,13 @@
@
<<RCAGG.dotabb>>=
-"RCAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=RCAGG"];
+"RCAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=RCAGG"];
"RCAGG" -> "HOAGG"
@
<<RCAGG.dotfull>>=
"RecursiveAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=RCAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=RCAGG"];
"RecursiveAggregate(a:Type)" -> "HomogeneousAggregate(a:Type)"
@
@@ -3421,13 +3421,13 @@
@
<<BRAGG.dotabb>>=
-"BRAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=BRAGG"];
+"BRAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=BRAGG"];
"BRAGG" -> "RCAGG"
@
<<BRAGG.dotfull>>=
"BinaryRecursiveAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=BRAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=BRAGG"];
"BinaryRecursiveAggregate(a:Type)" -> "RecursiveAggregate(a:Type)"
@
@@ -3527,13 +3527,13 @@
@
<<CABMON.dotabb>>=
"CABMON"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=CABMON"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=CABMON"];
"CABMON" -> "ABELMON"
@
<<CABMON.dotfull>>=
"CancellationAbelianMonoid()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=CABMON"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=CABMON"];
"CancellationAbelianMonoid()" -> "AbelianMonoid()"
@
@@ -3752,14 +3752,14 @@
@
<<DIOPS.dotabb>>=
-"DIOPS" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=DIOPS"];
+"DIOPS" [color=lightblue,href="bookvol10.2.pdf#nameddest=DIOPS"];
"DIOPS" -> "BGAGG"
"DIOPS" -> "CLAGG"
@
<<DIOPS.dotfull>>=
"DictionaryOperations(a:SetCategory)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=DIOPS"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=DIOPS"];
"DictionaryOperations(a:SetCategory)" -> "BagAggregate(a:SetCategory)"
"DictionaryOperations(a:SetCategory)" -> "Collection(a:SetCategory)"
@@ -3971,13 +3971,13 @@
@
<<DLAGG.dotabb>>=
-"DLAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=DLAGG"];
+"DLAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=DLAGG"];
"DLAGG" -> "RCAGG"
@
<<DLAGG.dotfull>>=
"DoublyLinkedAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=DLAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=DLAGG"];
"DoublyLinkedAggregate(a:Type)" -> "RecursiveAggregate(a:Type)"
@
@@ -4119,13 +4119,13 @@
@
<<GROUP.dotabb>>=
"GROUP"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=GROUP"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=GROUP"];
"GROUP" -> "MONOID"
@
<<GROUP.dotfull>>=
"Group()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=GROUP"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=GROUP"];
"Group()" -> "Monoid()"
@
@@ -4423,14 +4423,14 @@
@
<<LNAGG.dotabb>>=
-"LNAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=LNAGG"];
+"LNAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=LNAGG"];
"LNAGG" -> "IXAGG"
"LNAGG" -> "CLAGG"
@
<<LNAGG.dotfull>>=
"LinearAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=LNAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=LNAGG"];
"LinearAggregate(a:Type)" -> "IndexedAggregate(b:Integer,a:Type)"
"LinearAggregate(a:Type)" -> "Collection(a:Type)"
@@ -4543,14 +4543,14 @@
@
<<OASGP.dotabb>>=
"OASGP"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=OASGP"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=OASGP"];
"OASGP" -> "ORDSET"
"OASGP" -> "ABELMON"
@
<<OASGP.dotfull>>=
"OrderedAbelianSemiGroup()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=OASGP"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=OASGP"];
"OrderedAbelianSemiGroup()" -> "OrderedSet()"
"OrderedAbelianSemiGroup()" -> "AbelianMonoid()"
@@ -4683,16 +4683,17 @@
@
<<ORDMON.dotabb>>=
"ORDMON"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ORDMON"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ORDMON"];
"ORDMON" -> "ORDSET"
"ORDMON" -> "MONOID"
@
<<ORDMON.dotfull>>=
"OrderedMonoid()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ORDMON"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ORDMON"];
"OrderedMonoid()" -> "OrderedSet()"
"OrderedMonoid()" -> "Monoid()"
+
@
<<ORDMON.dotpic>>=
digraph pic {
@@ -4701,12 +4702,12 @@
node [shape=box, color=white, style=filled];
"OrderedMonoid()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ORDMON"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ORDMON"];
"OrderedMonoid()" -> "OrderedSet()"
"OrderedMonoid()" -> "Monoid()"
"OrderedSet()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ORDSET"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ORDSET"];
"OrderedSet()" -> "SetCategory()"
"Monoid()" [color=lightblue];
@@ -4862,21 +4863,21 @@
@
<<PRQAGG.dotabb>>=
"PRQAGG"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=PRQAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=PRQAGG"];
"PRQAGG" -> "BGAGG"
@
<<PRQAGG.dotfull>>=
"PriorityQueueAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=PRQAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=PRQAGG"];
"PriorityQueueAggregate(a:Type)" -> "BagAggregate(a:Type)"
"PriorityQueueAggregate(a:SetCategory)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=PRQAGG"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=PRQAGG"];
"PriorityQueueAggregate(a:SetCategory)" -> "PriorityQueueAggregate(a:Type)"
"PriorityQueueAggregate(a:OrderedSet)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=PRQAGG"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=PRQAGG"];
"PriorityQueueAggregate(a:OrderedSet)" ->
"PriorityQueueAggregate(a:SetCategory)"
@@ -5044,17 +5045,17 @@
@
<<QUAGG.dotabb>>=
-"QUAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=QUAGG"];
+"QUAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=QUAGG"];
"QUAGG" -> "BGAGG"
@
<<QUAGG.dotfull>>=
"QueueAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=QUAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=QUAGG"];
"QueueAggregate(a:Type)" -> "BagAggregate(a:Type)"
"QueueAggregate(a:SetCategory)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=QUAGG"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=QUAGG"];
"QueueAggregate(a:SetCategory)" -> "QueueAggregate(a:Type)"
@
@@ -5307,14 +5308,14 @@
@
<<SETAGG.dotabb>>=
"SETAGG"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=SETAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=SETAGG"];
"SETAGG" -> "SETCAT"
"SETAGG" -> "CLAGG"
@
<<SETAGG.dotfull>>=
"SetAggregate(a:SetCategory)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=SETAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=SETAGG"];
"SetAggregate(a:SetCategory)" -> "SetCategory()"
"SetAggregate(a:SetCategory)" -> "Collection(a:SetCategory)"
@@ -5343,7 +5344,7 @@
"CoercibleTo(a:Type)" -> "Category"
"Collection(a:SetCategory)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=CLAGG"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=CLAGG"];
"Collection(a:SetCategory)" -> "Collection(a:Type)"
"Collection(a:Type)" [color=lightblue];
@@ -5489,17 +5490,17 @@
@
<<SKAGG.dotabb>>=
-"SKAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=SKAGG"];
+"SKAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=SKAGG"];
"SKAGG" -> "BGAGG"
@
<<SKAGG.dotfull>>=
"StackAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=SKAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=SKAGG"];
"StackAggregate(a:Type)" -> "BagAggregate(a:Type)"
"StackAggregate(a:SetCategory)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=SKAGG"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=SKAGG"];
"StackAggregate(a:SetCategory)" -> "StackAggregate(a:Type)"
@
@@ -5947,13 +5948,13 @@
@
<<URAGG.dotabb>>=
-"URAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=URAGG"];
+"URAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=URAGG"];
"URAGG" -> "RCAGG"
@
<<URAGG.dotfull>>=
"UnaryRecursiveAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=URAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=URAGG"];
"UnaryRecursiveAggregate(a:Type)" -> "RecursiveAggregate(a:Type)"
@
@@ -6080,13 +6081,13 @@
@
<<ABELGRP.dotabb>>=
"ABELGRP"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ABELGRP"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ABELGRP"];
"ABELGRP" -> "CABMON"
@
<<ABELGRP.dotfull>>=
"AbelianGroup()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ABELGRP"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ABELGRP"];
"AbelianGroup()" -> "CancellationAbelianMonoid()"
@
@@ -6284,17 +6285,17 @@
@
<<DIAGG.dotabb>>=
-"DIAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=DIAGG"];
+"DIAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=DIAGG"];
"DIAGG" -> "DIOPS"
@
<<DIAGG.dotfull>>=
"Dictionary(a:SetCategory)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=DIAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=DIAGG"];
"Dictionary(a:SetCategory)" -> "DictionaryOperations(a:SetCategory)"
"Dictionary(Record(a:SetCategory,b:SetCategory))"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=DIAGG"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=DIAGG"];
"Dictionary(Record(a:SetCategory,b:SetCategory))" ->
"Dictionary(a:SetCategory)"
@@ -6517,19 +6518,19 @@
@
<<DQAGG.dotabb>>=
-"DQAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=DQAGG"];
+"DQAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=DQAGG"];
"DQAGG" -> "SKAGG"
"DQAGG" -> "QUAGG"
@
<<DQAGG.dotfull>>=
"DequeueAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=DQAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=DQAGG"];
"DequeueAggregate(a:Type)" -> "StackAggregate(a:Type)"
"DequeueAggregate(a:Type)" -> "QueueAggregate(a:Type)"
"DequeueAggregate(a:SetCategory)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=DQAGG"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=DQAGG"];
"DequeueAggregate(a:SetCategory)" -> "DequeueAggregate(a:Type)"
@
@@ -6805,13 +6806,13 @@
@
<<ELAGG.dotabb>>=
-"ELAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ELAGG"];
+"ELAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=ELAGG"];
"ELAGG" -> "LNAGG"
@
<<ELAGG.dotfull>>=
"ExtensibleLinearAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ELAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ELAGG"];
"ExtensibleLinearAggregate(a:Type)" -> "LinearAggregate(a:Type)"
@
@@ -7133,13 +7134,13 @@
@
<<FLAGG.dotabb>>=
-"FLAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=FLAGG"];
+"FLAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=FLAGG"];
"FLAGG" -> "LNAGG"
@
<<FLAGG.dotfull>>=
"FiniteLinearAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=FLAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=FLAGG"];
"FiniteLinearAggregate(a:Type)" -> "LinearAggregate(a:Type)"
@
@@ -7329,13 +7330,13 @@
@
<<MDAGG.dotabb>>=
-"MDAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=MDAGG"];
+"MDAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=MDAGG"];
"MDAGG" -> "DIOPS"
@
<<MDAGG.dotfull>>=
"MultiDictionary(a:SetCategory)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=MDAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=MDAGG"];
"MultiDictionary(a:SetCategory)" -> "DictionaryOperations(a:SetCategory)"
@
@@ -7445,14 +7446,14 @@
@
<<OAMON.dotabb>>=
-"OAMON" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=OAMON"];
+"OAMON" [color=lightblue,href="bookvol10.2.pdf#nameddest=OAMON"];
"OAMON" -> "OASGP"
"OAMON" -> "ABELMON"
@
<<OAMON.dotfull>>=
"OrderedAbelianMonoid()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=OAMON"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=OAMON"];
"OrderedAbelianMonoid()" -> "OrderedAbelianSemiGroup()"
"OrderedAbelianMonoid()" -> "AbelianMonoid()"
@@ -7812,14 +7813,14 @@
@
<<STAGG.dotabb>>=
-"STAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=STAGG"];
+"STAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=STAGG"];
"STAGG" -> "RCAGG"
"STAGG" -> "LNAGG"
@
<<STAGG.dotfull>>=
"StreamAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=STAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=STAGG"];
"StreamAggregate(a:Type)" -> "UnaryRecursiveAggregate(a:Type)"
"StreamAggregate(a:Type)" -> "LinearAggregate(a:Type)"
@@ -8299,23 +8300,23 @@
@
<<A1AGG.dotabb>>=
-"A1AGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=A1AGG"];
+"A1AGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=A1AGG"];
"A1AGG" -> "FLAGG"
@
<<A1AGG.dotfull>>=
"OneDimensionalArrayAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=A1AGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=A1AGG"];
"OneDimensionalArrayAggregate(a:Type)" ->
"FiniteLinearAggregate(a:Type)"
"OneDimensionalArrayAggregate(Character)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=A1AGG"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=A1AGG"];
"OneDimensionalArrayAggregate(Character)" ->
"OneDimensionalArrayAggregate(a:Type)"
"OneDimensionalArrayAggregate(Boolean)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=A1AGG"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=A1AGG"];
"OneDimensionalArrayAggregate(Boolean)" ->
"OneDimensionalArrayAggregate(a:Type)"
@@ -8613,14 +8614,14 @@
@
<<FSAGG.dotabb>>=
-"FSAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=FSAGG"];
+"FSAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=FSAGG"];
"FSAGG" -> "DIAGG"
"FSAGG" -> "SETAGG"
@
<<FSAGG.dotfull>>=
"FiniteSetAggregate(a:SetCategory)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=FSAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=FSAGG"];
"FiniteSetAggregate(a:SetCategory)" -> "Dictionary(a:SetCategory)"
"FiniteSetAggregate(a:SetCategory)" -> "SetAggregate(a:SetCategory)"
@@ -8835,13 +8836,13 @@
@
<<KDAGG.dotabb>>=
-"KDAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=KDAGG"];
+"KDAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=KDAGG"];
"KDAGG" -> "DIAGG"
@
<<KDAGG.dotfull>>=
"KeyedDictionary(a:SetCategory,b:SetCategory)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=KDAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=KDAGG"];
"KeyedDictionary(a:SetCategory,b:SetCategory)" ->
"Dictionary(Record(a:SetCategory,b:SetCategory))"
@@ -8961,17 +8962,17 @@
@
<<LMODULE.dotabb>>=
"LMODULE"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=LMODULE"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=LMODULE"];
"LMODULE" -> "ABELGRP"
@
<<LMODULE.dotfull>>=
"LeftModule(a:Rng)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=LMODULE"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=LMODULE"];
"LeftModule(a:Rng)" -> "AbelianGroup()"
"LeftModule(a:Ring)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=LMODULE"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=LMODULE"];
"LeftModule(a:Ring)" -> "LeftModule(a:Rng)"
@
@@ -9518,20 +9519,20 @@
@
<<LSAGG.dotabb>>=
-"LSAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=LSAGG"];
+"LSAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=LSAGG"];
"LSAGG" -> "FLAGG"
"LSAGG" -> "ELAGG"
@
<<LSAGG.dotfull>>=
"ListAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=LSAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=LSAGG"];
"ListAggregate(a:Type)" -> "StreamAggregate(a:Type)"
"ListAggregate(a:Type)" -> "FiniteLinearAggregate(a:Type)"
"ListAggregate(a:Type)" -> "ExtensibleLinearAggregate(a:Type)"
"ListAggregate(Record(a:SetCategory,b:SetCategory))"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=LSAGG"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=LSAGG"];
"ListAggregate(Record(a:SetCategory,b:SetCategory))" ->
"ListAggregate(a:Type)"
@@ -9719,14 +9720,14 @@
@
<<MSETAGG.dotabb>>=
"MSETAGG"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=MSETAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=MSETAGG"];
"MSETAGG" -> "MDAGG"
"MSETAGG" -> "SETAGG"
@
<<MSETAGG.dotfull>>=
"MultisetAggregate(a:SetCategory)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=MSETAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=MSETAGG"];
"MultisetAggregate(a:SetCategory)" -> "MultiDictionary(a:SetCategory)"
"MultisetAggregate(a:SetCategory)" -> "SetAggregate(a:SetCategory)"
@@ -9835,14 +9836,14 @@
@
<<OCAMON.dotabb>>=
"OCAMON"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=OCAMON"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=OCAMON"];
"OCAMON" -> "OAMON"
"OCAMON" -> "CABMON"
@
<<OCAMON.dotfull>>=
"OrderedCancellationAbelianMonoid()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=OCAMON"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=OCAMON"];
"OrderedCancellationAbelianMonoid()" -> "OrderedAbelianMonoid()"
"OrderedCancellationAbelianMonoid()" -> "CancellationAbelianMonoid()"
@@ -9956,17 +9957,17 @@
@
<<RMODULE.dotabb>>=
"RMODULE"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=RMODULE"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=RMODULE"];
"RMODULE" -> "ABELGRP"
@
<<RMODULE.dotfull>>=
"RightModule(a:Rng)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=RMODULE"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=RMODULE"];
"RightModule(a:Rng)" -> "AbelianGroup()"
"RightModule(a:Ring)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=RMODULE"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=RMODULE"];
"RightModule(a:Ring)" -> "RightModule(a:Rng)"
@
@@ -10073,13 +10074,13 @@
@
<<RNG.dotabb>>=
-"RNG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=RNG"];
+"RNG" [color=lightblue,href="bookvol10.2.pdf#nameddest=RNG"];
"RNG" -> "ABELGRP"
"RNG" -> "SGROUP"
@
<<RNG.dotfull>>=
-"Rng()" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=RNG"];
+"Rng()" [color=lightblue,href="bookvol10.2.pdf#nameddest=RNG"];
"Rng()" -> "AbelianGroup()"
"Rng()" -> "SemiGroup()"
@@ -10480,13 +10481,13 @@
@
<<SRAGG.dotabb>>=
-"SRAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=SRAGG"];
+"SRAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=SRAGG"];
"SRAGG" -> "A1AGG"
@
<<SRAGG.dotfull>>=
"StringAggregate()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=SRAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=SRAGG"];
"StringAggregate()" -> "OneDimensionalArrayAggregate(Character)"
@
@@ -10888,14 +10889,14 @@
@
<<TBAGG.dotabb>>=
-"TBAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=TBAGG"];
+"TBAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=TBAGG"];
"TBAGG" -> "KDAGG"
"TBAGG" -> "IXAGG"
@
<<TBAGG.dotfull>>=
"TableAggregate(a:SetCategory,b:SetCategory)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=TBAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=TBAGG"];
"TableAggregate(a:SetCategory,b:SetCategory)" ->
"KeyedDictionary(a:SetCategory,b:SetCategory)"
"TableAggregate(a:SetCategory,b:SetCategory)" ->
@@ -11406,14 +11407,14 @@
@
<<ALAGG.dotabb>>=
-"ALAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ALAGG"];
+"ALAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=ALAGG"];
"ALAGG" -> "TBAGG"
"ALAGG" -> "LSAGG"
@
<<ALAGG.dotfull>>=
"AssociationListAggregate(a:SetCategory,b:SetCategory)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ALAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ALAGG"];
"AssociationListAggregate(a:SetCategory,b:SetCategory)" ->
"TableAggregate(a:SetCategory,b:SetCategory)"
"AssociationListAggregate(a:SetCategory,b:SetCategory)" ->
@@ -11537,23 +11538,23 @@
@
<<BMODULE.dotabb>>=
"BMODULE"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=BMODULE"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=BMODULE"];
"BMODULE" -> "LMODULE"
"BMODULE" -> "RMODULE"
@
<<BMODULE.dotfull>>=
"BiModule(a:Ring,b:Ring)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=BMODULE"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=BMODULE"];
"BiModule(a:Ring,b:Ring)" -> "LeftModule(a:Ring)"
"BiModule(a:Ring,b:Ring)" -> "RightModule(a:Ring)"
"BiModule(a:CommutativeRing,b:CommutativeRing)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=BMODULE"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=BMODULE"];
"BiModule(a:CommutativeRing,b:CommutativeRing)" -> "BiModule(a:Ring,b:Ring)"
"BiModule(a:Ring,b:OrderedAbelianMonoid)"
- [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=BMODULE"];
+ [color=seagreen,href="bookvol10.2.pdf#nameddest=BMODULE"];
"BiModule(a:Ring,b:OrderedAbelianMonoid)" -> "BiModule(a:Ring,b:Ring)"
@
@@ -11564,7 +11565,7 @@
node [shape=box, color=white, style=filled];
"BiModule(a:Ring,b:Ring)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=BMODULE"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=BMODULE"];
"BiModule(a:Ring,b:Ring)" -> "LeftModule(a:Ring)"
"BiModule(a:Ring,b:Ring)" -> "RightModule(a:Ring)"
@@ -11682,14 +11683,14 @@
@
<<OAGROUP.dotabb>>=
"OAGROUP"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=OAGROUP"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=OAGROUP"];
"OAGROUP" -> "OCAMON"
"OAGROUP" -> "ABELGRP"
@
<<OAGROUP.dotfull>>=
"OrderedAbelianGroup()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=OAGROUP"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=OAGROUP"];
"OrderedAbelianGroup()" -> "OrderedCancellationAbelianMonoid()"
"OrderedAbelianGroup()" -> "AbelianGroup()"
@@ -11806,13 +11807,13 @@
@
<<OAMONS.dotabb>>=
"OAMONS"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=OAMONS"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=OAMONS"];
"OAMONS" -> "OCAMON"
@
<<OAMONS.dotfull>>=
"OrderedAbelianMonoidSup()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=OAMONS"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=OAMONS"];
"OrderedAbelianMonoidSup()" -> "OrderedCancellationAbelianMonoid()"
@
@@ -12035,14 +12036,14 @@
@
<<OMSAGG.dotabb>>=
"OMSAGG"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=OMSAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=OMSAGG"];
"OMSAGG" -> "MSETAGG"
"OMSAGG" -> "PRQAGG"
@
<<OMSAGG.dotfull>>=
"OrderedMultisetAggregate(a:SetCategory)"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=OMSAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=OMSAGG"];
"OrderedMultisetAggregate(a:SetCategory)" ->
"MultisetAggregate(a:SetCategory)"
"OrderedMultisetAggregate(a:SetCategory)" ->
@@ -12206,7 +12207,7 @@
@
<<RING.dotabb>>=
"RING"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=RING"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=RING"];
"RING" -> "RNG"
"RING" -> "MONOID"
"RING" -> "LMODULE"
@@ -12214,7 +12215,7 @@
@
<<RING.dotfull>>=
"Ring()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=RING"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=RING"];
"Ring()" -> "Rng()"
"Ring()" -> "Monoid()"
"Ring()" -> "LeftModule(a:Ring)"
@@ -12400,7 +12401,7 @@
@
<<ORDRING.dotabb>>=
"ORDRING"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ORDRING"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ORDRING"];
"ORDRING" -> "OAGROUP"
"ORDRING" -> "RING"
"ORDRING" -> "MONOID"
@@ -12408,7 +12409,7 @@
@
<<ORDRING.dotfull>>=
"OrderedRing()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ORDRING"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=ORDRING"];
"OrderedRing()" -> "OrderedAbelianGroup()"
"OrderedRing()" -> "Ring()"
"OrderedRing()" -> "Monoid()"
@@ -12510,7 +12511,7 @@
@
<<BTAGG.dotabb>>=
-"BTAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=BTAGG"];
+"BTAGG" [color=lightblue,href="bookvol10.2.pdf#nameddest=BTAGG"];
"BTAGG" -> "ORDSET"
"BTAGG" -> "LOGIC"
"BTAGG" -> "A1AGG"
@@ -12518,7 +12519,7 @@
@
<<BTAGG.dotfull>>=
"BitAggregate()"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=BTAGG"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=BTAGG"];
"BitAggregate()" -> "OrderedSet()"
"BitAggregate()" -> "Logic()"
"BitAggregate()" -> "OneDimensionalArrayAggregate(Boolean)"
@@ -12529,7 +12530,7 @@
\pageto{HomogeneousAggregate}{HOAGG}
<<EVALAB.dotfull>>=
"Evalable(a:Type)"
- [color="#00EE00",href="books/bookvol10.2.pamphlet#nameddest=EVALAB"];
+ [color="#00EE00",href="bookvol10.2.pdf#nameddest=EVALAB"];
@
\chapter{The bootstrap code}
@@ -16813,7 +16814,7 @@
node [shape=box, color=white, style=filled];
"CATEGORY"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=CATEGORY"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=CATEGORY"];
<<ABELGRP.dotabb>>
<<ABELMON.dotabb>>
@@ -16887,7 +16888,7 @@
node [shape=box, color=white, style=filled];
"Category"
- [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=CATEGORY"];
+ [color=lightblue,href="bookvol10.2.pdf#nameddest=CATEGORY"];
<<ABELGRP.dotfull>>
<<ABELMON.dotfull>>
Modified: trunk/axiom/books/bookvol7.1.pamphlet
===================================================================
--- trunk/axiom/books/bookvol7.1.pamphlet 2008-09-21 16:15:34 UTC (rev 979)
+++ trunk/axiom/books/bookvol7.1.pamphlet 2008-09-22 05:30:00 UTC (rev 980)
@@ -233,6 +233,7 @@
\pagepic{ps/v71releasenotes.eps}{releasenotes}
\pagefrom{Root Page}{RootPage}
\pageto{Online information}{onlineInformation}
+\pageto{September 2008}{sept2008}
\pageto{July 2008}{july2008}
\pageto{May 2008}{may2008}
\pageto{March 2008}{march2008}
@@ -244,6 +245,7 @@
\beginscroll
\beginmenu
\menudownlink{Online information}{onlineInformation}
+ \menudownlink{September 2008}{sept2008}
\menudownlink{July 2008}{july2008}
\menudownlink{May 2008}{may2008}
\menudownlink{March 2008}{march2008}
@@ -271,6 +273,153 @@
\end{page}
@
+\pagehead{sept2008}{releasenotes.ht}{September 23, 2008 Release Notes}
+\pagepic{ps/v71sept2008.eps}{sept2008}
+\pagefrom{What's New in Axiom}{releaseNotes}
+<<releasenotes.ht>>=
+\begin{page}{sept2008}{September 23, 2008 Release Notes}
+\beginscroll
+\begin{verbatim}
+September 2008 Release Notes
+
+Axiom website
+ The effort here is to improve the support for offline literate
+ documentation. The primary changes are the inclusion of graphs
+ and additional book volumes.
+
+* <" rel="nofollow">http://axiom-developer.org/axiom-website/documentation.html>
+ Contains the new algebra volumes and subvolumes.
+* <" rel="nofollow">http://axiom-developer.org/axiom-website/bookvol10.2abb.html>
+ Contains a "clickable" graph that indexes into the algebra.
+
+
+
+
+Graphviz, PDF, and HTML integration
+ The effort here is to unify these three technologies in a way
+ that simplifies the user interface and improves documentation
+
+* Graphviz is used if available but not required
+* Algebra graphs are automatically generated at build time
+ from algebra source files
+* Graphviz graphs now properly hyperlink into PDF files allowing
+ any node in a graph to link to any document page
+
+
+
+
+Book volume 0 (Jenks and Sutor)
+
+* <" rel="nofollow">http://axiom-developer.org/axiom-website/bookvol0.pdf>
+* replace \over with \frac
+
+
+
+Book volume 7.1 (Hyperdoc pages)
+ The effort here is to create a literate document that contains
+ all of the "live" pages used in hyperdoc. The PDF is being
+ constructed so that a user can effectively "browse" the static
+ hyperdoc pages, which are included, without a running Axiom.
+
+* <" rel="nofollow">http://axiom-developer.org/axiom-website/bookvol7.1.pdf>
+* The source for all of the pages is now contained in this book.
+* Hyperdoc now fetches the pages directly from the book.
+* The hyper page directory and all files are gone.
+* Some of the static page images are now inside the PDF
+* Pages have href links allowing "in-pdf" navigation of pages
+
+
+
+
+Book volume 10 (Algebra)
+ The effort here is to create a way to describe and deeply
+ document the algebra. This volume was split to better handle
+ the structure of Axiom's information.
+
+* Split into 5 volumes
+ - 10 Implementation
+ - 10.1 Theory
+ - 10.2 Categories
+ - 10.3 Domains
+ - 10.4 Packages
+
+
+
+
+Book volume 10.2 (Algebra Categories)
+ The effort here is to create fully indexed, cross-referenced,
+ graphical documentation for Axiom categories in a standalone
+ form. This is a "live" literate document which contains the
+ actual source code used to build the system.
+
+* <" rel="nofollow">http://axiom-developer.org/axiom-website/bookvol10.2.pdf>
+* Contains 60 categories so far
+* Has partial graphs for each category
+* Has list of exported functions
+* Has information about source of functions
+* Has index cross reference by function and category
+* Has PDF href links so that URLs work:
+ <" rel="nofollow">http://axiom-developer.org/axiom-website/bookvol10.2.pdf#nameddest=AGG>
+* Has forward/backward links between categories
+* Automatically generates "clickable" graphs:
+ <" rel="nofollow">http://axiom-developer.org/axiom-website/bookvol10.2abb.html>
+* Graph clicking automatically opens to the proper source code
+
+
+
+
+New algebra examples (Daly, Tsikas)
+ The effort here is to create "real time" documentation that
+ gives the end user an example of how to construct the proper
+ arguments and call a function. This puts examples into the
+ system so users don't need to consult other documents.
+
+* )d op someop shows examples of function usage
+* about 100 new function examples were added
+* new comment syntax added to allow automatic API testing
+
+
+
+
+Input Files
+ There is a new effort to automatically extract the algebra
+ examples in order to regression test the user API to the
+ algebra. In addition there is ongoing test work.
+
+* New input files (Hemmecke, Stumbo, Cyganski, Daly)
+ bini, biquat, ifthenelse, liu, overload, sqrt3, typetower
+* Changed input files (Hemmecke, Stumbo, Cyganski, Daly)
+ bern, function, linalg, regset, test, tutchap2
+
+
+
+
+Build changes
+
+* graphics does not depend on compress, done at build time
+* firefox html pages are now built before tests are run
+
+
+
+Algebra changes
+
+* FLAGG (FiniteLinearAggregate) -- removed a duplicate function
+
+
+
+Interpreter changes (Page)
+
+* add cost function to bottomUp output
+
+
+
+
+\end{verbatim}
+\endscroll
+\autobuttons
+\end{page}
+
+@
\pagehead{july2008}{releasenotes.ht}{July 23, 2008 Release Notes}
\pagepic{ps/v71july2008.eps}{july2008}
\pagefrom{What's New in Axiom}{releaseNotes}
Modified: trunk/axiom/books/ps/v71releasenotes.eps
===================================================================
--- trunk/axiom/books/ps/v71releasenotes.eps 2008-09-21 16:15:34 UTC (rev 979)
+++ trunk/axiom/books/ps/v71releasenotes.eps 2008-09-22 05:30:00 UTC (rev 980)
@@ -1,7 +1,7 @@
%!PS-Adobe-3.0 EPSF-3.0
%%Creator: GIMP PostScript file plugin V 1.17 by Peter Kirchgessner
-%%Title: whatsnew.eps
-%%CreationDate: Sat Jun 21 00:08:02 2008
+%%Title: v71releasenotes.eps
+%%CreationDate: Mon Jul 28 14:40:07 2008
%%DocumentData: Clean7Bit
%%LanguageLevel: 2
%%Pages: 1
@@ -29,7 +29,7 @@
{currentfile /ASCII85Decode filter /RunLengthDecode filter gstr readstring pop}
{currentfile /ASCII85Decode filter /RunLengthDecode filter bstr readstring pop}
true 3
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!BU8[l%/kcs+13$s+13hs8M6`c8pI~>
!B:&Xj+75]s+13$s+13hs8M$Z_`*)~>
+!BpJ^mCN>t!9F1Z!8IPP!;c`o!;c`o!;c`o!.k0$s+13$s7u]om/bd$J,~>
+!BU8[l+6op!9F1Z!8IPP!;c`o!;c`o!;c`o!.k0$s+13$s7u]oklK'jJ,~>
+!B:&Xj1>9j!9F1Z!8IPP!;c`o!;c`o!;c`o!.k0$s+13$s7u]oirR%VJ,~>
+!BpJ^mFqU=!!<0#!9jI_!9F1Z!8RVO!;ulo!;ulo!;ulo!.k0$s+13$s8)cpm/bd$J,~>
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+!B:&Xj4aP3!!<0#!9jI_!9F1Z!8RVO!;ulo!;ulo!;ulo!.k0$s+13$s8)cpirR%VJ,~>
+!BpJ^mHsrH!;ull!9jI_!9=+Z!8[\T!<3#t!<)rt!<<*!!;uls!<<*!!<)rt!<)rt!.k0$s+13$
+s82iqm/bd$J,~>
+!BU8[l0\ND!;ull!9jI_!9=+Z!8[\T!<3#t!<)rt!<<*!!;uls!<<*!!<)rt!<)rt!.k0$s+13$
+s82iqklK'jJ,~>
+!B:&Xj6cm>!;ull!9jI_!9=+Z!8[\T!<3#t!<)rt!<<*!!;uls!<<*!!<)rt!<)rt!.k0$s+13$
+s82iqirR%VJ,~>
+!BpJ^mHsrH!;uls!<)rs!<)rr!<)rs!!*&t!<3#o!;lfp!<3#t!!E6$!<<#urr;uu!<;utqu?Tp
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+!BU8[l0\ND!;uls!<)rs!<)rr!<)rs!!*&t!<3#o!;lfp!<3#t!!E6$!<<#urr;uu!<;utqu?Tp
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+!B:&Xj6cm>!;uls!<)rs!<)rr!<)rs!!*&t!<3#o!;lfp!<3#t!!E6$!<<#urr;uu!<;utqu?Tp
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+s8N)us8N)ts8N)us8N)ts8N)ts8N*!s8N(Ms+13$s+14Hs8MBdeieN~>
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+s8N)us8N)ts8N)us8N)ts8N)ts8N*!s8N(Ms+13$s+14Hs8M6`c8pI~>
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[truncated message content] |
|
From: <gi...@ax...> - 2008-09-22 05:19:47
|
Makefile | 2 +-
Makefile.pamphlet | 2 +-
books/bookvol10.2.pamphlet | 345 +++---
books/bookvol7.1.pamphlet | 149 +++
books/ps/v71releasenotes.eps | 351 +++--
books/ps/v71sept2008.eps | 2960 ++++++++++++++++++++++++++++++++++++++++++
6 files changed, 3494 insertions(+), 315 deletions(-)
New commits:
commit f5913c396d3ffdf877b5e6f8368854a638310022
Author: Tim Daly <da...@ax...>
Date: Mon Jul 28 15:01:01 2008 -0400
20080921 tpd books/bookvol10.2 use .pdf rather than .pamphlet in URL
20080921 tpd books/ps/v71sept2008.eps add new image for sept 2008
20080921 tpd books/ps/v71releasenotes.eps update image to include sept2008
20080921 tpd books/bookvol7.1 add september release notes
20080921 tpd Makefile.pamphlet September 2008 release number
20080921 tpd Makefile September 2008 release number
|
|
From: <da...@us...> - 2008-09-21 16:15:40
|
Revision: 979
http://axiom.svn.sourceforge.net/axiom/?rev=979&view=rev
Author: daly
Date: 2008-09-21 16:15:34 +0000 (Sun, 21 Sep 2008)
Log Message:
-----------
20080920 tpd books/ps/v102bimodule.ps diagram BMODULE
20080920 tpd books/ps/v102group.ps diagram GROUP
20080920 tpd books/ps/v102leftmodule.ps diagram LMODULE
20080920 tpd books/ps/v102orderedabeliangroup.ps diagram OAGROUP
20080920 tpd books/ps/v102orderedabelianmonoidsup.ps OAMONS
20080920 tpd books/ps/v102orderedcancellationabelianmonoid.ps OCAMON
20080920 tpd books/ps/v102orderedring.ps diagram ORDRING
20080920 tpd books/ps/v102rightmodule.ps diagram RMODULE
20080920 tpd books/ps/v102ring.ps diagram RING
20080920 tpd src/algebra/catdef.spad remove more categories
20080920 tpd books/bookvol10.2 add more categories
Modified Paths:
--------------
trunk/axiom/books/bookvol10.2.pamphlet
trunk/axiom/src/algebra/catdef.spad.pamphlet
Added Paths:
-----------
trunk/axiom/books/ps/v102bimodule.ps
trunk/axiom/books/ps/v102group.ps
trunk/axiom/books/ps/v102leftmodule.ps
trunk/axiom/books/ps/v102orderedabeliangroup.ps
trunk/axiom/books/ps/v102orderedabelianmonoidsup.ps
trunk/axiom/books/ps/v102orderedcancellationabelianmonoid.ps
trunk/axiom/books/ps/v102orderedring.ps
trunk/axiom/books/ps/v102rightmodule.ps
trunk/axiom/books/ps/v102ring.ps
Modified: trunk/axiom/books/bookvol10.2.pamphlet
===================================================================
--- trunk/axiom/books/bookvol10.2.pamphlet 2008-09-20 13:16:15 UTC (rev 978)
+++ trunk/axiom/books/bookvol10.2.pamphlet 2008-09-21 16:15:34 UTC (rev 979)
@@ -52,10 +52,12 @@
\ \\${\bf\Leftarrow{}}${``#1''} (#2) \ref{#1} on page~\pageref{#1}}
%%
%% cross will put the category and function in the index
+%% cross will leave the funcname so it can be put inline.
%%
\newcommand{\cross}[2]{% e.g. \pagefrom{cat}{funcname}
\index{#1!#2}%
-\index{#2!#1}}
+\index{#2!#1}%
+#2}
% special meanings for math characters
@@ -298,7 +300,8 @@
{\bf Exports:}\\
\begin{tabular}{ll}
- ?=? & ?\~{}=?
+\cross{BASTYPE}{?=?} &
+\cross{BASTYPE}{?\~{}=?}
\end{tabular}
These are directly exported but not implemented:
@@ -366,11 +369,7 @@
\pageto{SetCategory}{SETCAT}
\pagefrom{Category}{CATEGORY}
-{\bf Exports:}
-\begin{verbatim}
- coerce
-\end{verbatim}
-
+{\bf Exports:}\\
\cross{KOERCE}{coerce}
This is directly exported but not implemented:
@@ -430,11 +429,7 @@
\pageto{Collection}{CLAGG}
\pagefrom{Category}{CATEGORY}
-{\bf Exports:}
-\begin{verbatim}
- convert
-\end{verbatim}
-
+{\bf Exports:}\\
\cross{KONVERT}{convert}
This is directly exported but not implemented:
@@ -550,11 +545,7 @@
\pageto{EltableAggregate}{ELTAGG}
\pagefrom{Category}{CATEGORY}
-{\bf Exports:}
-\begin{verbatim}
- ?.?
-\end{verbatim}
-
+{\bf Exports:}\\
\cross{ELTAB}{?.?}
This syntax for elt is supported by the interpreter and compiler.
@@ -620,13 +611,11 @@
{\bf Exports:}\\
\begin{tabular}{lll}
- coerce & retract & retractIfCan
+\cross{RETRACT}{coerce} &
+\cross{RETRACT}{retract} &
+\cross{RETRACT}{retractIfCan}
\end{tabular}
-\cross{RETRACT}{coerce}
-\cross{RETRACT}{retract}
-\cross{RETRACT}{retractIfCan}
-
These are directly exported but not implemented:
\begin{verbatim}
coerce : S -> %
@@ -770,16 +759,14 @@
{\bf Exports:}\\
\begin{tabular}{llllll}
- empty? & eq? & less? & more? & sample & size?
+\cross{AGG}{empty?} &
+\cross{AGG}{eq?} &
+\cross{AGG}{less?} &
+\cross{AGG}{more?} &
+\cross{AGG}{sample} &
+\cross{AGG}{size?}
\end{tabular}
-\cross{AGG}{empty?}
-\cross{AGG}{eq?}
-\cross{AGG}{less?}
-\cross{AGG}{more?}
-\cross{AGG}{sample}
-\cross{AGG}{size?}
-
These are implemented by this category:
\begin{verbatim}
empty? : % -> Boolean
@@ -882,15 +869,13 @@
{\bf Exports:}\\
\begin{tabular}{lllll}
- elt & qelt & qsetelt! & setelt & ?.?
+\cross{ELTAGG}{elt} &
+\cross{ELTAGG}{qelt} &
+\cross{ELTAGG}{qsetelt!} &
+\cross{ELTAGG}{setelt} &
+\cross{ELTAGG}{?.?}
\end{tabular}
-\cross{ELTAGG}{elt}
-\cross{ELTAGG}{qelt}
-\cross{ELTAGG}{qsetelt!}
-\cross{ELTAGG}{setelt}
-\cross{ELTAGG}{?.?}
-
These are part of this category's direct exports:
\begin{verbatim}
elt : (%,Dom,Im) -> Im
@@ -1003,15 +988,13 @@
{\bf Exports:}\\
\begin{tabular}{lllll}
-coerce & hash & latex & ?=? & ?\~{}=?
+\cross{SETCAT}{coerce} &
+\cross{SETCAT}{hash} &
+\cross{SETCAT}{latex} &
+\cross{SETCAT}{?=?} &
+\cross{SETCAT}{?\~{}=?}
\end{tabular}
-\cross{SETCAT}{coerce}
-\cross{SETCAT}{hash}
-\cross{SETCAT}{latex}
-\cross{SETCAT}{?=?}
-\cross{SETCAT}{?\~{}=?}
-
These are implemented by this category:
\begin{verbatim}
hash : % -> SingleInteger
@@ -1106,18 +1089,16 @@
\pagefrom{SetCategory}{SETCAT}
{\bf Exports:}\\
-\begin{tabular}{lllllll}
- coerce & hash & latex & ?*? & ?+? & ?=? & ?\~{}=?
+\begin{tabular}{lllll}
+\cross{ABELSG}{coerce} &
+\cross{ABELSG}{hash} &
+\cross{ABELSG}{latex} &
+\cross{ABELSG}{?*?} &
+\cross{ABELSG}{?+?} \\
+\cross{ABELSG}{?=?} &
+\cross{ABELSG}{?\~{}=?} &&&
\end{tabular}
-\cross{ABELSG}{coerce}
-\cross{ABELSG}{hash}
-\cross{ABELSG}{latex}
-\cross{ABELSG}{?*?}
-\cross{ABELSG}{?+?}
-\cross{ABELSG}{?=?}
-\cross{ABELSG}{?\~{}=?}
-
These are directly exported but not implemented:
\begin{verbatim}
?+? : (%,%) -> %
@@ -1225,20 +1206,18 @@
\pagefrom{SetCategory}{SETCAT}
{\bf Exports:}\\
-\begin{tabular}{lllllllll}
- coerce & hash & index & latex & lookup & random & size & ?=? & ?\~{}=?
+\begin{tabular}{lllll}
+\cross{FINITE}{coerce}
+\cross{FINITE}{hash} &
+\cross{FINITE}{index} &
+\cross{FINITE}{latex} &
+\cross{FINITE}{lookup} &
+\cross{FINITE}{random} \\
+\cross{FINITE}{size} &
+\cross{FINITE}{?=?} &
+\cross{FINITE}{?\~{}=?} &&
\end{tabular}
-\cross{FINITE}{coerce}
-\cross{FINITE}{hash}
-\cross{FINITE}{index}
-\cross{FINITE}{latex}
-\cross{FINITE}{lookup}
-\cross{FINITE}{random}
-\cross{FINITE}{size}
-\cross{FINITE}{?=?}
-\cross{FINITE}{?\~{}=?}
-
These are directly exported but not implemented:
\begin{verbatim}
index : PositiveInteger -> %
@@ -1346,39 +1325,33 @@
\pagefrom{Evalable}{EVALAB}
\pagefrom{SetCategory}{SETCAT}
-
{\bf Exports:}\\
-\begin{tabular}{lllllll}
- any? & coerce & copy & count & empty & empty? & eq?\\
- eval & every? & hash & latex & less? & map & map!\\
- members & member? & more? & parts & sample & size? & \#?\\
- ?=? & ?\~{}=? & & & & &\\
+\begin{tabular}{lllll}
+\cross{HOAGG}{any?} &
+\cross{HOAGG}{coerce} &
+\cross{HOAGG}{copy} &
+\cross{HOAGG}{count} &
+\cross{HOAGG}{empty} \\
+\cross{HOAGG}{empty?} &
+\cross{HOAGG}{eq?} &
+\cross{HOAGG}{eval} &
+\cross{HOAGG}{every?} &
+\cross{HOAGG}{hash} \\
+\cross{HOAGG}{latex} &
+\cross{HOAGG}{less?} &
+\cross{HOAGG}{map} &
+\cross{HOAGG}{map!} &
+\cross{HOAGG}{members} \\
+\cross{HOAGG}{member?} &
+\cross{HOAGG}{more?} &
+\cross{HOAGG}{parts} &
+\cross{HOAGG}{sample} &
+\cross{HOAGG}{size?} \\
+\cross{HOAGG}{\#?} &
+\cross{HOAGG}{?=?} &
+\cross{HOAGG}{?\~{}=?} &&
\end{tabular}
-\cross{HOAGG}{any?}
-\cross{HOAGG}{coerce}
-\cross{HOAGG}{copy}
-\cross{HOAGG}{count}
-\cross{HOAGG}{empty}
-\cross{HOAGG}{empty?}
-\cross{HOAGG}{eq?}
-\cross{HOAGG}{eval}
-\cross{HOAGG}{every?}
-\cross{HOAGG}{hash}
-\cross{HOAGG}{latex}
-\cross{HOAGG}{less?}
-\cross{HOAGG}{map}
-\cross{HOAGG}{map!}
-\cross{HOAGG}{members}
-\cross{HOAGG}{member?}
-\cross{HOAGG}{more?}
-\cross{HOAGG}{parts}
-\cross{HOAGG}{sample}
-\cross{HOAGG}{size?}
-\cross{HOAGG}{\#?}
-\cross{HOAGG}{?=?}
-\cross{HOAGG}{?\~{}=?}
-
These are directly exported but not implemented:
\begin{verbatim}
map : ((S -> S),%) -> %
@@ -1570,23 +1543,20 @@
\pagefrom{SetCategory}{SETCAT}
{\bf Exports:}\\
-\begin{tabular}{llllll}
- coerce & hash & latex & max & min & ?$<$?\\
- ?$<=$? & ?=? & ?$>$? & ?$>=$? & ?\~{}=? &\\
+\begin{tabular}{lllll}
+\cross{ORDSET}{coerce} &
+\cross{ORDSET}{hash} &
+\cross{ORDSET}{latex} &
+\cross{ORDSET}{max} &
+\cross{ORDSET}{min} \\
+\cross{ORDSET}{?$<$?} &
+\cross{ORDSET}{?$<=$?} &
+\cross{ORDSET}{?=?} &
+\cross{ORDSET}{?$>$?} &
+\cross{ORDSET}{?$>=$?} \\
+\cross{ORDSET}{?\~{}=?} &&&&
\end{tabular}
-\cross{ORDSET}{coerce}
-\cross{ORDSET}{hash}
-\cross{ORDSET}{latex}
-\cross{ORDSET}{max}
-\cross{ORDSET}{min}
-\cross{ORDSET}{?$<$?}
-\cross{ORDSET}{?$<=$?}
-\cross{ORDSET}{?=?}
-\cross{ORDSET}{?$>$?}
-\cross{ORDSET}{?$>=$?}
-\cross{ORDSET}{?\~{}=?}
-
These are directly exported but not implemented:
\begin{verbatim}
?<? : (%,%) -> Boolean
@@ -1713,20 +1683,17 @@
\pagefrom{SetCategory}{SETCAT}
{\bf Exports:}\\
-\begin{tabular}{llll}
- coerce & hash & latex & ?*? \\
- ?**? & ?=? & ?\^{}? & ?\~{}=?
+\begin{tabular}{lllll}
+\cross{SGROUP}{coerce} &
+\cross{SGROUP}{hash} &
+\cross{SGROUP}{latex} &
+\cross{SGROUP}{?*?} &
+\cross{SGROUP}{?**?} \\
+\cross{SGROUP}{?=?} &
+\cross{SGROUP}{?\^{}?} &
+\cross{SGROUP}{?~=?} &&
\end{tabular}
-\cross{SGROUP}{coerce}
-\cross{SGROUP}{hash}
-\cross{SGROUP}{latex}
-\cross{SGROUP}{?*?}
-\cross{SGROUP}{?**?}
-\cross{SGROUP}{?=?}
-\cross{SGROUP}{?\^{}?}
-\cross{SGROUP}{?~=?}
-
These are directly exported but not implemented:
\begin{verbatim}
?*? : (%,%) -> %
@@ -1837,18 +1804,16 @@
\pagefrom{SetCategory}{SETCAT}
{\bf Exports:}\\
-\begin{tabular}{lllllll}
- coerce & hash & init & latex & nextItem & ?=? & ?\~{}=?
+\begin{tabular}{lllll}
+\cross{STEP}{coerce} &
+\cross{STEP}{hash} &
+\cross{STEP}{init} &
+\cross{STEP}{latex} &
+\cross{STEP}{?=?} \\
+\cross{STEP}{?~=?} &
+\cross{STEP}{nextItem} &&&
\end{tabular}
-\cross{STEP}{coerce}
-\cross{STEP}{hash}
-\cross{STEP}{init}
-\cross{STEP}{latex}
-\cross{STEP}{?=?}
-\cross{STEP}{?~=?}
-\cross{STEP}{nextItem}
-
These are directly exported but not implemented:
\begin{verbatim}
init : () -> %
@@ -1946,21 +1911,18 @@
{\bf Exports:}\\
\begin{tabular}{lllll}
- 0 & coerce & hash & latex & sample\\
- zero? & ?*? & ?+? & ?=? & ?\~{}=?
+\cross{ABELMON}{0} &
+\cross{ABELMON}{coerce} &
+\cross{ABELMON}{hash} &
+\cross{ABELMON}{latex} &
+\cross{ABELMON}{sample} \\
+\cross{ABELMON}{zero?} &
+\cross{ABELMON}{?*?} &
+\cross{ABELMON}{?+?} &
+\cross{ABELMON}{?=?} &
+\cross{ABELMON}{?\~{}=?} \\
\end{tabular}
-\cross{ABELMON}{0}
-\cross{ABELMON}{coerce}
-\cross{ABELMON}{hash}
-\cross{ABELMON}{latex}
-\cross{ABELMON}{sample}
-\cross{ABELMON}{zero?}
-\cross{ABELMON}{?*?}
-\cross{ABELMON}{?+?}
-\cross{ABELMON}{?=?}
-\cross{ABELMON}{?\~{}=?}
-
These are directly exported but not implemented:
\begin{verbatim}
0 : () -> %
@@ -2088,41 +2050,36 @@
\pagefrom{HomogeneousAggregate}{HOAGG}
{\bf Exports:}\\
-\begin{tabular}{lllllll}
- any? & bag & coerce & copy & count & empty & empty?\\
- eq? & eval & every? & extract! & hash & insert! & inspect\\
- latex & less? & map & map! & member? & members & more?\\
- parts & sample & size? & \#? & ?=? & ?\~{}=? &\\
+\begin{tabular}{lllll}
+\cross{BGAGG}{any?} &
+\cross{BGAGG}{bag} &
+\cross{BGAGG}{coerce} &
+\cross{BGAGG}{copy} &
+\cross{BGAGG}{count} \\
+\cross{BGAGG}{empty} &
+\cross{BGAGG}{empty?} &
+\cross{BGAGG}{eq?} &
+\cross{BGAGG}{eval} &
+\cross{BGAGG}{every?} \\
+\cross{BGAGG}{extract!} &
+\cross{BGAGG}{hash} &
+\cross{BGAGG}{insert!} &
+\cross{BGAGG}{inspect} &
+\cross{BGAGG}{latex} \\
+\cross{BGAGG}{less?} &
+\cross{BGAGG}{map} &
+\cross{BGAGG}{map!} &
+\cross{BGAGG}{member?} &
+\cross{BGAGG}{members} \\
+\cross{BGAGG}{more?} &
+\cross{BGAGG}{parts} &
+\cross{BGAGG}{sample} &
+\cross{BGAGG}{size?} &
+\cross{BGAGG}{\#?} \\
+\cross{BGAGG}{?=?} &
+\cross{BGAGG}{?\~{}=?} &&&
\end{tabular}
-\cross{BGAGG}{any?}
-\cross{BGAGG}{bag}
-\cross{BGAGG}{coerce}
-\cross{BGAGG}{copy}
-\cross{BGAGG}{count}
-\cross{BGAGG}{empty}
-\cross{BGAGG}{empty?}
-\cross{BGAGG}{eq?}
-\cross{BGAGG}{eval}
-\cross{BGAGG}{every?}
-\cross{BGAGG}{extract!}
-\cross{BGAGG}{hash}
-\cross{BGAGG}{insert!}
-\cross{BGAGG}{inspect}
-\cross{BGAGG}{latex}
-\cross{BGAGG}{less?}
-\cross{BGAGG}{map}
-\cross{BGAGG}{map!}
-\cross{BGAGG}{member?}
-\cross{BGAGG}{members}
-\cross{BGAGG}{more?}
-\cross{BGAGG}{parts}
-\cross{BGAGG}{sample}
-\cross{BGAGG}{size?}
-\cross{BGAGG}{\#?}
-\cross{BGAGG}{?=?}
-\cross{BGAGG}{?\~{}=?}
-
These are directly exported but not implemented:
\begin{verbatim}
extract! : % -> S
@@ -2258,45 +2215,39 @@
\pagefrom{HomogeneousAggregate}{HOAGG}
{\bf Exports:}\\
-\begin{tabular}{llllll}
- any? & coerce & construct & copy & convert & count\\
- empty & empty? & eq? & eval & every? & find\\
- hash & latex & less? & map & map! & member?\\
- members & more? & parts & reduce & remove & removeDuplicates\\
- sample & select & size? & \#? & ?=? & ?\~{}=?
+\begin{tabular}{lllll}
+\cross{CLAGG}{any?} &
+\cross{CLAGG}{coerce} &
+\cross{CLAGG}{construct} &
+\cross{CLAGG}{copy} &
+\cross{CLAGG}{convert} \\
+\cross{CLAGG}{count} &
+\cross{CLAGG}{empty} &
+\cross{CLAGG}{empty?} &
+\cross{CLAGG}{eq?} &
+\cross{CLAGG}{eval} \\
+\cross{CLAGG}{every?} &
+\cross{CLAGG}{find} &
+\cross{CLAGG}{hash} &
+\cross{CLAGG}{latex} &
+\cross{CLAGG}{less?} \\
+\cross{CLAGG}{map} &
+\cross{CLAGG}{map!} &
+\cross{CLAGG}{member?} &
+\cross{CLAGG}{members} &
+\cross{CLAGG}{more?} \\
+\cross{CLAGG}{parts} &
+\cross{CLAGG}{reduce} &
+\cross{CLAGG}{remove} &
+\cross{CLAGG}{removeDuplicates} &
+\cross{CLAGG}{sample} \\
+\cross{CLAGG}{select} &
+\cross{CLAGG}{size?} &
+\cross{CLAGG}{\#?} &
+\cross{CLAGG}{?=?} &
+\cross{CLAGG}{?\~{}=?} \\
\end{tabular}
-\cross{CLAGG}{any?}
-\cross{CLAGG}{coerce}
-\cross{CLAGG}{construct}
-\cross{CLAGG}{copy}
-\cross{CLAGG}{convert}
-\cross{CLAGG}{count}
-\cross{CLAGG}{empty}
-\cross{CLAGG}{empty?}
-\cross{CLAGG}{eq?}
-\cross{CLAGG}{eval}
-\cross{CLAGG}{every?}
-\cross{CLAGG}{find}
-\cross{CLAGG}{hash}
-\cross{CLAGG}{latex}
-\cross{CLAGG}{less?}
-\cross{CLAGG}{map}
-\cross{CLAGG}{map!}
-\cross{CLAGG}{member?}
-\cross{CLAGG}{members}
-\cross{CLAGG}{more?}
-\cross{CLAGG}{parts}
-\cross{CLAGG}{reduce}
-\cross{CLAGG}{remove}
-\cross{CLAGG}{removeDuplicates}
-\cross{CLAGG}{sample}
-\cross{CLAGG}{select}
-\cross{CLAGG}{size?}
-\cross{CLAGG}{\#?}
-\cross{CLAGG}{?=?}
-\cross{CLAGG}{?\~{}=?}
-
These are directly exported but not implemented:
\begin{verbatim}
construct: List S -> %
@@ -2506,53 +2457,46 @@
\pagefrom{HomogeneousAggregate}{HOAGG}
{\bf Exports:}\\
-\begin{tabular}{lllllll}
- any? & coerce & copy & count & elt & empty & empty? \\
- entries & entry? & eq? & eval & every? & fill! & first \\
- hash & index? & indices & latex & less? & map & map! \\
- maxIndex & member? & members & minIndex & more? & parts & qelt \\
- qsetelt! & sample & setelt & size? & swap! & ?.? & ?\~{}=?\\
- \#? & ?=? & & & & &\\
+\begin{tabular}{lllll}
+\cross{IXAGG}{any?} &
+\cross{IXAGG}{coerce} &
+\cross{IXAGG}{copy} &
+\cross{IXAGG}{count} &
+\cross{IXAGG}{elt} \\
+\cross{IXAGG}{empty} &
+\cross{IXAGG}{empty?} &
+\cross{IXAGG}{entries} &
+\cross{IXAGG}{entry?} &
+\cross{IXAGG}{eq?} \\
+\cross{IXAGG}{eval} &
+\cross{IXAGG}{every?} &
+\cross{IXAGG}{fill!} &
+\cross{IXAGG}{first} &
+\cross{IXAGG}{hash} \\
+\cross{IXAGG}{index?} &
+\cross{IXAGG}{indices} &
+\cross{IXAGG}{latex} &
+\cross{IXAGG}{less?} &
+\cross{IXAGG}{map} \\
+\cross{IXAGG}{map!} &
+\cross{IXAGG}{maxIndex} &
+\cross{IXAGG}{member?} &
+\cross{IXAGG}{members} &
+\cross{IXAGG}{minIndex} \\
+\cross{IXAGG}{more?} &
+\cross{IXAGG}{parts} &
+\cross{IXAGG}{qelt} &
+\cross{IXAGG}{qsetelt!} &
+\cross{IXAGG}{sample} \\
+\cross{IXAGG}{setelt} &
+\cross{IXAGG}{size?} &
+\cross{IXAGG}{swap!} &
+\cross{IXAGG}{?.?} &
+\cross{IXAGG}{?\~{}=?} \\
+\cross{IXAGG}{\#?} &
+\cross{IXAGG}{?=?} &&&
\end{tabular}
-\cross{IXAGG}{any?}
-\cross{IXAGG}{coerce}
-\cross{IXAGG}{copy}
-\cross{IXAGG}{count}
-\cross{IXAGG}{elt}
-\cross{IXAGG}{empty}
-\cross{IXAGG}{empty?}
-\cross{IXAGG}{entries}
-\cross{IXAGG}{entry?}
-\cross{IXAGG}{eq?}
-\cross{IXAGG}{eval}
-\cross{IXAGG}{every?}
-\cross{IXAGG}{fill!}
-\cross{IXAGG}{first}
-\cross{IXAGG}{hash}
-\cross{IXAGG}{index?}
-\cross{IXAGG}{indices}
-\cross{IXAGG}{latex}
-\cross{IXAGG}{less?}
-\cross{IXAGG}{map}
-\cross{IXAGG}{map!}
-\cross{IXAGG}{maxIndex}
-\cross{IXAGG}{member?}
-\cross{IXAGG}{members}
-\cross{IXAGG}{minIndex}
-\cross{IXAGG}{more?}
-\cross{IXAGG}{parts}
-\cross{IXAGG}{qelt}
-\cross{IXAGG}{qsetelt!}
-\cross{IXAGG}{sample}
-\cross{IXAGG}{setelt}
-\cross{IXAGG}{size?}
-\cross{IXAGG}{swap!}
-\cross{IXAGG}{?.?}
-\cross{IXAGG}{?\~{}=?}
-\cross{IXAGG}{\#?}
-\cross{IXAGG}{?=?}
-
These are directly exported but not implemented:
\begin{verbatim}
index? : (Index,%) -> Boolean
@@ -2770,30 +2714,28 @@
\pagepic{ps/v102monoid.ps}{MONOID}{0.75}
{\bf See:}\\
+\pageto{Group}{GROUP}
\pageto{OrderedMonoid}{ORDMON}
+\pageto{OrderedRing}{ORDRING}
+\pageto{Ring}{RING}
\pagefrom{SemiGroup}{SGROUP}
{\bf Exports:}\\
\begin{tabular}{lllll}
- 1 & coerce & hash & latex & one?\\
- recip & sample & ?*? & ?=? & ?\~{}=?\\
- ?**? & ?\^{}? & ?\^{}? &&\\
+\cross{MONOID}{1} &
+\cross{MONOID}{coerce} &
+\cross{MONOID}{hash} &
+\cross{MONOID}{latex} &
+\cross{MONOID}{one?} \\
+\cross{MONOID}{recip} &
+\cross{MONOID}{sample} &
+\cross{MONOID}{?*?} &
+\cross{MONOID}{?=?} &
+\cross{MONOID}{?\~{}=?} \\
+\cross{MONOID}{?**?} &
+\cross{MONOID}{?\^{}?} &&&
\end{tabular}
-\cross{MONOID}{1}
-\cross{MONOID}{coerce}
-\cross{MONOID}{hash}
-\cross{MONOID}{latex}
-\cross{MONOID}{one?}
-\cross{MONOID}{recip}
-\cross{MONOID}{sample}
-\cross{MONOID}{?*?}
-\cross{MONOID}{?=?}
-\cross{MONOID}{?\~{}=?}
-\cross{MONOID}{?**?}
-\cross{MONOID}{?\^{}?}
-
-
These are directly exported but not implemented:
\begin{verbatim}
1 : () -> %
@@ -2931,27 +2873,23 @@
{\bf Exports:}\\
\begin{tabular}{lllll}
- coerce & hash & index & latex & lookup \\
- max & min & random & size & ?\~{}=? \\
- ?$<$? & ?$<=$? & ?=? & ?$>$? & ?$>=$? \\
+\cross{ORDFIN}{coerce} &
+\cross{ORDFIN}{hash} &
+\cross{ORDFIN}{index} &
+\cross{ORDFIN}{latex} &
+\cross{ORDFIN}{lookup} \\
+\cross{ORDFIN}{max} &
+\cross{ORDFIN}{min} &
+\cross{ORDFIN}{random} &
+\cross{ORDFIN}{size} &
+\cross{ORDFIN}{?\~{}=?} \\
+\cross{ORDFIN}{?$<$?} &
+\cross{ORDFIN}{?$<=$?} &
+\cross{ORDFIN}{?=?} &
+\cross{ORDFIN}{?$>$?} &
+\cross{ORDFIN}{?$>=$?} \\
\end{tabular}
-\cross{ORDFIN}{coerce}
-\cross{ORDFIN}{hash}
-\cross{ORDFIN}{index}
-\cross{ORDFIN}{latex}
-\cross{ORDFIN}{lookup}
-\cross{ORDFIN}{max}
-\cross{ORDFIN}{min}
-\cross{ORDFIN}{random}
-\cross{ORDFIN}{size}
-\cross{ORDFIN}{?\~{}=?}
-\cross{ORDFIN}{?$<$?}
-\cross{ORDFIN}{?$<=$?}
-\cross{ORDFIN}{?=?}
-\cross{ORDFIN}{?$>$?}
-\cross{ORDFIN}{?$>=$?}
-
These exports come from OrderedSet():
\begin{verbatim}
coerce : % -> OutputForm
@@ -3050,52 +2988,45 @@
\pagefrom{HomogeneousAggregate}{HOAGG}
{\bf Exports:}\\
-\begin{tabular}{llllll}
- any? & child? & children & coerce & copy & count \\
- cyclic? & distance & empty & empty? & eq? & eval \\
- every? & hash & latex & leaf? & leaves & less? \\
- map & map! & member? & members & more? & nodes \\
- node? & parts & sample & setchildren! & setelt & setvalue!\\
- size? & value & ?.value & ?\~{}=? & \#? & ?=? \\
+\begin{tabular}{lllll}
+\cross{RCAGG}{any?} &
+\cross{RCAGG}{child?} &
+\cross{RCAGG}{children} &
+\cross{RCAGG}{coerce} &
+\cross{RCAGG}{copy} \\
+\cross{RCAGG}{count} &
+\cross{RCAGG}{cyclic?} &
+\cross{RCAGG}{distance} &
+\cross{RCAGG}{empty} &
+\cross{RCAGG}{empty?} \\
+\cross{RCAGG}{eq?} &
+\cross{RCAGG}{eval} &
+\cross{RCAGG}{every?} &
+\cross{RCAGG}{hash} &
+\cross{RCAGG}{latex} \\
+\cross{RCAGG}{leaf?} &
+\cross{RCAGG}{leaves} &
+\cross{RCAGG}{less?} &
+\cross{RCAGG}{map} &
+\cross{RCAGG}{map!} \\
+\cross{RCAGG}{member?} &
+\cross{RCAGG}{members} &
+\cross{RCAGG}{more?} &
+\cross{RCAGG}{nodes} &
+\cross{RCAGG}{node?} \\
+\cross{RCAGG}{parts} &
+\cross{RCAGG}{sample} &
+\cross{RCAGG}{setchildren!} &
+\cross{RCAGG}{setelt} &
+\cross{RCAGG}{setvalue!} \\
+\cross{RCAGG}{size?} &
+\cross{RCAGG}{value} &
+\cross{RCAGG}{?.value} &
+\cross{RCAGG}{?\~{}=?} &
+\cross{RCAGG}{\#?} \\
+\cross{RCAGG}{?=?} &&&&
\end{tabular}
-\cross{RCAGG}{any?}
-\cross{RCAGG}{child?}
-\cross{RCAGG}{children}
-\cross{RCAGG}{coerce}
-\cross{RCAGG}{copy}
-\cross{RCAGG}{count}
-\cross{RCAGG}{cyclic?}
-\cross{RCAGG}{distance}
-\cross{RCAGG}{empty}
-\cross{RCAGG}{empty?}
-\cross{RCAGG}{eq?}
-\cross{RCAGG}{eval}
-\cross{RCAGG}{every?}
-\cross{RCAGG}{hash}
-\cross{RCAGG}{latex}
-\cross{RCAGG}{leaf?}
-\cross{RCAGG}{leaves}
-\cross{RCAGG}{less?}
-\cross{RCAGG}{map}
-\cross{RCAGG}{map!}
-\cross{RCAGG}{member?}
-\cross{RCAGG}{members}
-\cross{RCAGG}{more?}
-\cross{RCAGG}{nodes}
-\cross{RCAGG}{node?}
-\cross{RCAGG}{parts}
-\cross{RCAGG}{sample}
-\cross{RCAGG}{setchildren!}
-\cross{RCAGG}{setelt}
-\cross{RCAGG}{setvalue!}
-\cross{RCAGG}{size?}
-\cross{RCAGG}{value}
-\cross{RCAGG}{?.value}
-\cross{RCAGG}{?\~{}=?}
-\cross{RCAGG}{\#?}
-\cross{RCAGG}{?=?}
-
These are directly exported but not implemented:
\begin{verbatim}
children : % -> List %
@@ -3262,66 +3193,51 @@
\pagefrom{RecursiveAggregate}{RCAGG}
{\bf Exports:}\\
-\begin{tabular}{llllll}
- any? & children & child? & coerce & copy & count \\
- count & cyclic? & distance & empty & empty? & eq? \\
- eval & eval & eval & eval & every? & hash \\
- latex & leaf? & leaves & left & less? & map \\
- map! & member? & members & more? & nodes & node? \\
- parts & right & sample & setchildren! & setelt & setelt \\
- setelt & setleft! & setright! & setvalue! & size? & value \\
- \#? & ?=? & ?\~{}=? & ?.right & ?.left & ?.value \\
+\begin{tabular}{lllll}
+\cross{BRAGG}{any?} &
+\cross{BRAGG}{children} &
+\cross{BRAGG}{child?} &
+\cross{BRAGG}{coerce} &
+\cross{BRAGG}{copy} \\
+\cross{BRAGG}{count} &
+\cross{BRAGG}{cyclic?} &
+\cross{BRAGG}{distance} &
+\cross{BRAGG}{empty} &
+\cross{BRAGG}{empty?} \\
+\cross{BRAGG}{eq?} &
+\cross{BRAGG}{eval} &
+\cross{BRAGG}{every?} &
+\cross{BRAGG}{hash} &
+\cross{BRAGG}{latex} \\
+\cross{BRAGG}{leaf?} &
+\cross{BRAGG}{leaves} &
+\cross{BRAGG}{left} &
+\cross{BRAGG}{less?} &
+\cross{BRAGG}{map} \\
+\cross{BRAGG}{map!} &
+\cross{BRAGG}{member?} &
+\cross{BRAGG}{members} &
+\cross{BRAGG}{more?} &
+\cross{BRAGG}{nodes} \\
+\cross{BRAGG}{node?} &
+\cross{BRAGG}{parts} &
+\cross{BRAGG}{right} &
+\cross{BRAGG}{sample} &
+\cross{BRAGG}{setchildren!} \\
+\cross{BRAGG}{setelt} &
+\cross{BRAGG}{setleft!} &
+\cross{BRAGG}{setright!} &
+\cross{BRAGG}{setvalue!} &
+\cross{BRAGG}{size?} \\
+\cross{BRAGG}{value} &
+\cross{BRAGG}{\#?} &
+\cross{BRAGG}{?=?} &
+\cross{BRAGG}{?\~{}=?} &
+\cross{BRAGG}{?.right} \\
+\cross{BRAGG}{?.left} &
+\cross{BRAGG}{?.value} &&&
\end{tabular}
-\cross{BRAGG}{any?}
-\cross{BRAGG}{children}
-\cross{BRAGG}{child?}
-\cross{BRAGG}{coerce}
-\cross{BRAGG}{copy}
-\cross{BRAGG}{count}
-\cross{BRAGG}{count}
-\cross{BRAGG}{cyclic?}
-\cross{BRAGG}{distance}
-\cross{BRAGG}{empty}
-\cross{BRAGG}{empty?}
-\cross{BRAGG}{eq?}
-\cross{BRAGG}{eval}
-\cross{BRAGG}{eval}
-\cross{BRAGG}{eval}
-\cross{BRAGG}{eval}
-\cross{BRAGG}{every?}
-\cross{BRAGG}{hash}
-\cross{BRAGG}{latex}
-\cross{BRAGG}{leaf?}
-\cross{BRAGG}{leaves}
-\cross{BRAGG}{left}
-\cross{BRAGG}{less?}
-\cross{BRAGG}{map}
-\cross{BRAGG}{map!}
-\cross{BRAGG}{member?}
-\cross{BRAGG}{members}
-\cross{BRAGG}{more?}
-\cross{BRAGG}{nodes}
-\cross{BRAGG}{node?}
-\cross{BRAGG}{parts}
-\cross{BRAGG}{right}
-\cross{BRAGG}{sample}
-\cross{BRAGG}{setchildren!}
-\cross{BRAGG}{setelt}
-\cross{BRAGG}{setelt}
-\cross{BRAGG}{setelt}
-\cross{BRAGG}{setleft!}
-\cross{BRAGG}{setright!}
-\cross{BRAGG}{setvalue!}
-\cross{BRAGG}{size?}
-\cross{BRAGG}{value}
-\cross{BRAGG}{\#?}
-\cross{BRAGG}{?=?}
-\cross{BRAGG}{?\~{}=?}
-\cross{BRAGG}{?.right}
-\cross{BRAGG}{?.left}
-\cross{BRAGG}{?.value}
-
These are directly exported but not implemented:
\begin{verbatim}
left : % -> %
@@ -3546,27 +3462,24 @@
{\bf See:}\\
\pageto{AbelianGroup}{ABELGRP}
+\pageto{OrderedCancellationAbelianMonoid}{OCAMON}
\pagefrom{AbelianMonoid}{ABELMON}
{\bf Exports:}\\
\begin{tabular}{lllll}
- 0 & coerce & hash & latex & sample\\
- subtractIfCan & zero? & ?\~{}=? & ?*? & ?+?\\
- ?=?&&&&
+\cross{CABMON}{0} &
+\cross{CABMON}{coerce} &
+\cross{CABMON}{hash} &
+\cross{CABMON}{latex} &
+\cross{CABMON}{sample} \\
+\cross{CABMON}{subtractIfCan} &
+\cross{CABMON}{zero?} &
+\cross{CABMON}{?\~{}=?} &
+\cross{CABMON}{?*?} &
+\cross{CABMON}{?+?} \\
+\cross{CABMON}{?=?} &&&&
\end{tabular}
-\cross{CABMON}{0}
-\cross{CABMON}{coerce}
-\cross{CABMON}{hash}
-\cross{CABMON}{latex}
-\cross{CABMON}{sample}
-\cross{CABMON}{subtractIfCan}
-\cross{CABMON}{zero?}
-\cross{CABMON}{?\~{}=?}
-\cross{CABMON}{?*?}
-\cross{CABMON}{?+?}
-\cross{CABMON}{?=?}
-
These are directly exported but not implemented:
\begin{verbatim}
subtractIfCan : (%,%) -> Union(%,"failed")
@@ -3677,54 +3590,46 @@
\pagefrom{Collection}{CLAGG}
{\bf Exports:}\\
-\begin{tabular}{llllll}
- any? & bag & coerce & construct & convert & copy \\
- count & dictionary & empty & empty? & eq? & eval \\
- every? & extract! & find & hash & insert! & inspect \\
- latex & less? & map & map! & member? & members \\
- more? & parts & reduce & remove & remove! & removeDuplicates \\
- sample & select & select! & size? & \#? & ?=? \\
- ?\~{}=? &&&&&\\
+\begin{tabular}{lllll}
+\cross{DIOPS}{any?} &
+\cross{DIOPS}{bag} &
+\cross{DIOPS}{coerce} &
+\cross{DIOPS}{construct} &
+\cross{DIOPS}{convert} \\
+\cross{DIOPS}{copy} &
+\cross{DIOPS}{count} &
+\cross{DIOPS}{dictionary} &
+\cross{DIOPS}{empty} &
+\cross{DIOPS}{empty?} \\
+\cross{DIOPS}{eq?} &
+\cross{DIOPS}{eval} &
+\cross{DIOPS}{every?} &
+\cross{DIOPS}{extract!} &
+\cross{DIOPS}{find} \\
+\cross{DIOPS}{hash} &
+\cross{DIOPS}{insert!} &
+\cross{DIOPS}{inspect} &
+\cross{DIOPS}{latex} &
+\cross{DIOPS}{less?} \\
+\cross{DIOPS}{map} &
+\cross{DIOPS}{map!} &
+\cross{DIOPS}{member?} &
+\cross{DIOPS}{members} &
+\cross{DIOPS}{more?} \\
+\cross{DIOPS}{parts} &
+\cross{DIOPS}{reduce} &
+\cross{DIOPS}{remove} &
+\cross{DIOPS}{remove!} &
+\cross{DIOPS}{removeDuplicates} \\
+\cross{DIOPS}{sample} &
+\cross{DIOPS}{select} &
+\cross{DIOPS}{select!} &
+\cross{DIOPS}{size?} &
+\cross{DIOPS}{\#?} \\
+\cross{DIOPS}{?=?} &
+\cross{DIOPS}{?\~{}=?} &&&
\end{tabular}
-\cross{DIOPS}{any?}
-\cross{DIOPS}{bag}
-\cross{DIOPS}{coerce}
-\cross{DIOPS}{construct}
-\cross{DIOPS}{convert}
-\cross{DIOPS}{copy}
-\cross{DIOPS}{count}
-\cross{DIOPS}{dictionary}
-\cross{DIOPS}{empty}
-\cross{DIOPS}{empty?}
-\cross{DIOPS}{eq?}
-\cross{DIOPS}{eval}
-\cross{DIOPS}{every?}
-\cross{DIOPS}{extract!}
-\cross{DIOPS}{find}
-\cross{DIOPS}{hash}
-\cross{DIOPS}{insert!}
-\cross{DIOPS}{inspect}
-\cross{DIOPS}{latex}
-\cross{DIOPS}{less?}
-\cross{DIOPS}{map}
-\cross{DIOPS}{map!}
-\cross{DIOPS}{member?}
-\cross{DIOPS}{members}
-\cross{DIOPS}{more?}
-\cross{DIOPS}{parts}
-\cross{DIOPS}{reduce}
-\cross{DIOPS}{remove}
-\cross{DIOPS}{remove!}
-\cross{DIOPS}{removeDuplicates}
-\cross{DIOPS}{sample}
-\cross{DIOPS}{select}
-\cross{DIOPS}{select!}
-\cross{DIOPS}{size?}
-\cross{DIOPS}{\#?}
-\cross{DIOPS}{?=?}
-\cross{DIOPS}{?\~{}=?}
-
These are directly exported but not implemented:
\begin{verbatim}
dictionary : List S -> %
@@ -3902,66 +3807,57 @@
\pagefrom{RecursiveAggregate}{RCAGG}
{\bf Exports:}\\
-\begin{tabular}{llllll}
- any? & children & child? & coerce & concat! & copy \\
- count & count & cyclic? & distance & empty & empty? \\
- eq? & eval & eval & eval & eval & every? \\
- hash & head & last & latex & leaf? & leaves \\
- less? & map & map! & member? & members & more? \\
- next & nodes & node? & parts & previous & sample \\
- setchildren! & setelt & setnext! & setprevious! & setvalue! & size? \\
- tail & value & \#? & ?=? & ?\~{}=? & ?.value \\
+\begin{tabular}{lllll}
+\cross{DLAGG}{any?} &
+\cross{DLAGG}{children} &
+\cross{DLAGG}{child?} &
+\cross{DLAGG}{coerce} &
+\cross{DLAGG}{concat!} \\
+\cross{DLAGG}{copy} &
+\cross{DLAGG}{count} &
+\cross{DLAGG}{count} &
+\cross{DLAGG}{cyclic?} &
+\cross{DLAGG}{distance} \\
+\cross{DLAGG}{empty} &
+\cross{DLAGG}{empty?} &
+\cross{DLAGG}{eq?} &
+\cross{DLAGG}{eval} &
+\cross{DLAGG}{eval} \\
+\cross{DLAGG}{eval} &
+\cross{DLAGG}{eval} &
+\cross{DLAGG}{every?} &
+\cross{DLAGG}{hash} &
+\cross{DLAGG}{head} \\
+\cross{DLAGG}{last} &
+\cross{DLAGG}{latex} &
+\cross{DLAGG}{leaf?} &
+\cross{DLAGG}{leaves} &
+\cross{DLAGG}{less?} \\
+\cross{DLAGG}{map} &
+\cross{DLAGG}{map!} &
+\cross{DLAGG}{member?} &
+\cross{DLAGG}{members} &
+\cross{DLAGG}{more?} \\
+\cross{DLAGG}{next} &
+\cross{DLAGG}{nodes} &
+\cross{DLAGG}{node?} &
+\cross{DLAGG}{parts} &
+\cross{DLAGG}{previous} \\
+\cross{DLAGG}{sample} &
+\cross{DLAGG}{setchildren!} &
+\cross{DLAGG}{setelt} &
+\cross{DLAGG}{setnext!} &
+\cross{DLAGG}{setprevious!} \\
+\cross{DLAGG}{setvalue!} &
+\cross{DLAGG}{size?} &
+\cross{DLAGG}{tail} &
+\cross{DLAGG}{value} &
+\cross{DLAGG}{\#?} \\
+\cross{DLAGG}{?=?} &
+\cross{DLAGG}{?\~{}=?} &
+\cross{DLAGG}{?.value} &&
\end{tabular}
-\cross{DLAGG}{any?}
-\cross{DLAGG}{children}
-\cross{DLAGG}{child?}
-\cross{DLAGG}{coerce}
-\cross{DLAGG}{concat!}
-\cross{DLAGG}{copy}
-\cross{DLAGG}{count}
-\cross{DLAGG}{count}
-\cross{DLAGG}{cyclic?}
-\cross{DLAGG}{distance}
-\cross{DLAGG}{empty}
-\cross{DLAGG}{empty?}
-\cross{DLAGG}{eq?}
-\cross{DLAGG}{eval}
-\cross{DLAGG}{eval}
-\cross{DLAGG}{eval}
-\cross{DLAGG}{eval}
-\cross{DLAGG}{every?}
-\cross{DLAGG}{hash}
-\cross{DLAGG}{head}
-\cross{DLAGG}{last}
-\cross{DLAGG}{latex}
-\cross{DLAGG}{leaf?}
-\cross{DLAGG}{leaves}
-\cross{DLAGG}{less?}
-\cross{DLAGG}{map}
-\cross{DLAGG}{map!}
-\cross{DLAGG}{member?}
-\cross{DLAGG}{members}
-\cross{DLAGG}{more?}
-\cross{DLAGG}{next}
-\cross{DLAGG}{nodes}
-\cross{DLAGG}{node?}
-\cross{DLAGG}{parts}
-\cross{DLAGG}{previous}
-\cross{DLAGG}{sample}
-\cross{DLAGG}{setchildren!}
-\cross{DLAGG}{setelt}
-\cross{DLAGG}{setnext!}
-\cross{DLAGG}{setprevious!}
-\cross{DLAGG}{setvalue!}
-\cross{DLAGG}{size?}
-\cross{DLAGG}{tail}
-\cross{DLAGG}{value}
-\cross{DLAGG}{\#?}
-\cross{DLAGG}{?=?}
-\cross{DLAGG}{?\~{}=?}
-\cross{DLAGG}{?.value}
-
These are directly exported but not implemented:
\begin{verbatim}
concat! : (%,%) -> % if $ has shallowlyMutable
@@ -4111,6 +4007,176 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{Group}{GROUP}
+\pagepic{ps/v102group.ps}{GROUP}{0.65}
+
+{\bf See:}\\
+\pagefrom{Monoid}{MONOID}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+\cross{GROUP}{1} &
+\cross{GROUP}{coerce} &
+\cross{GROUP}{commutator} &
+\cross{GROUP}{conjugate} &
+\cross{GROUP}{hash} \\
+\cross{GROUP}{inv} &
+\cross{GROUP}{latex} &
+\cross{GROUP}{one?} &
+\cross{GROUP}{recip} &
+\cross{GROUP}{sample} \\
+\cross{GROUP}{?\~{}=?} &
+\cross{GROUP}{?*?} &
+\cross{GROUP}{?**?} &
+\cross{GROUP}{?/?} &
+\cross{GROUP}{?=?} \\
+\cross{GROUP}{?\^{}?} &&&&
+\end{tabular}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ inv : % -> %
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ commutator : (%,%) -> %
+ conjugate : (%,%) -> %
+ recip : % -> Union(%,"failed")
+ ?/? : (%,%) -> %
+ ?^? : (%,Integer) -> %
+ ?**? : (%,Integer) -> %
+\end{verbatim}
+
+These exports come from Aggregate:
+\begin{verbatim}
+\end{verbatim}
+
+These exports come from Monoid():
+\begin{verbatim}
+ 1 : () -> %
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ one? : % -> Boolean
+ sample : () -> %
+ ?^? : (%,NonNegativeInteger) -> %
+ ?^? : (%,PositiveInteger) -> %
+ ?**? : (%,NonNegativeInteger) -> %
+ ?**? : (%,PositiveInteger) -> %
+ ?*? : (%,%) -> %
+ ?=? : (%,%) -> Boolean
+ ?~=? : (%,%) -> Boolean
+\end{verbatim}
+
+<<category GROUP Group>>=
+)abbrev category GROUP Group
+++ Author:
+++ Date Created:
+++ Date Last Updated:
+++ Basic Functions:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++ The class of multiplicative groups, i.e. monoids with
+++ multiplicative inverses.
+++
+++ Axioms:
+++ \spad{leftInverse("*":(%,%)->%,inv)}\tab{30}\spad{ inv(x)*x = 1 }
+++ \spad{rightInverse("*":(%,%)->%,inv)}\tab{30}\spad{ x*inv(x) = 1 }
+Group(): Category == Monoid with
+ inv: % -> %
+ ++ inv(x) returns the inverse of x.
+ "/": (%,%) -> %
+ ++ x/y is the same as x times the inverse of y.
+ "**": (%,Integer) -> %
+ ++ x**n returns x raised to the integer power n.
+ "^": (%,Integer) -> %
+ ++ x^n returns x raised to the integer power n.
+ unitsKnown
+ ++ unitsKnown asserts that recip only returns
+ ++ "failed" for non-units.
+ conjugate: (%,%) -> %
+ ++ conjugate(p,q) computes \spad{inv(q) * p * q}; this is
+ ++ 'right action by conjugation'.
+ commutator: (%,%) -> %
+ ++ commutator(p,q) computes \spad{inv(p) * inv(q) * p * q}.
+ add
+ import RepeatedSquaring(%)
+ x:% / y:% == x*inv(y)
+ recip(x:%) == inv(x)
+ _^(x:%, n:Integer):% == x ** n
+ x:% ** n:Integer ==
+ zero? n => 1
+ n<0 => expt(inv(x),(-n) pretend PositiveInteger)
+ expt(x,n pretend PositiveInteger)
+ conjugate(p,q) == inv(q) * p * q
+ commutator(p,q) == inv(p) * inv(q) * p * q
+
+@
+<<GROUP.dotabb>>=
+"GROUP"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=GROUP"];
+"GROUP" -> "MONOID"
+
+@
+<<GROUP.dotfull>>=
+"Group()"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=GROUP"];
+"Group()" -> "Monoid()"
+
+@
+<<GROUP.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"Group()" [color=lightblue];
+"Group()" -> "Monoid()"
+"Group()" -> "RepeatedSquaring(Group)"
+
+"Monoid()" [color=lightblue];
+"Monoid()" -> "SemiGroup()"
+
+"SemiGroup()" [color=lightblue];
+"SemiGroup()" -> "SetCategory()"
+"SemiGroup()" -> "RepeatedSquaring(SemiGroup)"
+
+"SetCategory()" [color=lightblue];
+"SetCategory()" -> "BasicType()"
+"SetCategory()" -> "CoercibleTo(OutputForm)"
+
+"BasicType()" [color=lightblue];
+"BasicType()" -> "Category"
+
+"CoercibleTo(OutputForm)" [color=seagreen];
+"CoercibleTo(OutputForm)" -> "CoercibleTo(a:Type)"
+
+"CoercibleTo(a:Type)" [color=lightblue];
+"CoercibleTo(a:Type)" -> "Category"
+
+"RepeatedSquaring(Group)" [color="#00EE00"];
+"RepeatedSquaring(Group)" -> "RepeatedSquaring(a:SetCategory)"
+
+"RepeatedSquaring(SemiGroup)" [color="#00EE00"];
+"RepeatedSquaring(SemiGroup)" -> "RepeatedSquaring(a:SetCategory)"
+
+"RepeatedSquaring(a:SetCategory)" [color="#00EE00"];
+"RepeatedSquaring(a:SetCategory)" -> "Package"
+
+"Package" [color="#00EE00"];
+
+"Category" [color=lightblue];
+
+}
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{LinearAggregate}{LNAGG}
\pagepic{ps/v102linearaggregate.ps}{LNAGG}{1.00}
@@ -4123,72 +4189,60 @@
{\bf Exports:}\\
\begin{tabular}{lllll}
- any? & coerce & concat & construct & convert \\
- copy & count & delete & elt & empty \\
- empty? & entries & entry? & eq? & eval \\
- every? & fill! & find & first & hash \\
- index? & indices & insert & latex & less? \\
- map & map! & maxIndex & member? & members \\
- minIndex & more? & new & parts & qelt \\
- qsetelt! & reduce & reduce & reduce & remove \\
- remove & removeDuplicates & sample & select & setelt \\
- setelt & size? & swap! & ?\~{}=? & \#? \\
- ?=? & ?.? &&&\\
+\cross{LNAGG}{any?} &
+\cross{LNAGG}{coerce} &
+\cross{LNAGG}{concat} &
+\cross{LNAGG}{construct} &
+\cross{LNAGG}{convert} \\
+\cross{LNAGG}{copy} &
+\cross{LNAGG}{count} &
+\cross{LNAGG}{delete} &
+\cross{LNAGG}{elt} &
+\cross{LNAGG}{empty} \\
+\cross{LNAGG}{empty?} &
+\cross{LNAGG}{entries} &
+\cross{LNAGG}{entry?} &
+\cross{LNAGG}{eq?} &
+\cross{LNAGG}{eval} \\
+\cross{LNAGG}{every?} &
+\cross{LNAGG}{fill!} &
+\cross{LNAGG}{find} &
+\cross{LNAGG}{first} &
+\cross{LNAGG}{hash} \\
+\cross{LNAGG}{index?} &
+\cross{LNAGG}{indices} &
+\cross{LNAGG}{insert} &
+\cross{LNAGG}{latex} &
+\cross{LNAGG}{less?} \\
+\cross{LNAGG}{map} &
+\cross{LNAGG}{map!} &
+\cross{LNAGG}{maxIndex} &
+\cross{LNAGG}{member?} &
+\cross{LNAGG}{members} \\
+\cross{LNAGG}{minIndex} &
+\cross{LNAGG}{more?} &
+\cross{LNAGG}{new} &
+\cross{LNAGG}{parts} &
+\cross{LNAGG}{qelt} \\
+\cross{LNAGG}{qsetelt!} &
+\cross{LNAGG}{reduce} &
+\cross{LNAGG}{reduce} &
+\cross{LNAGG}{reduce} &
+\cross{LNAGG}{remove} \\
+\cross{LNAGG}{remove} &
+\cross{LNAGG}{removeDuplicates} &
+\cross{LNAGG}{sample} &
+\cross{LNAGG}{select} &
+\cross{LNAGG}{setelt} \\
+\cross{LNAGG}{setelt} &
+\cross{LNAGG}{size?} &
+\cross{LNAGG}{swap!} &
+\cross{LNAGG}{?\~{}=?} &
+\cross{LNAGG}{\#?} \\
+\cross{LNAGG}{?=?} &
+\cross{LNAGG}{?.?} &&&
\end{tabular}
-\cross{LNAGG}{any?}
-\cross{LNAGG}{coerce}
-\cross{LNAGG}{concat}
-\cross{LNAGG}{construct}
-\cross{LNAGG}{convert}
-\cross{LNAGG}{copy}
-\cross{LNAGG}{count}
-\cross{LNAGG}{delete}
-\cross{LNAGG}{elt}
-\cross{LNAGG}{empty}
-\cross{LNAGG}{empty?}
-\cross{LNAGG}{entries}
-\cross{LNAGG}{entry?}
-\cross{LNAGG}{eq?}
-\cross{LNAGG}{eval}
-\cross{LNAGG}{every?}
-\cross{LNAGG}{fill!}
-\cross{LNAGG}{find}
-\cross{LNAGG}{first}
-\cross{LNAGG}{hash}
-\cross{LNAGG}{index?}
-\cross{LNAGG}{indices}
-\cross{LNAGG}{insert}
-\cross{LNAGG}{latex}
-\cross{LNAGG}{less?}
-\cross{LNAGG}{map}
-\cross{LNAGG}{map!}
-\cross{LNAGG}{maxIndex}
-\cross{LNAGG}{member?}
-\cross{LNAGG}{members}
-\cross{LNAGG}{minIndex}
-\cross{LNAGG}{more?}
-\cross{LNAGG}{new}
-\cross{LNAGG}{parts}
-\cross{LNAGG}{qelt}
-\cross{LNAGG}{qsetelt!}
-\cross{LNAGG}{reduce}
-\cross{LNAGG}{reduce}
-\cross{LNAGG}{reduce}
-\cross{LNAGG}{remove}
-\cross{LNAGG}{remove}
-\cross{LNAGG}{removeDuplicates}
-\cross{LNAGG}{sample}
-\cross{LNAGG}{select}
-\cross{LNAGG}{setelt}
-\cross{LNAGG}{setelt}
-\cross{LNAGG}{size?}
-\cross{LNAGG}{swap!}
-\cross{LNAGG}{?\~{}=?}
-\cross{LNAGG}{\#?}
-\cross{LNAGG}{?=?}
-\cross{LNAGG}{?.?}
-
These are directly exported but not implemented:
\begin{verbatim}
concat : (%,%) -> %
@@ -4425,28 +4479,25 @@
\pagefrom{OrderedSet}{ORDSET}
{\bf Exports:}\\
-\begin{tabular}{llllllll}
- 0 & coerce & hash & latex & max & min & sample & zero?\\
- ?\~{}=? & ?*? & ?+? & ?$<$? & ?$<=$? & ?=? & ?$>$? & ?$>=$?
+\begin{tabular}{lllll}
+\cross{OASGP}{0} &
+\cross{OASGP}{coerce} &
+\cross{OASGP}{hash} &
+\cross{OASGP}{latex} &
+\cross{OASGP}{max} \\
+\cross{OASGP}{min} &
+\cross{OASGP}{sample} &
+\cross{OASGP}{zero?} &
+\cross{OASGP}{?\~{}=?} &
+\cross{OASGP}{?*?} \\
+\cross{OASGP}{?+?} &
+\cross{OASGP}{?$<$?} &
+\cross{OASGP}{?$<=$?} &
+\cross{OASGP}{?=?} &
+\cross{OASGP}{?$>$?} \\
+\cross{OASGP}{?$>=$?} &&&&
\end{tabular}
-\cross{OASGP}{0}
-\cross{OASGP}{coerce}
-\cross{OASGP}{hash}
-\cross{OASGP}{latex}
-\cross{OASGP}{max}
-\cross{OASGP}{min}
-\cross{OASGP}{sample}
-\cross{OASGP}{zero?}
-\cross{OASGP}{?\~{}=?}
-\cross{OASGP}{?*?}
-\cross{OASGP}{?+?}
-\cross{OASGP}{?$<$?}
-\cross{OASGP}{?$<=$?}
-\cross{OASGP}{?=?}
-\cross{OASGP}{?$>$?}
-\cross{OASGP}{?$>=$?}
-
These exports come from OrderedSet():
\begin{verbatim}
coerce : % -> OutputForm
@@ -4559,31 +4610,27 @@
\pagefrom{OrderedSet}{ORDSET}
{\bf Exports:}\\
-\begin{tabular}{llllll}
- 1 & coerce & hash & latex & max & min\\
- one? & recip & sample & ?*? & ?**? & ?$<$?\\
- ?$<=$? & ?=? & ?$>$? & ?$>=$? & ?\~{}=? & ?\^{}?\\
+\begin{tabular}{lllll}
+\cross{ORDMON}{1} &
+\cross{ORDMON}{coerce} &
+\cross{ORDMON}{hash} &
+\cross{ORDMON}{latex} &
+\cross{ORDMON}{max} \\
+\cross{ORDMON}{min} &
+\cross{ORDMON}{one?} &
+\cross{ORDMON}{recip} &
+\cross{ORDMON}{sample} &
+\cross{ORDMON}{?*?} \\
+\cross{ORDMON}{?**?} &
+\cross{ORDMON}{?$<$?} &
+\cross{ORDMON}{?$<=$?} &
+\cross{ORDMON}{?=?} &
+\cross{ORDMON}{?$>$?} \\
+\cross{ORDMON}{?$>=$?} &
+\cross{ORDMON}{?\~{}=?} &
+\cross{ORDMON}{?\^{}?} &&
\end{tabular}
-\cross{ORDMON}{1}
-\cross{ORDMON}{coerce}
-\cross{ORDMON}{hash}
-\cross{ORDMON}{latex}
-\cross{ORDMON}{max}
-\cross{ORDMON}{min}
-\cross{ORDMON}{one?}
-\cross{ORDMON}{recip}
-\cross{ORDMON}{sample}
-\cross{ORDMON}{?*?}
-\cross{ORDMON}{?**?}
-\cross{ORDMON}{?$<$?}
-\cross{ORDMON}{?$<=$?}
-\cross{ORDMON}{?=?}
-\cross{ORDMON}{?$>$?}
-\cross{ORDMON}{?$>=$?}
-\cross{ORDMON}{?\~{}=?}
-\cross{ORDMON}{?\^{}?}
-
These exports come from Monoid():
\begin{verbatim}
1 : () -> %
@@ -4704,45 +4751,39 @@
\pagefrom{BagAggregate}{BGAGG}
{\bf Exports:}\\
-\begin{tabular}{lllllll}
- any? & bag & copy & coerce & count & empty & empty? \\
- eq? & eval & every? & extract! & hash & insert! & inspect \\
- latex & less? & map & map! & max & member? & members \\
- merge & merge! & more? & parts & sample & size? & \#? \\
- ?=? & ?\~{}=? &\\
+\begin{tabular}{lllll}
+\cross{PRQAGG}{any?} &
+\cross{PRQAGG}{bag} &
+\cross{PRQAGG}{copy} &
+\cross{PRQAGG}{coerce} &
+\cross{PRQAGG}{count} \\
+\cross{PRQAGG}{empty} &
+\cross{PRQAGG}{empty?} &
+\cross{PRQAGG}{eq?} &
+\cross{PRQAGG}{eval} &
+\cross{PRQAGG}{every?} \\
+\cross{PRQAGG}{extract!} &
+\cross{PRQAGG}{hash} &
+\cross{PRQAGG}{insert!} &
+\cross{PRQAGG}{inspect} &
+\cross{PRQAGG}{latex} \\
+\cross{PRQAGG}{less?} &
+\cross{PRQAGG}{map} &
+\cross{PRQAGG}{map!} &
+\cross{PRQAGG}{max} &
+\cross{PRQAGG}{member?} \\
+\cross{PRQAGG}{members} &
+\cross{PRQAGG}{merge} &
+\cross{PRQAGG}{merge!} &
+\cross{PRQAGG}{more?} &
+\cross{PRQAGG}{parts} \\
+\cross{PRQAGG}{sample} &
+\cross{PRQAGG}{size?} &
+\cross{PRQAGG}{\#?} &
+\cross{PRQAGG}{?=?} &
+\cross{PRQAGG}{?\~{}=?} \\
\end{tabular}
-\cross{PRQAGG}{any?}
-\cross{PRQAGG}{bag}
-\cross{PRQAGG}{copy}
-\cross{PRQAGG}{coerce}
-\cross{PRQAGG}{count}
-\cross{PRQAGG}{empty}
-\cross{PRQAGG}{empty?}
-\cross{PRQAGG}{eq?}
-\cross{PRQAGG}{eval}
-\cross{PRQAGG}{every?}
-\cross{PRQAGG}{extract!}
-\cross{PRQAGG}{hash}
-\cross{PRQAGG}{insert!}
-\cross{PRQAGG}{inspect}
-\cross{PRQAGG}{latex}
-\cross{PRQAGG}{less?}
-\cross{PRQAGG}{map}
-\cross{PRQAGG}{map!}
-\cross{PRQAGG}{max}
-\cross{PRQAGG}{member?}
-\cross{PRQAGG}{members}
-\cross{PRQAGG}{merge}
-\cross{PRQAGG}{merge!}
-\cross{PRQAGG}{more?}
-\cross{PRQAGG}{parts}
-\cross{PRQAGG}{sample}
-\cross{PRQAGG}{size?}
-\cross{PRQAGG}{\#?}
-\cross{PRQAGG}{?=?}
-\cross{PRQAGG}{?\~{}=?}
-
These are directly exported but not implemented:
\begin{verbatim}
max : % -> S
@@ -4874,48 +4915,42 @@
\pagefrom{BagAggregate}{BGAGG}
{\bf Exports:}\\
-\begin{tabular}{lllllll}
- any? & bag & back & coerce & copy & count & dequeue! \\
- empty & empty? & enqueue! & eq? & eval & every? & extract! \\
- front & hash & insert! & inspect & latex & length & less? \\
- map & map! & member? & members & more? & parts & rotate! \\
- sample & size? & \#? & ?=? & ?\~{}=? &&\\
+\begin{tabular}{lllll}
+\cross{QUAGG}{any?} &
+\cross{QUAGG}{bag} &
+\cross{QUAGG}{back} &
+\cross{QUAGG}{coerce} &
+\cross{QUAGG}{copy} \\
+\cross{QUAGG}{count} &
+\cross{QUAGG}{dequeue!} &
+\cross{QUAGG}{empty} &
+\cross{QUAGG}{empty?} &
+\cross{QUAGG}{enqueue!} \\
+\cross{QUAGG}{eq?} &
+\cross{QUAGG}{eval} &
+\cross{QUAGG}{every?} &
+\cross{QUAGG}{extract!} &
+\cross{QUAGG}{front} \\
+\cross{QUAGG}{hash} &
+\cross{QUAGG}{insert!} &
+\cross{QUAGG}{inspect} &
+\cross{QUAGG}{latex} &
+\cross{QUAGG}{length} \\
+\cross{QUAGG}{less?} &
+\cross{QUAGG}{map} &
+\cross{QUAGG}{map!} &
+\cross{QUAGG}{member?} &
+\cross{QUAGG}{members} \\
+\cross{QUAGG}{more?} &
+\cross{QUAGG}{parts} &
+\cross{QUAGG}{rotate!} &
+\cross{QUAGG}{sample} &
+\cross{QUAGG}{size?} \\
+\cross{QUAGG}{\#?} &
+\cross{QUAGG}{?=?} &
+\cross{QUAGG}{?\~{}=?} &&
\end{tabular}
-\cross{QUAGG}{any?}
-\cross{QUAGG}{bag}
-\cross{QUAGG}{back}
-\cross{QUAGG}{coerce}
-\cross{QUAGG}{copy}
-\cross{QUAGG}{count}
-\cross{QUAGG}{dequeue!}
-\cross{QUAGG}{empty}
-\cross{QUAGG}{empty?}
-\cross{QUAGG}{enqueue!}
-\cross{QUAGG}{eq?}
-\cross{QUAGG}{eval}
-\cross{QUAGG}{every?}
-\cross{QUAGG}{extract!}
-\cross{QUAGG}{front}
-\cross{QUAGG}{hash}
-\cross{QUAGG}{insert!}
-\cross{QUAGG}{inspect}
-\cross{QUAGG}{latex}
-\cross{QUAGG}{length}
-\cross{QUAGG}{less?}
-\cross{QUAGG}{map}
-\cross{QUAGG}{map!}
-\cross{QUAGG}{member?}
-\cross{QUAGG}{members}
-\cross{QUAGG}{more?}
-\cross{QUAGG}{parts}
-\cross{QUAGG}{rotate!}
-\cross{QUAGG}{sample}
-\cross{QUAGG}{size?}
-\cross{QUAGG}{\#?}
-\cross{QUAGG}{?=?}
-\cross{QUAGG}{?\~{}=?}
-
These are implemented by this category:
\begin{verbatim}
back : % -> S
@@ -5060,55 +5095,46 @@
{\bf Exports:}\\
\begin{tabular}{lllll}
- any? & brace & coerce & construct & convert\\
- copy & count & difference & empty & empty?\\
- eq? & eval & every? & find & hash\\
- intersect & latex & less? & map & map!\\
- member? & members & more? & parts & reduce\\
- remove & removeDuplicates & sample & select & set\\
- size? & subset? & symmetricDifference & union & \#?\\
- ?$<$? & ?=? & ?\~{}=? &&
+\cross{SETAGG}{any?} &
+\cross{SETAGG}{brace} &
+\cross{SETAGG}{coerce} &
+\cross{SETAGG}{construct} &
+\cross{SETAGG}{convert} \\
+\cross{SETAGG}{copy} &
+\cross{SETAGG}{count} &
+\cross{SETAGG}{difference} &
+\cross{SETAGG}{empty} &
+\cross{SETAGG}{empty?} \\
+\cross{SETAGG}{eq?} &
+\cross{SETAGG}{eval} &
+\cross{SETAGG}{every?} &
+\cross{SETAGG}{find} &
+\cross{SETAGG}{hash} \\
+\cross{SETAGG}{intersect} &
+\cross{SETAGG}{latex} &
+\cross{SETAGG}{less?} &
+\cross{SETAGG}{map} &
+\cross{SETAGG}{map!} \\
+\cross{SETAGG}{member?} &
+\cross{SETAGG}{members} &
+\cross{SETAGG}{more?} &
+\cross{SETAGG}{parts} &
+\cross{SETAGG}{reduce} \\
+\cross{SETAGG}{remove} &
+\cross{SETAGG}{removeDuplicates} &
+\cross{SETAGG}{sample} &
+\cross{SETAGG}{select} &
+\cross{SETAGG}{set} \\
+\cross{SETAGG}{size?} &
+\cross{SETAGG}{subset?} &
+\cross{SETAGG}{symmetricDifference} &
+\cross{SETAGG}{union} &
+\cross{SETAGG}{\#?} \\
+\cross{SETAGG}{?$<$?} &
+\cross{SETAGG}{?=?} &
+\cross{SETAGG}{?\~{}=?} &&
\end{tabular}
-\cross{SETAGG}{any?}
-\cross{SETAGG}{brace}
-\cross{SETAGG}{coerce}
-\cross{SETAGG}{construct}
-\cross{SETAGG}{convert}
-\cross{SETAGG}{copy}
-\cross{SETAGG}{count}
-\cross{SETAGG}{difference}
-\cross{SETAGG}{empty}
-\cross{SETAGG}{empty?}
-\cross{SETAGG}{eq?}
-\cross{SETAGG}{eval}
-\cross{SETAGG}{every?}
-\cross{SETAGG}{find}
-\cross{SETAGG}{hash}
-\cross{SETAGG}{intersect}
-\cross{SETAGG}{latex}
-\cross{SETAGG}{less?}
-\cross{SETAGG}{map}
-\cross{SETAGG}{map!}
-\cross{SETAGG}{member?}
-\cross{SETAGG}{members}
-\cross{SETAGG}{more?}
-\cross{SETAGG}{parts}
-\cross{SETAGG}{reduce}
-\cross{SETAGG}{remove}
-\cross{SETAGG}{removeDuplicates}
-\cross{SETAGG}{sample}
-\cross{SETAGG}{select}
-\cross{SETAGG}{set}
-\cross{SETAGG}{size?}
-\cross{SETAGG}{subset?}
-\cross{SETAGG}{symmetricDifference}
-\cross{SETAGG}{union}
-\cross{SETAGG}{\#?}
-\cross{SETAGG}{?$<$?}
-\cross{SETAGG}{?=?}
-\cross{SETAGG}{?\~{}=?}
-
These are directly exported but not implemented:
\begin{verbatim}
brace : List S -> %
@@ -5345,46 +5371,40 @@
\pagefrom{BagAggregate}{BGAGG}
{\bf Exports:}\\
-\begin{tabular}{lllllll}
- any? & bag & coerce & copy & count & depth & empty \\
- empty? & eq? & eval & every? & extract! & hash & insert! \\
- inspect & latex & less? & map & map! & member? & members \\
- more? & parts & pop! & push! & sample & size? & top \\
- \#? & ?=? & ?\~{}=? &&&&\\
+\begin{tabular}{lllll}
+\cross{SKAGG}{any?} &
+\cross{SKAGG}{bag} &
+\cross{SKAGG}{coerce} &
+\cross{SKAGG}{copy} &
+\cross{SKAGG}{count} \\
+\cross{SKAGG}{depth} &
+\cross{SKAGG}{empty} &
+\cross{SKAGG}{empty?} &
+\cross{SKAGG}{eq?} &
+\cross{SKAGG}{eval} \\
+\cross{SKAGG}{every?} &
+\cross{SKAGG}{extract!} &
+\cross{SKAGG}{hash} &
+\cross{SKAGG}{insert!} &
+\cross{SKAGG}{inspect} \\
+\cross{SKAGG}{latex} &
+\cross{SKAGG}{less?} &
+\cross{SKAGG}{map} &
+\cross{SKAGG}{map!} &
+\cross{SKAGG}{member?} \\
+\cross{SKAGG}{members} &
+\cross{SKAGG}{more?} &
+\cross{SKAGG}{parts} &
+\cross{SKAGG}{pop!} &
+\cross{SKAGG}{push!} \\
+\cross{SKAGG}{sample} &
+\cross{SKAGG}{size?} &
+\cross{SKAGG}{top} &
+\cross{SKAGG}{\#?} &
+\cross{SKAGG}{?=?} \\
+\cross{SKAGG}{?\~{}=?} &&&&
\end{tabular}
-\cross{SKAGG}{any?}
-\cross{SKAGG}{bag}
-\cross{SKAGG}{coerce}
-\cross{SKAGG}{copy}
-\cross{SKAGG}{count}
-\cross{SKAGG}{depth}
-\cross{SKAGG}{empty}
-\cross{SKAGG}{empty?}
-\cross{SKAGG}{eq?}
-\cross{SKAGG}{eval}
-\cross{SKAGG}{every?}
-\cross{SKAGG}{extract!}
-\cross{SKAGG}{hash}
-\cross{SKAGG}{insert!}
-\cross{SKAGG}{inspect}
-\cross{SKAGG}{latex}
-\cross{SKAGG}{less?}
-\cross{SKAGG}{map}
-\cross{SKAGG}{map!}
-\cross{SKAGG}{member?}
-\cross{SKAGG}{members}
-\cross{SKAGG}{more?}
-\cross{SKAGG}{parts}
-\cross{SKAGG}{pop!}
-\cross{SKAGG}{push!}
-\cross{SKAGG}{sample}
-\cross{SKAGG}{size?}
-\cross{SKAGG}{top}
-\cross{SKAGG}{\#?}
-\cross{SKAGG}{?=?}
-\cross{SKAGG}{?\~{}=?}
-
These are directly exported but not implemented:
\begin{verbatim}
depth : % -> NonNegativeInteger
@@ -5518,75 +5538,63 @@
{\bf Exports:}\\
\begin{tabular}{lllll}
- any? & children & child? & coerce & concat \\
- concat! & copy & count & cycleEntry & cycleLength\\
- cycleSplit! & cycleTail & cyclic? & distance & empty \\
- empty? & eq? & eval & every? & first \\
- hash & last & latex & leaf? & leaves \\
- less? & map & map! & member? & members \\
- more? & nodes & node? & parts & rest \\
- sample & second & setchildren! & setelt & setfirst! \\
- setlast! & setrest! & setvalue! & size? & split! \\
- tail & third & value & \#? & ?.last \\
- ?.rest & ?.first & ?.value & ?=? & ?\~{}=? \\
+\cross{URAGG}{any?} &
+\cross{URAGG}{children} &
+\cross{URAGG}{child?} &
+\cross{URAGG}{coerce} &
+\cross{URAGG}{concat} \\
+\cross{URAGG}{concat!} &
+\cross{URAGG}{copy} &
+\cross{URAGG}{count} &
+\cross{URAGG}{cycleEntry} &
+\cross{URAGG}{cycleLength} \\
+\cross{URAGG}{cycleSplit!} &
+\cross{URAGG}{cycleTail} &
+\cross{URAGG}{cyclic?} &
+\cross{URAGG}{distance} &
+\cross{URAGG}{empty} \\
+\cross{URAGG}{empty?} &
+\cross{URAGG}{eq?} &
+\cross{URAGG}{eval} &
+\cross{URAGG}{every?} &
+\cross{URAGG}{first} \\
+\cross{URAGG}{hash} &
+\cross{URAGG}{last} &
+\cross{URAGG}{latex} &
+\cross{URAGG}{leaf?} &
+\cross{URAGG}{leaves} \\
+\cross{URAGG}{less?} &
+\cross{URAGG}{map} &
+\cross{URAGG}{map!} &
+\cross{URAGG}{member?} &
+\cross{URAGG}{members} \\
+\cross{URAGG}{more?} &
+\cross{URAGG}{nodes} &
+\cross{URAGG}{node?} &
+\cross{URAGG}{parts} &
+\cross{URAGG}{rest} \\
+\cross{URAGG}{sample} &
+\cross{URAGG}{second} &
+\cross{URAGG}{setchildren!} &
+\cross{URAGG}{setelt} &
+\cross{URAGG}{setfirst!} \\
+\cross{URAGG}{setlast!} &
+\cross{URAGG}{setrest!} &
+\cross{URAGG}{setvalue!} &
+\cross{URAGG}{size?} &
+\cross{URAGG}{split!} \\
+\cross{URAGG}{tail} &
+\cross{URAGG}{third} &
+\cross{URAGG}{value} &
+\cross{URAGG}{\#?} &
+\cross{URAGG}{?.last} \\
+\cross{URAGG}{?.rest} &
+\cross{URAGG}{?.first} &
+\cross{URAGG}{?.value} &
+\cross{URAGG}{?=?} &
+\cross{URAGG}{?\~{}=?} \\
\end{tabular}
-\cross{URAGG}{any?}
-\cross{URAGG}{children}
-\cross{URAGG}{child?}
-\cross{URAGG}{coerce}
-\cross{URAGG}{concat}
-\cross{URAGG}{concat!}
-\cross{URAGG}{copy}
-\cross{URAGG}{count}
-\cross{URAGG}{cycleEntry}
-\cross{URAGG}{cycleLength}
-\cross{URAGG}{cycleSplit!}
-\cross{URAGG}{cycleTail}
-\cross{URAGG}{cyclic?}
-\cross{URAGG}{distance}
-\cross{URAGG}{empty}
-\cross{URAGG}{empty?}
-\cross{URAGG}{eq?}
-\cross{URAGG}{eval}
-\cross{URAGG}{every?}
-\cross{URAGG}{first}
-\cross{URAGG}{hash}
-\cross{URAGG}{last}
-\cross{URAGG}{latex}
-\cross{URAGG}{leaf?}
-\cross{URAGG}{leaves}
-\cross{URAGG}{less?}
-\cross{URAGG}{map}
-\cross{URAGG}{map!}
-\cross{URAGG}{member?}
-\cross{URAGG}{members}
-\cross{URAGG}{more?}
-\cross{URAGG}{nodes}
-\cross{URAGG}{node?}
-\cross{URAGG}{parts}
-\cross{URAGG}{rest}
-\cross{URAGG}{sample}
-\cross{URAGG}{second}
-\cross{URAGG}{setchildren!}
-\cross{URAGG}{setelt}
-\cross{URAGG}{setfirst!}
-\cross{URAGG}{setlast!}
-\cross{URAGG}{setrest!}
-\cross{URAGG}{setvalue!}
-\cross{URAGG}{size?}
-\cross{URAGG}{split!}
-\cross{URAGG}{tail}
-\cross{URAGG}{third}
-\cross{URAGG}{value}
-\cross{URAGG}{\#?}
-\cross{URAGG}{?.last}
-\cross{URAGG}{?.rest}
-\cross{URAGG}{?.first}
-\cross{URAGG}{?.value}
-\cross{URAGG}{?=?}
-\cross{URAGG}{?\~{}=?}
-
These are directly exported but not implemented:
\begin{verbatim}
concat : (S,%) -> %
@@ -5980,30 +5988,29 @@
\pagepic{ps/v102abeliangroup.ps}{ABELGRP}{0.75}
{\bf See:}\\
+\pageto{LeftModule}{LMODULE}
+\pageto{OrderedAbelianGroup}{OAGROUP}
+\pageto{RightModule}{RMODULE}
\pageto{Rng}{RNG}
\pagefrom{CancellationAbelianMonoid}{CABMON}
{\bf Exports:}\\
-\begin{tabular}{lllllll}
- 0 & coerce & hash & latex & sample & subtractIfCan & zero?\\
- ?\~{}=? & ?*? & ?+? & ?-? & -? & ?=? &
+\begin{tabular}{lllll}
+\cross{ABELGRP}{0} &
+\cross{ABELGRP}{coerce} &
+\cross{ABELGRP}{hash} &
+\cross{ABELGRP}{latex} &
+\cross{ABELGRP}{sample} \\
+\cross{ABELGRP}{subtractIfCan} &
+\cross{ABELGRP}{zero?} &
+\cross{ABELGRP}{?\~{}=?} &
+\cross{ABELGRP}{?*?} &
+\cross{ABELGRP}{?+?} \\
+\cross{ABELGRP}{?-?} &
+\cross{ABELGRP}{-?} &
+\cross{ABELGRP}{?=?} &&
\end{tabular}
-\cross{ABELGRP}{0}
-\cross{ABELGRP}{coerce}
-\cross{ABELGRP}{hash}
-\cross{ABELGRP}{latex}
-\cross{ABELGRP}{sample}
-\cross{ABELGRP}{subtractIfCan}
-\cross{ABELGRP}{zero?}
-\cross{ABELGRP}{?\~{}=?}
-\cross{ABELGRP}{?*?}
-\cross{ABELGRP}{?+?}
-\cross{ABELGRP}{?-?}
-\cross{ABELGRP}{-?}
-\cross{ABELGRP}{?=?}
-
-
These are directly exported but not implemented:
\begin{verbatim}
-? : % -> %
@@ -6128,55 +6135,46 @@
\pagefrom{DictionaryOperations}{DIOPS}
{\bf Exports:}\\
-\begin{tabular}{lllllll}
- any? & bag & coerce & construct & convert \\
- copy & count & dictionary & empty & empty? \\
- eq? & eval & every? & extract! & find \\
- hash & insert! & inspect & latex & less? \\
- map & map! & member? & members & more? \\
- parts & reduce & remove & remove! & removeDuplicates \\
- sample & select & select! & size? & \#? \\
- ?\~{}=? & ?=? &&&\\
+\begin{tabular}{lllll}
+\cross{DIAGG}{any?} &
+\cross{DIAGG}{bag} &
+\cross{DIAGG}{coerce} &
+\cross{DIAGG}{construct} &
+\cross{DIAGG}{convert} \\
+\cross{DIAGG}{copy} &
+\cross{DIAGG}{count} &
+\cross{DIAGG}{dictionary} &
+\cross{DIAGG}{empty} &
+\cross{DIAGG}{empty?} \\
+\cross{DIAGG}{eq?} &
+\cross{DIAGG}{eval} &
+\cross{DIAGG}{every?} &
+\cross{DIAGG}{extract!} &
+\cross{DIAGG}{find} \\
+\cross{DIAGG}{hash} &
+\cross{DIAGG}{insert!} &
+\cross{DIAGG}{inspect} &
+\cross{DIAGG}{latex} &
+\cross{DIAGG}{less?} \\
+\cross{DIAGG}{map} &
+\cross{DIAGG}{map!} &
+\cross{DIAGG}{member?} &
+\cross{DIAGG}{members} &
+\cross{DIAGG}{more?} \\
+\cross{DIAGG}{parts} &
+\cross{DIAGG}{reduce} &
+\cross{DIAGG}{remove} &
+\cross{DIAGG}{remove!} &
+\cross{DIAGG}{removeDuplicates} \\
+\cross{DIAGG}{sample} &
+\cross{DIAGG}{select} &
+\cross{DIAGG}{select!} &
+\cross{DIAGG}{size?} &
+\cross{DIAGG}{\#?} \\
+\cross{DIAGG}{?\~{}=?} &
+\cross{DIAGG}{?=?} &&&
\end{tabular}
-\cross{DIAGG}{any?}
-\cross{DIAGG}{bag}
-\cross{DIAGG}{coerce}
-\cross{DIAGG}{construct}
-\cross{DIAGG}{convert}
-\cross{DIAGG}{copy}
-\cross{DIAGG}{count}
-\cross{DIAGG}{dictionary}
-\cross{DIAGG}{empty}
-\cross{DIAGG}{empty?}
-\cross{DIAGG}{eq?}
-\cross{DIAGG}{eval}
-\cross{DIAGG}{every?}
-\cross{DIAGG}{extract!}
-\cross{DIAGG}{find}
-\cross{DIAGG}{hash}
-\cross{DIAGG}{insert!}
-\cross{DIAGG}{inspect}
-\cross{DIAGG}{latex}
-\cross{DIAGG}{less?}
-\cross{DIAGG}{map}
-\cross{DIAGG}{map!}
-\cross{DIAGG}{member?}
-\cross{DIAGG}{members}
-\cross{DIAGG}{more?}
-\cross{DIAGG}{parts}
-\cross{DIAGG}{reduce}
-\cross{DIAGG}{remove}
-\cross{DIAGG}{remove!}
-\cross{DIAGG}{removeDuplicates}
-\cross{DIAGG}{sample}
-\cross{DIAGG}{select}
-\cross{DIAGG}{select!}
-\cross{DIAGG}{size?}
-\cross{DIAGG}{\#?}
-\cross{DIAGG}{?\~{}=?}
-\cross{DIAGG}{?=?}
-
These are implemented by this category:
\begin{verbatim}
dictionary : List S -> %
@@ -6349,65 +6347,54 @@
{\bf Exports:}\\
\begin{tabular}{lllll}
- any? & back & bag & bottom! & coerce \\
- copy & count & depth & dequeue & dequeue! \\
- empty & empty? & enqueue! & eq? & eval \\
- every? & extract! & extractBottom! & extractTop! & front \\
- hash & height & insert! & insertBottom! & insertTop! \\
- inspect & latex & length & less? & map \\
- map! & members & member? & more? & parts \\
- pop! & push! & reverse! & rotate! & sample \\
- size? & top & top! & \#? & ?=? \\
- ?\~{}=? &&&&\\
+\cross{DQAGG}{any?} &
+\cross{DQAGG}{back} &
+\cross{DQAGG}{bag} &
+\cross{DQAGG}{bottom!} &
+\cross{DQAGG}{coerce} \\
+\cross{DQAGG}{copy} &
+\cross{DQAGG}{count} &
+\cross{DQAGG}{depth} &
+\cross{DQAGG}{dequeue} &
+\cross{DQAGG}{dequeue!} \\
+\cross{DQAGG}{empty} &
+\cross{DQAGG}{empty?} &
+\cross{DQAGG}{enqueue!} &
+\cross{DQAGG}{eq?} &
+\cross{DQAGG}{eval} \\
+\cross{DQAGG}{every?} &
+\cross{DQAGG}{extract!} &
+\cross{DQAGG}{extractBottom!} &
+\cross{DQAGG}{extractTop!} &
+\cross{DQAGG}{front} \\
+\cross{DQAGG}{hash} &
+\cross{DQAGG}{height} &
+\cross{DQAGG}{insert!} &
+\cross{DQAGG}{insertBottom!} &
+\cross{DQAGG}{insertTop!} \\
+\cross{DQAGG}{inspect} &
+\cross{DQAGG}{latex} &
+\cross{DQAGG}{length} &
+\cross{DQAGG}{less?} &
+\cross{DQAGG}{map} \\
+\cross{DQAGG}{map!} &
+\cross{DQAGG}{members} &
+\cross{DQAGG}{member?} &
+\cross{DQAGG}{more?} &
+\cross{DQAGG}{parts} \\
+\cross{DQAGG}{pop!} &
+\cross{DQAGG}{push!} &
+\cross{DQAGG}{reverse!} &
+\cross{DQAGG}{rotate!} &
+\cross{DQAGG}{sample} \\
+\cross{DQAGG}{size?} &
+\cross{DQAGG}{top} &
+\cross{DQAGG}{top!} &
+\cross{DQAGG}{\#?} &
+\cross{DQAGG}{?=?} \\
+\cross{DQAGG}{?\~{}=?} &&&&
\end{tabular}
-\cross{DQAGG}{any?}
-\cross{DQAGG}{back}
-\cross{DQAGG}{bag}
-\cross{DQAGG}{bottom!}
-\cross{DQAGG}{coerce}
-\cross{DQAGG}{copy}
-\cross{DQAGG}{count}
-\cross{DQAGG}{depth}
-\cross{DQAGG}{dequeue}
-\cross{DQAGG}{dequeue!}
-\cross{DQAGG}{empty}
-\cross{DQAGG}{empty?}
-\cross{DQAGG}{enqueue!}
-\cross{DQAGG}{eq?}
-\cross{DQAGG}{eval}
-\cross{DQAGG}{every?}
-\cross{DQAGG}{extract!}
-\cross{DQAGG}{extractBottom!}
-\cross{DQAGG}{extractTop!}
-\cross{DQAGG}{front}
-\cross{DQAGG}{hash}
-\cross{DQAGG}{height}
-\cross{DQAGG}{insert!}
-\cross{DQAGG}{insertBottom!}
-\cross{DQAGG}{insertTop!}
-\cross{DQAGG}{inspect}
-\cross{DQAGG}{latex}
-\cross{DQAGG}{length}
-\cross{DQAGG}{less?}
-\cross{DQAGG}{map}
-\cross{DQAGG}{map!}
-\cross{DQAGG}{members}
-\cross{DQAGG}{member?}
-\cross{DQAGG}{more?}
-\cross{DQAGG}{parts}
-\cross{DQAGG}{pop!}
-\cross{DQAGG}{push!}
-\cross{DQAGG}{reverse!}
-\cross{DQAGG}{rotate!}
-\cross{DQAGG}{sample}
-\cross{DQAGG}{size?}
-\cross{DQAGG}{top}
-\cross{DQAGG}{top!}
-\cross{DQAGG}{\#?}
-\cross{DQAGG}{?=?}
-\cross{DQAGG}{?\~{}=?}
-
These are directly exported but not implemented:
\begin{verbatim}
bottom! : % -> S
@@ -6582,75 +6569,63 @@
{\bf Exports:}\\
\begin{tabular}{lllll}
- any? & coerce & concat & concat! & construct \\
- copy & convert & count & delete & delete! \\
- elt & empty & empty? & entries & entry? \\
- eval & every? & eq? & fill! & find \\
- first & hash & index? & indices & insert \\
- insert! & latex & less? & map & map! \\
- maxIndex & member...
[truncated message content] |
|
From: <gi...@ax...> - 2008-09-21 16:14:21
|
books/bookvol10.2.pamphlet | 5301 +++++++++++++---------
books/ps/v102bimodule.ps | 636 +++
books/ps/v102group.ps | 791 ++++
books/ps/v102leftmodule.ps | 519 +++
books/ps/v102orderedabeliangroup.ps | 493 ++
books/ps/v102orderedabelianmonoidsup.ps | 652 +++
books/ps/v102orderedcancellationabelianmonoid.ps | 606 +++
books/ps/v102orderedring.ps | 832 ++++
books/ps/v102rightmodule.ps | 427 ++
books/ps/v102ring.ps | 744 +++
src/algebra/catdef.spad.pamphlet | 566 ---
11 files changed, 8943 insertions(+), 2624 deletions(-)
New commits:
commit 3d9ac8e5234807a8fbe3beafb68959182872ef55
Author: Tim Daly <da...@ax...>
Date: Mon Jul 28 07:08:09 2008 -0400
20080920 tpd books/ps/v102bimodule.ps diagram BMODULE
20080920 tpd books/ps/v102group.ps diagram GROUP
20080920 tpd books/ps/v102leftmodule.ps diagram LMODULE
20080920 tpd books/ps/v102orderedabeliangroup.ps diagram OAGROUP
20080920 tpd books/ps/v102orderedabelianmonoidsup.ps OAMONS
20080920 tpd books/ps/v102orderedcancellationabelianmonoid.ps OCAMON
20080920 tpd books/ps/v102orderedring.ps diagram ORDRING
20080920 tpd books/ps/v102rightmodule.ps diagram RMODULE
20080920 tpd books/ps/v102ring.ps diagram RING
20080920 tpd src/algebra/catdef.spad remove more categories
20080920 tpd books/bookvol10.2 add more categories
|
|
From: <gi...@ax...> - 2008-09-20 14:05:42
|
books/bookvol10.2.pamphlet | 3678 ++++++++++++++++++++++++-----
books/ps/v102abeliangroup.ps | 632 +++++
books/ps/v102abelianmonoid.ps | 678 ++++++
books/ps/v102cancellationabelianmonoid.ps | 729 ++++++
books/ps/v102finitesetaggregate.ps | 636 +++++
books/ps/v102monoid.ps | 678 ++++++
books/ps/v102multisetaggregate.ps | 540 +++++
books/ps/v102orderedabelianmonoid.ps | 494 ++++
books/ps/v102orderedabeliansemigroup.ps | 795 +++++++
books/ps/v102orderedfinite.ps | 606 +++++
books/ps/v102orderedmonoid.ps | 800 +++++++
books/ps/v102orderedmultisetaggregate.ps | 708 ++++++
books/ps/v102rng.ps | 653 +++++
books/ps/v102setaggregate.ps | 760 ++++++
books/ps/v102stepthrough.ps | 499 ++++
changelog | 16 +
src/algebra/catdef.spad.pamphlet | 847 -------
17 files changed, 12367 insertions(+), 1382 deletions(-)
New commits:
commit 53d317b9cbd45a5e6aff64939aa3a6fc114ff41c
Author: Tim Daly <da...@ax...>
Date: Sun Jul 27 13:31:22 2008 -0400
20080919 tpd books/ps/v102stepthrough.ps diagram STEP
20080919 tpd books/ps/v102setaggregate.ps diagram SETAGG
20080919 tpd books/ps/v102rng.ps diagram RNG
20080919 tpd books/ps/v102orderedmultisetaggregate.ps diagram OMSAGG
20080919 tpd books/ps/v102orderedmonoid.ps diagram ORDMON
20080919 tpd books/ps/v102orderedfinite.ps diagram ORDFIN
20080919 tpd books/ps/v102orderedabeliansemigroup.ps diagram OASGP
20080919 tpd books/ps/v102orderedabelianmonoid.ps diagram OAMON
20080919 tpd books/ps/v102multisetaggregate.ps diagram MSETAGG
20080919 tpd books/ps/v102monoid.ps diagram MONOID
20080919 tpd books/ps/v102finitesetaggregate.ps diagram FINITE
20080919 tpd books/ps/v102cancellationabelianmonoid.ps diagram CABMON
20080919 tpd books/ps/v102abelianmonoid.ps diagram ABELMON
20080919 tpd books/ps/v102abeliangroup.ps diagram ABELSG
20080919 tpd src/algebra/catdef.spad remove more categories
20080919 tpd books/bookvol10.2 add more categories
|
|
From: <da...@us...> - 2008-09-20 13:16:27
|
Revision: 978
http://axiom.svn.sourceforge.net/axiom/?rev=978&view=rev
Author: daly
Date: 2008-09-20 13:16:15 +0000 (Sat, 20 Sep 2008)
Log Message:
-----------
20080919 tpd books/ps/v102stepthrough.ps diagram STEP
20080919 tpd books/ps/v102setaggregate.ps diagram SETAGG
20080919 tpd books/ps/v102rng.ps diagram RNG
20080919 tpd books/ps/v102orderedmultisetaggregate.ps diagram OMSAGG
20080919 tpd books/ps/v102orderedmonoid.ps diagram ORDMON
20080919 tpd books/ps/v102orderedfinite.ps diagram ORDFIN
20080919 tpd books/ps/v102orderedabeliansemigroup.ps diagram OASGP
20080919 tpd books/ps/v102orderedabelianmonoid.ps diagram OAMON
20080919 tpd books/ps/v102multisetaggregate.ps diagram MSETAGG
20080919 tpd books/ps/v102monoid.ps diagram MONOID
20080919 tpd books/ps/v102finitesetaggregate.ps diagram FINITE
20080919 tpd books/ps/v102cancellationabelianmonoid.ps diagram CABMON
20080919 tpd books/ps/v102abelianmonoid.ps diagram ABELMON
20080919 tpd books/ps/v102abeliangroup.ps diagram ABELSG
20080919 tpd src/algebra/catdef.spad remove more categories
20080919 tpd books/bookvol10.2 add more categories
Modified Paths:
--------------
trunk/axiom/books/bookvol10.2.pamphlet
trunk/axiom/changelog
trunk/axiom/src/algebra/catdef.spad.pamphlet
Added Paths:
-----------
trunk/axiom/books/ps/v102abeliangroup.ps
trunk/axiom/books/ps/v102abelianmonoid.ps
trunk/axiom/books/ps/v102cancellationabelianmonoid.ps
trunk/axiom/books/ps/v102finitesetaggregate.ps
trunk/axiom/books/ps/v102monoid.ps
trunk/axiom/books/ps/v102multisetaggregate.ps
trunk/axiom/books/ps/v102orderedabelianmonoid.ps
trunk/axiom/books/ps/v102orderedabeliansemigroup.ps
trunk/axiom/books/ps/v102orderedfinite.ps
trunk/axiom/books/ps/v102orderedmonoid.ps
trunk/axiom/books/ps/v102orderedmultisetaggregate.ps
trunk/axiom/books/ps/v102rng.ps
trunk/axiom/books/ps/v102setaggregate.ps
trunk/axiom/books/ps/v102stepthrough.ps
Modified: trunk/axiom/books/bookvol10.2.pamphlet
===================================================================
--- trunk/axiom/books/bookvol10.2.pamphlet 2008-09-19 07:21:15 UTC (rev 977)
+++ trunk/axiom/books/bookvol10.2.pamphlet 2008-09-20 13:16:15 UTC (rev 978)
@@ -37,8 +37,8 @@
%%
%% pagepic adds an image and an index entry
%%
-\newcommand{\pagepic}[2]{% e.g. \pagepic{pathandfile}{abb}
-\includegraphics{#1}%
+\newcommand{\pagepic}[3]{% e.g. \pagepic{pathandfile}{abb}{scale}
+\includegraphics[scale=#3]{#1}%
\index{images!#2}}
%%
%% pageto is a forward link to a referenced page
@@ -290,9 +290,10 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{BasicType}{BASTYPE}
-\pagepic{ps/v102basictype.ps}{BASTYPE}
+\pagepic{ps/v102basictype.ps}{BASTYPE}{1.00}
{\bf See:}\\
+\pageto{SetCategory}{SETCAT}
\pagefrom{Category}{CATEGORY}
{\bf Exports:}\\
@@ -359,9 +360,10 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{CoercibleTo}{KOERCE}
-\pagepic{ps/v102koerce.ps}{KOERCE}
+\pagepic{ps/v102koerce.ps}{KOERCE}{1.00}
{\bf See:}\\
+\pageto{SetCategory}{SETCAT}
\pagefrom{Category}{CATEGORY}
{\bf Exports:}
@@ -422,7 +424,7 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{ConvertibleTo}{KONVERT}
-\pagepic{ps/v102konvert.ps}{KONVERT}
+\pagepic{ps/v102konvert.ps}{KONVERT}{1.00}
{\bf See:}\\
\pageto{Collection}{CLAGG}
@@ -542,9 +544,10 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{Eltable}{ELTAB}
-\pagepic{ps/v102eltab.ps}{ELTAB}
+\pagepic{ps/v102eltab.ps}{ELTAB}{1.00}
{\bf See:}\\
+\pageto{EltableAggregate}{ELTAGG}
\pagefrom{Category}{CATEGORY}
{\bf Exports:}
@@ -610,7 +613,7 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{RetractableTo}{RETRACT}
-\pagepic{ps/v102retractableto.ps}{RETRACT}
+\pagepic{ps/v102retractableto.ps}{RETRACT}{1.00}
{\bf See:}\\
\pagefrom{Category}{CATEGORY}
@@ -718,7 +721,7 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{Type}{TYPE}
-\pagepic{ps/v102type.ps}{TYPE}
+\pagepic{ps/v102type.ps}{TYPE}{1.00}
{\bf See:}\\
\pageto{Aggregate}{AGG}
@@ -759,7 +762,7 @@
\chapter{Category Layer 2}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{Aggregate}{AGG}
-\pagepic{ps/v102agg.ps}{AGG}
+\pagepic{ps/v102agg.ps}{AGG}{1.00}
{\bf See:}\\
\pageto{HomogeneousAggregate}{HOAGG}
@@ -871,9 +874,7 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{EltableAggregate}{ELTAGG}
-%\pagepic{ps/v102eltableaggregate.ps}{ELTAGG}
-\includegraphics[scale=0.75]{ps/v102eltableaggregate.ps}
-\index{images!STAGG}
+\pagepic{ps/v102eltableaggregate.ps}{ELTAGG}{0.75}
{\bf See:}\\
\pageto{IndexedAggregate}{IXAGG}
@@ -987,7 +988,7 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{SetCategory}{SETCAT}
-\pagepic{ps/v102setcategory.ps}{SETCAT}
+\pagepic{ps/v102setcategory.ps}{SETCAT}{1.00}
{\bf See:}\\
\pageto{AbelianSemiGroup}{ABELSG}
@@ -995,6 +996,10 @@
\pageto{HomogeneousAggregate}{HOAGG}
\pageto{OrderedSet}{ORDSET}
\pageto{SemiGroup}{SGROUP}
+\pageto{SetAggregate}{SETAGG}
+\pageto{StepThrough}{STEP}
+\pagefrom{BasicType}{BASTYPE}
+\pagefrom{CoercibleTo}{KOERCE}
{\bf Exports:}\\
\begin{tabular}{lllll}
@@ -1094,9 +1099,10 @@
\chapter{Category Layer 3}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{AbelianSemiGroup}{ABELSG}
-\pagepic{ps/v102abeliansemigroup.ps}{ABELSG}
+\pagepic{ps/v102abeliansemigroup.ps}{ABELSG}{1.00}
{\bf See:}\\
+\pageto{AbelianMonoid}{ABELMON}
\pagefrom{SetCategory}{SETCAT}
{\bf Exports:}\\
@@ -1212,9 +1218,10 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{Finite}{FINITE}
-\pagepic{ps/v102finite.ps}{FINITE}
+\pagepic{ps/v102finite.ps}{FINITE}{1.00}
{\bf See:}\\
+\pageto{OrderedFinite}{ORDFIN}
\pagefrom{SetCategory}{SETCAT}
{\bf Exports:}\\
@@ -1328,7 +1335,7 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{HomogeneousAggregate}{HOAGG}
-\pagepic{ps/v102homogeneousaggregate.ps}{HOAGG}
+\pagepic{ps/v102homogeneousaggregate.ps}{HOAGG}{1.00}
{\bf See:}\\
\pageto{BagAggregate}{BGAGG}
@@ -1420,7 +1427,7 @@
if S has EVALAB S and S has SETCAT
\end{verbatim}
-These exports come from SetCategory:
+These exports come from SetCategory():
\begin{verbatim}
hash : % -> SingleInteger if S has SETCAT
?~=? : (%,%) -> Boolean if S has SETCAT
@@ -1554,15 +1561,18 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{OrderedSet}{ORDSET}
-\pagepic{ps/v102orderedset.ps}{ORDSET}
+\pagepic{ps/v102orderedset.ps}{ORDSET}{1.00}
{\bf See:}\\
+\pageto{OrderedAbelianSemiGroup}{OASGP}
+\pageto{OrderedFinite}{ORDFIN}
+\pageto{OrderedMonoid}{ORDMON}
\pagefrom{SetCategory}{SETCAT}
{\bf Exports:}\\
\begin{tabular}{llllll}
- coerce & hash & latex & max & min & ?<?\\
- ?<=? & ?=? & ?>? & ?>=? & ?\~{}=? &\\
+ coerce & hash & latex & max & min & ?$<$?\\
+ ?$<=$? & ?=? & ?$>$? & ?$>=$? & ?\~{}=? &\\
\end{tabular}
\cross{ORDSET}{coerce}
@@ -1570,11 +1580,11 @@
\cross{ORDSET}{latex}
\cross{ORDSET}{max}
\cross{ORDSET}{min}
-\cross{ORDSET}{?<?}
-\cross{ORDSET}{?<=?}
+\cross{ORDSET}{?$<$?}
+\cross{ORDSET}{?$<=$?}
\cross{ORDSET}{?=?}
-\cross{ORDSET}{?>?}
-\cross{ORDSET}{?>=?}
+\cross{ORDSET}{?$>$?}
+\cross{ORDSET}{?$>=$?}
\cross{ORDSET}{?\~{}=?}
These are directly exported but not implemented:
@@ -1616,7 +1626,6 @@
++ pair of elements \spad{(a,b)}
++ exactly one of the following relations holds \spad{a<b or a=b or b<a}
++ and the relation is transitive, i.e. \spad{a<b and b<c => a<c}.
-
OrderedSet(): Category == SetCategory with
--operations
"<": (%,%) -> Boolean
@@ -1688,9 +1697,7 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{SemiGroup}{SGROUP}
-%\pagepic{ps/v102semigroup.ps}{SGROUP}
-\includegraphics[scale=0.75]{ps/v102semigroup.ps}
-\index{images!SGROUP}
+\pagepic{ps/v102semigroup.ps}{SGROUP}{0.75}
A Semigroup is defined as a set $S$ with a binary multiplicative
operator ``*''. A Semigroup $G(S,*)$ is:
@@ -1701,6 +1708,8 @@
\end{itemize}
{\bf See:}\\
+\pageto{Monoid}{MONOID}
+\pageto{Rng}{RNG}
\pagefrom{SetCategory}{SETCAT}
{\bf Exports:}\\
@@ -1820,10 +1829,256 @@
}
@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{StepThrough}{STEP}
+\pagepic{ps/v102stepthrough.ps}{STEP}{1.00}
+
+{\bf See:}\\
+\pagefrom{SetCategory}{SETCAT}
+
+{\bf Exports:}\\
+\begin{tabular}{lllllll}
+ coerce & hash & init & latex & nextItem & ?=? & ?\~{}=?
+\end{tabular}
+
+\cross{STEP}{coerce}
+\cross{STEP}{hash}
+\cross{STEP}{init}
+\cross{STEP}{latex}
+\cross{STEP}{?=?}
+\cross{STEP}{?~=?}
+\cross{STEP}{nextItem}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ init : () -> %
+ nextItem : % -> Union(%,"failed")
+\end{verbatim}
+
+These exports come from SetCategory():
+\begin{verbatim}
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ ?=? : (%,%) -> Boolean
+ ?~=? : (%,%) -> Boolean
+\end{verbatim}
+
+<<category STEP StepThrough>>=
+)abbrev category STEP StepThrough
+++ Author:
+++ Date Created:
+++ Date Last Updated:
+++ Basic Functions:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++ A class of objects which can be 'stepped through'.
+++ Repeated applications of \spadfun{nextItem} is guaranteed never to
+++ return duplicate items and only return "failed" after exhausting
+++ all elements of the domain.
+++ This assumes that the sequence starts with \spad{init()}.
+++ For infinite domains, repeated application
+++ of \spadfun{nextItem} is not required to reach all possible domain elements
+++ starting from any initial element.
+++
+++ Conditional attributes:
+++ infinite\tab{15}repeated \spad{nextItem}'s are never "failed".
+StepThrough(): Category == SetCategory with
+ --operations
+ init: constant -> %
+ ++ init() chooses an initial object for stepping.
+ nextItem: % -> Union(%,"failed")
+ ++ nextItem(x) returns the next item, or "failed" if domain is exhausted.
+
+@
+<<STEP.dotabb>>=
+"STEP" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=STEP"];
+"STEP" -> "SETCAT"
+
+@
+<<STEP.dotfull>>=
+"StepThrough()"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=STEP"];
+"StepThrough()" -> "SetCategory()"
+
+@
+<<STEP.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"StepThrough()" [color=lightblue];
+"StepThrough()" -> "SetCategory()"
+
+"SetCategory()" [color=lightblue];
+"SetCategory()" -> "BasicType()"
+"SetCategory()" -> "CoercibleTo(OutputForm)"
+
+"BasicType()" [color=lightblue];
+"BasicType()" -> "Category"
+
+"CoercibleTo(OutputForm)" [color=seagreen];
+"CoercibleTo(OutputForm)" -> "CoercibleTo(a:Type)"
+
+"CoercibleTo(a:Type)" [color=lightblue];
+"CoercibleTo(a:Type)" -> "Category"
+
+"Category" [color=lightblue];
+
+}
+
+@
\chapter{Category Layer 4}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{AbelianMonoid}{ABELMON}
+\pagepic{ps/v102abelianmonoid.ps}{ABELMON}{0.75}
+
+{\bf See:}\\
+\pageto{CancellationAbelianMonoid}{CABMON}
+\pageto{OrderedAbelianMonoid}{OAMON}
+\pageto{OrderedAbelianSemiGroup}{OASGP}
+\pagefrom{AbelianSemiGroup}{ABELSG}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+ 0 & coerce & hash & latex & sample\\
+ zero? & ?*? & ?+? & ?=? & ?\~{}=?
+\end{tabular}
+
+\cross{ABELMON}{0}
+\cross{ABELMON}{coerce}
+\cross{ABELMON}{hash}
+\cross{ABELMON}{latex}
+\cross{ABELMON}{sample}
+\cross{ABELMON}{zero?}
+\cross{ABELMON}{?*?}
+\cross{ABELMON}{?+?}
+\cross{ABELMON}{?=?}
+\cross{ABELMON}{?\~{}=?}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ 0 : () -> %
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ sample : () -> %
+ zero? : % -> Boolean
+ ?*? : (PositiveInteger,%) -> %
+ ?*? : (NonNegativeInteger,%) -> %
+\end{verbatim}
+
+These exports come from AbelianSemiGroup():
+\begin{verbatim}
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ ?=? : (%,%) -> Boolean
+ ?~=? : (%,%) -> Boolean
+ ?+? : (%,%) -> %
+\end{verbatim}
+
+<<category ABELMON AbelianMonoid>>=
+)abbrev category ABELMON AbelianMonoid
+++ Author:
+++ Date Created:
+++ Date Last Updated:
+++ Basic Functions:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++ The class of multiplicative monoids, i.e. semigroups with an
+++ additive identity element.
+++
+++ Axioms:
+++ \spad{leftIdentity("+":(%,%)->%,0)}\tab{30}\spad{ 0+x=x }
+++ \spad{rightIdentity("+":(%,%)->%,0)}\tab{30}\spad{ x+0=x }
+-- following domain must be compiled with subsumption disabled
+-- define SourceLevelSubset to be EQUAL
+AbelianMonoid(): Category == AbelianSemiGroup with
+ --operations
+ 0: constant -> %
+ ++ 0 is the additive identity element.
+ sample: constant -> %
+ ++ sample yields a value of type %
+ zero?: % -> Boolean
+ ++ zero?(x) tests if x is equal to 0.
+ "*": (NonNegativeInteger,%) -> %
+ ++ n * x is left-multiplication by a non negative integer
+ add
+ import RepeatedDoubling(%)
+ zero? x == x = 0
+ n:PositiveInteger * x:% == (n::NonNegativeInteger) * x
+ sample() == 0
+ if not (% has Ring) then
+ n:NonNegativeInteger * x:% ==
+ zero? n => 0
+ double(n pretend PositiveInteger,x)
+
+@
+<<ABELMON.dotabb>>=
+"ABELMON"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ABELMON"];
+"ABELMON" -> "ABELSG"
+
+@
+<<ABELMON.dotfull>>=
+"AbelianMonoid()"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ABELMON"];
+"AbelianMonoid()" -> "AbelianSemiGroup()"
+
+@
+<<ABELMON.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"AbelianMonoid()" [color=lightblue];
+"AbelianMonoid()" -> "AbelianSemiGroup()"
+
+"AbelianSemiGroup()" [color=lightblue];
+"AbelianSemiGroup()" -> "SetCategory()"
+"AbelianSemiGroup()" -> "RepeatedDoubling(AbelianSemiGroup)"
+
+"SetCategory()" [color=lightblue];
+"SetCategory()" -> "BasicType()"
+"SetCategory()" -> "CoercibleTo(OutputForm)"
+
+"BasicType()" [color=lightblue];
+"BasicType()" -> "Category"
+
+"CoercibleTo(OutputForm)" [color=seagreen];
+"CoercibleTo(OutputForm)" ->
+ "CoercibleTo(a:Type)"
+
+"CoercibleTo(a:Type)" [color=lightblue];
+"CoercibleTo(a:Type)" -> "Category"
+
+"RepeatedDoubling(AbelianSemiGroup)" [color="#00EE00"];
+"RepeatedDoubling(AbelianSemiGroup)" -> "RepeatedDoubling(a:SetCategory)"
+
+"RepeatedDoubling(a:SetCategory)" [color="#00EE00"];
+"RepeatedDoubling(a:SetCategory)" -> "Package"
+
+"Package" [color="#00EE00"];
+
+"Category" [color=lightblue];
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{BagAggregate}{BGAGG}
-\pagepic{ps/v102bagaggregate.ps}{BGAGG}
+\pagepic{ps/v102bagaggregate.ps}{BGAGG}{1.00}
{\bf See:}\\
\pageto{DictionaryOperations}{DIOPS}
@@ -1880,7 +2135,7 @@
bag : List S -> %
\end{verbatim}
-These exports come from HomogeneousAggregate:
+These exports come from HomogeneousAggregate(S:Type):
\begin{verbatim}
any? : ((S -> Boolean),%) -> Boolean
if $ has finiteAggregate
@@ -1993,11 +2248,12 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{Collection}{CLAGG}
-\pagepic{ps/v102collection.ps}{CLAGG}
+\pagepic{ps/v102collection.ps}{CLAGG}{1.00}
{\bf See:}\\
\pageto{DictionaryOperations}{DIOPS}
\pageto{LinearAggregate}{LNAGG}
+\pageto{SetAggregate}{SETAGG}
\pagefrom{ConvertibleTo}{KONVERT}
\pagefrom{HomogeneousAggregate}{HOAGG}
@@ -2066,7 +2322,7 @@
#? : % -> NonNegativeInteger if $ has finiteAggregate
\end{verbatim}
-These exports come from HomogeneousAggregate(a:Type):
+These exports come from HomogeneousAggregate(S:Type):
\begin{verbatim}
coerce : % -> OutputForm if S has SETCAT
copy : % -> %
@@ -2091,16 +2347,16 @@
map! : ((S -> S),%) -> % if $ has shallowlyMutable
member? : (S,%) -> Boolean
if S has SETCAT and $ has finiteAggregate
- sample : () -> %
members : % -> List S if $ has finiteAggregate
more? : (%,NonNegativeInteger) -> Boolean
parts : % -> List S if $ has finiteAggregate
+ sample : () -> %
size? : (%,NonNegativeInteger) -> Boolean
?=? : (%,%) -> Boolean if S has SETCAT
?~=? : (%,%) -> Boolean if S has SETCAT
\end{verbatim}
-These exports come from ConvertibleTo(a:Type):
+These exports come from ConvertibleTo(S:Type):
\begin{verbatim}
convert : % -> InputForm if S has KONVERT INFORM
\end{verbatim}
@@ -2241,7 +2497,7 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{IndexedAggregate}{IXAGG}
-\pagepic{ps/v102indexedaggregate.ps}{IXAGG}
+\pagepic{ps/v102indexedaggregate.ps}{IXAGG}{1.00}
{\bf See:}\\
\pageto{LinearAggregate}{LNAGG}
@@ -2318,7 +2574,7 @@
swap! : (%,Index,Index) -> Void if $ has shallowlyMutable
\end{verbatim}
-These exports come from HomogeneousAggregate(a:Type):
+These exports come from HomogeneousAggregate(Entry:Type):
\begin{verbatim}
any? : ((Entry -> Boolean),%) -> Boolean
if $ has finiteAggregate
@@ -2356,7 +2612,7 @@
?=? : (%,%) -> Boolean if Entry has SETCAT
\end{verbatim}
-These exports come from EltableAggregate(a:SetCategory,b:Type):
+These exports come from EltableAggregate(Index:SetCategory,Entry:Type):
\begin{verbatim}
qelt : (%,Index) -> Entry
qsetelt! : (%,Index,Entry) -> Entry if $ has shallowlyMutable
@@ -2510,8 +2766,282 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{Monoid}{MONOID}
+\pagepic{ps/v102monoid.ps}{MONOID}{0.75}
+
+{\bf See:}\\
+\pageto{OrderedMonoid}{ORDMON}
+\pagefrom{SemiGroup}{SGROUP}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+ 1 & coerce & hash & latex & one?\\
+ recip & sample & ?*? & ?=? & ?\~{}=?\\
+ ?**? & ?\^{}? & ?\^{}? &&\\
+\end{tabular}
+
+\cross{MONOID}{1}
+\cross{MONOID}{coerce}
+\cross{MONOID}{hash}
+\cross{MONOID}{latex}
+\cross{MONOID}{one?}
+\cross{MONOID}{recip}
+\cross{MONOID}{sample}
+\cross{MONOID}{?*?}
+\cross{MONOID}{?=?}
+\cross{MONOID}{?\~{}=?}
+\cross{MONOID}{?**?}
+\cross{MONOID}{?\^{}?}
+
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ 1 : () -> %
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ one? : % -> Boolean
+ recip : % -> Union(%,"failed")
+ sample : () -> %
+ ?^? : (%,NonNegativeInteger) -> %
+ ?**? : (%,NonNegativeInteger) -> %
+\end{verbatim}
+
+These exports come from SemiGroup():
+\begin{verbatim}
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ ?*? : (%,%) -> %
+ ?**? : (%,PositiveInteger) -> %
+ ?^? : (%,PositiveInteger) -> %
+ ?=? : (%,%) -> Boolean
+ ?~=? : (%,%) -> Boolean
+\end{verbatim}
+
+<<category MONOID Monoid>>=
+)abbrev category MONOID Monoid
+++ Author:
+++ Date Created:
+++ Date Last Updated:
+++ Basic Functions:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++ The class of multiplicative monoids, i.e. semigroups with a
+++ multiplicative identity element.
+++
+++ Axioms:
+++ \spad{leftIdentity("*":(%,%)->%,1)}\tab{30}\spad{1*x=x}
+++ \spad{rightIdentity("*":(%,%)->%,1)}\tab{30}\spad{x*1=x}
+++
+++ Conditional attributes:
+++ unitsKnown\tab{15}\spadfun{recip} only returns "failed" on non-units
+Monoid(): Category == SemiGroup with
+ 1: constant -> %
+ ++ 1 is the multiplicative identity.
+ sample: constant -> %
+ ++ sample yields a value of type %
+ one?: % -> Boolean
+ ++ one?(x) tests if x is equal to 1.
+ "**": (%,NonNegativeInteger) -> %
+ ++ x**n returns the repeated product
+ ++ of x n times, i.e. exponentiation.
+ "^" : (%,NonNegativeInteger) -> %
+ ++ x^n returns the repeated product
+ ++ of x n times, i.e. exponentiation.
+ recip: % -> Union(%,"failed")
+ ++ recip(x) tries to compute the multiplicative inverse for x
+ ++ or "failed" if it cannot find the inverse (see unitsKnown).
+ add
+ import RepeatedSquaring(%)
+ _^(x:%, n:NonNegativeInteger):% == x ** n
+ one? x == x = 1
+ sample() == 1
+ recip x ==
+ (x = 1) => x
+ "failed"
+ x:% ** n:NonNegativeInteger ==
+ zero? n => 1
+ expt(x,n pretend PositiveInteger)
+
+@
+<<MONOID.dotabb>>=
+"MONOID"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=MONOID"];
+"MONOID" -> "SGROUP"
+
+@
+<<MONOID.dotfull>>=
+"Monoid()"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=MONOID"];
+"Monoid()" -> "SemiGroup()"
+
+@
+<<MONOID.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"Monoid()" [color=lightblue];
+"Monoid()" -> "SemiGroup()"
+
+"SemiGroup()" [color=lightblue];
+"SemiGroup()" -> "SetCategory()"
+"SemiGroup()" -> "RepeatedSquaring(SemiGroup)"
+
+"SetCategory()" [color=lightblue];
+"SetCategory()" -> "BasicType()"
+"SetCategory()" -> "CoercibleTo(OutputForm)"
+
+"BasicType()" [color=lightblue];
+"BasicType()" -> "Category"
+
+"CoercibleTo(OutputForm)" [color=seagreen];
+"CoercibleTo(OutputForm)" -> "CoercibleTo(a:Type)"
+
+"CoercibleTo(a:Type)" [color=lightblue];
+"CoercibleTo(a:Type)" -> "Category"
+
+"RepeatedSquaring(SemiGroup)" [color="#00EE00"];
+"RepeatedSquaring(SemiGroup)" -> "RepeatedSquaring(a:SetCategory)"
+
+"RepeatedSquaring(a:SetCategory)" [color="#00EE00"];
+"RepeatedSquaring(a:SetCategory)" -> "Package"
+
+"Package" [color="#00EE00"];
+
+"Category" [color=lightblue];
+
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{OrderedFinite}{ORDFIN}
+\pagepic{ps/v102orderedfinite.ps}{ORDFIN}{1.00}
+
+{\bf See:}\\
+\pagefrom{Finite}{FINITE}
+\pagefrom{OrderedSet}{ORDSET}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+ coerce & hash & index & latex & lookup \\
+ max & min & random & size & ?\~{}=? \\
+ ?$<$? & ?$<=$? & ?=? & ?$>$? & ?$>=$? \\
+\end{tabular}
+
+\cross{ORDFIN}{coerce}
+\cross{ORDFIN}{hash}
+\cross{ORDFIN}{index}
+\cross{ORDFIN}{latex}
+\cross{ORDFIN}{lookup}
+\cross{ORDFIN}{max}
+\cross{ORDFIN}{min}
+\cross{ORDFIN}{random}
+\cross{ORDFIN}{size}
+\cross{ORDFIN}{?\~{}=?}
+\cross{ORDFIN}{?$<$?}
+\cross{ORDFIN}{?$<=$?}
+\cross{ORDFIN}{?=?}
+\cross{ORDFIN}{?$>$?}
+\cross{ORDFIN}{?$>=$?}
+
+These exports come from OrderedSet():
+\begin{verbatim}
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ max : (%,%) -> %
+ min : (%,%) -> %
+ ?=? : (%,%) -> Boolean
+ ?~=? : (%,%) -> Boolean
+ ?<? : (%,%) -> Boolean
+ ?<=? : (%,%) -> Boolean
+ ?>? : (%,%) -> Boolean
+ ?>=? : (%,%) -> Boolean
+\end{verbatim}
+
+These exports come from Finite():
+\begin{verbatim}
+ index : PositiveInteger -> %
+ lookup : % -> PositiveInteger
+ random : () -> %
+ size : () -> NonNegativeInteger
+\end{verbatim}
+
+<<category ORDFIN OrderedFinite>>=
+)abbrev category ORDFIN OrderedFinite
+++ Author:
+++ Date Created:
+++ Date Last Updated:
+++ Basic Functions:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++ Ordered finite sets.
+
+OrderedFinite(): Category == Join(OrderedSet, Finite)
+
+@
+<<ORDFIN.dotabb>>=
+"ORDFIN"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ORDFIN"];
+"ORDFIN" -> "ORDSET"
+"ORDFIN" -> "FINITE"
+
+@
+<<ORDFIN.dotfull>>=
+"OrderedFinite()"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ORDFIN"];
+"OrderedFinite()" -> "OrderedSet()"
+"OrderedFinite()" -> "Finite()"
+
+@
+<<ORDFIN.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"OrderedFinite()" [color=lightblue];
+"OrderedFinite()" -> "OrderedSet()"
+"OrderedFinite()" -> "Finite()"
+
+"Finite()" [color=lightblue];
+"Finite()" -> "SetCategory()"
+
+"OrderedSet()" [color=lightblue];
+"OrderedSet()" -> "SetCategory()"
+
+"SetCategory()" [color=lightblue];
+"SetCategory()" -> "BasicType()"
+"SetCategory()" -> "CoercibleTo(OutputForm)"
+
+"BasicType()" [color=lightblue];
+"BasicType()" -> "Category"
+
+"CoercibleTo(OutputForm)" [color=seagreen];
+"CoercibleTo(OutputForm)" -> "CoercibleTo(a:Type)"
+
+"CoercibleTo(a:Type)" [color=lightblue];
+"CoercibleTo(a:Type)" -> "Category"
+
+"Category" [color=lightblue];
+
+}
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{RecursiveAggregate}{RCAGG}
-\pagepic{ps/v102recursiveaggregate.ps}{RCAGG}
+\pagepic{ps/v102recursiveaggregate.ps}{RCAGG}{1.00}
{\bf See:}\\
\pageto{BinaryRecursiveAggregate}{BRAGG}
@@ -2587,7 +3117,7 @@
?.value : (%,value) -> S
\end{verbatim}
-These exports come from HomogeneousAggregate(a:Type):
+These exports come from HomogeneousAggregate(S:Type):
\begin{verbatim}
any? : ((S -> Boolean),%) -> Boolean
if $ has finiteAggregate
@@ -2726,7 +3256,7 @@
\chapter{Category Layer 5}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{BinaryRecursiveAggregate}{BRAGG}
-\pagepic{ps/v102binaryrecursiveaggregate.ps}{BRAGG}
+\pagepic{ps/v102binaryrecursiveaggregate.ps}{BRAGG}{1.00}
{\bf See:}\\
\pagefrom{RecursiveAggregate}{RCAGG}
@@ -2819,7 +3349,7 @@
?.left : (%,left) -> %
\end{verbatim}
-These exports come from RecursiveAggregate(a:Type)
+These exports come from RecursiveAggregate(S:Type)
\begin{verbatim}
any? : ((S -> Boolean),%) -> Boolean
if $ has finiteAggregate
@@ -3011,8 +3541,134 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{CancellationAbelianMonoid}{CABMON}
+\pagepic{ps/v102cancellationabelianmonoid.ps}{CABMON}{0.75}
+
+{\bf See:}\\
+\pageto{AbelianGroup}{ABELGRP}
+\pagefrom{AbelianMonoid}{ABELMON}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+ 0 & coerce & hash & latex & sample\\
+ subtractIfCan & zero? & ?\~{}=? & ?*? & ?+?\\
+ ?=?&&&&
+\end{tabular}
+
+\cross{CABMON}{0}
+\cross{CABMON}{coerce}
+\cross{CABMON}{hash}
+\cross{CABMON}{latex}
+\cross{CABMON}{sample}
+\cross{CABMON}{subtractIfCan}
+\cross{CABMON}{zero?}
+\cross{CABMON}{?\~{}=?}
+\cross{CABMON}{?*?}
+\cross{CABMON}{?+?}
+\cross{CABMON}{?=?}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ subtractIfCan : (%,%) -> Union(%,"failed")
+\end{verbatim}
+
+These exports come from AbelianMonoid():
+\begin{verbatim}
+ 0 : () -> %
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ sample : () -> %
+ zero? : % -> Boolean
+ ?*? : (NonNegativeInteger,%) -> %
+ ?*? : (PositiveInteger,%) -> %
+ ?~=? : (%,%) -> Boolean
+ ?+? : (%,%) -> %
+ ?=? : (%,%) -> Boolean
+\end{verbatim}
+
+<<category CABMON CancellationAbelianMonoid>>=
+)abbrev category CABMON CancellationAbelianMonoid
+++ Author:
+++ Date Created:
+++ Date Last Updated:
+++ Basic Functions:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References: Davenport & Trager I
+++ Description:
+++ This is an \spadtype{AbelianMonoid} with the cancellation property, i.e.
+++ \spad{ a+b = a+c => b=c }.
+++ This is formalised by the partial subtraction operator,
+++ which satisfies the axioms listed below:
+++
+++ Axioms:
+++ \spad{c = a+b <=> c-b = a}
+CancellationAbelianMonoid(): Category == AbelianMonoid with
+ subtractIfCan: (%,%) -> Union(%,"failed")
+ ++ subtractIfCan(x, y) returns an element z such that \spad{z+y=x}
+ ++ or "failed" if no such element exists.
+
+@
+<<CABMON.dotabb>>=
+"CABMON"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=CABMON"];
+"CABMON" -> "ABELMON"
+
+@
+<<CABMON.dotfull>>=
+"CancellationAbelianMonoid()"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=CABMON"];
+"CancellationAbelianMonoid()" -> "AbelianMonoid()"
+
+@
+<<CABMON.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"CancellationAbelianMonoid()" [color=lightblue];
+"CancellationAbelianMonoid()" -> "AbelianMonoid()"
+
+"AbelianMonoid()" [color=lightblue];
+"AbelianMonoid()" -> "AbelianSemiGroup()"
+
+"AbelianSemiGroup()" [color=lightblue];
+"AbelianSemiGroup()" -> "SetCategory()"
+"AbelianSemiGroup()" -> "RepeatedDoubling(AbelianSemiGroup)"
+
+"SetCategory()" [color=lightblue];
+"SetCategory()" -> "BasicType()"
+"SetCategory()" -> "CoercibleTo(OutputForm)"
+
+"BasicType()" [color=lightblue];
+"BasicType()" -> "Category"
+
+"CoercibleTo(OutputForm)" [color=seagreen];
+"CoercibleTo(OutputForm)" ->
+ "CoercibleTo(a:Type)"
+
+"CoercibleTo(a:Type)" [color=lightblue];
+"CoercibleTo(a:Type)" -> "Category"
+
+"RepeatedDoubling(AbelianSemiGroup)" [color="#00EE00"];
+"RepeatedDoubling(AbelianSemiGroup)" -> "RepeatedDoubling(a:SetCategory)"
+
+"RepeatedDoubling(a:SetCategory)" [color="#00EE00"];
+"RepeatedDoubling(a:SetCategory)" -> "Package"
+
+"Package" [color="#00EE00"];
+
+"Category" [color=lightblue];
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{DictionaryOperations}{DIOPS}
-\pagepic{ps/v102dictionaryoperations.ps}{DIOPS}
+\pagepic{ps/v102dictionaryoperations.ps}{DIOPS}{1.00}
{\bf See:}\\
\pageto{Dictionary}{DIAGG}
@@ -3085,7 +3741,7 @@
dictionary : () -> %
\end{verbatim}
-These exports come from BagAggregate(a:SetCategory):
+These exports come from BagAggregate(S:SetCategory):
\begin{verbatim}
any? : ((S -> Boolean),%) -> Boolean
if $ has finiteAggregate
@@ -3126,7 +3782,7 @@
?~=? : (%,%) -> Boolean if S has SETCAT
\end{verbatim}
-These exports come from Collection(a:SetCategory)
+These exports come from Collection(S:SetCategory)
\begin{verbatim}
convert : % -> InputForm if S has KONVERT INFORM
find : ((S -> Boolean),%) -> Union(S,"failed")
@@ -3240,7 +3896,7 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{DoublyLinkedAggregate}{DLAGG}
-\pagepic{ps/v102doublylinkedaggregate.ps}{DLAGG}
+\pagepic{ps/v102doublylinkedaggregate.ps}{DLAGG}{1.00}
{\bf See:}\\
\pagefrom{RecursiveAggregate}{RCAGG}
@@ -3318,7 +3974,7 @@
tail : % -> %
\end{verbatim}
-These exports come from RecursiveAggregate(a:Type):
+These exports come from RecursiveAggregate(S:Type):
\begin{verbatim}
any? : ((S -> Boolean),%) -> Boolean
if $ has finiteAggregate
@@ -3456,7 +4112,7 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{LinearAggregate}{LNAGG}
-\pagepic{ps/v102linearaggregate.ps}{LNAGG}
+\pagepic{ps/v102linearaggregate.ps}{LNAGG}{1.00}
{\bf See:}\\
\pageto{ExtensibleLinearAggregate}{ELAGG}
@@ -3557,7 +4213,7 @@
maxIndex : % -> Integer if Integer has ORDSET
\end{verbatim}
-These exports come from IndexedAggregate(a:SetCategory,b:Type)
+These exports come from IndexedAggregate(Integer,S:Type)
\begin{verbatim}
any? : ((S -> Boolean),%) -> Boolean
if $ has finiteAggregate
@@ -3608,7 +4264,7 @@
?=? : (%,%) -> Boolean if S has SETCAT
\end{verbatim}
-These exports come from Collection(a:Type):
+These exports come from Collection(S:Type):
\begin{verbatim}
construct : List S -> %
convert : % -> InputForm if S has KONVERT INFORM
@@ -3759,11 +4415,292 @@
}
@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{OrderedAbelianSemiGroup}{OASGP}
+\pagepic{ps/v102orderedabeliansemigroup.ps}{OASGP}{0.75}
+
+{\bf See:}\\
+\pageto{OrderedAbelianMonoid}{OAMON}
+\pagefrom{AbelianMonoid}{ABELMON}
+\pagefrom{OrderedSet}{ORDSET}
+
+{\bf Exports:}\\
+\begin{tabular}{llllllll}
+ 0 & coerce & hash & latex & max & min & sample & zero?\\
+ ?\~{}=? & ?*? & ?+? & ?$<$? & ?$<=$? & ?=? & ?$>$? & ?$>=$?
+\end{tabular}
+
+\cross{OASGP}{0}
+\cross{OASGP}{coerce}
+\cross{OASGP}{hash}
+\cross{OASGP}{latex}
+\cross{OASGP}{max}
+\cross{OASGP}{min}
+\cross{OASGP}{sample}
+\cross{OASGP}{zero?}
+\cross{OASGP}{?\~{}=?}
+\cross{OASGP}{?*?}
+\cross{OASGP}{?+?}
+\cross{OASGP}{?$<$?}
+\cross{OASGP}{?$<=$?}
+\cross{OASGP}{?=?}
+\cross{OASGP}{?$>$?}
+\cross{OASGP}{?$>=$?}
+
+These exports come from OrderedSet():
+\begin{verbatim}
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ max : (%,%) -> %
+ min : (%,%) -> %
+ ?<? : (%,%) -> Boolean
+ ?>? : (%,%) -> Boolean
+ ?<=? : (%,%) -> Boolean
+ ?>=? : (%,%) -> Boolean
+ ?=? : (%,%) -> Boolean
+ ?~=? : (%,%) -> Boolean
+\end{verbatim}
+
+These exports come from AbelianMonoid():
+\begin{verbatim}
+ 0 : () -> %
+ sample : () -> %
+ zero? : % -> Boolean
+ ?*? : (NonNegativeInteger,%) -> %
+ ?*? : (PositiveInteger,%) -> %
+ ?+? : (%,%) -> %
+\end{verbatim}
+
+<<category OASGP OrderedAbelianSemiGroup>>=
+)abbrev category OASGP OrderedAbelianSemiGroup
+++ Author:
+++ Date Created:
+++ Date Last Updated:
+++ Basic Functions:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++ Ordered sets which are also abelian semigroups, such that the addition
+++ preserves the ordering.
+++ \spad{ x < y => x+z < y+z}
+OrderedAbelianSemiGroup(): Category == Join(OrderedSet, AbelianMonoid)
+
+@
+<<OASGP.dotabb>>=
+"OASGP"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=OASGP"];
+"OASGP" -> "ORDSET"
+"OASGP" -> "ABELMON"
+
+@
+<<OASGP.dotfull>>=
+"OrderedAbelianSemiGroup()"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=OASGP"];
+"OrderedAbelianSemiGroup()" -> "OrderedSet()"
+"OrderedAbelianSemiGroup()" -> "AbelianMonoid()"
+
+@
+<<OASGP.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"OrderedAbelianSemiGroup()" [color=lightblue];
+"OrderedAbelianSemiGroup()" -> "OrderedSet()"
+"OrderedAbelianSemiGroup()" -> "AbelianMonoid()"
+
+"OrderedSet()" [color=lightblue];
+"OrderedSet()" -> "SetCategory()"
+
+"AbelianMonoid()" [color=lightblue];
+"AbelianMonoid()" -> "AbelianSemiGroup()"
+
+"AbelianSemiGroup()" [color=lightblue];
+"AbelianSemiGroup()" -> "SetCategory()"
+"AbelianSemiGroup()" -> "RepeatedDoubling(AbelianSemiGroup)"
+
+"SetCategory()" [color=lightblue];
+"SetCategory()" -> "BasicType()"
+"SetCategory()" -> "CoercibleTo(OutputForm)"
+
+"BasicType()" [color=lightblue];
+"BasicType()" -> "Category"
+
+"CoercibleTo(OutputForm)" [color=seagreen];
+"CoercibleTo(OutputForm)" ->
+ "CoercibleTo(a:Type)"
+
+"CoercibleTo(a:Type)" [color=lightblue];
+"CoercibleTo(a:Type)" -> "Category"
+
+"RepeatedDoubling(AbelianSemiGroup)" [color="#00EE00"];
+"RepeatedDoubling(AbelianSemiGroup)" -> "RepeatedDoubling(a:SetCategory)"
+
+"RepeatedDoubling(a:SetCategory)" [color="#00EE00"];
+"RepeatedDoubling(a:SetCategory)" -> "Package"
+
+"Package" [color="#00EE00"];
+
+"Category" [color=lightblue];
+}
+
+@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{OrderedMonoid}{ORDMON}
+\pagepic{ps/v102orderedmonoid.ps}{ORDMON}{0.75}
+
+{\bf See:}\\
+\pagefrom{Monoid}{MONOID}
+\pagefrom{OrderedSet}{ORDSET}
+
+{\bf Exports:}\\
+\begin{tabular}{llllll}
+ 1 & coerce & hash & latex & max & min\\
+ one? & recip & sample & ?*? & ?**? & ?$<$?\\
+ ?$<=$? & ?=? & ?$>$? & ?$>=$? & ?\~{}=? & ?\^{}?\\
+\end{tabular}
+
+\cross{ORDMON}{1}
+\cross{ORDMON}{coerce}
+\cross{ORDMON}{hash}
+\cross{ORDMON}{latex}
+\cross{ORDMON}{max}
+\cross{ORDMON}{min}
+\cross{ORDMON}{one?}
+\cross{ORDMON}{recip}
+\cross{ORDMON}{sample}
+\cross{ORDMON}{?*?}
+\cross{ORDMON}{?**?}
+\cross{ORDMON}{?$<$?}
+\cross{ORDMON}{?$<=$?}
+\cross{ORDMON}{?=?}
+\cross{ORDMON}{?$>$?}
+\cross{ORDMON}{?$>=$?}
+\cross{ORDMON}{?\~{}=?}
+\cross{ORDMON}{?\^{}?}
+
+These exports come from Monoid():
+\begin{verbatim}
+ 1 : () -> %
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ one? : % -> Boolean
+ recip : % -> Union(%,"failed")
+ sample : () -> %
+ ?*? : (%,%) -> %
+ ?^? : (%,PositiveInteger) -> %
+ ?^? : (%,NonNegativeInteger) -> %
+ ?**? : (%,PositiveInteger) -> %
+ ?**? : (%,NonNegativeInteger) -> %
+ ?=? : (%,%) -> Boolean
+ ?~=? : (%,%) -> Boolean
+\end{verbatim}
+
+These exports come from OrderedSet():
+\begin{verbatim}
+ max : (%,%) -> %
+ min : (%,%) -> %
+ ?<? : (%,%) -> Boolean
+ ?<=? : (%,%) -> Boolean
+ ?>? : (%,%) -> Boolean
+ ?>=? : (%,%) -> Boolean
+\end{verbatim}
+
+<<category ORDMON OrderedMonoid>>=
+)abbrev category ORDMON OrderedMonoid
+++ Author:
+++ Date Created:
+++ Date Last Updated:
+++ Basic Functions:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++ Ordered sets which are also monoids, such that multiplication
+++ preserves the ordering.
+++
+++ Axioms:
+++ \spad{x < y => x*z < y*z}
+++ \spad{x < y => z*x < z*y}
+
+OrderedMonoid(): Category == Join(OrderedSet, Monoid)
+
+@
+<<ORDMON.dotabb>>=
+"ORDMON"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ORDMON"];
+"ORDMON" -> "ORDSET"
+"ORDMON" -> "MONOID"
+
+@
+<<ORDMON.dotfull>>=
+"OrderedMonoid()"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ORDMON"];
+"OrderedMonoid()" -> "OrderedSet()"
+"OrderedMonoid()" -> "Monoid()"
+@
+<<ORDMON.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"OrderedMonoid()"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ORDMON"];
+"OrderedMonoid()" -> "OrderedSet()"
+"OrderedMonoid()" -> "Monoid()"
+
+"OrderedSet()"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ORDSET"];
+"OrderedSet()" -> "SetCategory()"
+
+"Monoid()" [color=lightblue];
+"Monoid()" -> "SemiGroup()"
+
+"SemiGroup()" [color=lightblue];
+"SemiGroup()" -> "SetCategory()"
+"SemiGroup()" -> "RepeatedSquaring(SemiGroup)"
+
+"SetCategory()" [color=lightblue];
+"SetCategory()" -> "BasicType()"
+"SetCategory()" -> "CoercibleTo(OutputForm)"
+
+"BasicType()" [color=lightblue];
+"BasicType()" -> "Category"
+
+"CoercibleTo(OutputForm)" [color=seagreen];
+"CoercibleTo(OutputForm)" -> "CoercibleTo(a:Type)"
+
+"CoercibleTo(a:Type)" [color=lightblue];
+"CoercibleTo(a:Type)" -> "Category"
+
+"RepeatedSquaring(SemiGroup)" [color="#00EE00"];
+"RepeatedSquaring(SemiGroup)" -> "RepeatedSquaring(a:SetCategory)"
+
+"RepeatedSquaring(a:SetCategory)" [color="#00EE00"];
+"RepeatedSquaring(a:SetCategory)" -> "Package"
+
+"Package" [color="#00EE00"];
+
+"Category" [color=lightblue];
+
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{PriorityQueueAggregate}{PRQAGG}
-\pagepic{ps/v102priorityqueueaggregate.ps}{PRQAGG}
+\pagepic{ps/v102priorityqueueaggregate.ps}{PRQAGG}{1.00}
{\bf See:}\\
+\pageto{OrderedMultisetAggregate}{OMSAGG}
\pagefrom{BagAggregate}{BGAGG}
{\bf Exports:}\\
@@ -3813,7 +4750,7 @@
merge! : (%,%) -> %
\end{verbatim}
-These exports come from PriorityQueueAggregate(a:Type):
+These exports come from BagAggregate(S:OrderedSet):
\begin{verbatim}
any? : ((S -> Boolean),%) -> Boolean
if $ has finiteAggregate
@@ -3930,7 +4867,7 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{QueueAggregate}{QUAGG}
-\pagepic{ps/v102queueaggregate.ps}{QUAGG}
+\pagepic{ps/v102queueaggregate.ps}{QUAGG}{1.00}
{\bf See:}\\
\pageto{DequeueAggregate}{DQAGG}
@@ -3989,7 +4926,7 @@
rotate! : % -> %
\end{verbatim}
-These exports come from BagAggregate(a:Type):
+These exports come from BagAggregate(S:Type):
\begin{verbatim}
any? : ((S -> Boolean),%) -> Boolean
if $ has finiteAggregate
@@ -4112,8 +5049,296 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{SetAggregate}{SETAGG}
+\pagepic{ps/v102setaggregate.ps}{SETAGG}{1.00}
+
+{\bf See:}\\
+\pageto{FiniteSetAggregate}{FSAGG}
+\pageto{MultisetAggregate}{MSETAGG}
+\pagefrom{Collection}{CLAGG}
+\pagefrom{SetCategory}{SETCAT}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+ any? & brace & coerce & construct & convert\\
+ copy & count & difference & empty & empty?\\
+ eq? & eval & every? & find & hash\\
+ intersect & latex & less? & map & map!\\
+ member? & members & more? & parts & reduce\\
+ remove & removeDuplicates & sample & select & set\\
+ size? & subset? & symmetricDifference & union & \#?\\
+ ?$<$? & ?=? & ?\~{}=? &&
+\end{tabular}
+
+\cross{SETAGG}{any?}
+\cross{SETAGG}{brace}
+\cross{SETAGG}{coerce}
+\cross{SETAGG}{construct}
+\cross{SETAGG}{convert}
+\cross{SETAGG}{copy}
+\cross{SETAGG}{count}
+\cross{SETAGG}{difference}
+\cross{SETAGG}{empty}
+\cross{SETAGG}{empty?}
+\cross{SETAGG}{eq?}
+\cross{SETAGG}{eval}
+\cross{SETAGG}{every?}
+\cross{SETAGG}{find}
+\cross{SETAGG}{hash}
+\cross{SETAGG}{intersect}
+\cross{SETAGG}{latex}
+\cross{SETAGG}{less?}
+\cross{SETAGG}{map}
+\cross{SETAGG}{map!}
+\cross{SETAGG}{member?}
+\cross{SETAGG}{members}
+\cross{SETAGG}{more?}
+\cross{SETAGG}{parts}
+\cross{SETAGG}{reduce}
+\cross{SETAGG}{remove}
+\cross{SETAGG}{removeDuplicates}
+\cross{SETAGG}{sample}
+\cross{SETAGG}{select}
+\cross{SETAGG}{set}
+\cross{SETAGG}{size?}
+\cross{SETAGG}{subset?}
+\cross{SETAGG}{symmetricDifference}
+\cross{SETAGG}{union}
+\cross{SETAGG}{\#?}
+\cross{SETAGG}{?$<$?}
+\cross{SETAGG}{?=?}
+\cross{SETAGG}{?\~{}=?}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ brace : List S -> %
+ brace : () -> %
+ difference : (%,%) -> %
+ intersect : (%,%) -> %
+ set : List S -> %
+ set : () -> %
+ subset? : (%,%) -> Boolean
+ union : (%,%) -> %
+ ?<? : (%,%) -> Boolean
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ difference : (%,S) -> %
+ symmetricDifference : (%,%) -> %
+ union : (S,%) -> %
+ union : (%,S) -> %
+\end{verbatim}
+
+These exports come from SetCategory():
+\begin{verbatim}
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ ?=? : (%,%) -> Boolean
+ ?~=? : (%,%) -> Boolean
+\end{verbatim}
+
+These exports come from Collection(S:SetCategory):
+\begin{verbatim}
+ any? : ((S -> Boolean),%) -> Boolean
+ if $ has finiteAggregate
+ construct : List S -> %
+ convert : % -> InputForm if S has KONVERT INFORM
+ copy : % -> %
+ count : ((S -> Boolean),%) -> NonNegativeInteger
+ if $ has finiteAggregate
+ count : (S,%) -> NonNegativeInteger
+ if S has SETCAT
+ and $ has finiteAggregate
+ empty : () -> %
+ empty? : % -> Boolean
+ eq? : (%,%) -> Boolean
+ eval : (%,List Equation S) -> %
+ if S has EVALAB S
+ and S has SETCAT
+ eval : (%,Equation S) -> %
+ if S has EVALAB S
+ and S has SETCAT
+ eval : (%,S,S) -> %
+ if S has EVALAB S
+ and S has SETCAT
+ eval : (%,List S,List S) -> %
+ if S has EVALAB S
+ and S has SETCAT
+ every? : ((S -> Boolean),%) -> Boolean
+ if $ has finiteAggregate
+ find : ((S -> Boolean),%) -> Union(S,"failed")
+ less? : (%,NonNegativeInteger) -> Boolean
+ map : ((S -> S),%) -> %
+ map! : ((S -> S),%) -> % if $ has shallowlyMutable
+ members : % -> List S if $ has finiteAggregate
+ member? : (S,%) -> Boolean
+ if S has SETCAT and $ has finiteAggregate
+ more? : (%,NonNegativeInteger) -> Boolean
+ parts : % -> List S if $ has finiteAggregate
+ reduce : (((S,S) -> S),%,S,S) -> S
+ if S has SETCAT
+ and $ has finiteAggregate
+ reduce : (((S,S) -> S),%,S) -> S
+ if $ has finiteAggregate
+ reduce : (((S,S) -> S),%) -> S
+ if $ has finiteAggregate
+ remove : ((S -> Boolean),%) -> %
+ if $ has finiteAggregate
+ remove : (S,%) -> %
+ if S has SETCAT
+ and $ has finiteAggregate
+ removeDuplicates : % -> %
+ if S has SETCAT
+ and $ has finiteAggregate
+ sample : () -> %
+ select : ((S -> Boolean),%) -> %
+ if $ has finiteAggregate
+ size? : (%,NonNegativeInteger) -> Boolean
+ #? : % -> NonNegativeInteger
+ if $ has finiteAggregate
+\end{verbatim}
+
+<<category SETAGG SetAggregate>>=
+)abbrev category SETAGG SetAggregate
+++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
+++ Date Created: August 87 through August 88
+++ Date Last Updated: 14 Oct, 1993 by RSS
+++ Basic Operations:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++ A set category lists a collection of set-theoretic operations
+++ useful for both finite sets and multisets.
+++ Note however that finite sets are distinct from multisets.
+++ Although the operations defined for set categories are
+++ common to both, the relationship between the two cannot
+++ be described by inclusion or inheritance.
+SetAggregate(S:SetCategory):
+ Category == Join(SetCategory, Collection(S)) with
+ partiallyOrderedSet
+ "<" : (%, %) -> Boolean
+ ++ s < t returns true if all elements of set aggregate s are also
+ ++ elements of set aggregate t.
+ brace : () -> %
+ ++ brace()$D (otherwise written {}$D)
+ ++ creates an empty set aggregate of type D.
+ ++ This form is considered obsolete. Use \axiomFun{set} instead.
+ brace : List S -> %
+ ++ brace([x,y,...,z])
+ ++ creates a set aggregate containing items x,y,...,z.
+ ++ This form is considered obsolete. Use \axiomFun{set} instead.
+ set : () -> %
+ ++ set()$D creates an empty set aggregate of type D.
+ set : List S -> %
+ ++ set([x,y,...,z]) creates a set aggregate containing items x,y,...,z.
+ intersect: (%, %) -> %
+ ++ intersect(u,v) returns the set aggregate w consisting of
+ ++ elements common to both set aggregates u and v.
+ ++ Note: equivalent to the notation (not currently supported)
+ ++ {x for x in u | member?(x,v)}.
+ difference : (%, %) -> %
+ ++ difference(u,v) returns the set aggregate w consisting of
+ ++ elements in set aggregate u but not in set aggregate v.
+ ++ If u and v have no elements in common, \axiom{difference(u,v)}
+ ++ returns a copy of u.
+ ++ Note: equivalent to the notation (not currently supported)
+ ++ \axiom{{x for x in u | not member?(x,v)}}.
+ difference : (%, S) -> %
+ ++ difference(u,x) returns the set aggregate u with element x removed.
+ ++ If u does not contain x, a copy of u is returned.
+ ++ Note: \axiom{difference(s, x) = difference(s, {x})}.
+ symmetricDifference : (%, %) -> %
+ ++ symmetricDifference(u,v) returns the set aggregate of elements x
+ ++ which are members of set aggregate u or set aggregate v but
+ ++ not both. If u and v have no elements in common,
+ ++ \axiom{symmetricDifference(u,v)} returns a copy of u.
+ ++ Note: \axiom{symmetricDifference(u,v) =
+ ++ union(difference(u,v),difference(v,u))}
+ subset? : (%, %) -> Boolean
+ ++ subset?(u,v) tests if u is a subset of v.
+ ++ Note: equivalent to
+ ++ \axiom{reduce(and,{member?(x,v) for x in u},true,false)}.
+ union : (%, %) -> %
+ ++ union(u,v) returns the set aggregate of elements which are members
+ ++ of either set aggregate u or v.
+ union : (%, S) -> %
+ ++ union(u,x) returns the set aggregate u with the element x added.
+ ++ If u already contains x, \axiom{union(u,x)} returns a copy of u.
+ union : (S, %) -> %
+ ++ union(x,u) returns the set aggregate u with the element x added.
+ ++ If u already contains x, \axiom{union(x,u)} returns a copy of u.
+ add
+ symmetricDifference(x, y) == union(difference(x, y), difference(y, x))
+ union(s:%, x:S) == union(s, {x})
+ union(x:S, s:%) == union(s, {x})
+ difference(s:%, x:S) == difference(s, {x})
+
+@
+<<SETAGG.dotabb>>=
+"SETAGG"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=SETAGG"];
+"SETAGG" -> "SETCAT"
+"SETAGG" -> "CLAGG"
+
+@
+<<SETAGG.dotfull>>=
+"SetAggregate(a:SetCategory)"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=SETAGG"];
+"SetAggregate(a:SetCategory)" -> "SetCategory()"
+"SetAggregate(a:SetCategory)" -> "Collection(a:SetCategory)"
+
+@
+<<SETAGG.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"SetAggregate(a:SetCategory)" [color=lightblue];
+"SetAggregate(a:SetCategory)" -> "SetCategory()"
+"SetAggregate(a:SetCategory)" -> "Collection(a:SetCategory)"
+
+"SetCategory()" [color=lightblue];
+"SetCategory()" -> "BasicType()"
+"SetCategory()" -> "CoercibleTo(OutputForm)"
+
+"BasicType()" [color=lightblue];
+"BasicType()" -> "Category"
+
+"CoercibleTo(OutputForm)" [color=seagreen];
+"CoercibleTo(OutputForm)" -> "CoercibleTo(a:Type)"
+
+"CoercibleTo(a:Type)" [color=lightblue];
+"CoercibleTo(a:Type)" -> "Category"
+
+"Collection(a:SetCategory)"
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=CLAGG"];
+"Collection(a:SetCategory)" -> "Collection(a:Type)"
+
+"Collection(a:Type)" [color=lightblue];
+"Collection(a:Type)" -> "HomogeneousAggregate(a:Type)"
+
+"HomogeneousAggregate(a:Type)" [color=lightblue];
+"HomogeneousAggregate(a:Type)" -> "Aggregate()"
+
+"Aggregate()" [color=lightblue];
+"Aggregate()" -> "Type()"
+
+"Type()" [color=lightblue];
+"Type()" -> "Category"
+
+"Category" [color=lightblue];
+
+}
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{StackAggregate}{SKAGG}
-\pagepic{ps/v102stackaggregate.ps}{SKAGG}
+\pagepic{ps/v102stackaggregate.ps}{SKAGG}{1.00}
{\bf See:}\\
\pageto{DequeueAggregate}{DQAGG}
@@ -4168,7 +5393,7 @@
top : % -> S
\end{verbatim}
-These exports come from BagAggregate(a:Type):
+These exports come from BagAggregate(S:Type):
\begin{verbatim}
any? : ((S -> Boolean),%) -> Boolean
if $ has finiteAggregate
@@ -4285,7 +5510,7 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{UnaryRecursiveAggregate}{URAGG}
-\pagepic{ps/v102unaryrecursiveaggregate.ps}{URAGG}
+\pagepic{ps/v102unaryrecursiveaggregate.ps}{URAGG}{1.00}
{\bf See:}\\
\pageto{StreamAggregate}{STAGG}
@@ -4409,7 +5634,7 @@
?.rest : (%,rest) -> %
\end{verbatim}
-These exports come from RecursiveAggregate(a:Type):
+These exports come from RecursiveAggregate(S:Type):
\begin{verbatim}
any? : ((S -> Boolean),%) -> Boolean
if $ has finiteAggregate
@@ -4751,10 +5976,154 @@
@
\chapter{Category Layer 6}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{AbelianGroup}{ABELGRP}
+\pagepic{ps/v102abeliangroup.ps}{ABELGRP}{0.75}
+
+{\bf See:}\\
+\pageto{Rng}{RNG}
+\pagefrom{CancellationAbelianMonoid}{CABMON}
+
+{\bf Exports:}\\
+\begin{tabular}{lllllll}
+ 0 & coerce & hash & latex & sample & subtractIfCan & zero?\\
+ ?\~{}=? & ?*? & ?+? & ?-? & -? & ?=? &
+\end{tabular}
+
+\cross{ABELGRP}{0}
+\cross{ABELGRP}{coerce}
+\cross{ABELGRP}{hash}
+\cross{ABELGRP}{latex}
+\cross{ABELGRP}{sample}
+\cross{ABELGRP}{subtractIfCan}
+\cross{ABELGRP}{zero?}
+\cross{ABELGRP}{?\~{}=?}
+\cross{ABELGRP}{?*?}
+\cross{ABELGRP}{?+?}
+\cross{ABELGRP}{?-?}
+\cross{ABELGRP}{-?}
+\cross{ABELGRP}{?=?}
+
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ -? : % -> %
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ subtractIfCan : (%,%) -> Union(%,"failed")
+ ?*? : (Integer,%) -> %
+ ?*? : (NonNegativeInteger,%) -> %
+ ?-? : (%,%) -> %
+\end{verbatim}
+
+These exports come from CancellationAbelianMonoid():
+\begin{verbatim}
+ 0 : () -> %
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ sample : () -> %
+ zero? : % -> Boolean
+ ?~=? : (%,%) -> Boolean
+ ?*? : (PositiveInteger,%) -> %
+ ?+? : (%,%) -> %
+ ?=? : (%,%) -> Boolean
+\end{verbatim}
+
+<<category ABELGRP AbelianGroup>>=
+)abbrev category ABELGRP AbelianGroup
+++ Author:
+++ Date Created:
+++ Date Last Updated:
+++ Basic Functions:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++ The class of abelian groups, i.e. additive monoids where
+++ each element has an additive inverse.
+++
+++ Axioms:
+++ \spad{-(-x) = x}
+++ \spad{x+(-x) = 0}
+-- following domain must be compiled with subsumption disabled
+AbelianGroup(): Category == CancellationAbelianMonoid with
+ "-": % -> %
+ ++ -x is the additive inverse of x.
+ "-": (%,%) -> %
+ ++ x-y is the difference of x and y
+ ++ i.e. \spad{x + (-y)}.
+ -- subsumes the partial subtraction from previous
+ "*": (Integer,%) -> %
+ ++ n*x is the product of x by the integer n.
+ add
+ (x:% - y:%):% == x+(-y)
+ subtractIfCan(x:%, y:%):Union(%, "failed") == (x-y)::Union(%,"failed")
+ n:NonNegativeInteger * x:% == (n::Integer) * x
+ import RepeatedDoubling(%)
+ if not (% has Ring) then
+ n:Integer * x:% ==
+ zero? n => 0
+ n>0 => double(n pretend PositiveInteger,x)
+ double((-n) pretend PositiveInteger,-x)
+
+@
+<<ABELGRP.dotabb>>=
+"ABELGRP"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ABELGRP"];
+"ABELGRP" -> "CABMON"
+
+@
+<<ABELGRP.dotfull>>=
+"AbelianGroup()"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ABELGRP"];
+"AbelianGroup()" -> "CancellationAbelianMonoid()"
+
+@
+<<ABELGRP.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"AbelianGroup()" [color=lightblue];
+"AbelianGroup()" -> "CancellationAbelianMonoid()"
+"AbelianGroup()" -> "RepeatedDoubling(AbelianGroup)"
+
+"RepeatedDoubling(AbelianGroup)" [color="#00EE00"];
+"RepeatedDoubling(AbelianGroup)" -> "RepeatedDoubling(a:SetCategory)"
+
+"RepeatedDoubling(AbelianSemiGroup)" [color="#00EE00"];
+"RepeatedDoubling(AbelianSemiGroup)" -> "RepeatedDoubling(a:SetCategory)"
+
+"RepeatedDoubling(a:SetCategory)" [color="#00EE00"];
+"RepeatedDoubling(a:SetCategory)" -> "Package"
+
+"Package" [color="#00EE00"];
+
+"CancellationAbelianMonoid()" [color=lightblue];
+"CancellationAbelianMonoid()" -> "AbelianMonoid()"
+
+"AbelianMonoid()" [color=lightblue];
+"AbelianMonoid()" -> "AbelianSemiGroup()"
+
+"AbelianSemiGroup()" [color=lightblue];
+"AbelianSemiGroup()" -> "SETCAT..."
+"AbelianSemiGroup()" -> "RepeatedDoubling(AbelianSemiGroup)"
+
+"SETCAT..." [color=lightblue];
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{Dictionary}{DIAGG}
-\pagepic{ps/v102dictionary.ps}{DIAGG}
+\pagepic{ps/v102dictionary.ps}{DIAGG}{1.00}
{\bf See:}\\
+\pageto{FiniteSetAggregate}{FSAGG}
\pageto{KeyedDictionary}{KDAGG}
\pagefrom{DictionaryOperations}{DIOPS}
@@ -4816,7 +6185,7 @@
remove! : ((S -> Boolean),%) -> % if $ has finiteAggregate
\end{verbatim}
-These exports come from DictionaryOperations(a:SetCategory):
+These exports come from DictionaryOperations(S:SetCategory):
\begin{verbatim}
any? : ((S -> Boolean),%) -> Boolean
if $ has finiteAggregate
@@ -4972,7 +6341,7 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{DequeueAggregate}{DQAGG}
-\pagepic{ps/v102dequeueaggregate.ps}{DQAGG}
+\pagepic{ps/v102dequeueaggregate.ps}{DQAGG}{1.00}
{\bf See:}\\
\pagefrom{QueueAggregate}{QUAGG}
@@ -5053,7 +6422,7 @@
top! : % -> S
\end{verbatim}
-These exports come from StackAggregate(a:Type):
+These exports come from StackAggregate(S:Type):
\begin{verbatim}
any? : ((S -> Boolean),%) -> Boolean
if $ has finiteAggregate
@@ -5100,7 +6469,7 @@
?~=? : (%,%) -> Boolean if S has SETCAT
\end{verbatim}
-These exports come from QueueAggregate(a:Type):
+These exports come from QueueAggregate(S:Type):
\begin{verbatim}
back : % -> S
dequeue! : % -> S
@@ -5205,7 +6574,7 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{ExtensibleLinearAggregate}{ELAGG}
-\pagepic{ps/v102extensiblelinearaggregate.ps}{ELAGG}
+\pagepic{ps/v102extensiblelinearaggregate.ps}{ELAGG}{1.00}
{\bf See:}\\
\pageto{ListAggregate}{LSAGG}
@@ -5313,7 +6682,7 @@
select : ((S -> Boolean),%) -> % if $ has finiteAggregate
\end{verbatim}
-These exports come from LinearAggregate(a:Type):
+These exports come from LinearAggregate(S:Type):
\begin{verbatim}
any? : ((S -> Boolean),%) -> Boolean
if $ has finiteAggregate
@@ -5503,7 +6872,7 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{FiniteLinearAggregate}{FLAGG}
-\pagepic{ps/v102finitelinearaggregate.ps}{FLAGG}
+\pagepic{ps/v102finitelinearaggregate.ps}{FLAGG}{1.00}
{\bf See:}\\
\pageto{OneDimensionalArrayAggregate}{A1AGG}
@@ -5583,11 +6952,11 @@
\cross{FLAGG}{\#?}
\cross{FLAGG}{?.?}
\cross{FLAGG}{?.?}
-\cross{FLAGG}{?<?}
-\cross{FLAGG}{?<=?}
+\cross{FLAGG}{?$<$?}
+\cross{FLAGG}{?$<=$?}
\cross{FLAGG}{?=?}
-\cross{FLAGG}{?>?}
-\cross{FLAGG}{?>=?}
+\cross{FLAGG}{?$>$?}
+\cross{FLAGG}{?$>=$?}
\cross{FLAGG}{?\~{}=?}
These are directly exported but not implemented:
@@ -5615,7 +6984,7 @@
if S has ORDSET and $ has shallowlyMutable
\end{verbatim}
-These exports come from LinearAggregate(a:Type):
+These exports come from LinearAggregate(S:Type):
\begin{verbatim}
any? : ((S -> Boolean),%) -> Boolean
if $ has finiteAggregate
@@ -5846,9 +7215,10 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{MultiDictionary}{MDAGG}
-\pagepic{ps/v102multidictionary.ps}{MDAGG}
+\pagepic{ps/v102multidictionary.ps}{MDAGG}{1.00}
{\bf See:}\\
+\pageto{MultisetAggregate}{MSETAGG}
\pagefrom{DictionaryOperations}{DIOPS}
{\bf Exports:}\\
@@ -5857,10 +7227,10 @@
copy & count & dictionary & duplicates & empty\\
empty? & eq? & eval & every? & extract!\\
find & hash & insert! & inspect & latex\\
- less? & map & map! & member? & members\\
+ less? & map & map! & member? & members\\
more? & parts & reduce & remove & remove! \\
- removeDuplicates & sample & select & select! & size? \\
- \#? & ?=? & ?\~{}=? &&\\
+ removeDuplicates & removeDuplicates! & sample & select & select!\\
+ size? & \#? & ?=? & ?\~{}=? &\\
\end{tabular}
\cross{MDAGG}{any?}
@@ -5894,6 +7264,7 @@
\cross{MDAGG}{remove}
\cross{MDAGG}{remove!}
\cross{MDAGG}{removeDuplicates}
+\cross{MDAGG}{removeDuplicates!}
\cross{MDAGG}{sample}
\cross{MDAGG}{select}
\cross{MDAGG}{select!}
@@ -5906,10 +7277,10 @@
\begin{verbatim}
insert! : (S,%,NonNegativeInteger) -> %
removeDuplicates! : % -> %
- duplicates : % -> List Record(entry: S,count: NonNegativeInteger)
+ duplicates : % -> List Record(entry:S,count:NonNegativeInteger)
\end{verbatim}
-These exports come from DictionaryOperations(a:SetCategory):
+These exports come from DictionaryOperations(S:SetCategory):
\begin{verbatim}
any? : ((S -> Boolean),%) -> Boolean
if $ has finiteAggregate
@@ -6047,10 +7418,122 @@
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{OrderedAbelianMonoid}{OAMON}
+\pagepic{ps/v102orderedabelianmonoid.ps}{OAMON}{1.00}
+
+{\bf See:}\\
+\pagefrom{AbelianMonoid}{ABELMON}
+\pagefrom{OrderedAbelianSemiGroup}{OASGP}
+
+{\bf Exports:}\\
+\begin{tabular}{lllllll}
+ 0 ...
[truncated message content] |
|
From: <gi...@ax...> - 2008-09-19 00:17:24
|
books/bookvol10.2.pamphlet | 1212 ++++++++++++++++++++++++++--------
books/ps/v102finite.ps | 494 ++++++++++++++
books/ps/v102homogeneousaggregate.ps | 428 ++++++++----
books/ps/v102orderedset.ps | 494 ++++++++++++++
books/ps/v102semigroup.ps | 632 ++++++++++++++++++
changelog | 6 +
src/algebra/catdef.spad.pamphlet | 141 ----
7 files changed, 2837 insertions(+), 570 deletions(-)
New commits:
commit bb976a5dc350cae3e256b868b2bed008d9c74923
Author: Tim Daly <da...@ax...>
Date: Sat Jul 26 19:22:36 2008 -0400
20080918 tpd books/ps/v102semigroup.ps diagram SGROUP
20080918 tpd books/ps/v102orderedset.ps diagram ORDSET
20080918 tpd books/ps/v102finite.ps diagram FINITE
20080918 tpd src/algebra/catdef.spad remove FINITE, ORDSET, SGROUP
20080918 tpd books/ps/v102homogeneousaggregate.ps corrected diagram
20080918 tpd books/bookvol10.2 add FINITE, ORDSET, SGROUP
|
|
From: <da...@us...> - 2008-09-18 10:15:23
|
Revision: 976
http://axiom.svn.sourceforge.net/axiom/?rev=976&view=rev
Author: daly
Date: 2008-09-18 17:15:34 +0000 (Thu, 18 Sep 2008)
Log Message:
-----------
20080917 tpd src/algebra/catdef.spad remove BASTYPE, SETCAT, ABELSG
20080917 tpd books/ps/v102abeliansemigroup.ps ABELSG graph
20080917 tpd books/ps/v102setcategory.ps SETCAT graph
20080917 tpd books/ps/v102basictype.ps BASTYPE graph
20080917 tpd books/bookvol10.2 add pdf destinations
20080917 tpd books/bookvol10.2 add BASTYPE, SETCAT, ABELSG
Modified Paths:
--------------
trunk/axiom/books/bookvol10.2.pamphlet
trunk/axiom/changelog
trunk/axiom/src/algebra/catdef.spad.pamphlet
Added Paths:
-----------
trunk/axiom/books/ps/v102abeliansemigroup.ps
trunk/axiom/books/ps/v102basictype.ps
trunk/axiom/books/ps/v102setcategory.ps
Modified: trunk/axiom/books/bookvol10.2.pamphlet
===================================================================
--- trunk/axiom/books/bookvol10.2.pamphlet 2008-09-18 05:28:06 UTC (rev 975)
+++ trunk/axiom/books/bookvol10.2.pamphlet 2008-09-18 17:15:34 UTC (rev 976)
@@ -6,9 +6,29 @@
\makeindex
\usepackage{graphicx}
%%
+%% Note that this file will eventually generate a dvi file
+%% which will eventually be processed by dvipdfm to create a pdf.
+%% The categories/domains/packages will be placed in a graphviz graph.
+%% The graphviz dot syntax allows an href parameter.
+%% The href parameter will reference this file.
+%% pdf href syntax allows named destinations.
+%% This macro creates a named destination using \special
+%% Thus, you reference http://thispdf#nameddest=ABBREV
+%% and you end up at the right page.
+%% This macro is called implicitly by \pagehead so every
+%% category/domain/package can be referenced by fullname or abbrev.
+%%
+%% dest will give the ability to use nameddest= in html pdfs
+%%
+\newcommand{\dest}[1]{% e.g. \dest{abb}
+\special{pdf:dest (#1) [ @thispage /FitH @ypos ]}}
+%%
+%%
%% pagehead consolidates standard page indexing
%%
\newcommand{\pagehead}[2]{% e.g. \pagehead{name}{abb}
+\dest{#1}%
+\dest{#2}%
\section{#1 (#2)}
\label{#1}%
\label{#2}%
@@ -36,7 +56,6 @@
\newcommand{\cross}[2]{% e.g. \pagefrom{cat}{funcname}
\index{#1!#2}%
\index{#2!#1}}
-%%
% special meanings for math characters
@@ -262,6 +281,7 @@
This is the root of the category hierarchy and is not represented by code.
{\bf See:}\\
+\pageto{BasicType}{BASTYPE}
\pageto{Eltable}{ELTAB}
\pageto{CoercibleTo}{KOERCE}
\pageto{ConvertibleTo}{KONVERT}
@@ -269,6 +289,75 @@
\pageto{Type}{TYPE}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{BasicType}{BASTYPE}
+\pagepic{ps/v102basictype.ps}{BASTYPE}
+
+{\bf See:}\\
+\pagefrom{Category}{CATEGORY}
+
+{\bf Exports:}\\
+\begin{tabular}{ll}
+ ?=? & ?\~{}=?
+\end{tabular}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ ?=? : (%,%) -> Boolean
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ ?~=? : (%,%) -> Boolean
+\end{verbatim}
+
+<<category BASTYPE BasicType>>=
+)abbrev category BASTYPE BasicType
+--% BasicType
+++ Author:
+++ Date Created:
+++ Date Last Updated:
+++ Basic Functions:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++ \spadtype{BasicType} is the basic category for describing a collection
+++ of elements with \spadop{=} (equality).
+BasicType(): Category == with
+ "=": (%,%) -> Boolean ++ x=y tests if x and y are equal.
+ "~=": (%,%) -> Boolean ++ x~=y tests if x and y are not equal.
+ add
+ _~_=(x:%,y:%) : Boolean == not(x=y)
+
+@
+<<BASTYPE.dotabb>>=
+"BASTYPE"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=BASTYPE"];
+"BASTYPE" -> "CATEGORY"
+
+@
+<<BASTYPE.dotfull>>=
+"BasicType()"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=BASTYPE"];
+"BasicType()" -> "Category"
+
+@
+<<BASTYPE.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"BasicType()" [color=lightblue];
+"BasicType()" -> "Category"
+
+"Category" [color=lightblue];
+}
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{CoercibleTo}{KOERCE}
\pagepic{ps/v102koerce.ps}{KOERCE}
@@ -302,17 +391,20 @@
@
<<KOERCE.dotabb>>=
-"KOERCE" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"KOERCE" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=KOERCE"];
"KOERCE" -> "CATEGORY"
@
<<KOERCE.dotfull>>=
-"CoercibleTo(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"CoercibleTo(a:Type)"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=KOERCE"];
"CoercibleTo(a:Type)" -> "Category"
-"CoercibleTo(OutputForm)" [color=seagreen,href="books/bookvol10.2.pamphlet"];
+"CoercibleTo(OutputForm)"
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KOERCE"];
"CoercibleTo(OutputForm)" ->
"CoercibleTo(a:Type)"
+
@
<<KOERCE.dotpic>>=
digraph pic {
@@ -320,10 +412,10 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"CoercibleTo(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"CoercibleTo(a:Type)" [color=lightblue];
"CoercibleTo(a:Type)" -> "Category"
-"Category" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Category" [color=lightblue];
}
@
@@ -363,73 +455,74 @@
@
<<KONVERT.dotabb>>=
-"KONVERT" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"KONVERT"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
"KONVERT" -> "CATEGORY"
@
<<KONVERT.dotfull>>=
"ConvertibleTo(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
"ConvertibleTo(a:Type)" -> "Category"
"ConvertibleTo(DoubleFloat)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
"ConvertibleTo(DoubleFloat)" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(Float)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
"ConvertibleTo(Float)" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(InputForm)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
"ConvertibleTo(InputForm)" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(Integer)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
"ConvertibleTo(Integer)" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(Pattern(Integer))"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
"ConvertibleTo(Pattern(Integer))" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(Pattern(Float))"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
"ConvertibleTo(Pattern(Float))" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(Complex(Float))"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
"ConvertibleTo(Complex(Float))" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(Complex(DoubleFloat))"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
"ConvertibleTo(Complex(DoubleFloat))" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(String)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
"ConvertibleTo(String)" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(Symbol)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
"ConvertibleTo(Symbol)" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(SExpression)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
"ConvertibleTo(SExpression)" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(Pattern(Base))"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
"ConvertibleTo(Pattern(Base))" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(List(Integer))"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
"ConvertibleTo(List(Integer))" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(List(Character))"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
"ConvertibleTo(List(Character))" -> "ConvertibleTo(a:Type)"
"ConvertibleTo(UnivariatePolynomialCategory(CommutativeRing))"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=KONVERT"];
"ConvertibleTo(UnivariatePolynomialCategory(CommutativeRing))" ->
"ConvertibleTo(a:Type)"
@
@@ -439,11 +532,10 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"ConvertibleTo(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"ConvertibleTo(a:Type)" [color=lightblue];
"ConvertibleTo(a:Type)" -> "Category"
-"Category" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Category" [color=lightblue];
}
@
@@ -491,13 +583,13 @@
@
<<ELTAB.dotabb>>=
-"ELTAB" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"ELTAB" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ELTAB"];
"ELTAB" -> "CATEGORY"
@
<<ELTAB.dotfull>>=
"Eltable(a:SetCategory,b:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ELTAB"];
"Eltable(a:SetCategory,b:Type)" -> "Category"
@
@@ -507,11 +599,10 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"Eltable(a:SetCategory,b:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Eltable(a:SetCategory,b:Type)" [color=lightblue];
"Eltable(a:SetCategory,b:Type)" -> "Category"
-"Category" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Category" [color=lightblue];
}
@
@@ -568,45 +659,46 @@
@
<<RETRACT.dotabb>>=
-"RETRACT" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"RETRACT"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=RETRACT"];
"RETRACT" -> "CATEGORY"
@
<<RETRACT.dotfull>>=
"RetractableTo(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=RETRACT"];
"RetractableTo(a:Type)" -> "Category"
"RetractableTo(SetCategory)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=RETRACT"];
"RetractableTo(SetCategory)" -> "RetractableTo(a:Type)"
"RetractableTo(Symbol)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=RETRACT"];
"RetractableTo(Symbol)" -> "RetractableTo(a:Type)"
"RetractableTo(Integer)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=RETRACT"];
"RetractableTo(Integer)" -> "RetractableTo(a:Type)"
"RetractableTo(NonNegativeInteger)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=RETRACT"];
"RetractableTo(NonNegativeInteger)" -> "RetractableTo(a:Type)"
"RetractableTo(Fraction(Integer))"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=RETRACT"];
"RetractableTo(Fraction(Integer))" -> "RetractableTo(a:Type)"
"RetractableTo(Float)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=RETRACT"];
"RetractableTo(Float)" -> "RetractableTo(a:Type)"
"RetractableTo(Kernel(ExpressionSpace))"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=RETRACT"];
"RetractableTo(Kernel(ExpressionSpace))" -> "RetractableTo(a:Type)"
"RetractableTo(CommutativeRing)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=RETRACT"];
"RetractableTo(CommutativeRing)" -> "RetractableTo(a:Type)"
@
<<RETRACT.dotpic>>=
@@ -615,11 +707,10 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"RetractableTo(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"RetractableTo(a:Type)" [color=lightblue];
"RetractableTo(a:Type)" -> "Category"
-"Category" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Category" [color=lightblue];
}
@
@@ -641,12 +732,12 @@
@
<<TYPE.dotabb>>=
-"TYPE" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"TYPE" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=TYPE"];
"TYPE" -> "CATEGORY"
@
<<TYPE.dotfull>>=
-"Type()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Type()" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=TYPE"];
"Type()" -> "Category"
@
@@ -656,10 +747,10 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"Type()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Type()" [color=lightblue];
"Type()" -> "Category"
-"Category" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Category" [color=lightblue];
}
@
@@ -748,12 +839,13 @@
@
<<AGG.dotabb>>=
-"AGG" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"AGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=AGG"];
"AGG" -> "TYPE"
@
<<AGG.dotfull>>=
-"Aggregate()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Aggregate()"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=AGG"];
"Aggregate()" -> "Type()"
@
@@ -763,13 +855,13 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"Aggregate()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Aggregate()" [color=lightblue];
"Aggregate()" -> "Type()"
-"Type()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Type()" [color=lightblue];
"Type()" -> "Category"
-"Category" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Category" [color=lightblue];
}
@
@@ -862,13 +954,13 @@
@
<<ELTAGG.dotabb>>=
-"ELTAGG" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"ELTAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ELTAGG"];
"ELTAGG" -> "ELTAB"
@
<<ELTAGG.dotfull>>=
"EltableAggregate(a:SetCategory,b:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ELTAGG"];
"EltableAggregate(a:SetCategory,b:Type)" -> "Eltable(a:SetCategory,b:Type)"
@
@@ -878,20 +970,237 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"EltableAggregate(a:SetCategory,b:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"EltableAggregate(a:SetCategory,b:Type)" [color=lightblue];
"EltableAggregate(a:SetCategory,b:Type)" -> "Eltable(a:SetCategory,b:Type)"
-"Eltable(a:SetCategory,b:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Eltable(a:SetCategory,b:Type)" [color=lightblue];
"Eltable(a:SetCategory,b:Type)" -> "Category"
-"Category" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Category" [color=lightblue];
}
@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{SetCategory}{SETCAT}
+\pagepic{ps/v102setcategory.ps}{SETCAT}
+
+{\bf See:}\\
+\pageto{AbelianSemiGroup}{ABELSG}
+\pageto{HomogeneousAggregate}{HOAGG}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+coerce & hash & latex & ?=? & ?\~{}=?
+\end{tabular}
+
+\cross{SETCAT}{coerce}
+\cross{SETCAT}{hash}
+\cross{SETCAT}{latex}
+\cross{SETCAT}{?=?}
+\cross{SETCAT}{?\~{}=?}
+
+These are implemented by this category:
+\begin{verbatim}
+ hash : % -> SingleInteger
+ latex : % -> String
+\end{verbatim}
+
+These exports come from BasicType():
+\begin{verbatim}
+ ?=? : (%,%) -> Boolean
+ ?~=? : (%,%) -> Boolean
+\end{verbatim}
+
+These exports come from CoercibleTo(OutputForm):
+\begin{verbatim}
+ coerce : % -> OutputForm
+\end{verbatim}
+
+<<category SETCAT SetCategory>>=
+)abbrev category SETCAT SetCategory
+++ Author:
+++ Date Created:
+++ Date Last Updated:
+++ 09/09/92 RSS added latex and hash
+++ Basic Functions:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++ \spadtype{SetCategory} is the basic category for describing a collection
+++ of elements with \spadop{=} (equality) and \spadfun{coerce} to output form.
+++
+++ Conditional Attributes:
+++ canonical\tab{15}data structure equality is the same as \spadop{=}
+SetCategory(): Category == Join(BasicType,CoercibleTo OutputForm) with
+ --operations
+ hash: % -> SingleInteger ++ hash(s) calculates a hash code for s.
+ latex: % -> String ++ latex(s) returns a LaTeX-printable output
+ ++ representation of s.
+ add
+ hash(s : %): SingleInteger == 0$SingleInteger
+ latex(s : %): String == "\mbox{\bf Unimplemented}"
+
+@
+<<SETCAT.dotabb>>=
+"SETCAT" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=SETCAT"];
+"SETCAT" -> "BASTYPE"
+"SETCAT" -> "KOERCE"
+
+@
+<<SETCAT.dotfull>>=
+"SetCategory()"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=SETCAT"];
+"SetCategory()" -> "BasicType()"
+"SetCategory()" -> "CoercibleTo(OutputForm)"
+
+@
+<<SETCAT.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"SetCategory()" [color=lightblue];
+"SetCategory()" -> "BasicType()"
+"SetCategory()" -> "CoercibleTo(OutputForm)"
+
+"BasicType()" [color=lightblue];
+"BasicType()" -> "Category"
+
+"CoercibleTo(OutputForm)" [color=seagreen];
+"CoercibleTo(OutputForm)" -> "CoercibleTo(a:Type)"
+
+"CoercibleTo(a:Type)" [color=lightblue];
+"CoercibleTo(a:Type)" -> "Category"
+
+"Category" [color=lightblue];
+
+}
+
+@
\chapter{Category Layer 3}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{AbelianSemiGroup}{ABELSG}
+\pagepic{ps/v102abeliansemigroup.ps}{ABELSG}
+
+{\bf See:}\\
+\pagefrom{SetCategory}{SETCAT}
+
+{\bf Exports:}\\
+\begin{tabular}{lllllll}
+ coerce & hash & latex & ?*? & ?+? & ?=? & ?\~{}=?
+\end{tabular}
+
+\cross{ABELSG}{coerce}
+\cross{ABELSG}{hash}
+\cross{ABELSG}{latex}
+\cross{ABELSG}{?*?}
+\cross{ABELSG}{?+?}
+\cross{ABELSG}{?=?}
+\cross{ABELSG}{?\~{}=?}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ ?+? : (%,%) -> %
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ ?*? : (PositiveInteger,%) -> %
+\end{verbatim}
+
+These exports come from SetCategory():
+\begin{verbatim}
+ coerce : % -> OutputForm
+ hash : % -> SingleInteger
+ latex : % -> String
+ ?=? : (%,%) -> Boolean
+ ?~=? : (%,%) -> Boolean
+\end{verbatim}
+
+<<category ABELSG AbelianSemiGroup>>=
+)abbrev category ABELSG AbelianSemiGroup
+++ Author:
+++ Date Created:
+++ Date Last Updated:
+++ Basic Functions:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++ the class of all additive (commutative) semigroups, i.e.
+++ a set with a commutative and associative operation \spadop{+}.
+++
+++ Axioms:
+++ \spad{associative("+":(%,%)->%)}\tab{30}\spad{ (x+y)+z = x+(y+z) }
+++ \spad{commutative("+":(%,%)->%)}\tab{30}\spad{ x+y = y+x }
+AbelianSemiGroup(): Category == SetCategory with
+ --operations
+ "+": (%,%) -> % ++ x+y computes the sum of x and y.
+ "*": (PositiveInteger,%) -> %
+ ++ n*x computes the left-multiplication of x by the positive integer n.
+ ++ This is equivalent to adding x to itself n times.
+ add
+ import RepeatedDoubling(%)
+ if not (% has Ring) then
+ n:PositiveInteger * x:% == double(n,x)
+
+@
+<<ABELSG.dotabb>>=
+"ABELSG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ABELSG"];
+"ABELSG" -> "SETCAT"
+"ABELSG" -> "REPDB"
+
+@
+<<ABELSG.dotfull>>=
+"AbelianSemiGroup()"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ABELSG"];
+"AbelianSemiGroup()" -> "SetCategory()"
+"AbelianSemiGroup()" -> "RepeatedDoubling(S:SetCategory)"
+
+<<ABELSG.dotpic>>=
+digraph pic {
+ fontsize=10;
+ bgcolor="#FFFF66";
+ node [shape=box, color=white, style=filled];
+
+"AbelianSemiGroup()" [color=lightblue];
+"AbelianSemiGroup()" -> "SetCategory()"
+"AbelianSemiGroup()" -> "RepeatedDoubling(S:AbelianSemiGroup)"
+
+"SetCategory()" [color=lightblue];
+"SetCategory()" -> "BasicType()"
+"SetCategory()" -> "CoercibleTo(OutputForm)"
+
+"BasicType()" [color=lightblue];
+"BasicType()" -> "Category"
+
+"CoercibleTo(OutputForm)" [color=seagreen];
+"CoercibleTo(OutputForm)" ->
+ "CoercibleTo(a:Type)"
+
+"CoercibleTo(a:Type)" [color=lightblue];
+"CoercibleTo(a:Type)" -> "Category"
+
+"RepeatedDoubling(S:AbelianSemiGroup)" [color="#00EE00"];
+"RepeatedDoubling(S:AbelianSemiGroup)" -> "RepeatedDoubling(S:SetCategory)"
+
+"RepeatedDoubling(S:SetCategory)" [color="#00EE00"];
+"RepeatedDoubling(S:SetCategory)" -> "Package"
+
+"Package" [color="#00EE00"];
+
+"Category" [color=lightblue];
+}
+
+@
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagehead{HomogeneousAggregate}{HOAGG}
\pagepic{ps/v102homogeneousaggregate.ps}{HOAGG}
@@ -1070,13 +1379,13 @@
@
<<HOAGG.dotabb>>=
-"HOAGG" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"HOAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=HOAGG"];
"HOAGG" -> "AGG"
@
<<HOAGG.dotfull>>=
"HomogeneousAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=HOAGG"];
"HomogeneousAggregate(a:Type)" -> "Aggregate()"
@
@@ -1086,23 +1395,22 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"HomogeneousAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"HomogeneousAggregate(a:Type)" [color=lightblue];
"HomogeneousAggregate(a:Type)" -> "Aggregate()"
"HomogeneousAggregate(a:Type)" -> "Evalable(a:Type)"
-"HomogeneousAggregate(a:Type)" -> "SetCategory"
+"HomogeneousAggregate(a:Type)" -> "SetCategory()"
-"Evalable(a:Type)" [color="#00EE00",href="books/bookvol10.2.pamphlet"];
+"Evalable(a:Type)" [color="#00EE00"];
-"SetCategory" [color="#00EE00",href="books/bookvol10.2.pamphlet"];
+"SetCategory()" [color="#00EE00"];
-"Aggregate()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Aggregate()" [color=lightblue];
"Aggregate()" -> "Type()"
-"Type()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Type()" [color=lightblue];
"Type()" -> "Category"
-"Category" [color=lightblue,href="books/bookvol10.pamphlet"];
+"Category" [color=lightblue];
}
@@ -1242,16 +1550,17 @@
@
<<BGAGG.dotabb>>=
-"BGAGG" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"BGAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=BGAGG"];
"BGAGG" -> "HOAGG"
@
<<BGAGG.dotfull>>=
-"BagAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"BagAggregate(a:Type)"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=BGAGG"];
"BagAggregate(a:Type)" -> "HomogeneousAggregate(a:Type)"
"BagAggregate(a:SetCategory)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=BGAGG"];
"BagAggregate(a:SetCategory)" -> "BagAggregate(a:Type)"
@
@@ -1261,20 +1570,19 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"BagAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"BagAggregate(a:Type)" [color=lightblue];
"BagAggregate(a:Type)" -> "HomogeneousAggregate(a:Type)"
-"HomogeneousAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"HomogeneousAggregate(a:Type)" [color=lightblue];
"HomogeneousAggregate(a:Type)" -> "Aggregate()"
-"Aggregate()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Aggregate()" [color=lightblue];
"Aggregate()" -> "Type()"
-"Type()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Type()" [color=lightblue];
"Type()" -> "Category"
-"Category" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Category" [color=lightblue];
}
@
@@ -1483,15 +1791,17 @@
@
<<CLAGG.dotabb>>=
-"CLAGG" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"CLAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=CLAGG"];
"CLAGG" -> "HOAGG"
@
<<CLAGG.dotfull>>=
-"Collection(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Collection(a:Type)"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=CLAGG"];
"Collection(a:Type)" -> "HomogeneousAggregate(a:Type)"
-"Collection(a:SetCategory)" [color=seagreen,href="books/bookvol10.2.pamphlet"];
+"Collection(a:SetCategory)"
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=CLAGG"];
"Collection(a:SetCategory)" -> "Collection(a:Type)"
@
@@ -1501,29 +1811,26 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"Collection(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Collection(a:Type)" [color=lightblue];
"Collection(a:Type)" -> "HomogeneousAggregate(a:Type)"
"Collection(a:Type)" -> "ConvertibleTo(InputForm)"
-"HomogeneousAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"HomogeneousAggregate(a:Type)" [color=lightblue];
"HomogeneousAggregate(a:Type)" -> "Aggregate()"
-"Aggregate()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Aggregate()" [color=lightblue];
"Aggregate()" -> "Type()"
-"Type()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Type()" [color=lightblue];
"Type()" -> "Category"
-"ConvertibleTo(InputForm)"
- [color="#00EE00",href="books/bookvol10.2.pamphlet"];
+"ConvertibleTo(InputForm)" [color="#00EE00"];
"ConvertibleTo(InputForm)" -> "ConvertibleTo(a:Type)"
-"ConvertibleTo(a:Type)"
- [color="#00EE00",href="books/bookvol10.2.pamphlet"];
+"ConvertibleTo(a:Type)" [color="#00EE00"];
"ConvertibleTo(a:Type)" -> "Category"
-"Category" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Category" [color=lightblue];
}
@
@@ -1741,26 +2048,26 @@
@
<<IXAGG.dotabb>>=
-"IXAGG" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"IXAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=IXAGG"];
"IXAGG" -> "HOAGG"
"IXAGG" -> "ELTAGG"
@
<<IXAGG.dotfull>>=
"IndexedAggregate(a:SetCategory,b:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=IXAGG"];
"IndexedAggregate(a:SetCategory,b:Type)" ->
"HomogeneousAggregate(a:Type)"
"IndexedAggregate(a:SetCategory,b:Type)" ->
"EltableAggregate(a:SetCategory,b:Type)"
"IndexedAggregate(a:SetCategory,b:SetCategory)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=IXAGG"];
"IndexedAggregate(a:SetCategory,b:SetCategory)" ->
"IndexedAggregate(a:SetCategory,b:Type)"
"IndexedAggregate(b:Integer,a:Type)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=IXAGG"];
"IndexedAggregate(b:Integer,a:Type)" ->
"IndexedAggregate(a:SetCategory,b:Type)"
@@ -1771,32 +2078,28 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"IndexedAggregate(a:SetCategory,b:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"IndexedAggregate(a:SetCategory,b:Type)" [color=lightblue];
"IndexedAggregate(a:SetCategory,b:Type)" ->
"HomogeneousAggregate(a:Type)"
"IndexedAggregate(a:SetCategory,b:Type)" ->
"EltableAggregate(a:SetCategory,b:Type)"
-"HomogeneousAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"HomogeneousAggregate(a:Type)" [color=lightblue];
"HomogeneousAggregate(a:Type)" -> "Aggregate()"
-"EltableAggregate(a:SetCategory,b:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"EltableAggregate(a:SetCategory,b:Type)" [color=lightblue];
"EltableAggregate(a:SetCategory,b:Type)" -> "Eltable(a:SetCategory,b:Type)"
-"Eltable(a:SetCategory,b:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Eltable(a:SetCategory,b:Type)" [color=lightblue];
"Eltable(a:SetCategory,b:Type)" -> "Category"
-"Aggregate()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Aggregate()" [color=lightblue];
"Aggregate()" -> "Type()"
-"Type()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Type()" [color=lightblue];
"Type()" -> "Category"
-"Category" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Category" [color=lightblue];
}
@
@@ -1982,13 +2285,13 @@
@
<<RCAGG.dotabb>>=
-"RCAGG" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"RCAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=RCAGG"];
"RCAGG" -> "HOAGG"
@
<<RCAGG.dotfull>>=
"RecursiveAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=RCAGG"];
"RecursiveAggregate(a:Type)" -> "HomogeneousAggregate(a:Type)"
@
@@ -1998,21 +2301,19 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"RecursiveAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"RecursiveAggregate(a:Type)" [color=lightblue];
"RecursiveAggregate(a:Type)" -> "HomogeneousAggregate(a:Type)"
-"HomogeneousAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"HomogeneousAggregate(a:Type)" [color=lightblue];
"HomogeneousAggregate(a:Type)" -> "Aggregate()"
-"Aggregate()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Aggregate()" [color=lightblue];
"Aggregate()" -> "Type()"
-"Type()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Type()" [color=lightblue];
"Type()" -> "Category"
-"Category" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Category" [color=lightblue];
}
@
@@ -2268,13 +2569,13 @@
@
<<BRAGG.dotabb>>=
-"BRAGG" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"BRAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=BRAGG"];
"BRAGG" -> "RCAGG"
@
<<BRAGG.dotfull>>=
"BinaryRecursiveAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=BRAGG"];
"BinaryRecursiveAggregate(a:Type)" -> "RecursiveAggregate(a:Type)"
@
@@ -2284,25 +2585,22 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"BinaryRecursiveAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"BinaryRecursiveAggregate(a:Type)" [color=lightblue];
"BinaryRecursiveAggregate(a:Type)" -> "RecursiveAggregate(a:Type)"
-"RecursiveAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"RecursiveAggregate(a:Type)" [color=lightblue];
"RecursiveAggregate(a:Type)" -> "HomogeneousAggregate(a:Type)"
-"HomogeneousAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"HomogeneousAggregate(a:Type)" [color=lightblue];
"HomogeneousAggregate(a:Type)" -> "Aggregate()"
-"Aggregate()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Aggregate()" [color=lightblue];
"Aggregate()" -> "Type()"
-"Type()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Type()" [color=lightblue];
"Type()" -> "Category"
-"Category" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Category" [color=lightblue];
}
@
@@ -2487,14 +2785,14 @@
@
<<DIOPS.dotabb>>=
-"DIOPS" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"DIOPS" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=DIOPS"];
"DIOPS" -> "BGAGG"
"DIOPS" -> "CLAGG"
@
<<DIOPS.dotfull>>=
"DictionaryOperations(a:SetCategory)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=DIOPS"];
"DictionaryOperations(a:SetCategory)" -> "BagAggregate(a:SetCategory)"
"DictionaryOperations(a:SetCategory)" -> "Collection(a:SetCategory)"
@@ -2505,35 +2803,32 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"DictionaryOperations(a:SetCategory)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"DictionaryOperations(a:SetCategory)" [color=lightblue];
"DictionaryOperations(a:SetCategory)" -> "BagAggregate(a:SetCategory)"
"DictionaryOperations(a:SetCategory)" -> "Collection(a:SetCategory)"
-"BagAggregate(a:SetCategory)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+"BagAggregate(a:SetCategory)" [color=seagreen];
"BagAggregate(a:SetCategory)" -> "BagAggregate(a:Type)"
-"BagAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"BagAggregate(a:Type)" [color=lightblue];
"BagAggregate(a:Type)" -> "HomogeneousAggregate(a:Type)"
-"Collection(a:SetCategory)" [color=seagreen,href="books/bookvol10.2.pamphlet"];
+"Collection(a:SetCategory)" [color=seagreen];
"Collection(a:SetCategory)" -> "Collection(a:Type)"
-"Collection(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Collection(a:Type)" [color=lightblue];
"Collection(a:Type)" -> "HomogeneousAggregate(a:Type)"
-"HomogeneousAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"HomogeneousAggregate(a:Type)" [color=lightblue];
"HomogeneousAggregate(a:Type)" -> "Aggregate()"
-"Aggregate()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Aggregate()" [color=lightblue];
"Aggregate()" -> "Type()"
-"Type()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Type()" [color=lightblue];
"Type()" -> "Category"
-"Category" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Category" [color=lightblue];
}
@
@@ -2718,13 +3013,13 @@
@
<<DLAGG.dotabb>>=
-"DLAGG" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"DLAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=DLAGG"];
"DLAGG" -> "RCAGG"
@
<<DLAGG.dotfull>>=
"DoublyLinkedAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=DLAGG"];
"DoublyLinkedAggregate(a:Type)" -> "RecursiveAggregate(a:Type)"
@
@@ -2734,25 +3029,22 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"DoublyLinkedAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"DoublyLinkedAggregate(a:Type)" [color=lightblue];
"DoublyLinkedAggregate(a:Type)" -> "RecursiveAggregate(a:Type)"
-"RecursiveAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"RecursiveAggregate(a:Type)" [color=lightblue];
"RecursiveAggregate(a:Type)" -> "HomogeneousAggregate(a:Type)"
-"HomogeneousAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"HomogeneousAggregate(a:Type)" [color=lightblue];
"HomogeneousAggregate(a:Type)" -> "Aggregate()"
-"Aggregate()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Aggregate()" [color=lightblue];
"Aggregate()" -> "Type()"
-"Type()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Type()" [color=lightblue];
"Type()" -> "Category"
-"Category" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Category" [color=lightblue];
}
@
@@ -3013,13 +3305,14 @@
@
<<LNAGG.dotabb>>=
-"LNAGG" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"LNAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=LNAGG"];
"LNAGG" -> "IXAGG"
"LNAGG" -> "CLAGG"
@
<<LNAGG.dotfull>>=
-"LinearAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"LinearAggregate(a:Type)"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=LNAGG"];
"LinearAggregate(a:Type)" -> "IndexedAggregate(b:Integer,a:Type)"
"LinearAggregate(a:Type)" -> "Collection(a:Type)"
@@ -3030,34 +3323,31 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"LinearAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"LinearAggregate(a:Type)" [color=lightblue];
"LinearAggregate(a:Type)" -> "IndexedAggregate(b:Integer,a:Type)"
"LinearAggregate(a:Type)" -> "Collection(a:Type)"
-"IndexedAggregate(b:Integer,a:Type)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+"IndexedAggregate(b:Integer,a:Type)" [color=seagreen];
"IndexedAggregate(b:Integer,a:Type)" ->
"IndexedAggregate(a:SetCategory,b:Type)"
-"IndexedAggregate(a:SetCategory,b:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"IndexedAggregate(a:SetCategory,b:Type)" [color=lightblue];
"IndexedAggregate(a:SetCategory,b:Type)" ->
"HomogeneousAggregate(a:Type)"
-"Collection(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Collection(a:Type)" [color=lightblue];
"Collection(a:Type)" -> "HomogeneousAggregate(a:Type)"
-"HomogeneousAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"HomogeneousAggregate(a:Type)" [color=lightblue];
"HomogeneousAggregate(a:Type)" -> "Aggregate()"
-"Aggregate()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Aggregate()" [color=lightblue];
"Aggregate()" -> "Type()"
-"Type()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Type()" [color=lightblue];
"Type()" -> "Category"
-"Category" [color=lightblue,href="books/bookvol10.pamphlet"];
+"Category" [color=lightblue];
}
@
@@ -3185,21 +3475,21 @@
@
<<PRQAGG.dotabb>>=
-"PRQAGG" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"PRQAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=PRQAGG"];
"PRQAGG" -> "BGAGG"
@
<<PRQAGG.dotfull>>=
"PriorityQueueAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=PRQAGG"];
"PriorityQueueAggregate(a:Type)" -> "BagAggregate(a:Type)"
"PriorityQueueAggregate(a:SetCategory)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=PRQAGG"];
"PriorityQueueAggregate(a:SetCategory)" -> "PriorityQueueAggregate(a:Type)"
"PriorityQueueAggregate(a:OrderedSet)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=PRQAGG"];
"PriorityQueueAggregate(a:OrderedSet)" ->
"PriorityQueueAggregate(a:SetCategory)"
@@ -3210,24 +3500,22 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"PriorityQueueAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"PriorityQueueAggregate(a:Type)" [color=lightblue];
"PriorityQueueAggregate(a:Type)" -> "BagAggregate(a:Type)"
-"BagAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"BagAggregate(a:Type)" [color=lightblue];
"BagAggregate(a:Type)" -> "HomogeneousAggregate(a:Type)"
-"HomogeneousAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"HomogeneousAggregate(a:Type)" [color=lightblue];
"HomogeneousAggregate(a:Type)" -> "Aggregate()"
-"Aggregate()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Aggregate()" [color=lightblue];
"Aggregate()" -> "Type()"
-"Type()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Type()" [color=lightblue];
"Type()" -> "Category"
-"Category" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Category" [color=lightblue];
}
@
@@ -3374,16 +3662,17 @@
@
<<QUAGG.dotabb>>=
-"QUAGG" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"QUAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=QUAGG"];
"QUAGG" -> "BGAGG"
@
<<QUAGG.dotfull>>=
-"QueueAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"QueueAggregate(a:Type)"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=QUAGG"];
"QueueAggregate(a:Type)" -> "BagAggregate(a:Type)"
"QueueAggregate(a:SetCategory)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=QUAGG"];
"QueueAggregate(a:SetCategory)" -> "QueueAggregate(a:Type)"
@
@@ -3393,23 +3682,22 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"QueueAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"QueueAggregate(a:Type)" [color=lightblue];
"QueueAggregate(a:Type)" -> "BagAggregate(a:Type)"
-"BagAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"BagAggregate(a:Type)" [color=lightblue];
"BagAggregate(a:Type)" -> "HomogeneousAggregate(a:Type)"
-"HomogeneousAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"HomogeneousAggregate(a:Type)" [color=lightblue];
"HomogeneousAggregate(a:Type)" -> "Aggregate()"
-"Aggregate()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Aggregate()" [color=lightblue];
"Aggregate()" -> "Type()"
-"Type()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Type()" [color=lightblue];
"Type()" -> "Category"
-"Category" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Category" [color=lightblue];
}
@
@@ -3546,16 +3834,17 @@
@
<<SKAGG.dotabb>>=
-"SKAGG" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"SKAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=SKAGG"];
"SKAGG" -> "BGAGG"
@
<<SKAGG.dotfull>>=
-"StackAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"StackAggregate(a:Type)"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=SKAGG"];
"StackAggregate(a:Type)" -> "BagAggregate(a:Type)"
"StackAggregate(a:SetCategory)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=SKAGG"];
"StackAggregate(a:SetCategory)" -> "StackAggregate(a:Type)"
@
@@ -3565,23 +3854,22 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"StackAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"StackAggregate(a:Type)" [color=lightblue];
"StackAggregate(a:Type)" -> "BagAggregate(a:Type)"
-"BagAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"BagAggregate(a:Type)" [color=lightblue];
"BagAggregate(a:Type)" -> "HomogeneousAggregate(a:Type)"
-"HomogeneousAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"HomogeneousAggregate(a:Type)" [color=lightblue];
"HomogeneousAggregate(a:Type)" -> "Aggregate()"
-"Aggregate()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Aggregate()" [color=lightblue];
"Aggregate()" -> "Type()"
-"Type()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Type()" [color=lightblue];
"Type()" -> "Category"
-"Category" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Category" [color=lightblue];
}
@
@@ -4016,13 +4304,13 @@
@
<<URAGG.dotabb>>=
-"URAGG" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"URAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=URAGG"];
"URAGG" -> "RCAGG"
@
<<URAGG.dotfull>>=
"UnaryRecursiveAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=URAGG"];
"UnaryRecursiveAggregate(a:Type)" -> "RecursiveAggregate(a:Type)"
@
@@ -4032,25 +4320,22 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"UnaryRecursiveAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"UnaryRecursiveAggregate(a:Type)" [color=lightblue];
"UnaryRecursiveAggregate(a:Type)" -> "RecursiveAggregate(a:Type)"
-"RecursiveAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"RecursiveAggregate(a:Type)" [color=lightblue];
"RecursiveAggregate(a:Type)" -> "HomogeneousAggregate(a:Type)"
-"HomogeneousAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"HomogeneousAggregate(a:Type)" [color=lightblue];
"HomogeneousAggregate(a:Type)" -> "Aggregate()"
-"Aggregate()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Aggregate()" [color=lightblue];
"Aggregate()" -> "Type()"
-"Type()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Type()" [color=lightblue];
"Type()" -> "Category"
-"Category" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Category" [color=lightblue];
}
@
@@ -4222,17 +4507,17 @@
@
<<DIAGG.dotabb>>=
-"DIAGG" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"DIAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=DIAGG"];
"DIAGG" -> "DIOPS"
@
<<DIAGG.dotfull>>=
"Dictionary(a:SetCategory)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=DIAGG"];
"Dictionary(a:SetCategory)" -> "DictionaryOperations(a:SetCategory)"
"Dictionary(Record(a:SetCategory,b:SetCategory))"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=DIAGG"];
"Dictionary(Record(a:SetCategory,b:SetCategory))" ->
"Dictionary(a:SetCategory)"
@@ -4243,39 +4528,35 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"Dictionary(a:SetCategory)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Dictionary(a:SetCategory)" [color=lightblue];
"Dictionary(a:SetCategory)" -> "DictionaryOperations(a:SetCategory)"
-"DictionaryOperations(a:SetCategory)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"DictionaryOperations(a:SetCategory)" [color=lightblue];
"DictionaryOperations(a:SetCategory)" -> "BagAggregate(a:SetCategory)"
"DictionaryOperations(a:SetCategory)" -> "Collection(a:SetCategory)"
-"BagAggregate(a:SetCategory)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+"BagAggregate(a:SetCategory)" [color=seagreen];
"BagAggregate(a:SetCategory)" -> "BagAggregate(a:Type)"
-"BagAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"BagAggregate(a:Type)" [color=lightblue];
"BagAggregate(a:Type)" -> "HomogeneousAggregate(a:Type)"
-"Collection(a:SetCategory)" [color=seagreen,href="books/bookvol10.2.pamphlet"];
+"Collection(a:SetCategory)" [color=seagreen];
"Collection(a:SetCategory)" -> "Collection(a:Type)"
-"Collection(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Collection(a:Type)" [color=lightblue];
"Collection(a:Type)" -> "HomogeneousAggregate(a:Type)"
-"HomogeneousAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"HomogeneousAggregate(a:Type)" [color=lightblue];
"HomogeneousAggregate(a:Type)" -> "Aggregate()"
-"Aggregate()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Aggregate()" [color=lightblue];
"Aggregate()" -> "Type()"
-"Type()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Type()" [color=lightblue];
"Type()" -> "Category"
-"Category" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Category" [color=lightblue];
}
@
@@ -4470,18 +4751,19 @@
@
<<DQAGG.dotabb>>=
-"DQAGG" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"DQAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=DQAGG"];
"DQAGG" -> "SKAGG"
"DQAGG" -> "QUAGG"
@
<<DQAGG.dotfull>>=
-"DequeueAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"DequeueAggregate(a:Type)"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=DQAGG"];
"DequeueAggregate(a:Type)" -> "StackAggregate(a:Type)"
"DequeueAggregate(a:Type)" -> "QueueAggregate(a:Type)"
"DequeueAggregate(a:SetCategory)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=DQAGG"];
"DequeueAggregate(a:SetCategory)" -> "DequeueAggregate(a:Type)"
@
@@ -4491,24 +4773,23 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"DequeueAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"DequeueAggregate(a:Type)" [color=lightblue];
"DequeueAggregate(a:Type)" -> "StackAggregate(a:Type)"
"DequeueAggregate(a:Type)" -> "QueueAggregate(a:Type)"
-"StackAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"StackAggregate(a:Type)" [color=lightblue];
"StackAggregate(a:Type)" -> "BagAggregate(a:Type)"
-"QueueAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"QueueAggregate(a:Type)" [color=lightblue];
"QueueAggregate(a:Type)" -> "BagAggregate(a:Type)"
-"BagAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"BagAggregate(a:Type)" [color=lightblue];
"BagAggregate(a:Type)" -> "HomogeneousAggregate(a:Type)"
-"HomogeneousAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"HomogeneousAggregate(a:Type)" [color=lightblue];
"HomogeneousAggregate(a:Type)" -> "..."
-"..." [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"..." [color=lightblue];
}
@
@@ -4769,13 +5050,13 @@
@
<<ELAGG.dotabb>>=
-"ELAGG" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"ELAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ELAGG"];
"ELAGG" -> "LNAGG"
@
<<ELAGG.dotfull>>=
"ExtensibleLinearAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=ELAGG"];
"ExtensibleLinearAggregate(a:Type)" -> "LinearAggregate(a:Type)"
@
@@ -4785,32 +5066,28 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"ExtensibleLinearAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"ExtensibleLinearAggregate(a:Type)" [color=lightblue];
"ExtensibleLinearAggregate(a:Type)" -> "LinearAggregate(a:Type)"
-"LinearAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"LinearAggregate(a:Type)" [color=lightblue];
"LinearAggregate(a:Type)" -> "IndexedAggregate(b:Integer,a:Type)"
"LinearAggregate(a:Type)" -> "Collection(a:Type)"
-"IndexedAggregate(b:Integer,a:Type)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+"IndexedAggregate(b:Integer,a:Type)" [color=seagreen];
"IndexedAggregate(b:Integer,a:Type)" ->
"IndexedAggregate(a:SetCategory,b:Type)"
-"IndexedAggregate(a:SetCategory,b:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"IndexedAggregate(a:SetCategory,b:Type)" [color=lightblue];
"IndexedAggregate(a:SetCategory,b:Type)" ->
"HomogeneousAggregate(a:Type)"
-"Collection(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Collection(a:Type)" [color=lightblue];
"Collection(a:Type)" -> "HomogeneousAggregate(a:Type)"
-"HomogeneousAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"HomogeneousAggregate(a:Type)" [color=lightblue];
"HomogeneousAggregate(a:Type)" -> "..."
-"..." [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"..." [color=lightblue];
}
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -5112,13 +5389,13 @@
@
<<FLAGG.dotabb>>=
-"FLAGG" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"FLAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=FLAGG"];
"FLAGG" -> "LNAGG"
@
<<FLAGG.dotfull>>=
"FiniteLinearAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=FLAGG"];
"FiniteLinearAggregate(a:Type)" -> "LinearAggregate(a:Type)"
@
@@ -5128,35 +5405,31 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"FiniteLinearAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"FiniteLinearAggregate(a:Type)" [color=lightblue];
"FiniteLinearAggregate(a:Type)" -> "LinearAggregate(a:Type)"
"FiniteLinearAggregate(a:Type)" -> "OrderedSet"
-"OrderedSet" [color="#00EE00",href="books/bookvol10.2.pamphlet"];
+"OrderedSet" [color="#00EE00"];
-"LinearAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"LinearAggregate(a:Type)" [color=lightblue];
"LinearAggregate(a:Type)" -> "IndexedAggregate(b:Integer,a:Type)"
"LinearAggregate(a:Type)" -> "Collection(a:Type)"
-"IndexedAggregate(b:Integer,a:Type)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+"IndexedAggregate(b:Integer,a:Type)" [color=seagreen];
"IndexedAggregate(b:Integer,a:Type)" ->
"IndexedAggregate(a:SetCategory,b:Type)"
-"IndexedAggregate(a:SetCategory,b:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"IndexedAggregate(a:SetCategory,b:Type)" [color=lightblue];
"IndexedAggregate(a:SetCategory,b:Type)" ->
"HomogeneousAggregate(a:Type)"
-"Collection(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Collection(a:Type)" [color=lightblue];
"Collection(a:Type)" -> "HomogeneousAggregate(a:Type)"
-"HomogeneousAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"HomogeneousAggregate(a:Type)" [color=lightblue];
"HomogeneousAggregate(a:Type)" -> "..."
-"..." [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"..." [color=lightblue];
}
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -5165,7 +5438,6 @@
{\bf See:}\\
\pagefrom{DictionaryOperations}{DIOPS}
-<<category MDAGG MultiDictionary>>=
{\bf Exports:}\\
\begin{tabular}{lllll}
@@ -5214,9 +5486,9 @@
\cross{MDAGG}{select}
\cross{MDAGG}{select!}
\cross{MDAGG}{size?}
-\cross{MDAGG}{#?}
+\cross{MDAGG}{\#?}
\cross{MDAGG}{?=?}
-\cross{MDAGG}{?~=?}
+\cross{MDAGG}{?\~{}=?}
These are directly exported but not implemented:
\begin{verbatim}
@@ -5288,6 +5560,7 @@
?~=? : (%,%) -> Boolean if S has SETCAT
\end{verbatim}
+<<category MDAGG MultiDictionary>>=
)abbrev category MDAGG MultiDictionary
++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
++ Date Created: August 87 through August 88
@@ -5319,13 +5592,13 @@
@
<<MDAGG.dotabb>>=
-"MDAGG" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"MDAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=MDAGG"];
"MDAGG" -> "DIOPS"
@
<<MDAGG.dotfull>>=
"MultiDictionary(a:SetCategory)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=MDAGG"];
"MultiDictionary(a:SetCategory)" -> "DictionaryOperations(a:SetCategory)"
@
@@ -5335,33 +5608,29 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"MultiDictionary(a:SetCategory)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"MultiDictionary(a:SetCategory)" [color=lightblue];
"MultiDictionary(a:SetCategory)" -> "DictionaryOperations(a:SetCategory)"
-"DictionaryOperations(a:SetCategory)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"DictionaryOperations(a:SetCategory)" [color=lightblue];
"DictionaryOperations(a:SetCategory)" -> "BagAggregate(a:SetCategory)"
"DictionaryOperations(a:SetCategory)" -> "Collection(a:SetCategory)"
-"BagAggregate(a:SetCategory)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+"BagAggregate(a:SetCategory)" [color=seagreen];
"BagAggregate(a:SetCategory)" -> "BagAggregate(a:Type)"
-"BagAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"BagAggregate(a:Type)" [color=lightblue];
"BagAggregate(a:Type)" -> "HomogeneousAggregate(a:Type)"
-"Collection(a:SetCategory)" [color=seagreen,href="books/bookvol10.2.pamphlet"];
+"Collection(a:SetCategory)" [color=seagreen];
"Collection(a:SetCategory)" -> "Collection(a:Type)"
-"Collection(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Collection(a:Type)" [color=lightblue];
"Collection(a:Type)" -> "HomogeneousAggregate(a:Type)"
-"HomogeneousAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"HomogeneousAggregate(a:Type)" [color=lightblue];
"HomogeneousAggregate(a:Type)" -> "..."
-"..." [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"..." [color=lightblue];
}
@
@@ -5684,13 +5953,14 @@
@
<<STAGG.dotabb>>=
-"STAGG" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"STAGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=STAGG"];
"STAGG" -> "RCAGG"
"STAGG" -> "LNAGG"
@
<<STAGG.dotfull>>=
-"StreamAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"StreamAggregate(a:Type)"
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=STAGG"];
"StreamAggregate(a:Type)" -> "UnaryRecursiveAggregate(a:Type)"
"StreamAggregate(a:Type)" -> "LinearAggregate(a:Type)"
@@ -5701,40 +5971,35 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"StreamAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"StreamAggregate(a:Type)" [color=lightblue];
"StreamAggregate(a:Type)" -> "UnaryRecursiveAggregate(a:Type)"
"StreamAggregate(a:Type)" -> "LinearAggregate(a:Type)"
-"UnaryRecursiveAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"UnaryRecursiveAggregate(a:Type)" [color=lightblue];
"UnaryRecursiveAggregate(a:Type)" -> "RecursiveAggregate(a:Type)"
-"RecursiveAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"RecursiveAggregate(a:Type)" [color=lightblue];
"RecursiveAggregate(a:Type)" -> "HomogeneousAggregate(a:Type)"
-"LinearAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"LinearAggregate(a:Type)" [color=lightblue];
"LinearAggregate(a:Type)" -> "IndexedAggregate(b:Integer,a:Type)"
"LinearAggregate(a:Type)" -> "Collection(a:Type)"
-"IndexedAggregate(b:Integer,a:Type)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+"IndexedAggregate(b:Integer,a:Type)" [color=seagreen];
"IndexedAggregate(b:Integer,a:Type)" ->
"IndexedAggregate(a:SetCategory,b:Type)"
-"IndexedAggregate(a:SetCategory,b:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"IndexedAggregate(a:SetCategory,b:Type)" [color=lightblue];
"IndexedAggregate(a:SetCategory,b:Type)" ->
"HomogeneousAggregate(a:Type)"
-"Collection(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"Collection(a:Type)" [color=lightblue];
"Collection(a:Type)" -> "HomogeneousAggregate(a:Type)"
-"HomogeneousAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"HomogeneousAggregate(a:Type)" [color=lightblue];
"HomogeneousAggregate(a:Type)" -> "..."
-"..." [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"..." [color=lightblue];
}
@
@@ -6189,23 +6454,23 @@
@
<<A1AGG.dotabb>>=
-"A1AGG" [color=lightblue,style=filled];
+"A1AGG" [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=A1AGG"];
"A1AGG" -> "FLAGG"
@
<<A1AGG.dotfull>>=
"OneDimensionalArrayAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+ [color=lightblue,href="books/bookvol10.2.pamphlet#nameddest=A1AGG"];
"OneDimensionalArrayAggregate(a:Type)" ->
"FiniteLinearAggregate(a:Type)"
"OneDimensionalArrayAggregate(Character)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=A1AGG"];
"OneDimensionalArrayAggregate(Character)" ->
"OneDimensionalArrayAggregate(a:Type)"
"OneDimensionalArrayAggregate(Boolean)"
- [color=seagreen,href="books/bookvol10.2.pamphlet"];
+ [color=seagreen,href="books/bookvol10.2.pamphlet#nameddest=A1AGG"];
"OneDimensionalArrayAggregate(Boolean)" ->
"OneDimensionalArrayAggregate(a:Type)"
@@ -6216,25 +6481,22 @@
bgcolor="#FFFF66";
node [shape=box, color=white, style=filled];
-"OneDimensionalArrayAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"OneDimensionalArrayAggregate(a:Type)" [color=lightblue];
"OneDimensionalArrayAggregate(a:Type)" ->
"FiniteLinearAggregate(a:Type)"
-"FiniteLinearAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"FiniteLinearAggregate(a:Type)" [color=lightblue];
"FiniteLinearAggregate(a:Type)" -> "LinearAggregate(a:Type)"
-"LinearAggregate(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
+"LinearAggregate(a:Type)" [color=lightblue];
"LinearAggregate(a:Type)" -> "IndexedAggregate(b:Integer,a:Type)"
"LinearAggregate(a:Type)" -> "CLAGG..."
-"IndexedAggregate(b:Integer,...
[truncated message content] |
|
From: <gi...@ax...> - 2008-09-18 10:12:46
|
books/bookvol10.2.pamphlet | 1324 ++++++++++++++++++++++++++------------
books/ps/v102abeliansemigroup.ps | 677 +++++++++++++++++++
books/ps/v102basictype.ps | 299 +++++++++
books/ps/v102setcategory.ps | 473 ++++++++++++++
changelog | 6 +
src/algebra/catdef.spad.pamphlet | 352 +----------
6 files changed, 2368 insertions(+), 763 deletions(-)
New commits:
commit 6bb671be4caa43995e0d35bc7a2f4d8323a9a6cb
Author: Tim Daly <da...@ax...>
Date: Sat Jul 26 11:44:02 2008 -0400
20080917 tpd src/algebra/catdef.spad remove BASTYPE, SETCAT, ABELSG
20080917 tpd books/ps/v102abeliansemigroup.ps ABELSG graph
20080917 tpd books/ps/v102setcategory.ps SETCAT graph
20080917 tpd books/ps/v102basictype.ps BASTYPE graph
20080917 tpd books/bookvol10.2 add pdf destinations
20080917 tpd books/bookvol10.2 add BASTYPE, SETCAT, ABELSG
|
|
From: <da...@us...> - 2008-09-18 05:27:56
|
Revision: 975
http://axiom.svn.sourceforge.net/axiom/?rev=975&view=rev
Author: daly
Date: 2008-09-18 05:28:06 +0000 (Thu, 18 Sep 2008)
Log Message:
-----------
20080917 wsp src/algebra/mkfunc.spad add parse to InputForm
Modified Paths:
--------------
trunk/axiom/changelog
trunk/axiom/src/algebra/mkfunc.spad.pamphlet
Modified: trunk/axiom/changelog
===================================================================
--- trunk/axiom/changelog 2008-09-17 04:37:14 UTC (rev 974)
+++ trunk/axiom/changelog 2008-09-18 05:28:06 UTC (rev 975)
@@ -1,3 +1,4 @@
+20080917 wsp src/algebra/mkfunc.spad add parse to InputForm
20080917 tpd books/bookvol10.2 remove duplicate function def in FLAGG
20080916 tpd books/ps/v102streamaggregate.ps
20080916 tpd books/ps/v102listaggregate.ps
Modified: trunk/axiom/src/algebra/mkfunc.spad.pamphlet
===================================================================
--- trunk/axiom/src/algebra/mkfunc.spad.pamphlet 2008-09-17 04:37:14 UTC (rev 974)
+++ trunk/axiom/src/algebra/mkfunc.spad.pamphlet 2008-09-18 05:28:06 UTC (rev 975)
@@ -68,6 +68,8 @@
++ unparse(f) returns a string s such that the parser
++ would transform s to f.
++ Error: if f is not the parsed form of a string.
+ parse : String -> %
+ ++ parse is the inverse of unparse. It parses a string to InputForm.
declare : List % -> Symbol
++ declare(t) returns a name f such that f has been
++ declared to the interpreter to be of type t, but has
@@ -139,6 +141,9 @@
atom?(s:% := form2String(x)$Lisp) => strsym s
concat [strsym a for a in destruct s]
+ parse(s:String):% ==
+ ncParseFromString(s)$Lisp
+
declare signature ==
declare(name := new()$Symbol, signature)$Lisp
name
This was sent by the SourceForge.net collaborative development platform, the world's largest Open Source development site.
|
|
From: <gi...@ax...> - 2008-09-18 05:26:33
|
changelog | 1 +
src/algebra/mkfunc.spad.pamphlet | 5 +++++
2 files changed, 6 insertions(+), 0 deletions(-)
New commits:
commit 39c0f541b0cd43eca6884b45b6e8d8da1efc4885
Author: Tim Daly <da...@ax...>
Date: Sat Jul 26 01:32:52 2008 -0400
20080917 wsp src/algebra/mkfunc.spad add parse to InputForm
|
|
From: <gi...@ax...> - 2008-09-17 04:36:18
|
books/bookvol10.2.pamphlet | 1 -
changelog | 1 +
2 files changed, 1 insertions(+), 1 deletions(-)
New commits:
commit 7489943c8fed0cccd0cbc992a97b96a4719c1be2
Author: Tim Daly <da...@ax...>
Date: Fri Jul 25 23:08:25 2008 -0400
20080917 tpd books/bookvol10.2 remove duplicate function def in FLAGG
|
|
From: <da...@us...> - 2008-09-17 04:33:51
|
Revision: 973
http://axiom.svn.sourceforge.net/axiom/?rev=973&view=rev
Author: daly
Date: 2008-09-17 04:34:02 +0000 (Wed, 17 Sep 2008)
Log Message:
-----------
20080916 tpd books/ps/v102streamaggregate.ps
20080916 tpd books/ps/v102listaggregate.ps
20080916 tpd books/ps/v102finitelinearaggregate.ps corrected diagram
20080916 tpd books/ps/v102collection.ps corrected diagram
20080916 tpd books/bookvol10.2 more documentation
Modified Paths:
--------------
trunk/axiom/books/bookvol10.2.pamphlet
trunk/axiom/books/ps/v102collection.ps
trunk/axiom/books/ps/v102finitelinearaggregate.ps
trunk/axiom/books/ps/v102listaggregate.ps
trunk/axiom/books/ps/v102streamaggregate.ps
trunk/axiom/changelog
Modified: trunk/axiom/books/bookvol10.2.pamphlet
===================================================================
--- trunk/axiom/books/bookvol10.2.pamphlet 2008-09-13 05:27:50 UTC (rev 972)
+++ trunk/axiom/books/bookvol10.2.pamphlet 2008-09-17 04:34:02 UTC (rev 973)
@@ -9,7 +9,7 @@
%% pagehead consolidates standard page indexing
%%
\newcommand{\pagehead}[2]{% e.g. \pagehead{name}{abb}
-\section{#1}
+\section{#1 (#2)}
\label{#1}%
\label{#2}%
\index{{#1}}%
@@ -26,12 +26,19 @@
\newcommand{\pageto}[2]{% e.g. \pageto{abb}{name}
\ \\${\bf\Rightarrow{}}${``#1''} (#2) \ref{#1} on page~\pageref{#1}}
%%
-%% pageback is a backward link to a referencing page
+%% pagefrom is a backward link to a referencing page
%%
\newcommand{\pagefrom}[2]{% e.g. \pagefrom{name}{abb}
\ \\${\bf\Leftarrow{}}${``#1''} (#2) \ref{#1} on page~\pageref{#1}}
%%
+%% cross will put the category and function in the index
+%%
+\newcommand{\cross}[2]{% e.g. \pagefrom{cat}{funcname}
+\index{#1!#2}%
+\index{#2!#1}}
+%%
+
% special meanings for math characters
\providecommand{\N}{\mbox{\bbold N}}
\providecommand{\Natural}{\mbox{\bbold N}}
@@ -273,6 +280,8 @@
coerce
\end{verbatim}
+\cross{KOERCE}{coerce}
+
This is directly exported but not implemented:
\begin{verbatim}
coerce : % -> S
@@ -323,6 +332,7 @@
\pagepic{ps/v102konvert.ps}{KONVERT}
{\bf See:}\\
+\pageto{Collection}{CLAGG}
\pagefrom{Category}{CATEGORY}
{\bf Exports:}
@@ -330,6 +340,8 @@
convert
\end{verbatim}
+\cross{KONVERT}{convert}
+
This is directly exported but not implemented:
\begin{verbatim}
convert : % -> S
@@ -447,12 +459,15 @@
?.?
\end{verbatim}
+\cross{ELTAB}{?.?}
+
This syntax for elt is supported by the interpreter and compiler.
This is directly exported but not implemented:
\begin{verbatim}
?.? : (%,S) -> Index
\end{verbatim}
+
<<category ELTAB Eltable>>=
)abbrev category ELTAB Eltable
++ Author: Michael Monagan; revised by Manuel Bronstein and Manuel Bronstein
@@ -512,6 +527,10 @@
coerce & retract & retractIfCan
\end{tabular}
+\cross{RETRACT}{coerce}
+\cross{RETRACT}{retract}
+\cross{RETRACT}{retractIfCan}
+
These are directly exported but not implemented:
\begin{verbatim}
coerce : S -> %
@@ -658,6 +677,13 @@
empty? & eq? & less? & more? & sample & size?
\end{tabular}
+\cross{AGG}{empty?}
+\cross{AGG}{eq?}
+\cross{AGG}{less?}
+\cross{AGG}{more?}
+\cross{AGG}{sample}
+\cross{AGG}{size?}
+
These are implemented by this category:
\begin{verbatim}
empty? : % -> Boolean
@@ -762,6 +788,12 @@
elt & qelt & qsetelt! & setelt & ?.?
\end{tabular}
+\cross{ELTAGG}{elt}
+\cross{ELTAGG}{qelt}
+\cross{ELTAGG}{qsetelt!}
+\cross{ELTAGG}{setelt}
+\cross{ELTAGG}{?.?}
+
These are part of this category's direct exports:
\begin{verbatim}
elt : (%,Dom,Im) -> Im
@@ -869,15 +901,42 @@
\pageto{IndexedAggregate}{IXAGG}
\pageto{RecursiveAggregate}{RCAGG}
\pagefrom{Aggregate}{AGG}
+\pagefrom{Evalable}{EVALAB}
+\pagefrom{SetCategory}{SETCAT}
+
{\bf Exports:}\\
\begin{tabular}{lllllll}
any? & coerce & copy & count & empty & empty? & eq?\\
eval & every? & hash & latex & less? & map & map!\\
members & member? & more? & parts & sample & size? & \#?\\
- ?$=$? & ?\~{}=? & & & & &\\
+ ?=? & ?\~{}=? & & & & &\\
\end{tabular}
+\cross{HOAGG}{any?}
+\cross{HOAGG}{coerce}
+\cross{HOAGG}{copy}
+\cross{HOAGG}{count}
+\cross{HOAGG}{empty}
+\cross{HOAGG}{empty?}
+\cross{HOAGG}{eq?}
+\cross{HOAGG}{eval}
+\cross{HOAGG}{every?}
+\cross{HOAGG}{hash}
+\cross{HOAGG}{latex}
+\cross{HOAGG}{less?}
+\cross{HOAGG}{map}
+\cross{HOAGG}{map!}
+\cross{HOAGG}{members}
+\cross{HOAGG}{member?}
+\cross{HOAGG}{more?}
+\cross{HOAGG}{parts}
+\cross{HOAGG}{sample}
+\cross{HOAGG}{size?}
+\cross{HOAGG}{\#?}
+\cross{HOAGG}{?=?}
+\cross{HOAGG}{?\~{}=?}
+
These are directly exported but not implemented:
\begin{verbatim}
map : ((S -> S),%) -> %
@@ -887,14 +946,19 @@
These are implemented by this category:
\begin{verbatim}
- any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
+ any? : ((S -> Boolean),%) -> Boolean
+ if $ has finiteAggregate
coerce : % -> OutputForm if S has SETCAT
- count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
- count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
- eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+ count : (S,%) -> NonNegativeInteger
+ if S has SETCAT and $ has finiteAggregate
+ count : ((S -> Boolean),%) -> NonNegativeInteger
+ if $ has finiteAggregate
+ eval : (%,List Equation S) -> %
+ if S has EVALAB S and S has SETCAT
every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
members : % -> List S if $ has finiteAggregate
- member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
+ member? : (S,%) -> Boolean
+ if S has SETCAT and $ has finiteAggregate
#? : % -> NonNegativeInteger if $ has finiteAggregate
?=? : (%,%) -> Boolean if S has SETCAT
\end{verbatim}
@@ -913,9 +977,12 @@
These exports come from Evalable(a:Type):
\begin{verbatim}
- eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
- eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
- eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
+ eval : (%,List S,List S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,S,S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,Equation S) -> %
+ if S has EVALAB S and S has SETCAT
\end{verbatim}
These exports come from SetCategory:
@@ -1022,13 +1089,13 @@
"HomogeneousAggregate(a:Type)"
[color=lightblue,href="books/bookvol10.2.pamphlet"];
"HomogeneousAggregate(a:Type)" -> "Aggregate()"
-"Evalable(a:Type)"
- [color="#00EE00",href="books/bookvol10.pamphlet"];
"HomogeneousAggregate(a:Type)" -> "Evalable(a:Type)"
-"SetCategory"
- [color="#00EE00",href="books/bookvol10.pamphlet"];
"HomogeneousAggregate(a:Type)" -> "SetCategory"
+"Evalable(a:Type)" [color="#00EE00",href="books/bookvol10.2.pamphlet"];
+
+"SetCategory" [color="#00EE00",href="books/bookvol10.2.pamphlet"];
+
"Aggregate()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
"Aggregate()" -> "Type()"
@@ -1060,6 +1127,34 @@
parts & sample & size? & \#? & ?=? & ?\~{}=? &\\
\end{tabular}
+\cross{BGAGG}{any?}
+\cross{BGAGG}{bag}
+\cross{BGAGG}{coerce}
+\cross{BGAGG}{copy}
+\cross{BGAGG}{count}
+\cross{BGAGG}{empty}
+\cross{BGAGG}{empty?}
+\cross{BGAGG}{eq?}
+\cross{BGAGG}{eval}
+\cross{BGAGG}{every?}
+\cross{BGAGG}{extract!}
+\cross{BGAGG}{hash}
+\cross{BGAGG}{insert!}
+\cross{BGAGG}{inspect}
+\cross{BGAGG}{latex}
+\cross{BGAGG}{less?}
+\cross{BGAGG}{map}
+\cross{BGAGG}{map!}
+\cross{BGAGG}{member?}
+\cross{BGAGG}{members}
+\cross{BGAGG}{more?}
+\cross{BGAGG}{parts}
+\cross{BGAGG}{sample}
+\cross{BGAGG}{size?}
+\cross{BGAGG}{\#?}
+\cross{BGAGG}{?=?}
+\cross{BGAGG}{?\~{}=?}
+
These are directly exported but not implemented:
\begin{verbatim}
extract! : % -> S
@@ -1074,18 +1169,25 @@
These exports come from HomogeneousAggregate:
\begin{verbatim}
- any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
+ any? : ((S -> Boolean),%) -> Boolean
+ if $ has finiteAggregate
coerce : % -> OutputForm if S has SETCAT
copy : % -> %
- count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
- count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
+ count : (S,%) -> NonNegativeInteger
+ if S has SETCAT and $ has finiteAggregate
+ count : ((S -> Boolean),%) -> NonNegativeInteger
+ if $ has finiteAggregate
empty : () -> %
empty? : % -> Boolean
eq? : (%,%) -> Boolean
- eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
- eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
- eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
- eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+ eval : (%,List S,List S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,S,S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,Equation S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,List Equation S) -> %
+ if S has EVALAB S and S has SETCAT
every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
hash : % -> SingleInteger if S has SETCAT
latex : % -> String if S has SETCAT
@@ -1093,7 +1195,8 @@
map : ((S -> S),%) -> %
map! : ((S -> S),%) -> % if $ has shallowlyMutable
members : % -> List S if $ has finiteAggregate
- member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
+ member? : (S,%) -> Boolean
+ if S has SETCAT and $ has finiteAggregate
more? : (%,NonNegativeInteger) -> Boolean
parts : % -> List S if $ has finiteAggregate
sample : () -> %
@@ -1182,7 +1285,113 @@
{\bf See:}\\
\pageto{DictionaryOperations}{DIOPS}
\pageto{LinearAggregate}{LNAGG}
+\pagefrom{ConvertibleTo}{KONVERT}
\pagefrom{HomogeneousAggregate}{HOAGG}
+
+{\bf Exports:}\\
+\begin{tabular}{llllll}
+ any? & coerce & construct & copy & convert & count\\
+ empty & empty? & eq? & eval & every? & find\\
+ hash & latex & less? & map & map! & member?\\
+ members & more? & parts & reduce & remove & removeDuplicates\\
+ sample & select & size? & \#? & ?=? & ?\~{}=?
+\end{tabular}
+
+\cross{CLAGG}{any?}
+\cross{CLAGG}{coerce}
+\cross{CLAGG}{construct}
+\cross{CLAGG}{copy}
+\cross{CLAGG}{convert}
+\cross{CLAGG}{count}
+\cross{CLAGG}{empty}
+\cross{CLAGG}{empty?}
+\cross{CLAGG}{eq?}
+\cross{CLAGG}{eval}
+\cross{CLAGG}{every?}
+\cross{CLAGG}{find}
+\cross{CLAGG}{hash}
+\cross{CLAGG}{latex}
+\cross{CLAGG}{less?}
+\cross{CLAGG}{map}
+\cross{CLAGG}{map!}
+\cross{CLAGG}{member?}
+\cross{CLAGG}{members}
+\cross{CLAGG}{more?}
+\cross{CLAGG}{parts}
+\cross{CLAGG}{reduce}
+\cross{CLAGG}{remove}
+\cross{CLAGG}{removeDuplicates}
+\cross{CLAGG}{sample}
+\cross{CLAGG}{select}
+\cross{CLAGG}{size?}
+\cross{CLAGG}{\#?}
+\cross{CLAGG}{?=?}
+\cross{CLAGG}{?\~{}=?}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ construct: List S -> %
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ any? : ((S -> Boolean),%) -> Boolean
+ if $ has finiteAggregate
+ count : ((S -> Boolean),%) -> NonNegativeInteger
+ if $ has finiteAggregate
+ every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
+ find : ((S -> Boolean),%) -> Union(S,"failed")
+ reduce : (((S,S) -> S),%,S,S) -> S
+ if S has SETCAT and $ has finiteAggregate
+ reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate
+ reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate
+ remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate
+ remove : ((S -> Boolean),%) -> % if $ has finiteAggregate
+ removeDuplicates : % -> %
+ if S has SETCAT and $ has finiteAggregate
+ select : ((S -> Boolean),%) -> % if $ has finiteAggregate
+ #? : % -> NonNegativeInteger if $ has finiteAggregate
+\end{verbatim}
+
+These exports come from HomogeneousAggregate(a:Type):
+\begin{verbatim}
+ coerce : % -> OutputForm if S has SETCAT
+ copy : % -> %
+ count : (S,%) -> NonNegativeInteger
+ if S has SETCAT and $ has finiteAggregate
+ empty : () -> %
+ empty? : % -> Boolean
+ eq? : (%,%) -> Boolean
+ eval : (%,List S,List S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,S,S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,Equation S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,List Equation S) -> %
+ if S has EVALAB S and S has SETCAT
+ every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
+ hash : % -> SingleInteger if S has SETCAT
+ latex : % -> String if S has SETCAT
+ less? : (%,NonNegativeInteger) -> Boolean
+ map : ((S -> S),%) -> %
+ map! : ((S -> S),%) -> % if $ has shallowlyMutable
+ member? : (S,%) -> Boolean
+ if S has SETCAT and $ has finiteAggregate
+ sample : () -> %
+ members : % -> List S if $ has finiteAggregate
+ more? : (%,NonNegativeInteger) -> Boolean
+ parts : % -> List S if $ has finiteAggregate
+ size? : (%,NonNegativeInteger) -> Boolean
+ ?=? : (%,%) -> Boolean if S has SETCAT
+ ?~=? : (%,%) -> Boolean if S has SETCAT
+\end{verbatim}
+
+These exports come from ConvertibleTo(a:Type):
+\begin{verbatim}
+ convert : % -> InputForm if S has KONVERT INFORM
+\end{verbatim}
+
<<category CLAGG Collection>>=
)abbrev category CLAGG Collection
++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
@@ -1294,6 +1503,7 @@
"Collection(a:Type)" [color=lightblue,href="books/bookvol10.2.pamphlet"];
"Collection(a:Type)" -> "HomogeneousAggregate(a:Type)"
+"Collection(a:Type)" -> "ConvertibleTo(InputForm)"
"HomogeneousAggregate(a:Type)"
[color=lightblue,href="books/bookvol10.2.pamphlet"];
@@ -1305,6 +1515,14 @@
"Type()" [color=lightblue,href="books/bookvol10.2.pamphlet"];
"Type()" -> "Category"
+"ConvertibleTo(InputForm)"
+ [color="#00EE00",href="books/bookvol10.2.pamphlet"];
+"ConvertibleTo(InputForm)" -> "ConvertibleTo(a:Type)"
+
+"ConvertibleTo(a:Type)"
+ [color="#00EE00",href="books/bookvol10.2.pamphlet"];
+"ConvertibleTo(a:Type)" -> "Category"
+
"Category" [color=lightblue,href="books/bookvol10.2.pamphlet"];
}
@@ -1318,6 +1536,122 @@
\pageto{TableAggregate}{TBAGG}
\pagefrom{EltableAggregate}{ELTAGG}
\pagefrom{HomogeneousAggregate}{HOAGG}
+
+{\bf Exports:}\\
+\begin{tabular}{lllllll}
+ any? & coerce & copy & count & elt & empty & empty? \\
+ entries & entry? & eq? & eval & every? & fill! & first \\
+ hash & index? & indices & latex & less? & map & map! \\
+ maxIndex & member? & members & minIndex & more? & parts & qelt \\
+ qsetelt! & sample & setelt & size? & swap! & ?.? & ?\~{}=?\\
+ \#? & ?=? & & & & &\\
+\end{tabular}
+
+\cross{IXAGG}{any?}
+\cross{IXAGG}{coerce}
+\cross{IXAGG}{copy}
+\cross{IXAGG}{count}
+\cross{IXAGG}{elt}
+\cross{IXAGG}{empty}
+\cross{IXAGG}{empty?}
+\cross{IXAGG}{entries}
+\cross{IXAGG}{entry?}
+\cross{IXAGG}{eq?}
+\cross{IXAGG}{eval}
+\cross{IXAGG}{every?}
+\cross{IXAGG}{fill!}
+\cross{IXAGG}{first}
+\cross{IXAGG}{hash}
+\cross{IXAGG}{index?}
+\cross{IXAGG}{indices}
+\cross{IXAGG}{latex}
+\cross{IXAGG}{less?}
+\cross{IXAGG}{map}
+\cross{IXAGG}{map!}
+\cross{IXAGG}{maxIndex}
+\cross{IXAGG}{member?}
+\cross{IXAGG}{members}
+\cross{IXAGG}{minIndex}
+\cross{IXAGG}{more?}
+\cross{IXAGG}{parts}
+\cross{IXAGG}{qelt}
+\cross{IXAGG}{qsetelt!}
+\cross{IXAGG}{sample}
+\cross{IXAGG}{setelt}
+\cross{IXAGG}{size?}
+\cross{IXAGG}{swap!}
+\cross{IXAGG}{?.?}
+\cross{IXAGG}{?\~{}=?}
+\cross{IXAGG}{\#?}
+\cross{IXAGG}{?=?}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ index? : (Index,%) -> Boolean
+ indices : % -> List Index
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ elt : (%,Index,Entry) -> Entry
+ entries : % -> List Entry
+ entry? : (Entry,%) -> Boolean
+ if $ has finiteAggregate and Entry has SETCAT
+ fill! : (%,Entry) -> % if $ has shallowlyMutable
+ first : % -> Entry if Index has ORDSET
+ map : ((Entry -> Entry),%) -> %
+ map! : ((Entry -> Entry),%) -> % if $ has shallowlyMutable
+ maxIndex : % -> Index if Index has ORDSET
+ minIndex : % -> Index if Index has ORDSET
+ swap! : (%,Index,Index) -> Void if $ has shallowlyMutable
+\end{verbatim}
+
+These exports come from HomogeneousAggregate(a:Type):
+\begin{verbatim}
+ any? : ((Entry -> Boolean),%) -> Boolean
+ if $ has finiteAggregate
+ coerce : % -> OutputForm if Entry has SETCAT
+ copy : % -> %
+ count : (Entry,%) -> NonNegativeInteger
+ if Entry has SETCAT and $ has finiteAggregate
+ count : ((Entry -> Boolean),%) -> NonNegativeInteger
+ if $ has finiteAggregate
+ empty : () -> %
+ empty? : % -> Boolean
+ eq? : (%,%) -> Boolean
+ eval : (%,List Entry,List Entry) -> %
+ if Entry has EVALAB Entry and Entry has SETCAT
+ eval : (%,Entry,Entry) -> %
+ if Entry has EVALAB Entry and Entry has SETCAT
+ eval : (%,Equation Entry) -> %
+ if Entry has EVALAB Entry and Entry has SETCAT
+ eval : (%,List Equation Entry) -> %
+ if Entry has EVALAB Entry and Entry has SETCAT
+ every? : ((Entry -> Boolean),%) -> Boolean
+ if $ has finiteAggregate
+ hash : % -> SingleInteger if Entry has SETCAT
+ latex : % -> String if Entry has SETCAT
+ less? : (%,NonNegativeInteger) -> Boolean
+ member? : (Entry,%) -> Boolean
+ if Entry has SETCAT and $ has finiteAggregate
+ members : % -> List Entry if $ has finiteAggregate
+ more? : (%,NonNegativeInteger) -> Boolean
+ parts : % -> List Entry if $ has finiteAggregate
+ sample : () -> %
+ size? : (%,NonNegativeInteger) -> Boolean
+ ?~=? : (%,%) -> Boolean if Entry has SETCAT
+ #? : % -> NonNegativeInteger if $ has finiteAggregate
+ ?=? : (%,%) -> Boolean if Entry has SETCAT
+\end{verbatim}
+
+These exports come from EltableAggregate(a:SetCategory,b:Type):
+\begin{verbatim}
+ qelt : (%,Index) -> Entry
+ qsetelt! : (%,Index,Entry) -> Entry if $ has shallowlyMutable
+ setelt : (%,Index,Entry) -> Entry if $ has shallowlyMutable
+ ?.? : (%,Index) -> Entry
+\end{verbatim}
+
<<category IXAGG IndexedAggregate>>=
)abbrev category IXAGG IndexedAggregate
++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
@@ -1473,9 +1807,116 @@
{\bf See:}\\
\pageto{BinaryRecursiveAggregate}{BRAGG}
\pageto{DoublyLinkedAggregate}{DLAGG}
-\pageto{StreamAggregate}{STAGG}
\pageto{UnaryRecursiveAggregate}{URAGG}
\pagefrom{HomogeneousAggregate}{HOAGG}
+
+{\bf Exports:}\\
+\begin{tabular}{llllll}
+ any? & child? & children & coerce & copy & count \\
+ cyclic? & distance & empty & empty? & eq? & eval \\
+ every? & hash & latex & leaf? & leaves & less? \\
+ map & map! & member? & members & more? & nodes \\
+ node? & parts & sample & setchildren! & setelt & setvalue!\\
+ size? & value & ?.value & ?\~{}=? & \#? & ?=? \\
+\end{tabular}
+
+\cross{RCAGG}{any?}
+\cross{RCAGG}{child?}
+\cross{RCAGG}{children}
+\cross{RCAGG}{coerce}
+\cross{RCAGG}{copy}
+\cross{RCAGG}{count}
+\cross{RCAGG}{cyclic?}
+\cross{RCAGG}{distance}
+\cross{RCAGG}{empty}
+\cross{RCAGG}{empty?}
+\cross{RCAGG}{eq?}
+\cross{RCAGG}{eval}
+\cross{RCAGG}{every?}
+\cross{RCAGG}{hash}
+\cross{RCAGG}{latex}
+\cross{RCAGG}{leaf?}
+\cross{RCAGG}{leaves}
+\cross{RCAGG}{less?}
+\cross{RCAGG}{map}
+\cross{RCAGG}{map!}
+\cross{RCAGG}{member?}
+\cross{RCAGG}{members}
+\cross{RCAGG}{more?}
+\cross{RCAGG}{nodes}
+\cross{RCAGG}{node?}
+\cross{RCAGG}{parts}
+\cross{RCAGG}{sample}
+\cross{RCAGG}{setchildren!}
+\cross{RCAGG}{setelt}
+\cross{RCAGG}{setvalue!}
+\cross{RCAGG}{size?}
+\cross{RCAGG}{value}
+\cross{RCAGG}{?.value}
+\cross{RCAGG}{?\~{}=?}
+\cross{RCAGG}{\#?}
+\cross{RCAGG}{?=?}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ children : % -> List %
+ cyclic? : % -> Boolean
+ distance : (%,%) -> Integer
+ nodes : % -> List %
+ leaf? : % -> Boolean
+ leaves : % -> List S
+ node? : (%,%) -> Boolean if S has SETCAT
+ setchildren! : (%,List %) -> % if $ has shallowlyMutable
+ setvalue! : (%,S) -> S if $ has shallowlyMutable
+ value : % -> S
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ child? : (%,%) -> Boolean if S has SETCAT
+ setelt : (%,value,S) -> S if $ has shallowlyMutable
+ ?.value : (%,value) -> S
+\end{verbatim}
+
+These exports come from HomogeneousAggregate(a:Type):
+\begin{verbatim}
+ any? : ((S -> Boolean),%) -> Boolean
+ if $ has finiteAggregate
+ coerce : % -> OutputForm if S has SETCAT
+ copy : % -> %
+ count : (S,%) -> NonNegativeInteger
+ if S has SETCAT and $ has finiteAggregate
+ count : ((S -> Boolean),%) -> NonNegativeInteger
+ if $ has finiteAggregate
+ empty : () -> %
+ empty? : % -> Boolean
+ eq? : (%,%) -> Boolean
+ eval : (%,List S,List S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,S,S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,Equation S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,List Equation S) -> %
+ if S has EVALAB S and S has SETCAT
+ every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
+ hash : % -> SingleInteger if S has SETCAT
+ latex : % -> String if S has SETCAT
+ less? : (%,NonNegativeInteger) -> Boolean
+ map : ((S -> S),%) -> %
+ map! : ((S -> S),%) -> % if $ has shallowlyMutable
+ member? : (S,%) -> Boolean
+ if S has SETCAT and $ has finiteAggregate
+ members : % -> List S if $ has finiteAggregate
+ more? : (%,NonNegativeInteger) -> Boolean
+ parts : % -> List S if $ has finiteAggregate
+ sample : () -> %
+ size? : (%,NonNegativeInteger) -> Boolean
+ ?~=? : (%,%) -> Boolean if S has SETCAT
+ #? : % -> NonNegativeInteger if $ has finiteAggregate
+ ?=? : (%,%) -> Boolean if S has SETCAT
+\end{verbatim}
+
<<category RCAGG RecursiveAggregate>>=
)abbrev category RCAGG RecursiveAggregate
++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
@@ -1582,6 +2023,136 @@
{\bf See:}\\
\pagefrom{RecursiveAggregate}{RCAGG}
+
+{\bf Exports:}\\
+\begin{tabular}{llllll}
+ any? & children & child? & coerce & copy & count \\
+ count & cyclic? & distance & empty & empty? & eq? \\
+ eval & eval & eval & eval & every? & hash \\
+ latex & leaf? & leaves & left & less? & map \\
+ map! & member? & members & more? & nodes & node? \\
+ parts & right & sample & setchildren! & setelt & setelt \\
+ setelt & setleft! & setright! & setvalue! & size? & value \\
+ \#? & ?=? & ?\~{}=? & ?.right & ?.left & ?.value \\
+\end{tabular}
+
+\cross{BRAGG}{any?}
+\cross{BRAGG}{children}
+\cross{BRAGG}{child?}
+\cross{BRAGG}{coerce}
+\cross{BRAGG}{copy}
+\cross{BRAGG}{count}
+\cross{BRAGG}{count}
+\cross{BRAGG}{cyclic?}
+\cross{BRAGG}{distance}
+\cross{BRAGG}{empty}
+\cross{BRAGG}{empty?}
+\cross{BRAGG}{eq?}
+\cross{BRAGG}{eval}
+\cross{BRAGG}{eval}
+\cross{BRAGG}{eval}
+\cross{BRAGG}{eval}
+\cross{BRAGG}{every?}
+\cross{BRAGG}{hash}
+\cross{BRAGG}{latex}
+\cross{BRAGG}{leaf?}
+\cross{BRAGG}{leaves}
+\cross{BRAGG}{left}
+\cross{BRAGG}{less?}
+\cross{BRAGG}{map}
+\cross{BRAGG}{map!}
+\cross{BRAGG}{member?}
+\cross{BRAGG}{members}
+\cross{BRAGG}{more?}
+\cross{BRAGG}{nodes}
+\cross{BRAGG}{node?}
+\cross{BRAGG}{parts}
+\cross{BRAGG}{right}
+\cross{BRAGG}{sample}
+\cross{BRAGG}{setchildren!}
+\cross{BRAGG}{setelt}
+\cross{BRAGG}{setelt}
+\cross{BRAGG}{setelt}
+\cross{BRAGG}{setleft!}
+\cross{BRAGG}{setright!}
+\cross{BRAGG}{setvalue!}
+\cross{BRAGG}{size?}
+\cross{BRAGG}{value}
+\cross{BRAGG}{\#?}
+\cross{BRAGG}{?=?}
+\cross{BRAGG}{?\~{}=?}
+\cross{BRAGG}{?.right}
+\cross{BRAGG}{?.left}
+\cross{BRAGG}{?.value}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ left : % -> %
+ right : % -> %
+ setelt : (%,right,%) -> % if $ has shallowlyMutable
+ setelt : (%,left,%) -> % if $ has shallowlyMutable
+ setleft! : (%,%) -> % if $ has shallowlyMutable
+ setright! : (%,%) -> % if $ has shallowlyMutable
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ children : % -> List %
+ coerce : % -> OutputForm if S has SETCAT
+ cyclic? : % -> Boolean
+ leaf? : % -> Boolean
+ leaves : % -> List S
+ member? : (S,%) -> Boolean
+ if S has SETCAT and $ has finiteAggregate
+ nodes : % -> List %
+ node? : (%,%) -> Boolean if S has SETCAT
+ #? : % -> NonNegativeInteger if $ has finiteAggregate
+ ?=? : (%,%) -> Boolean if S has SETCAT
+ ?.right : (%,right) -> %
+ ?.left : (%,left) -> %
+\end{verbatim}
+
+These exports come from RecursiveAggregate(a:Type)
+\begin{verbatim}
+ any? : ((S -> Boolean),%) -> Boolean
+ if $ has finiteAggregate
+ child? : (%,%) -> Boolean if S has SETCAT
+ copy : % -> %
+ count : (S,%) -> NonNegativeInteger
+ if S has SETCAT and $ has finiteAggregate
+ count : ((S -> Boolean),%) -> NonNegativeInteger
+ if $ has finiteAggregate
+ distance : (%,%) -> Integer
+ empty : () -> %
+ empty? : % -> Boolean
+ eq? : (%,%) -> Boolean
+ eval : (%,List S,List S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,S,S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,Equation S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,List Equation S) -> %
+ if S has EVALAB S and S has SETCAT
+ every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
+ hash : % -> SingleInteger if S has SETCAT
+ latex : % -> String if S has SETCAT
+ less? : (%,NonNegativeInteger) -> Boolean
+ map : ((S -> S),%) -> %
+ map! : ((S -> S),%) -> % if $ has shallowlyMutable
+ members : % -> List S if $ has finiteAggregate
+ more? : (%,NonNegativeInteger) -> Boolean
+ parts : % -> List S if $ has finiteAggregate
+ sample : () -> %
+ setchildren! : (%,List %) -> % if $ has shallowlyMutable
+ setelt : (%,value,S) -> S if $ has shallowlyMutable
+ setvalue! : (%,S) -> S if $ has shallowlyMutable
+ size? : (%,NonNegativeInteger) -> Boolean
+ value : % -> S
+ ?~=? : (%,%) -> Boolean if S has SETCAT
+ ?.value : (%,value) -> S
+\end{verbatim}
+
<<category BRAGG BinaryRecursiveAggregate>>=
)abbrev category BRAGG BinaryRecursiveAggregate
++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
@@ -1744,6 +2315,128 @@
\pageto{MultiDictionary}{MDAGG}
\pagefrom{BagAggregate}{BGAGG}
\pagefrom{Collection}{CLAGG}
+
+{\bf Exports:}\\
+\begin{tabular}{llllll}
+ any? & bag & coerce & construct & convert & copy \\
+ count & dictionary & empty & empty? & eq? & eval \\
+ every? & extract! & find & hash & insert! & inspect \\
+ latex & less? & map & map! & member? & members \\
+ more? & parts & reduce & remove & remove! & removeDuplicates \\
+ sample & select & select! & size? & \#? & ?=? \\
+ ?\~{}=? &&&&&\\
+\end{tabular}
+
+\cross{DIOPS}{any?}
+\cross{DIOPS}{bag}
+\cross{DIOPS}{coerce}
+\cross{DIOPS}{construct}
+\cross{DIOPS}{convert}
+\cross{DIOPS}{copy}
+\cross{DIOPS}{count}
+\cross{DIOPS}{dictionary}
+\cross{DIOPS}{empty}
+\cross{DIOPS}{empty?}
+\cross{DIOPS}{eq?}
+\cross{DIOPS}{eval}
+\cross{DIOPS}{every?}
+\cross{DIOPS}{extract!}
+\cross{DIOPS}{find}
+\cross{DIOPS}{hash}
+\cross{DIOPS}{insert!}
+\cross{DIOPS}{inspect}
+\cross{DIOPS}{latex}
+\cross{DIOPS}{less?}
+\cross{DIOPS}{map}
+\cross{DIOPS}{map!}
+\cross{DIOPS}{member?}
+\cross{DIOPS}{members}
+\cross{DIOPS}{more?}
+\cross{DIOPS}{parts}
+\cross{DIOPS}{reduce}
+\cross{DIOPS}{remove}
+\cross{DIOPS}{remove!}
+\cross{DIOPS}{removeDuplicates}
+\cross{DIOPS}{sample}
+\cross{DIOPS}{select}
+\cross{DIOPS}{select!}
+\cross{DIOPS}{size?}
+\cross{DIOPS}{\#?}
+\cross{DIOPS}{?=?}
+\cross{DIOPS}{?\~{}=?}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ dictionary : List S -> %
+ remove! : ((S -> Boolean),%) -> % if $ has finiteAggregate
+ remove! : (S,%) -> % if $ has finiteAggregate
+ select! : ((S -> Boolean),%) -> % if $ has finiteAggregate
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ coerce : % -> OutputForm if S has SETCAT
+ construct : List S -> %
+ copy : % -> %
+ dictionary : () -> %
+\end{verbatim}
+
+These exports come from BagAggregate(a:SetCategory):
+\begin{verbatim}
+ any? : ((S -> Boolean),%) -> Boolean
+ if $ has finiteAggregate
+ bag : List S -> %
+ count : (S,%) -> NonNegativeInteger
+ if S has SETCAT and $ has finiteAggregate
+ count : ((S -> Boolean),%) -> NonNegativeInteger
+ if $ has finiteAggregate
+ empty : () -> %
+ empty? : % -> Boolean
+ eq? : (%,%) -> Boolean
+ eval : (%,List S,List S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,S,S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,Equation S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,List Equation S) -> %
+ if S has EVALAB S and S has SETCAT
+ every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
+ extract! : % -> S
+ hash : % -> SingleInteger if S has SETCAT
+ insert! : (S,%) -> %
+ inspect : % -> S
+ latex : % -> String if S has SETCAT
+ less? : (%,NonNegativeInteger) -> Boolean
+ map : ((S -> S),%) -> %
+ map! : ((S -> S),%) -> % if $ has shallowlyMutable
+ member? : (S,%) -> Boolean
+ if S has SETCAT and $ has finiteAggregate
+ members : % -> List S if $ has finiteAggregate
+ more? : (%,NonNegativeInteger) -> Boolean
+ parts : % -> List S if $ has finiteAggregate
+ sample : () -> %
+ size? : (%,NonNegativeInteger) -> Boolean
+ #? : % -> NonNegativeInteger if $ has finiteAggregate
+ ?=? : (%,%) -> Boolean if S has SETCAT
+ ?~=? : (%,%) -> Boolean if S has SETCAT
+\end{verbatim}
+
+These exports come from Collection(a:SetCategory)
+\begin{verbatim}
+ convert : % -> InputForm if S has KONVERT INFORM
+ find : ((S -> Boolean),%) -> Union(S,"failed")
+ reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate
+ reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate
+ reduce : (((S,S) -> S),%,S,S) -> S
+ if S has SETCAT and $ has finiteAggregate
+ remove : ((S -> Boolean),%) -> % if $ has finiteAggregate
+ remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate
+ removeDuplicates : % -> %
+ if S has SETCAT and $ has finiteAggregate
+ select : ((S -> Boolean),%) -> % if $ has finiteAggregate
+\end{verbatim}
+
<<category DIOPS DictionaryOperations>>=
)abbrev category DIOPS DictionaryOperations
++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
@@ -1850,6 +2543,132 @@
{\bf See:}\\
\pagefrom{RecursiveAggregate}{RCAGG}
+
+{\bf Exports:}\\
+\begin{tabular}{llllll}
+ any? & children & child? & coerce & concat! & copy \\
+ count & count & cyclic? & distance & empty & empty? \\
+ eq? & eval & eval & eval & eval & every? \\
+ hash & head & last & latex & leaf? & leaves \\
+ less? & map & map! & member? & members & more? \\
+ next & nodes & node? & parts & previous & sample \\
+ setchildren! & setelt & setnext! & setprevious! & setvalue! & size? \\
+ tail & value & \#? & ?=? & ?\~{}=? & ?.value \\
+\end{tabular}
+
+\cross{DLAGG}{any?}
+\cross{DLAGG}{children}
+\cross{DLAGG}{child?}
+\cross{DLAGG}{coerce}
+\cross{DLAGG}{concat!}
+\cross{DLAGG}{copy}
+\cross{DLAGG}{count}
+\cross{DLAGG}{count}
+\cross{DLAGG}{cyclic?}
+\cross{DLAGG}{distance}
+\cross{DLAGG}{empty}
+\cross{DLAGG}{empty?}
+\cross{DLAGG}{eq?}
+\cross{DLAGG}{eval}
+\cross{DLAGG}{eval}
+\cross{DLAGG}{eval}
+\cross{DLAGG}{eval}
+\cross{DLAGG}{every?}
+\cross{DLAGG}{hash}
+\cross{DLAGG}{head}
+\cross{DLAGG}{last}
+\cross{DLAGG}{latex}
+\cross{DLAGG}{leaf?}
+\cross{DLAGG}{leaves}
+\cross{DLAGG}{less?}
+\cross{DLAGG}{map}
+\cross{DLAGG}{map!}
+\cross{DLAGG}{member?}
+\cross{DLAGG}{members}
+\cross{DLAGG}{more?}
+\cross{DLAGG}{next}
+\cross{DLAGG}{nodes}
+\cross{DLAGG}{node?}
+\cross{DLAGG}{parts}
+\cross{DLAGG}{previous}
+\cross{DLAGG}{sample}
+\cross{DLAGG}{setchildren!}
+\cross{DLAGG}{setelt}
+\cross{DLAGG}{setnext!}
+\cross{DLAGG}{setprevious!}
+\cross{DLAGG}{setvalue!}
+\cross{DLAGG}{size?}
+\cross{DLAGG}{tail}
+\cross{DLAGG}{value}
+\cross{DLAGG}{\#?}
+\cross{DLAGG}{?=?}
+\cross{DLAGG}{?\~{}=?}
+\cross{DLAGG}{?.value}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ concat! : (%,%) -> % if $ has shallowlyMutable
+ head : % -> %
+ last : % -> S
+ next : % -> %
+ previous : % -> %
+ setnext! : (%,%) -> % if $ has shallowlyMutable
+ setprevious! : (%,%) -> % if $ has shallowlyMutable
+ tail : % -> %
+\end{verbatim}
+
+These exports come from RecursiveAggregate(a:Type):
+\begin{verbatim}
+ any? : ((S -> Boolean),%) -> Boolean
+ if $ has finiteAggregate
+ children : % -> List %
+ child? : (%,%) -> Boolean if S has SETCAT
+ coerce : % -> OutputForm if S has SETCAT
+ copy : % -> %
+ count : (S,%) -> NonNegativeInteger
+ if S has SETCAT and $ has finiteAggregate
+ count : ((S -> Boolean),%) -> NonNegativeInteger
+ if $ has finiteAggregate
+ cyclic? : % -> Boolean
+ distance : (%,%) -> Integer
+ empty : () -> %
+ empty? : % -> Boolean
+ eq? : (%,%) -> Boolean
+ eval : (%,List S,List S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,S,S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,Equation S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,List Equation S) -> %
+ if S has EVALAB S and S has SETCAT
+ every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
+ hash : % -> SingleInteger if S has SETCAT
+ latex : % -> String if S has SETCAT
+ leaf? : % -> Boolean
+ leaves : % -> List S
+ less? : (%,NonNegativeInteger) -> Boolean
+ map : ((S -> S),%) -> %
+ map! : ((S -> S),%) -> % if $ has shallowlyMutable
+ member? : (S,%) -> Boolean
+ if S has SETCAT and $ has finiteAggregate
+ members : % -> List S if $ has finiteAggregate
+ more? : (%,NonNegativeInteger) -> Boolean
+ nodes : % -> List %
+ node? : (%,%) -> Boolean if S has SETCAT
+ parts : % -> List S if $ has finiteAggregate
+ sample : () -> %
+ setchildren! : (%,List %) -> % if $ has shallowlyMutable
+ setelt : (%,value,S) -> S if $ has shallowlyMutable
+ setvalue! : (%,S) -> S if $ has shallowlyMutable
+ size? : (%,NonNegativeInteger) -> Boolean
+ value : % -> S
+ #? : % -> NonNegativeInteger if $ has finiteAggregate
+ ?=? : (%,%) -> Boolean if S has SETCAT
+ ?~=? : (%,%) -> Boolean if S has SETCAT
+ ?.value : (%,value) -> S
+\end{verbatim}
+
<<category DLAGG DoublyLinkedAggregate>>=
)abbrev category DLAGG DoublyLinkedAggregate
++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
@@ -1947,6 +2766,166 @@
\pageto{StreamAggregate}{STAGG}
\pagefrom{Collection}{CLAGG}
\pagefrom{IndexedAggregate}{IXAGG}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+ any? & coerce & concat & construct & convert \\
+ copy & count & delete & elt & empty \\
+ empty? & entries & entry? & eq? & eval \\
+ every? & fill! & find & first & hash \\
+ index? & indices & insert & latex & less? \\
+ map & map! & maxIndex & member? & members \\
+ minIndex & more? & new & parts & qelt \\
+ qsetelt! & reduce & reduce & reduce & remove \\
+ remove & removeDuplicates & sample & select & setelt \\
+ setelt & size? & swap! & ?\~{}=? & \#? \\
+ ?=? & ?.? &&&\\
+\end{tabular}
+
+\cross{LNAGG}{any?}
+\cross{LNAGG}{coerce}
+\cross{LNAGG}{concat}
+\cross{LNAGG}{construct}
+\cross{LNAGG}{convert}
+\cross{LNAGG}{copy}
+\cross{LNAGG}{count}
+\cross{LNAGG}{delete}
+\cross{LNAGG}{elt}
+\cross{LNAGG}{empty}
+\cross{LNAGG}{empty?}
+\cross{LNAGG}{entries}
+\cross{LNAGG}{entry?}
+\cross{LNAGG}{eq?}
+\cross{LNAGG}{eval}
+\cross{LNAGG}{every?}
+\cross{LNAGG}{fill!}
+\cross{LNAGG}{find}
+\cross{LNAGG}{first}
+\cross{LNAGG}{hash}
+\cross{LNAGG}{index?}
+\cross{LNAGG}{indices}
+\cross{LNAGG}{insert}
+\cross{LNAGG}{latex}
+\cross{LNAGG}{less?}
+\cross{LNAGG}{map}
+\cross{LNAGG}{map!}
+\cross{LNAGG}{maxIndex}
+\cross{LNAGG}{member?}
+\cross{LNAGG}{members}
+\cross{LNAGG}{minIndex}
+\cross{LNAGG}{more?}
+\cross{LNAGG}{new}
+\cross{LNAGG}{parts}
+\cross{LNAGG}{qelt}
+\cross{LNAGG}{qsetelt!}
+\cross{LNAGG}{reduce}
+\cross{LNAGG}{reduce}
+\cross{LNAGG}{reduce}
+\cross{LNAGG}{remove}
+\cross{LNAGG}{remove}
+\cross{LNAGG}{removeDuplicates}
+\cross{LNAGG}{sample}
+\cross{LNAGG}{select}
+\cross{LNAGG}{setelt}
+\cross{LNAGG}{setelt}
+\cross{LNAGG}{size?}
+\cross{LNAGG}{swap!}
+\cross{LNAGG}{?\~{}=?}
+\cross{LNAGG}{\#?}
+\cross{LNAGG}{?=?}
+\cross{LNAGG}{?.?}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ concat : (%,%) -> %
+ concat : List % -> %
+ delete : (%,Integer) -> %
+ delete : (%,UniversalSegment Integer) -> %
+ insert : (%,%,Integer) -> %
+ map : (((S,S) -> S),%,%) -> %
+ new : (NonNegativeInteger,S) -> %
+ setelt : (%,UniversalSegment Integer,S) -> S
+ if $ has shallowlyMutable
+ ?.? : (%,UniversalSegment Integer) -> %
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ concat : (%,S) -> %
+ concat : (S,%) -> %
+ index? : (Integer,%) -> Boolean
+ indices : % -> List Integer
+ insert : (S,%,Integer) -> %
+ maxIndex : % -> Integer if Integer has ORDSET
+\end{verbatim}
+
+These exports come from IndexedAggregate(a:SetCategory,b:Type)
+\begin{verbatim}
+ any? : ((S -> Boolean),%) -> Boolean
+ if $ has finiteAggregate
+ coerce : % -> OutputForm if S has SETCAT
+ copy : % -> %
+ count : (S,%) -> NonNegativeInteger
+ if S has SETCAT and $ has finiteAggregate
+ count : ((S -> Boolean),%) -> NonNegativeInteger
+ if $ has finiteAggregate
+ elt : (%,Integer,S) -> S
+ empty : () -> %
+ empty? : % -> Boolean
+ entries : % -> List S
+ entry? : (S,%) -> Boolean
+ if $ has finiteAggregate and S has SETCAT
+ eq? : (%,%) -> Boolean
+ eval : (%,List S,List S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,S,S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,Equation S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,List Equation S) -> %
+ if S has EVALAB S and S has SETCAT
+ every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
+ fill! : (%,S) -> % if $ has shallowlyMutable
+ first : % -> S if Integer has ORDSET
+ hash : % -> SingleInteger if S has SETCAT
+ latex : % -> String if S has SETCAT
+ less? : (%,NonNegativeInteger) -> Boolean
+ map : ((S -> S),%) -> %
+ map! : ((S -> S),%) -> % if $ has shallowlyMutable
+ member? : (S,%) -> Boolean
+ if S has SETCAT and $ has finiteAggregate
+ members : % -> List S if $ has finiteAggregate
+ minIndex : % -> Integer if Integer has ORDSET
+ more? : (%,NonNegativeInteger) -> Boolean
+ parts : % -> List S if $ has finiteAggregate
+ qelt : (%,Integer) -> S
+ qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable
+ sample : () -> %
+ setelt : (%,Integer,S) -> S if $ has shallowlyMutable
+ size? : (%,NonNegativeInteger) -> Boolean
+ swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable
+ #? : % -> NonNegativeInteger if $ has finiteAggregate
+ ?.? : (%,Integer) -> S
+ ?~=? : (%,%) -> Boolean if S has SETCAT
+ ?=? : (%,%) -> Boolean if S has SETCAT
+\end{verbatim}
+
+These exports come from Collection(a:Type):
+\begin{verbatim}
+ construct : List S -> %
+ convert : % -> InputForm if S has KONVERT INFORM
+ find : ((S -> Boolean),%) -> Union(S,"failed")
+ reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate
+ reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate
+ reduce : (((S,S) -> S),%,S,S) -> S
+ if S has SETCAT and $ has finiteAggregate
+ remove : ((S -> Boolean),%) -> % if $ has finiteAggregate
+ remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate
+ removeDuplicates : % -> %
+ if S has SETCAT and $ has finiteAggregate
+ select : ((S -> Boolean),%) -> % if $ has finiteAggregate
+\end{verbatim}
+
<<category LNAGG LinearAggregate>>=
)abbrev category LNAGG LinearAggregate
++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
@@ -2088,6 +3067,97 @@
{\bf See:}\\
\pagefrom{BagAggregate}{BGAGG}
+
+{\bf Exports:}\\
+\begin{tabular}{lllllll}
+ any? & bag & copy & coerce & count & empty & empty? \\
+ eq? & eval & every? & extract! & hash & insert! & inspect \\
+ latex & less? & map & map! & max & member? & members \\
+ merge & merge! & more? & parts & sample & size? & \#? \\
+ ?=? & ?\~{}=? &\\
+\end{tabular}
+
+\cross{PRQAGG}{any?}
+\cross{PRQAGG}{bag}
+\cross{PRQAGG}{copy}
+\cross{PRQAGG}{coerce}
+\cross{PRQAGG}{count}
+\cross{PRQAGG}{empty}
+\cross{PRQAGG}{empty?}
+\cross{PRQAGG}{eq?}
+\cross{PRQAGG}{eval}
+\cross{PRQAGG}{every?}
+\cross{PRQAGG}{extract!}
+\cross{PRQAGG}{hash}
+\cross{PRQAGG}{insert!}
+\cross{PRQAGG}{inspect}
+\cross{PRQAGG}{latex}
+\cross{PRQAGG}{less?}
+\cross{PRQAGG}{map}
+\cross{PRQAGG}{map!}
+\cross{PRQAGG}{max}
+\cross{PRQAGG}{member?}
+\cross{PRQAGG}{members}
+\cross{PRQAGG}{merge}
+\cross{PRQAGG}{merge!}
+\cross{PRQAGG}{more?}
+\cross{PRQAGG}{parts}
+\cross{PRQAGG}{sample}
+\cross{PRQAGG}{size?}
+\cross{PRQAGG}{\#?}
+\cross{PRQAGG}{?=?}
+\cross{PRQAGG}{?\~{}=?}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ max : % -> S
+ merge : (%,%) -> %
+ merge! : (%,%) -> %
+\end{verbatim}
+
+These exports come from PriorityQueueAggregate(a:Type):
+\begin{verbatim}
+ any? : ((S -> Boolean),%) -> Boolean
+ if $ has finiteAggregate
+ bag : List S -> %
+ coerce : % -> OutputForm if S has SETCAT
+ copy : % -> %
+ count : (S,%) -> NonNegativeInteger
+ if S has SETCAT and $ has finiteAggregate
+ count : ((S -> Boolean),%) -> NonNegativeInteger
+ if $ has finiteAggregate
+ empty : () -> %
+ empty? : % -> Boolean
+ eq? : (%,%) -> Boolean
+ eval : (%,List S,List S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,S,S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,Equation S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,List Equation S) -> %
+ if S has EVALAB S and S has SETCAT
+ every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
+ extract! : % -> S
+ hash : % -> SingleInteger if S has SETCAT
+ insert! : (S,%) -> %
+ inspect : % -> S
+ latex : % -> String if S has SETCAT
+ less? : (%,NonNegativeInteger) -> Boolean
+ map : ((S -> S),%) -> %
+ map! : ((S -> S),%) -> % if $ has shallowlyMutable
+ member? : (S,%) -> Boolean
+ if S has SETCAT and $ has finiteAggregate
+ members : % -> List S if $ has finiteAggregate
+ more? : (%,NonNegativeInteger) -> Boolean
+ parts : % -> List S if $ has finiteAggregate
+ sample : () -> %
+ size? : (%,NonNegativeInteger) -> Boolean
+ #? : % -> NonNegativeInteger if $ has finiteAggregate
+ ?=? : (%,%) -> Boolean if S has SETCAT
+ ?~=? : (%,%) -> Boolean if S has SETCAT
+\end{verbatim}
+
<<category PRQAGG PriorityQueueAggregate>>=
)abbrev category PRQAGG PriorityQueueAggregate
++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
@@ -2168,6 +3238,103 @@
{\bf See:}\\
\pageto{DequeueAggregate}{DQAGG}
\pagefrom{BagAggregate}{BGAGG}
+
+{\bf Exports:}\\
+\begin{tabular}{lllllll}
+ any? & bag & back & coerce & copy & count & dequeue! \\
+ empty & empty? & enqueue! & eq? & eval & every? & extract! \\
+ front & hash & insert! & inspect & latex & length & less? \\
+ map & map! & member? & members & more? & parts & rotate! \\
+ sample & size? & \#? & ?=? & ?\~{}=? &&\\
+\end{tabular}
+
+\cross{QUAGG}{any?}
+\cross{QUAGG}{bag}
+\cross{QUAGG}{back}
+\cross{QUAGG}{coerce}
+\cross{QUAGG}{copy}
+\cross{QUAGG}{count}
+\cross{QUAGG}{dequeue!}
+\cross{QUAGG}{empty}
+\cross{QUAGG}{empty?}
+\cross{QUAGG}{enqueue!}
+\cross{QUAGG}{eq?}
+\cross{QUAGG}{eval}
+\cross{QUAGG}{every?}
+\cross{QUAGG}{extract!}
+\cross{QUAGG}{front}
+\cross{QUAGG}{hash}
+\cross{QUAGG}{insert!}
+\cross{QUAGG}{inspect}
+\cross{QUAGG}{latex}
+\cross{QUAGG}{length}
+\cross{QUAGG}{less?}
+\cross{QUAGG}{map}
+\cross{QUAGG}{map!}
+\cross{QUAGG}{member?}
+\cross{QUAGG}{members}
+\cross{QUAGG}{more?}
+\cross{QUAGG}{parts}
+\cross{QUAGG}{rotate!}
+\cross{QUAGG}{sample}
+\cross{QUAGG}{size?}
+\cross{QUAGG}{\#?}
+\cross{QUAGG}{?=?}
+\cross{QUAGG}{?\~{}=?}
+
+These are implemented by this category:
+\begin{verbatim}
+ back : % -> S
+ dequeue! : % -> S
+ enqueue! : (S,%) -> S
+ front : % -> S
+ length : % -> NonNegativeInteger
+ rotate! : % -> %
+\end{verbatim}
+
+These exports come from BagAggregate(a:Type):
+\begin{verbatim}
+ any? : ((S -> Boolean),%) -> Boolean
+ if $ has finiteAggregate
+ bag : List S -> %
+ coerce : % -> OutputForm if S has SETCAT
+ copy : % -> %
+ count : (S,%) -> NonNegativeInteger
+ if S has SETCAT and $ has finiteAggregate
+ count : ((S -> Boolean),%) -> NonNegativeInteger
+ if $ has finiteAggregate
+ empty : () -> %
+ empty? : % -> Boolean
+ eq? : (%,%) -> Boolean
+ eval : (%,List S,List S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,S,S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,Equation S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,List Equation S) -> %
+ if S has EVALAB S and S has SETCAT
+ every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
+ extract! : % -> S
+ hash : % -> SingleInteger if S has SETCAT
+ insert! : (S,%) -> %
+ inspect : % -> S
+ latex : % -> String if S has SETCAT
+ less? : (%,NonNegativeInteger) -> Boolean
+ map : ((S -> S),%) -> %
+ map! : ((S -> S),%) -> % if $ has shallowlyMutable
+ member? : (S,%) -> Boolean
+ if S has SETCAT and $ has finiteAggregate
+ members : % -> List S if $ has finiteAggregate
+ more? : (%,NonNegativeInteger) -> Boolean
+ parts : % -> List S if $ has finiteAggregate
+ sample : () -> %
+ size? : (%,NonNegativeInteger) -> Boolean
+ #? : % -> NonNegativeInteger if $ has finiteAggregate
+ ?=? : (%,%) -> Boolean if S has SETCAT
+ ?~=? : (%,%) -> Boolean if S has SETCAT
+\end{verbatim}
+
<<category QUAGG QueueAggregate>>=
)abbrev category QUAGG QueueAggregate
++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
@@ -2253,6 +3420,99 @@
{\bf See:}\\
\pageto{DequeueAggregate}{DQAGG}
\pagefrom{BagAggregate}{BGAGG}
+
+{\bf Exports:}\\
+\begin{tabular}{lllllll}
+ any? & bag & coerce & copy & count & depth & empty \\
+ empty? & eq? & eval & every? & extract! & hash & insert! \\
+ inspect & latex & less? & map & map! & member? & members \\
+ more? & parts & pop! & push! & sample & size? & top \\
+ \#? & ?=? & ?\~{}=? &&&&\\
+\end{tabular}
+
+\cross{SKAGG}{any?}
+\cross{SKAGG}{bag}
+\cross{SKAGG}{coerce}
+\cross{SKAGG}{copy}
+\cross{SKAGG}{count}
+\cross{SKAGG}{depth}
+\cross{SKAGG}{empty}
+\cross{SKAGG}{empty?}
+\cross{SKAGG}{eq?}
+\cross{SKAGG}{eval}
+\cross{SKAGG}{every?}
+\cross{SKAGG}{extract!}
+\cross{SKAGG}{hash}
+\cross{SKAGG}{insert!}
+\cross{SKAGG}{inspect}
+\cross{SKAGG}{latex}
+\cross{SKAGG}{less?}
+\cross{SKAGG}{map}
+\cross{SKAGG}{map!}
+\cross{SKAGG}{member?}
+\cross{SKAGG}{members}
+\cross{SKAGG}{more?}
+\cross{SKAGG}{parts}
+\cross{SKAGG}{pop!}
+\cross{SKAGG}{push!}
+\cross{SKAGG}{sample}
+\cross{SKAGG}{size?}
+\cross{SKAGG}{top}
+\cross{SKAGG}{\#?}
+\cross{SKAGG}{?=?}
+\cross{SKAGG}{?\~{}=?}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ depth : % -> NonNegativeInteger
+ pop! : % -> S
+ push! : (S,%) -> S
+ top : % -> S
+\end{verbatim}
+
+These exports come from BagAggregate(a:Type):
+\begin{verbatim}
+ any? : ((S -> Boolean),%) -> Boolean
+ if $ has finiteAggregate
+ bag : List S -> %
+ coerce : % -> OutputForm if S has SETCAT
+ copy : % -> %
+ count : (S,%) -> NonNegativeInteger
+ if S has SETCAT and $ has finiteAggregate
+ count : ((S -> Boolean),%) -> NonNegativeInteger
+ if $ has finiteAggregate
+ empty : () -> %
+ empty? : % -> Boolean
+ eq? : (%,%) -> Boolean
+ eval : (%,List S,List S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,S,S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,Equation S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,List Equation S) -> %
+ if S has EVALAB S and S has SETCAT
+ every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
+ extract! : % -> S
+ hash : % -> SingleInteger if S has SETCAT
+ insert! : (S,%) -> %
+ inspect : % -> S
+ latex : % -> String if S has SETCAT
+ less? : (%,NonNegativeInteger) -> Boolean
+ map : ((S -> S),%) -> %
+ map! : ((S -> S),%) -> % if $ has shallowlyMutable
+ member? : (S,%) -> Boolean
+ if S has SETCAT and $ has finiteAggregate
+ members : % -> List S if $ has finiteAggregate
+ more? : (%,NonNegativeInteger) -> Boolean
+ parts : % -> List S if $ has finiteAggregate
+ sample : () -> %
+ size? : (%,NonNegativeInteger) -> Boolean
+ #? : % -> NonNegativeInteger if $ has finiteAggregate
+ ?=? : (%,%) -> Boolean if S has SETCAT
+ ?~=? : (%,%) -> Boolean if S has SETCAT
+\end{verbatim}
+
<<category SKAGG StackAggregate>>=
)abbrev category SKAGG StackAggregate
++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
@@ -2330,7 +3590,167 @@
\pagepic{ps/v102unaryrecursiveaggregate.ps}{URAGG}
{\bf See:}\\
+\pageto{StreamAggregate}{STAGG}
\pagefrom{RecursiveAggregate}{RCAGG}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+ any? & children & child? & coerce & concat \\
+ concat! & copy & count & cycleEntry & cycleLength\\
+ cycleSplit! & cycleTail & cyclic? & distance & empty \\
+ empty? & eq? & eval & every? & first \\
+ hash & last & latex & leaf? & leaves \\
+ less? & map & map! & member? & members \\
+ more? & nodes & node? & parts & rest \\
+ sample & second & setchildren! & setelt & setfirst! \\
+ setlast! & setrest! & setvalue! & size? & split! \\
+ tail & third & value & \#? & ?.last \\
+ ?.rest & ?.first & ?.value & ?=? & ?\~{}=? \\
+\end{tabular}
+
+\cross{URAGG}{any?}
+\cross{URAGG}{children}
+\cross{URAGG}{child?}
+\cross{URAGG}{coerce}
+\cross{URAGG}{concat}
+\cross{URAGG}{concat!}
+\cross{URAGG}{copy}
+\cross{URAGG}{count}
+\cross{URAGG}{cycleEntry}
+\cross{URAGG}{cycleLength}
+\cross{URAGG}{cycleSplit!}
+\cross{URAGG}{cycleTail}
+\cross{URAGG}{cyclic?}
+\cross{URAGG}{distance}
+\cross{URAGG}{empty}
+\cross{URAGG}{empty?}
+\cross{URAGG}{eq?}
+\cross{URAGG}{eval}
+\cross{URAGG}{every?}
+\cross{URAGG}{first}
+\cross{URAGG}{hash}
+\cross{URAGG}{last}
+\cross{URAGG}{latex}
+\cross{URAGG}{leaf?}
+\cross{URAGG}{leaves}
+\cross{URAGG}{less?}
+\cross{URAGG}{map}
+\cross{URAGG}{map!}
+\cross{URAGG}{member?}
+\cross{URAGG}{members}
+\cross{URAGG}{more?}
+\cross{URAGG}{nodes}
+\cross{URAGG}{node?}
+\cross{URAGG}{parts}
+\cross{URAGG}{rest}
+\cross{URAGG}{sample}
+\cross{URAGG}{second}
+\cross{URAGG}{setchildren!}
+\cross{URAGG}{setelt}
+\cross{URAGG}{setfirst!}
+\cross{URAGG}{setlast!}
+\cross{URAGG}{setrest!}
+\cross{URAGG}{setvalue!}
+\cross{URAGG}{size?}
+\cross{URAGG}{split!}
+\cross{URAGG}{tail}
+\cross{URAGG}{third}
+\cross{URAGG}{value}
+\cross{URAGG}{\#?}
+\cross{URAGG}{?.last}
+\cross{URAGG}{?.rest}
+\cross{URAGG}{?.first}
+\cross{URAGG}{?.value}
+\cross{URAGG}{?=?}
+\cross{URAGG}{?\~{}=?}
+
+These are directly exported but not implemented:
+\begin{verbatim}
+ concat : (S,%) -> %
+ concat! : (%,S) -> % if $ has shallowlyMutable
+ concat! : (%,%) -> % if $ has shallowlyMutable
+ first : % -> S
+ first : (%,NonNegativeInteger) -> %
+ rest : % -> %
+ setfirst! : (%,S) -> S if $ has shallowlyMutable
+\end{verbatim}
+
+These are implemented by this category:
+\begin{verbatim}
+ children : % -> List %
+ concat : (%,%) -> %
+ cycleEntry : % -> %
+ cycleLength : % -> NonNegativeInteger
+ cycleSplit! : % -> % if $ has shallowlyMutable
+ cycleTail : % -> %
+ cyclic? : % -> Boolean
+ last : % -> S
+ last : (%,NonNegativeInteger) -> %
+ leaf? : % -> Boolean
+ less? : (%,NonNegativeInteger) -> Boolean
+ more? : (%,NonNegativeInteger) -> Boolean
+ nodes : % -> List %
+ node? : (%,%) -> Boolean if S has SETCAT
+ rest : (%,NonNegativeInteger) -> %
+ second : % -> S
+ setchildren! : (%,List %) -> % if $ has shallowlyMutable
+ setelt : (%,first,S) -> S if $ has shallowlyMutable
+ setelt : (%,last,S) -> S if $ has shallowlyMutable
+ setelt : (%,rest,%) -> % if $ has shallowlyMutable
+ setlast! : (%,S) -> S if $ has shallowlyMutable
+ setvalue! : (%,S) -> S if $ has shallowlyMutable
+ size? : (%,NonNegativeInteger) -> Boolean
+ split! : (%,Integer) -> % if $ has shallowlyMutable
+ tail : % -> %
+ third : % -> S
+ value : % -> S
+ #? : % -> NonNegativeInteger if $ has finiteAggregate
+ ?=? : (%,%) -> Boolean if S has SETCAT
+ ?.first : (%,first) -> S
+ ?.last : (%,last) -> S
+ ?.rest : (%,rest) -> %
+\end{verbatim}
+
+These exports come from RecursiveAggregate(a:Type):
+\begin{verbatim}
+ any? : ((S -> Boolean),%) -> Boolean
+ if $ has finiteAggregate
+ child? : (%,%) -> Boolean if S has SETCAT
+ coerce : % -> OutputForm if S has SETCAT
+ copy : % -> %
+ count : (S,%) -> NonNegativeInteger
+ if S has SETCAT and $ has finiteAggregate
+ count : ((S -> Boolean),%) -> NonNegativeInteger
+ if $ has finiteAggregate
+ distance : (%,%) -> Integer
+ empty : () -> %
+ empty? : % -> Boolean
+ eq? : (%,%) -> Boolean
+ eval : (%,List S,List S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,S,S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,Equation S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,List Equation S) -> %
+ if S has EVALAB S and S has SETCAT
+ every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
+ hash : % -> SingleInteger if S has SETCAT
+ latex : % -> String if S has SETCAT
+ leaves : % -> List S
+ map : ((S -> S),%) -> %
+ map! : ((S -> S),%) -> % if $ has shallowlyMutable
+ member? : (S,%) -> Boolean
+ if S has SETCAT and $ has finiteAggregate
+ members : % -> List S if $ has finiteAggregate
+ parts : % -> List S if $ has finiteAggregate
+ sample : () -> %
+ setelt : (%,value,S) -> S if $ has shallowlyMutable
+ setrest! : (%,%) -> % if $ has shallowlyMutable
+ ?.value : (%,value) -> S
+ ?~=? : (%,%) -> Boolean if S has SETCAT
+\end{verbatim}
+
<<category URAGG UnaryRecursiveAggregate>>=
)abbrev category URAGG UnaryRecursiveAggregate
++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
@@ -2642,6 +4062,121 @@
{\bf See:}\\
\pageto{KeyedDictionary}{KDAGG}
\pagefrom{DictionaryOperations}{DIOPS}
+
+{\bf Exports:}\\
+\begin{tabular}{lllllll}
+ any? & bag & coerce & construct & convert \\
+ copy & count & dictionary & empty & empty? \\
+ eq? & eval & every? & extract! & find \\
+ hash & insert! & inspect & latex & less? \\
+ map & map! & member? & members & more? \\
+ parts & reduce & remove & remove! & removeDuplicates \\
+ sample & select & select! & size? & \#? \\
+ ?\~{}=? & ?=? &&&\\
+\end{tabular}
+
+\cross{DIAGG}{any?}
+\cross{DIAGG}{bag}
+\cross{DIAGG}{coerce}
+\cross{DIAGG}{construct}
+\cross{DIAGG}{convert}
+\cross{DIAGG}{copy}
+\cross{DIAGG}{count}
+\cross{DIAGG}{dictionary}
+\cross{DIAGG}{empty}
+\cross{DIAGG}{empty?}
+\cross{DIAGG}{eq?}
+\cross{DIAGG}{eval}
+\cross{DIAGG}{every?}
+\cross{DIAGG}{extract!}
+\cross{DIAGG}{find}
+\cross{DIAGG}{hash}
+\cross{DIAGG}{insert!}
+\cross{DIAGG}{inspect}
+\cross{DIAGG}{latex}
+\cross{DIAGG}{less?}
+\cross{DIAGG}{map}
+\cross{DIAGG}{map!}
+\cross{DIAGG}{member?}
+\cross{DIAGG}{members}
+\cross{DIAGG}{more?}
+\cross{DIAGG}{parts}
+\cross{DIAGG}{reduce}
+\cross{DIAGG}{remove}
+\cross{DIAGG}{remove!}
+\cross{DIAGG}{removeDuplicates}
+\cross{DIAGG}{sample}
+\cross{DIAGG}{select}
+\cross{DIAGG}{select!}
+\cross{DIAGG}{size?}
+\cross{DIAGG}{\#?}
+\cross{DIAGG}{?\~{}=?}
+\cross{DIAGG}{?=?}
+
+These are implemented by this category:
+\begin{verbatim}
+ dictionary : List S -> %
+ select! : ((S -> Boolean),%) -> % if $ has finiteAggregate
+ ?=? : (%,%) -> Boolean if S has SETCAT
+ remove! : ((S -> Boolean),%) -> % if $ has finiteAggregate
+\end{verbatim}
+
+These exports come from DictionaryOperations(a:SetCategory):
+\begin{verbatim}
+ any? : ((S -> Boolean),%) -> Boolean
+ if $ has finiteAggregate
+ bag : List S -> %
+ coerce : % -> OutputForm if S has SETCAT
+ construct : List S -> %
+ convert : % -> InputForm if S has KONVERT INFORM
+ copy : % -> %
+ count : (S,%) -> NonNegativeInteger
+ if S has SETCAT and $ has finiteAggregate
+ count : ((S -> Boolean),%) -> NonNegativeInteger
+ if $ has finiteAggregate
+ dictionary : () -> %
+ empty : () -> %
+ empty? : % -> Boolean
+ eq? : (%,%) -> Boolean
+ eval : (%,List S,List S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,S,S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,Equation S) -> %
+ if S has EVALAB S and S has SETCAT
+ eval : (%,List Equation S) -> %
+ if S has EVALAB S and S has SETCAT
+ every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
+ extract! : % -> S
+ find : ((S -> Boolean),%) -> Union(S,"failed")
+ hash : % -> SingleInteger if S has SETCAT
+ insert! : (S,%) -> %
+ inspect : % -> S
+ latex : % -> String if S has SETCAT
+ less? : (%,NonNegativeInteger) -> Boolean
+ map : ((S -> S),%) -> %
+ map! : ((S -> S),%) -> % if $ has shallowlyMutable
+ member? : (S,%) -> Boolean
+ if S has SETCAT and $ has finiteAggregate
+ members : % -> List S if $ has finiteAggregate
+ more? : (%,NonNegativeInteger) -> Boolean
+ parts : % -> List S if $ has finiteAggregate
+ reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate
+ reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate
+ reduce : (((S,S) -> S),%,S,S) -> S
+ if S has SETCAT and $ has finiteAggregate
+ remove : ((S -> Boolean),%) -> % if $ has finiteAggregate
+ remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate
+ remove! : (S,%) -> % if $ has finiteAggregate
+ removeDuplicates : % -> %
+ if S has SETCAT and $ has finiteAggregate
+ sample : () -> %
+ select : ((S -> Boolean),%) -> % if $ has finiteAggregate
+ size? : (%,NonNegativeInteger) -> Boolean
+ #? : % -> NonNegativeInteger if $ has finiteAggregate
+ ?~=? : (%,%) -> Boolean if S has SETCAT
+\end{verbatim}
+
<<category DIAGG Dictionary>>=
)abbrev category DIAGG Dictionary
++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
@@ -2751,6 +4286,139 @@
{\bf See:}\\
\pagefrom{QueueAggregate}{QUAGG}
\pagefrom{StackAggregate}{SKAGG}
+
+{\bf Exports:}\\
+\begin{tabular}{lllll}
+ any? & back & bag & bottom! & coerce \\
+ copy & count & depth & dequeue & dequeue! \\
+ empty & empty? & enqueue! & eq? & eval \\...
[truncated message content] |
|
From: <gi...@ax...> - 2008-09-17 04:11:43
|
books/bookvol10.2.pamphlet | 4122 +++++++++++++++++++++++++++++++--
books/ps/v102collection.ps | 289 ++-
books/ps/v102finitelinearaggregate.ps | 115 +-
books/ps/v102listaggregate.ps | 491 ++--
books/ps/v102streamaggregate.ps | 403 ++--
changelog | 5 +
6 files changed, 4741 insertions(+), 684 deletions(-)
New commits:
commit f48c67d0e07f3c861db98e417cb8251dcef93fb2
Author: Tim Daly <da...@ax...>
Date: Fri Jul 25 22:49:42 2008 -0400
20080916 tpd books/ps/v102streamaggregate.ps
20080916 tpd books/ps/v102listaggregate.ps
20080916 tpd books/ps/v102finitelinearaggregate.ps corrected diagram
20080916 tpd books/ps/v102collection.ps corrected diagram
20080916 tpd books/bookvol10.2 more documentation
|
|
From: <da...@us...> - 2008-09-13 05:27:52
|
Revision: 972
http://axiom.svn.sourceforge.net/axiom/?rev=972&view=rev
Author: daly
Date: 2008-09-13 05:27:50 +0000 (Sat, 13 Sep 2008)
Log Message:
-----------
20080912 tpd books/Makefile add bookvol10 subvolumes
20080912 tpd books/bookvol10.4 added
20080912 tpd books/bookvol10.3 added
20080912 tpd books/bookvol10.2 added
20080912 tpd books/bookvol10.1 added
20080912 tpd books/bookvol10 split
20080912 tpd books/ps/v102keyeddictionary.ps updated
20080912 tpd books/ps/v102homogeneousaggregate.ps updated
20080912 tpd books/ps/v102homogeneousaggregate.ps updated
20080912 tpd books/ps/v10* renamed to books/ps/v102*
Modified Paths:
--------------
trunk/axiom/books/Makefile.pamphlet
trunk/axiom/books/bookvol10.pamphlet
trunk/axiom/changelog
trunk/axiom/src/Makefile.pamphlet
Added Paths:
-----------
trunk/axiom/books/bookvol10.1.pamphlet
trunk/axiom/books/bookvol10.2.pamphlet
trunk/axiom/books/bookvol10.3.pamphlet
trunk/axiom/books/bookvol10.4.pamphlet
trunk/axiom/books/ps/v102agg.ps
trunk/axiom/books/ps/v102associationlistaggregate.ps
trunk/axiom/books/ps/v102bagaggregate.ps
trunk/axiom/books/ps/v102binaryrecursiveaggregate.ps
trunk/axiom/books/ps/v102collection.ps
trunk/axiom/books/ps/v102dequeueaggregate.ps
trunk/axiom/books/ps/v102dictionary.ps
trunk/axiom/books/ps/v102dictionaryoperations.ps
trunk/axiom/books/ps/v102doublylinkedaggregate.ps
trunk/axiom/books/ps/v102eltab.ps
trunk/axiom/books/ps/v102eltableaggregate.ps
trunk/axiom/books/ps/v102extensiblelinearaggregate.ps
trunk/axiom/books/ps/v102finitelinearaggregate.ps
trunk/axiom/books/ps/v102homogeneousaggregate.ps
trunk/axiom/books/ps/v102indexedaggregate.ps
trunk/axiom/books/ps/v102keyeddictionary.ps
trunk/axiom/books/ps/v102koerce.ps
trunk/axiom/books/ps/v102konvert.ps
trunk/axiom/books/ps/v102linearaggregate.ps
trunk/axiom/books/ps/v102listaggregate.ps
trunk/axiom/books/ps/v102multidictionary.ps
trunk/axiom/books/ps/v102onedimensionalarrayaggregate.ps
trunk/axiom/books/ps/v102priorityqueueaggregate.ps
trunk/axiom/books/ps/v102queueaggregate.ps
trunk/axiom/books/ps/v102recursiveaggregate.ps
trunk/axiom/books/ps/v102retractableto.ps
trunk/axiom/books/ps/v102stackaggregate.ps
trunk/axiom/books/ps/v102streamaggregate.ps
trunk/axiom/books/ps/v102stringaggregate.ps
trunk/axiom/books/ps/v102tableaggregate.ps
trunk/axiom/books/ps/v102type.ps
trunk/axiom/books/ps/v102unaryrecursiveaggregate.ps
Removed Paths:
-------------
trunk/axiom/books/ps/v10agg.ps
trunk/axiom/books/ps/v10associationlistaggregate.ps
trunk/axiom/books/ps/v10bagaggregate.ps
trunk/axiom/books/ps/v10binaryrecursiveaggregate.ps
trunk/axiom/books/ps/v10collection.ps
trunk/axiom/books/ps/v10dequeueaggregate.ps
trunk/axiom/books/ps/v10dictionary.ps
trunk/axiom/books/ps/v10dictionaryoperations.ps
trunk/axiom/books/ps/v10doublylinkedaggregate.ps
trunk/axiom/books/ps/v10eltab.ps
trunk/axiom/books/ps/v10eltableaggregate.ps
trunk/axiom/books/ps/v10extensiblelinearaggregate.ps
trunk/axiom/books/ps/v10finitelinearaggregate.ps
trunk/axiom/books/ps/v10homogeneousaggregate.ps
trunk/axiom/books/ps/v10indexedaggregate.ps
trunk/axiom/books/ps/v10keyeddictionary.ps
trunk/axiom/books/ps/v10koerce.ps
trunk/axiom/books/ps/v10konvert.ps
trunk/axiom/books/ps/v10linearaggregate.ps
trunk/axiom/books/ps/v10listaggregate.ps
trunk/axiom/books/ps/v10multidictionary.ps
trunk/axiom/books/ps/v10onedimensionalarrayaggregate.ps
trunk/axiom/books/ps/v10priorityqueueaggregate.ps
trunk/axiom/books/ps/v10queueaggregate.ps
trunk/axiom/books/ps/v10recursiveaggregate.ps
trunk/axiom/books/ps/v10retractableto.ps
trunk/axiom/books/ps/v10stackaggregate.ps
trunk/axiom/books/ps/v10streamaggregate.ps
trunk/axiom/books/ps/v10stringaggregate.ps
trunk/axiom/books/ps/v10tableaggregate.ps
trunk/axiom/books/ps/v10type.ps
trunk/axiom/books/ps/v10unaryrecursiveaggregate.ps
Modified: trunk/axiom/books/Makefile.pamphlet
===================================================================
--- trunk/axiom/books/Makefile.pamphlet 2008-09-12 01:26:14 UTC (rev 971)
+++ trunk/axiom/books/Makefile.pamphlet 2008-09-13 05:27:50 UTC (rev 972)
@@ -26,7 +26,8 @@
${PDF}/bookvol3.pdf ${PDF}/bookvol4.pdf ${PDF}/bookvol5.pdf \
${PDF}/bookvol6.pdf ${PDF}/bookvol7.pdf ${PDF}/bookvol7.1.pdf \
${PDF}/bookvol8.pdf ${PDF}/bookvol9.pdf ${PDF}/bookvol10.pdf \
- ${PDF}/bookvol11.pdf ${PDF}/bookvol12.pdf
+ ${PDF}/bookvol10.1.pdf ${PDF}/bookvol10.2.pdf ${PDF}/bookvol10.3.pdf \
+ ${PDF}/bookvol10.4.pdf ${PDF}/bookvol11.pdf ${PDF}/bookvol12.pdf
all: ${PDF}/axiom.sty ${BOOKS} ${PDF}/toc.pdf
@@ -104,7 +105,11 @@
"{\\bf Volume ~ 7.1}: Axiom {\\sl Hyperdoc Pages}\\\\" >>toc.toc ; \
echo "{\\bf Volume ~ 8}: Axiom {\\sl Graphics}\\\\" >>toc.toc ; \
echo "{\\bf Volume ~ 9}: Axiom {\\sl Compiler}\\\\" >>toc.toc ; \
- echo "{\\bf Volume 10}: Axiom {\\sl Algebra}\\\\" >>toc.toc ; \
+ echo "{\\bf Volume 10}: Axiom {\\sl Algebra: Implementation}\\\\" >>toc.toc ; \
+ echo "{\\bf Volume 10.1}: Axiom {\\sl Algebra: Theory}\\\\" >>toc.toc ; \
+ echo "{\\bf Volume 10.1}: Axiom {\\sl Algebra: Categories}\\\\" >>toc.toc ; \
+ echo "{\\bf Volume 10.1}: Axiom {\\sl Algebra: Domains}\\\\" >>toc.toc ; \
+ echo "{\\bf Volume 10.1}: Axiom {\\sl Algebra: Packages}\\\\" >>toc.toc ; \
echo "{\\bf Volume 11}: Axiom {\\sl Browser}\\\\" >>toc.toc ; \
echo "{\\bf Volume 12}: Axiom {\\sl Crystal}\\\\" >>toc.toc ; \
echo "\\newpage" >>toc.toc ; \
@@ -154,8 +159,20 @@
<<sed pattern>>
<bookvol9.toc >>toc.toc ; \
echo "\\newpage" >>toc.toc ; \
- echo "\\section*{Volume 10: Axiom Algebra}" >>toc.toc ; \
+ echo "\\section*{Volume 10: Axiom Algebra: Implementation}" >>toc.toc ; \
<<sed pattern>>
+ echo "\\newpage" >>toc.toc ; \
+ echo "\\section*{Volume 10.1: Axiom Algebra: Theory}" >>toc.toc ; \
+<<sed pattern>>
+ echo "\\newpage" >>toc.toc ; \
+ echo "\\section*{Volume 10.2: Axiom Algebra: Categories}" >>toc.toc ; \
+<<sed pattern>>
+ echo "\\newpage" >>toc.toc ; \
+ echo "\\section*{Volume 10.3: Axiom Algebra: Domains}" >>toc.toc ; \
+<<sed pattern>>
+ echo "\\newpage" >>toc.toc ; \
+ echo "\\section*{Volume 10.4: Axiom Algebra: Packages}" >>toc.toc ; \
+<<sed pattern>>
<bookvol10.toc >>toc.toc ; \
echo "\\newpage" >>toc.toc ; \
echo "\\section*{Volume 11: Axiom Browser}" >>toc.toc ; \
Added: trunk/axiom/books/bookvol10.1.pamphlet
===================================================================
--- trunk/axiom/books/bookvol10.1.pamphlet (rev 0)
+++ trunk/axiom/books/bookvol10.1.pamphlet 2008-09-13 05:27:50 UTC (rev 972)
@@ -0,0 +1,2090 @@
+\documentclass[dvipdfm]{book}
+\usepackage{hyperref}
+\usepackage{amssymb}
+\usepackage{axiom}
+\usepackage{makeidx}
+\makeindex
+\usepackage{graphicx}
+%%
+%% pagehead consolidates standard page indexing
+%%
+\newcommand{\pagehead}[2]{% e.g. \pagehead{name}{abb}
+\section{#1}
+\label{#1}%
+\label{#2}%
+\index{{#1}}%
+\index{{#2}}}%
+%%
+%% pagepic adds an image and an index entry
+%%
+\newcommand{\pagepic}[2]{% e.g. \pagepic{pathandfile}{abb}
+\includegraphics{#1}%
+\index{images!#2}}
+%%
+%% pageto is a forward link to a referenced page
+%%
+\newcommand{\pageto}[2]{% e.g. \pageto{abb}{name}
+\ \\${\bf\Rightarrow{}}${``#1''} (#2) \ref{#1} on page~\pageref{#1}}
+%%
+%% pageback is a backward link to a referencing page
+%%
+\newcommand{\pagefrom}[2]{% e.g. \pagefrom{name}{abb}
+\ \\${\bf\Leftarrow{}}${``#1''} (#2) \ref{#1} on page~\pageref{#1}}
+%%
+% special meanings for math characters
+\providecommand{\N}{\mbox{\bbold N}}
+\providecommand{\Natural}{\mbox{\bbold N}}
+\providecommand{\Z}{\mbox{\bbold Z}}
+\providecommand{\Integer}{\mbox{\bbold Z}}
+\providecommand{\Rational}{\mbox{\bbold Q}}
+\providecommand{\Q}{\mbox{\bbold Q}}
+\providecommand{\Complex}{\mbox{\bbold C}}
+\providecommand{\C}{{\mathcal C}}
+\providecommand{\Real}{\mbox{\bbold R}}
+\providecommand{\F}{{\mathcal F}}
+\providecommand{\R}{{\mathcal R}}
+\begin{document}
+\begin{titlepage}
+\center{\includegraphics{ps/axiomfront.ps}}
+\vskip 0.1in
+\includegraphics{ps/bluebayou.ps}\\
+\vskip 0.1in
+{\Huge{The 30 Year Horizon}}
+\vskip 0.1in
+$$
+\begin{array}{lll}
+Manuel\ Bronstein & William\ Burge & Timothy\ Daly \\
+James\ Davenport & Michael\ Dewar & Martin\ Dunstan \\
+Albrecht\ Fortenbacher & Patrizia\ Gianni & Johannes\ Grabmeier \\
+Jocelyn\ Guidry & Richard\ Jenks & Larry\ Lambe \\
+Michael\ Monagan & Scott\ Morrison & William\ Sit \\
+Jonathan\ Steinbach & Robert\ Sutor & Barry\ Trager \\
+Stephen\ Watt & Jim\ Wen & Clifton\ Williamson
+\end{array}
+$$
+\center{\large{Volume 10: Axiom Algebra: Theory}}
+\end{titlepage}
+\pagenumbering{roman}
+\begin{verbatim}
+Portions Copyright (c) 2005 Timothy Daly
+
+The Blue Bayou image Copyright (c) 2004 Jocelyn Guidry
+
+Portions Copyright (c) 2004 Martin Dunstan
+
+Portions Copyright (c) 1991-2002,
+The Numerical ALgorithms Group Ltd.
+All rights reserved.
+
+This book and the Axiom software is licensed as follows:
+
+Redistribution and use in source and binary forms, with or
+without modification, are permitted provided that the following
+conditions are
+met:
+
+ - Redistributions of source code must retain the above
+ copyright notice, this list of conditions and the
+ following disclaimer.
+
+ - Redistributions in binary form must reproduce the above
+ copyright notice, this list of conditions and the
+ following disclaimer in the documentation and/or other
+ materials provided with the distribution.
+
+ - Neither the name of The Numerical ALgorithms Group Ltd.
+ nor the names of its contributors may be used to endorse
+ or promote products derived from this software without
+ specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
+CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,
+INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
+WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+SUCH DAMAGE.
+
+\end{verbatim}
+
+Inclusion of names in the list of credits is based on historical
+information and is as accurate as possible. Inclusion of names
+does not in any way imply an endorsement but represents historical
+influence on Axiom development.
+\vfill
+\eject
+\begin{tabular}{lll}
+Cyril Alberga & Roy Adler & Richard Anderson\\
+George Andrews & Henry Baker & Stephen Balzac\\
+Yurij Baransky & David R. Barton & Gerald Baumgartner\\
+Gilbert Baumslag & Fred Blair & Vladimir Bondarenko\\
+Mark Botch & Alexandre Bouyer & Peter A. Broadbery\\
+Martin Brock & Manuel Bronstein & Florian Bundschuh\\
+William Burge & Quentin Carpent & Bob Caviness\\
+Bruce Char & Cheekai Chin & David V. Chudnovsky\\
+Gregory V. Chudnovsky & Josh Cohen & Christophe Conil\\
+Don Coppersmith & George Corliss & Robert Corless\\
+Gary Cornell & Meino Cramer & Claire Di Crescenzo\\
+Timothy Daly Sr. & Timothy Daly Jr. & James H. Davenport\\
+Jean Della Dora & Gabriel Dos Reis & Michael Dewar\\
+Claire DiCrescendo & Sam Dooley & Lionel Ducos\\
+Martin Dunstan & Brian Dupee & Dominique Duval\\
+Robert Edwards & Heow Eide-Goodman & Lars Erickson\\
+Richard Fateman & Bertfried Fauser & Stuart Feldman\\
+Brian Ford & Albrecht Fortenbacher & George Frances\\
+Constantine Frangos & Timothy Freeman & Korrinn Fu\\
+Marc Gaetano & Rudiger Gebauer & Kathy Gerber\\
+Patricia Gianni & Holger Gollan & Teresa Gomez-Diaz\\
+Laureano Gonzalez-Vega& Stephen Gortler & Johannes Grabmeier\\
+Matt Grayson & James Griesmer & Vladimir Grinberg\\
+Oswald Gschnitzer & Jocelyn Guidry & Steve Hague\\
+Vilya Harvey & Satoshi Hamaguchi & Martin Hassner\\
+Ralf Hemmecke & Henderson & Antoine Hersen\\
+Pietro Iglio & Richard Jenks & Kai Kaminski\\
+Grant Keady & Tony Kennedy & Paul Kosinski\\
+Klaus Kusche & Bernhard Kutzler & Larry Lambe\\
+Frederic Lehobey & Michel Levaud & Howard Levy\\
+Rudiger Loos & Michael Lucks & Richard Luczak\\
+Camm Maguire & Bob McElrath & Michael McGettrick\\
+Ian Meikle & David Mentre & Victor S. Miller\\
+Gerard Milmeister & Mohammed Mobarak & H. Michael Moeller\\
+Michael Monagan & Marc Moreno-Maza & Scott Morrison\\
+Mark Murray & William Naylor & C. Andrew Neff\\
+John Nelder & Godfrey Nolan & Arthur Norman\\
+Jinzhong Niu & Michael O'Connor & Kostas Oikonomou\\
+Julian A. Padget & Bill Page & Jaap Weel\\
+Susan Pelzel & Michel Petitot & Didier Pinchon\\
+Claude Quitte & Norman Ramsey & Michael Richardson\\
+Renaud Rioboo & Jean Rivlin & Nicolas Robidoux\\
+Simon Robinson & Michael Rothstein & Martin Rubey\\
+Philip Santas & Alfred Scheerhorn & William Schelter\\
+Gerhard Schneider & Martin Schoenert & Marshall Schor\\
+Fritz Schwarz & Nick Simicich & William Sit\\
+Elena Smirnova & Jonathan Steinbach & Christine Sundaresan\\
+Robert Sutor & Moss E. Sweedler & Eugene Surowitz\\
+James Thatcher & Baldir Thomas & Mike Thomas\\
+Dylan Thurston & Barry Trager & Themos T. Tsikas\\
+Gregory Vanuxem & Bernhard Wall & Stephen Watt\\
+Juergen Weiss & M. Weller & Mark Wegman\\
+James Wen & Thorsten Werther & Michael Wester\\
+John M. Wiley & Berhard Will & Clifton J. Williamson\\
+Stephen Wilson & Shmuel Winograd & Robert Wisbauer\\
+Sandra Wityak & Waldemar Wiwianka & Knut Wolf\\
+Clifford Yapp & David Yun & Richard Zippel\\
+Evelyn Zoernack & Bruno Zuercher & Dan Zwillinger
+\end{tabular}
+\eject
+\tableofcontents
+\vfill
+\eject
+\setlength{\parindent}{0em}
+\setlength{\parskip}{1ex}
+{\Large{\bf New Foreword}}
+\vskip .25in
+
+On October 1, 2001 Axiom was withdrawn from the market and ended
+life as a commercial product.
+On September 3, 2002 Axiom was released under the Modified BSD
+license, including this document.
+On August 27, 2003 Axiom was released as free and open source
+software available for download from the Free Software Foundation's
+website, Savannah.
+
+Work on Axiom has had the generous support of the Center for
+Algorithms and Interactive Scientific Computation (CAISS) at
+City College of New York. Special thanks go to Dr. Gilbert
+Baumslag for his support of the long term goal.
+
+The online version of this documentation is roughly 1000 pages.
+In order to make printed versions we've broken it up into three
+volumes. The first volume is tutorial in nature. The second volume
+is for programmers. The third volume is reference material. We've
+also added a fourth volume for developers. All of these changes
+represent an experiment in print-on-demand delivery of documentation.
+Time will tell whether the experiment succeeded.
+
+Axiom has been in existence for over thirty years. It is estimated to
+contain about three hundred man-years of research and has, as of
+September 3, 2003, 143 people listed in the credits. All of these
+people have contributed directly or indirectly to making Axiom
+available. Axiom is being passed to the next generation. I'm looking
+forward to future milestones.
+
+With that in mind I've introduced the theme of the ``30 year horizon''.
+We must invent the tools that support the Computational Mathematician
+working 30 years from now. How will research be done when every bit of
+mathematical knowledge is online and instantly available? What happens
+when we scale Axiom by a factor of 100, giving us 1.1 million domains?
+How can we integrate theory with code? How will we integrate theorems
+and proofs of the mathematics with space-time complexity proofs and
+running code? What visualization tools are needed? How do we support
+the conceptual structures and semantics of mathematics in effective
+ways? How do we support results from the sciences? How do we teach
+the next generation to be effective Computational Mathematicians?
+
+The ``30 year horizon'' is much nearer than it appears.
+
+\vskip .25in
+%\noindent
+Tim Daly\\
+CAISS, City College of New York\\
+November 10, 2003 ((iHy))
+\vfill
+\eject
+\pagenumbering{arabic}
+\setcounter{chapter}{0} % Chapter 1
+\chapter{Integration}
+An {\sl elementary function}
+\index{elementary function}
+of a variable $x$ is a function that can
+be obtained from the rational functions in $x$ by repeatedly adjoining
+a finite number of nested logarithms, exponentials, and algebraic
+numbers or functions. Since $\sqrt{-1}$ is elementary, the
+trigonometric functions and their inverses are also elementary (when
+they are rewritten using complex exponentials and logarithms) as well
+as all the ``usual'' functions of calculus. For example,
+\begin{equation}
+\sin(x+\tan(x^3-\sqrt{x^3-x+1}))
+\end{equation}
+is elementary when rewritten as
+\[
+\frac{\sqrt{-1}}{2}(e^{t-x\sqrt{-1}}-e^{x\sqrt{-1}-t})
+{\rm\ where\ }
+t=\frac{1-e^{2\sqrt{-1}(x^3-\sqrt{x^3-x+1})}}
+{1+e^{2\sqrt{-1}(x^3-\sqrt{x^3-x+1})}}
+\]
+This tutorial describes recent algorithmic solutions to the {\sl
+problem of integration in finite terms}:
+\index{integration in finite terms}
+to decide in a finite number
+of steps whether a given elementary funcction has an elementary
+indefinite integral, and to compute it explicitly if it exists. While
+this problem was studied extensively by Abel and Liouville during the
+last century, the difficulties posed by algebraic functions caused
+Hardy (1916) to state that ``there is reason to suppose that no such
+method can be given''. This conjecture was eventually disproved by
+Risch (1970), who described an algorithm for this problem in a series
+of reports \cite{12,13,14,15}. In the past 30 years, this procedure
+has been repeatedly improved, extended and refined, yielding practical
+algorithms that are now becoming standard and are implemented in most
+of the major computer algebra systems. In this tutorial, we outline
+the above algorithms for various classes of elementary functions,
+starting with rational functions and progressively increasing the
+class of functions up to general elementary functions. Proofs of
+correctness of the algorithms presented here can be found in several
+of the references, and are generally too long and too detailed to be
+described in this tutorial.
+
+{\bf Notations}: we write $x$ for the variable of integration, and '
+for the derivation $d/dx$. $\mathbb{Z}$,$\mathbb{Q}$,$\mathbb{R}$,and
+$\mathbb{C}$ denote respectively the integers, rational, real and
+complex numbers. All fields are commutative and, except when mentioned
+explicitly otherwise, have characteristic 0. If $K$ is a field, then
+$\overline{K}$ denotes its algebraic closure. For a polynomial $p$,
+pp($p$) denotes the primitive
+part of $p$, {\sl i. e.} $p$ divided by the gcd of its coefficients.
+\section{Rational Functions}
+By a {\sl rational function}, we mean a quotient of polynomials in the
+integration variable $x$. This means that other functions can appear
+in the integrand, provided they do not involve $x$, hence that the
+coefficients of our polynomials in $x$ lie in an arbitrary field $K$
+satisfying: $\forall{a} \in K,\ a^{'}=0$.
+
+\subsection{The full partial-fraction algorithm}
+This method, which dates back to Newton, Leibniz, and Bernoulli,
+should not be used in practice, yet it remains the method found in
+most calculus tests and is often taught. Its major drawback is the
+factorization of the denominator of the integrand over the real or
+complex numbers. We outline it because it provides the theoretical
+foundations for all the subsequent algorithms. Let
+$f \in \mathbb{R}(x)$ be our integrand, and write
+$f=P+A/D$ where $P, A, D \in \mathbb{R}[x]$, $gcd(A,D)=1$, and
+$deg(A) < deg(D)$. Let
+\[
+D=c\prod_{i=1}^n(x-a_i)^{e_i}\prod_{j=1}^m(x^2+b_jx+c_j)^{f_j}
+\]
+be the irreducible factorization of $D$ over $\mathbb{R}$, where $c$,
+the $a_i$'s, $b_j$'s and $c_j$'s are in $\mathbb{R}$ and the $e_i$'s
+and $f_j$'s are positive integers. Computing the partial fraction
+decomposition of $f$, we get
+\[
+f=P+\sum_{i=1}^n\sum_{k=1}^{e_i}\frac{A_{ik}}{(x-a_i)^k}
++\sum_{j=1}^m\sum_{k=1}^{f_i}\frac{B_{jk}x+C_{jk}}{(x^2+b_jx+c_j)^k}
+\]
+where the $A_{ik}$'s, $B_{jk}$'s, and $C_{jk}$'s are in
+$\mathbb{R}$. Hence,
+\[
+\int{f}=\int{P}+\sum_{i=1}^n\sum_{k=1}^{e_i}\int{\frac{A_{ik}}{(x-a_i)^k}}
++\sum_{j=1}^m\sum_{k=1}^{f_i}\int{\frac{B_{jk}x+C_{jk}}{(x^2+b_jx+c_j)^k}}
+\]
+Computing $\int{P}$ poses no problem (it will for any other class of
+functions), and for the other terms we have
+\begin{equation}
+\int{\frac{A_{ik}}{(x-a_i)^k}}=\left\{
+\begin{array}{lc}
+A_{ik}(x-a_i)^{1-k}/(1-k)&{\rm if\ } k > 1\\
+A_{i1}\log(x-a_i)&{\rm if\ } k = 1\\
+\end{array}
+\right.
+\end{equation}
+and, noting that $b_j^2-4c_j < 0$ since $x^2+b_jx+c_j$ is irreducible
+in $\mathbb{R}$[x].
+\[
+\int\frac{B_{j1}x+C_{j1}}{(x^2+b_jx+c_j)}=
+\frac{B_{j1}}{2}\log(x^2+b_jx+c_j)
++\frac{2C_{j1}-b_jB_{j1}}{\sqrt{4c_j-b_j^2}}
+arctan\left(\frac{2x+b_j}{\sqrt{4c_j-b_j^2}}\right)
+\]
+and for $k > 1$,
+\[
+\begin{array}{lcl}
+\displaystyle
+\int{\frac{B_{jk}x+C_{jk}}{(x^2+b_jx+c_j)^k}}&=&
+\displaystyle\frac{(2C_{jk}-b_jB_{jk})x+b_jC_{jk}-2c_jB_{jk}}
+{(k-1)(4c_j-b_j^2)(x^2+b_jx+c_j)^{k-1}}\\
+&&\displaystyle+\int{\frac{(2k-3)(2C_{jk}-b_jB_{jk})}
+{(k-1)(4c_j-b_j^2)(x^2+b_jx+c_j)^{k-1}}}\\
+\end{array}
+\]
+This last formula is then used recursively until $k=1$.
+
+An alternative is to factor $D$ linearly over $\mathbb{C}$:
+$D=\prod_{i=1}^q(x-\alpha_i)^{e_i}$, and then use (2) on each term of
+\begin{equation}
+f=P+\sum_{i=1}^q\sum_{j=1}^{e_i}\frac{A_{ij}}{(x-\alpha_i)^j}
+\end{equation}
+Note that this alternative is applicable to coefficients in any field
+$K$, if we factor $D$ linearly over its algebraic closure
+$\overline{K}$, and is equivalent to expanding $f$ into its Laurent
+series at all its finite poles, since that series at
+$x=\alpha_i \in \overline{K}$ is
+\[
+f=\frac{A_{ie_i}}{(x-\alpha_i)^{e_i}}
++\cdots
++\frac{A_{i2}}{(x-\alpha_i)^2}
++\frac{A_{i1}}{(x-\alpha_i)}
++\cdots
+\]
+where the $A_{ij}$'s are the same as those in (3). Thus, this approach
+can be seen as expanding the integrand into series around all the
+poles (including $\infty$), then integrating the series termwise, and
+then interpolating for the answer, by summing all the polar terms,
+obtaining the integral of (3). In addition, this alternative shows
+that any rational function $f \in K(x)$ has an elementary integral of
+the form
+\begin{equation}
+\int{f}=v+c_1\log(u_1)+\cdots+c_m\log(u_m)
+\end{equation}
+where $v,u_1,\ldots,u_m \in \overline{K}(x)$ are the rational
+functions, and $c_1,\ldots,c_m \in \overline{K}$ are constants. The
+original Risch algorithm is essentially a generalization of this
+approach that searches for integrals of arbitrary elementary functions
+in a form similar to (4).
+
+\subsection{The Hermite reduction}
+The major computational inconvenience of the full partial fraction
+approach is the need to factor polynomials over $\mathbb{R}$,
+$\mathbb{C}$, or $\overline{K}$, thereby introducing algebraic numbers
+even if the integrand and its integral are both in $\mathbb{Q}(x)$. On
+the other hand, introducing algebraic numbers may be necessary, for
+example it is proven in \cite{14} that any field containing an
+integral of $1/(x^2+2)$ must also contain $\sqrt{2}$. Modern research
+has yielded so-called ``rational'' algorithms that
+\begin{itemize}
+\item compute as much of the integral as possible with all
+calculations being done in $K(x)$, and
+\item compute the minimal algebraic extension of $K$ necessary to
+express the integral
+\end{itemize}
+The first rational algorithms for integration date back to the
+$19^{{\rm th}}$ century, when both Hermite\cite{6} and
+Ostrogradsky\cite{11} invented methods for computing the $v$ of (4)
+entirely within $K(x)$. We describe here only Hermite's method, since
+it is the one that has been generalized to arbitrary elementary
+functions. The basic idea is that if an irreducible $p \in K[x]$
+appears with multiplicity $k > 1$ in the factorization of the
+denominator of the integrand, then (2) implies that it appears with
+multiplicity $k-1$ in the denominator of the integral. Furthermore, it
+is possible to compute the product of all such irreducibles for each
+$k$ without factoring the denominator into irreducibles by computing
+its {\sl squarefree factorization}, {\sl i.e} a factorization
+$D=D_1D_2^2\cdots D_m^m$, where each $D_i$ is squarefree and
+$gcd(D_i,D_j)=1$ for $i \ne j$. A straightforward way to compute it is
+as follows: let $R=gcd(D,D^{'})$, then $R=D_2D_2^3\cdots D_m^{m-1}$, so
+$D/R=D_1D_2\cdots D_m$ and $gcd(R,D/R)=D_2\cdots D_m$, which implies
+finally that
+\[
+D_1=\frac{D/R}{gcd(R,D/R)}
+\]
+Computing recursively a squarefree factorization of $R$ completes the
+one for $D$. Note that \cite{23} presents a more efficient method for
+this decomposition. Let now $f \in K(x)$ be our integrand, and write
+$f=P+A/D$ where $P,A,D \in K[x]$, $gcd(A,D)=1$, and $deg(A)<deg(D)$.
+Let $D=D_1D_2^2\cdots D_m^m$ be a squarefree factorization of $D$ and
+suppose that $m \ge 2$ (otherwise $D$ is already squarefree). Let then
+$V=D_m$ and $U=D/V^m$. Since $gcd(UV^{'},V)=1$, we can use the
+extended Euclidean algorithm to find $B,C \in K[x]$ such that
+\[
+\frac{A}{1-m}=BUV^{'}+CV
+\]
+and $deg(B) < deg(V)$. Multiplying both sides by $(1-m)/(UV^m)$ gives
+\[
+\frac{A}{UV^m}=\frac{(1-m)BV^{'}}{V^m}+\frac{(1-m)C}{UV^{m-1}}
+\]
+so, adding and subtracting $B^{'}/V^{m-1}$ to the right hand side, we
+get
+\[
+\frac{A}{UV^m}=\left(\frac{B^{'}}{V^{m-1}}-\frac{(m-1)BV^{'}}{V^m}\right)
++\frac{(1-m)C-UB^{'}}{UV^{m-1}}
+\]
+and integrating both sides yields
+\[
+\int\frac{A}{UV^m}=\frac{B}{V^{m-1}}+\int\frac{(1-m)C-UB^{'}}{UV^{m-1}}
+\]
+so the integrand is reduced to one with a smaller power of $V$ in the
+denominator. This process is repeated until the denominator is
+squarefree, yielding $g,h \in K(x)$ such that $f=g^{'}+h$ and $h$ has
+a squarefree denominator.
+
+\subsection{The Rothstein-Trager and Lazard-Rioboo-Trager algorithms}
+Following the Hermite reduction, we only have to integrate fractions
+of the form $f=A/D$ with $deg(A)<deg(D)$ and $D$ squarefree. It
+follows from (2) that
+\[
+\int{f}=\sum_{i=1}^n a_i\log(x-\alpha_i)
+\]
+where the $\alpha_i$'s are the zeros of $D$ in $\overline{K}$, and the
+$a_i$'s are the residues of $f$ at the $\alpha_i$'s. The problem
+is then to compute those residues without splitting $D$. Rothstein
+\cite{18} and Trager \cite{19} independently proved that the
+$\alpha_i$'s are exactly the zeros of
+\begin{equation}
+R=resultant_x(D,A-tD^{'}) \in K[t]
+\end{equation}
+and that the splitting field of $R$ over $K$ is indeed the minimal
+algebraic extension of $K$ necessary to express the integral in the
+form (4). The integral is then given by
+\begin{equation}
+\int\frac{A}{D}=\sum_{i=1}^m\sum_{a|R_i(a)=0}a\log(\gcd(D,A-aD^{'}))
+\end{equation}
+where $R=\prod_{i=1}^m R_i^{e_i}$ is the irreducible factorization of
+$R$ over $K$. Note that this algorithm requires factoring $R$ into
+irreducibles over $K$, and computing greatest common divisors in
+$(K[t]/(R_i))[x]$, hence computing with algebraic numbers. Trager and
+Lazard \& Rioboo \cite{7} independently discovered that those
+computations can be avoided, if one uses the subresultant PRS
+algorithm to compute the resultant of (5): let
+$(R_0,R_1,\ldots R_k\ne 0,0,\ldots)$ be the subresultant PRS with
+respect to $x$ of $D$ and $A-tD^{'}$ and $R=Q_1Q_2^2\ldots Q_m^m$ be a
+{\sl squarefree} factorization of their resultant. Then,
+\[
+\sum_{a|Q_i(a)=0} a\log(\gcd(D,A-aD^{'}))=\hbox{\hskip 5.0cm}
+\]
+\[
+\left\{
+\begin{array}{ll}
+\sum_{a|Q_i(a)=0} a \log(D) & {\rm if\ }i = deg(D)\\
+\sum_{a|Q_i(a)=0} a \log({\rm pp}_x(R_{k_i})(a,x))&
+{\rm where\ }deg(R_{k_i})=i,1 \le k_i \le n\\
+&{\rm if\ }i < deg(D)
+\end{array}
+\right.
+\]
+Evaluating ${\rm pp}_x(R_{k_i})$ at $t=a$ where $a$ is a root of $Q_i$
+is equivalent to reducing each coefficient with respect to $x$ of
+${\rm pp}_x(R_{k_i})$ module $Q_i$, hence computing in the algebraic
+extension $K[t]/(Q_i)$. Even this step can be avoided: it is in fact
+sufficient to ensure that $Q_i$ and the leading coefficient with
+respect to $x$ of $R_{k_i}$ do not have a nontrivial common factor,
+which implies then that the remainder by $Q_i$ is nonzero, see
+\cite{10} for details and other alternatives for computing
+${\rm pp}_x(R_{k_i})(a,x)$
+
+\section{Algebraic Functions}
+By an {\sl algebraic function}, we mean an element of a finitely
+generated algebraic extension $E$ of the rational function field
+$K(x)$. This includes nested radicals and implicit algebraic
+functions, not all of which can be expressed by radicals. It turns out
+that the algorithms we used for rational functions can be extended to
+algebraic functions, but with several difficulties, the first one
+being to define the proper analogues of polynomials, numerators and
+denominators. Since $E$ is algebraic over $K(x)$, for any
+$\alpha \in E$, there exists a polynomial $p \in K[x][y]$ such that
+$p(x,\alpha)=0$. We say that $\alpha \in E$ is {\sl integral over}
+$K[x]$ if there is a polynomial $p \in K[x][y]$, {\sl monic in y},
+such that $p(x,\alpha)=0$. Integral elements are analogous to
+polynomials in that their value is defined for any
+$x \in \overline{K}$ (unlike non-integral elements, which must have at
+least one pole in $\overline{K}$). The set
+\[
+{\bf O}_{K[x]} = \{\alpha \in E {\rm\ such\ that\ }\alpha
+{\rm\ is\ integral\ over\ }K[x]\}
+\]
+is called the {\sl integral closure of} $K[x]$ {\sl in E}. It is a
+ring and a finitely generated $K[x]$-module. Let $\alpha \in E^{*}$ be
+any element and $p=\sum_{i=0}^m a_iy^i \in K[x][y]$ be such that
+$p(x,\alpha)=0$ and $a_m \ne 0$. Then, $q(x,a_my)=0$ where
+$q=y^m+\sum_{i=0}^{m-1} a_ia_m^{m-i-1}y^i$ is monic in $y$,
+so $a_my \in {\bf O}_{K[x]}$. We need a canonical representation
+for algebraic functions similar to quotients of polynomials for
+rational functions. Expressions as quotients of integral functions are
+not unique, for example, $\sqrt{x}/x=x/\sqrt{x}$. Hoever, $E$ is a
+finite-dimensional vector space over $K(x)$, so let $n=[E:K(x)]$ and
+$w=(w_1,\ldots,w_n)$ be any basis for $E$ over $K(x)$. By the above
+remark, there are $a_1,\ldots,a_n \in K(x)^{*}$ such that
+$a_iw_i \in {\bf O}_{K[x]}$ for each $i$. Since
+$(a_1w_1,\ldots,a_nw_n)$ is also a basis for $E$ over $K(x)$, we can
+assume without loss of generality that the basis $w$ is composed of
+integral elements. Any $\alpha \in E$ can be written uniquely as
+$\alpha = \sum_{i=1}^n f_iw_i$ for $f_1,\ldots,f_n \in K(x)$, and
+putting the $f_i$'s over a monic common denominator $D \in K[x]$, we
+get an expression
+\[
+\alpha = \frac{A_1w_1+\ldots+A_nw_n}{D}
+\]
+where $A_1,\ldots,A_n \in K[x]$ and $\gcd(D,A_1,\ldots,A_n)=1$. We
+call $\sum_{i=1}^n A_iw_i \in {\bf O}_{K[x]}$ and
+$D \in K[x]$ respectively the {\sl numerator} and {\sl denominator} of
+$\alpha$ with respect to $w$. They are defined uniquely once the basis
+$w$ is fixed.
+\subsection{The Hermite reduction}
+Now that we have numerators and denominators for algebraic functions,
+we can attempt to generalize the Hermite reduction of the previous
+section, so let $f \in E$ be our integrand,
+$w=(w_1,\ldots,w_n) \in {{\bf O}_{K[n]}}^{n}$ be a basis for $E$
+over $K(x)$ and let $\sum_{i=1}^m A_iw_i \in {\bf O}_{K[x]}$
+and $D \in K[x]$ be the numerator and denominator of $f$ with respect
+to $w$, Let $D=D_1D_2^2\ldots D_m^m$ be a squarefree factorization of
+$D$ and suppose that $m \ge 2$. Let then $V=D_m$ and $U=D/V^m$, and we
+ask whether we can compute
+$B=\sum_{i=1}^n B_iw_i \in {\bf O}_{K[x]}$ and $h \in E$ such
+that $deg(B_i) < deg(V)$ for each $i$,
+\begin{equation}
+\int\frac{\sum_{i=1}^n A_iw_i}{UV^m}=\frac{B}{V^{m-1}}+\int{h}
+\end{equation}
+and the denominator of $h$ with respect to $w$ has no factor of order
+$m$ or higher. This turns out to reduce to solving the following
+linear system
+\begin{equation}
+f_1S_1+\ldots+f_nS_n=A_1w_1+\ldots+A_nw_n
+\end{equation}
+for $f_1,\ldots,f_n \in K(x)$, where
+\begin{equation}
+S_i=UV^m\left(\frac{w_i}{V^{m-1}}\right)^{'}\quad{\rm for\ }1\le i\le n
+\end{equation}
+Indeed, suppose that (8) has a solution $f_1,\ldots,f_n \in K(x)$, and
+write $f_i=T_i/Q$, where $Q,T_1,\ldots,T_n \in K[x]$ and
+$\gcd(Q,T_1,\ldots,T_n)=1$. Suppose further that $\gcd(Q,V)=1$. Then,
+we can use the extended Euclidean algorithm to find $A,R \in K[x]$
+such that $AV+RQ=1$, and Euclidean division to find $Q_i,B_i \in K[x]$
+such that $deg(B_i)<deg(V)$ when $B_i \ne 0$ and $RT_i=VQ_i+B_i$ for
+each $i$. We then have
+\[
+\begin{array}{lcl}
+h&=&\displaystyle
+f-\left(\frac{\sum_{i=1}^n B_iw_i}{V^{m-1}}\right)^{'}\\
+&&\\
+&=&\displaystyle
+\frac{\sum_{i=1}^nA_iw_i}{UV^m}
+-\frac{\sum_{i=1}^nB_i^{'}w_i}{V^{m-1}}
+-\sum_{i=1}^n(RT_i-VQ_i)\left(\frac{w_i}{V^{m-1}}\right)^{'}\\
+&&\\
+&=&\displaystyle
+\frac{\sum_{i=1}^nA_iw_i}{UV^m}
+-\frac{R\sum_{i=1}^nT_iS_i}{UV^m}
++V\sum_{i=1}^nQ_i\left(\frac{w_i}{V^{m-1}}\right)^{'}
+-\frac{\sum_{i=1}^nB_i^{'}w_i}{V^{m-1}}\\
+&&\\
+&=&\displaystyle
+\frac{(1-RQ)\sum_{i=1}^nA_iw_i}{UV^m}
++\frac{\sum_{i=1}^nQ_iw_i^{'}}{V^{m-2}}
+-(m-1)V^{'}\frac{\sum_{i=1}^nQ_iw_i}{V^{m-1}}
+-\frac{\sum_{i=1}^nB_i^{'}w_i}{V^{m-1}}\\
+&&\\
+&=&\displaystyle
+\frac{\sum_{i=1}^nAA_iw_i}{UV^{m-1}}
+-\frac{\sum_{i=1}^n((m-1)V^{'}Q_i+B_i^{'})w_i}{V^{m-1}}
++\frac{\sum_{i=1}^nQ_iw_i^{'}}{V^{m-2}}
+\end{array}
+\]
+Hence, if in addition the denominator of $h$ has no factor of order
+$m$ or higher, then $B=\sum_{i=1}^nB_iw_i \in {\bf O}_{K[x]}$
+and $h$ solve (7) and we have reduced the integrand. Unfortunately, it
+can happen that the denominator of $h$ has a factor of order $m$ or
+higher, or that (8) has no solution in $K(x)$ whose denominator is
+coprime with $V$, as the following example shows.
+
+\noindent
+{\bf Example 1} Let $E=K(x)[y]/(y^4+(x^2+x)y-x^2)$ {\sl with basis}
+$w=(1,y,y^2,y^3)$ {\sl over} $K(x)$ {\sl and consider the integrand}
+\[
+f=\frac{y^3}{x^2}=\frac{w_4}{x^2}\in E
+\]
+We have $D=x^2$, so $U=1,V=x$ and $m=2$.
+Then, $S_1=x^2(1/x)^{'}=-1$,
+\[
+\begin{array}{lcl}
+\displaystyle S_2&=&x^2\left(\frac{y}{x}\right)^{'}\\
+&&\\
+\displaystyle &=&\frac{24(1-x^2)y^3+32x(1-x)y^2-(9x^4+45x^3+209x^2+63x+18)y
+-18x(x^3+x^2-x-1)}{27x^4+108x^3+418x^2+108x+27}\\
+&&\\
+\displaystyle S_3&=&x^2\left(\frac{y^2}{x}\right)^{'}\\
+&&\\
+\displaystyle &=&
+\frac{64x(1-x)y^3+9(x^4+2x^3-2x-1)y^2+12x(x^3+x^2-x-1)y+48x^2(1-x^2)}
+{27x^4+108x^3+418x^2+108x+27}\\
+&&\\
+and&&\\
+&&\\
+\displaystyle S_4&=&x^2\left(\frac{y^3}{x}\right)^{'}\\
+&&\\
+\displaystyle &=&\frac{(27x^4+81x^3+209x^2+27x)y^3+18x(x^3+x^2-x-1)y^2
++24x^2(x^2-1)y+96x^3(1-x)}
+{27x^4+108x^3+418x^2+108x+27}
+\end{array}
+\]
+{\sl so (8) becomes}
+\begin{equation}
+M
+\left(
+\begin{array}{c}
+f_1\\
+f_2\\
+f_3\\
+f_4
+\end{array}
+\right)=
+\left(
+\begin{array}{c}
+0\\
+0\\
+0\\
+1
+\end{array}
+\right)
+\end{equation}
+{\sl where}
+\[
+M=\left(
+\begin{array}{cccc}
+\displaystyle -1&\frac{-18x(x^3+x^2-x-1)}{F}&\frac{48x^2(1-x^2)}{F}
+&\frac{96x^3(1-x)}{F}\\
+\displaystyle 0&\frac{-(9x^4+45x^3+209x^2+63x+18)}{F}
+&\frac{12x(x^3+x^2-x-1)}{F}&\frac{24x^2(x^2-1)}{F}\\
+\displaystyle 0&\frac{32x(1-x)}{F}&\frac{9(x^4+2x^3-2x-1)}{F}
+&\frac{18x(x^3+x^2-x-1)}{F}\\
+\displaystyle 0&\frac{24(1-x^2)}{F}&\frac{64x(1-x)}{F}
+&\frac{(27x^4+81x^3+209x^2+27x)}{F}
+\end{array}
+\right)
+\]
+and $F=27x^4+108x^3+418x^2+108x+27$. The system (10) admits a unique
+solution $f_1=f_2=0, f_3=-2$ and $f_4=(x+1)/x$, whose denominator is
+not coprime with $V$, so the Hermite reduction is not applicable.
+
+The above problem was first solved by Trager \cite{20}, who proved
+that if $w$ is an {\sl integral basis, i.e.} its elements generate
+${\bf O}_{K[x]}$ over $K[x]$, then the system (8) always has a
+unique solution in $K(x)$ when $m > 1$, and that solution always has a
+denominator coprime with V. Furthermore, the denominator of each
+$w_i^{'}$ must be squarefree, implying that the denominator of $h$ is
+a factor of $FUV^{m-1}$ where $F \in K[x]$ is squarefree and coprime
+with $UV$. He also described an algorithm for computing an integral
+basis, a necessary preprocessing for his Hermite reduction. The main
+problem with that approach is that computing the integral basis,
+whether by the method of \cite{20} or the local alternative \cite{21},
+can be in general more expansive than the rest of the reduction
+process. We describe here the lazy Hermite reduction \cite{5}, which
+avoids the precomputation of an integral basis. It is based on the
+observation that if $m > 1$ and (8) does not have a solution allowing
+us to perform the reduction, then either
+\begin{itemize}
+\item the $S_i$'s are linearly dependent over $K(x)$, or
+\item (8) has a unique solution in $K(x)$ whose denominator has a
+nontrivial common factor with $V$, or
+\item the denominator of some $w_i$ is not squarefree
+\end{itemize}
+In all of the above cases, we can replace our basis $w$ by a new one,
+also made up of integral elements, so that that $K[x]$-module
+generated by the new basis strictly contains the one generated by $w$:
+
+\noindent
+{\bf Theorem 1 (\cite{5})} {\sl Suppose that $m \ge 2$ and that
+$\{S_1,\ldots,S_n\}$ as given by (9) are linearly dependent over $K(x)$,
+and let $T_1,\ldots,T_n \in K[x]$ be not all 0 and such that
+$\sum_{i=1}^n T_iS_i=0$. Then,
+\[
+w_0=\frac{U}{V}\sum_{i=1}^n T_iw_i \in {\bf O}_{K[x]}
+\]
+Furthermore, if $\gcd(T_1,\ldots,T_n)=1$ then
+$w_0 \notin K[x]w_1+\cdots+K[x]w_n$.}
+
+\noindent
+{\bf Theorem 2 (\cite{5})} {\sl Suppose that $m \ge 2$ and that
+$\{S_1,\ldots,S_n\}$ as given by (9) are linearly independent over
+$K(x)$, and let $Q,T_1,\ldots,T_n \in K[x]$ be such that
+\[
+\sum_{i=1}^n A_iw_i = \frac{1}{Q}\sum_{i=1}^n T_iS_i
+\]
+Then,
+\[
+w_0=\frac{U(V/\gcd(V,Q))}{\gcd(V,Q)}\sum_{i=1}^n T_iw_i \in
+{\bf O}_{K[x]}
+\]
+Furthermore,
+if $\gcd(Q,T_1,\ldots,T_n)=1$ and $\deg(\gcd(V,Q)) \ge 1$, then
+$w_0 \notin K[x]w_1+\cdots+K[x]w_n$.}
+
+{\bf Theorem 3 (\cite{5})} {\sl Suppose that the denominator $F$ of
+some $w_i$ is not squarefree, and let $F=F_1F_2^2\cdots F_k^k$ be its
+squarefree factorization. Then,}
+\[
+w_0=F_1\cdots F_kw_i^{'} \in {\bf O}_{K[x]} \backslash
+(K[x]w_1+\cdots+K[x]w_n).
+\]
+
+The lazy Hermite reduction proceeds by solving the system (8) in
+$K(x)$. Either the reduction will succeed, or one of the above
+theorems produces an element
+$w_0 \in {\bf O}_{K[x]} \backslash (K[x]w_1+\cdots+K[x]w_n).$ Let then
+$\sum_{i=1}^n C_iw_i$ and $F$ be the numerator and denominator of
+$w_0$ with respect to $w$. Using Hermitian row reduction, we can zero
+out the last row of
+\[
+\left(
+\begin{array}{cccc}
+F & & &\\
+ &F & &\\
+ & &\ddots&\\
+ & & &F\\
+C_1&C_2&\cdots&C_n
+\end{array}
+\right)
+\]
+obtaining a matrix of the form
+\[
+\left(
+\begin{array}{cccc}
+C_{1,1} & C_{1,2} & \cdots & C_{1,n}\\
+C_{2,1} & C_{2,2} & \cdots & C_{2,n}\\
+\vdots & \vdots & & \vdots\\
+C_{n,1} & C_{n,2} & \cdots & C_{n,n}\\
+0 & 0 & \cdots & 0\\
+\end{array}
+\right)
+\]
+with $C_{ij} \in K[x]$. Let $\overline{w}_i=(\sum_{j=1}^n
+C_{ij}w_j)/F$
+for $1 \le i \le n$. Then,
+$\overline{w}=(\overline{w}_1,\ldots,\overline{w}_n)$ is a basis for
+$E$ over $K$ and
+\[
+K[x]\overline{w}_1+\cdots+K[x]\overline{w}_n=K[x]w_1+\cdots+K[x]w_n+K[x]w_0
+\]
+is a submodule of ${\bf O}_{K[x]}$, which strictly contains
+$K[x]w_1+\cdots+K[x]w_n$, since it contains $w_0$. Any strictly
+increasing chain of submodules of ${\bf O}_{K[x]}$ must
+stabilize after a finite number of steps, which means that this
+process produces a basis for which either the Hermite reduction can be
+carried out, or for which $f$ has a squarefree denominator.
+
+\noindent
+{\bf Example 2} Continuing example 1 for which the Hermite reduction
+failed, Theorem 2 implies that
+\[
+w_0=\frac{1}{x}(-2xw_3+(x+1)w_4)=(-2xy^2+(x+1)y^3)x \in {\bf O}_{K[x]}
+\]
+Performing a Hermitian row reduction on
+\[
+\left(
+\begin{array}{cccc}
+x& & & \\
+ &x& & \\
+ & &x & \\
+ & & &x\\
+0&0&-2x&x+1\\
+\end{array}
+\right)
+\]
+yields
+\[
+\left(
+\begin{array}{cccc}
+x& & & \\
+ &x& & \\
+ & &x& \\
+ & & &1\\
+0&0&0&0\\
+\end{array}
+\right)
+\]
+so the new basis is $\overline{w}=(1,y,y^2,y^3/x)$, and the
+denominator of $f$ with respect to $\overline{w}$ is 1, which is
+squarefree.
+
+\subsection{Simple radical extensions}
+The integration algorithm becomes easier when $E$ is a simple radical
+extension of $K(x)$, {\sl i.e.} $E=K(x)[y]/(y^n-a)$ for some
+$a \in K(x)$. Write $a=A/D$ where $A,D \in K[x]$, and let
+$AD^{n-1}=A_1A_2^2\cdots A_k^k$ be a squarefree factorization of
+$AD^{n-1}$. Writing $i=nq_i+r_i$, for $1 \le i \le k$, where
+$0 \le r_i < n$, let $F=A_1^{q_1}\cdots A_k^{q_k}$,
+$H=A_1^{r_1}\cdots A_k^{r_k}$ and $z=yD/F$. Then,
+\[
+z^n=\left(y\frac{D}{F}\right)^n=\frac{y^nD^n}{F^n}=\frac{AD^{n-1}}{F}
+=A_1^{r_1}\cdots A_k^{r_k}=H
+\]
+Since $r_i < n$ for each $i$, the squarefree factorization of $H$ is
+of the form $H=H_1H_2^2\cdots H_m^m$ with $m<n$. An integral basis is
+then $w=(w_1,\ldots,w_n)$ where
+\begin{equation}
+w_i=\frac{z^{i-1}}{\prod_{j=1}^m H_j^{\lfloor(i-1)j/n\rfloor}}\quad
+1 \le i \le n
+\end{equation}
+and the Hermite reductions with respect to the above basis is always
+guaranteed to succeed. Furthermore, when using that basis, the system
+(8) becomes diagonal and its solution can be written explicitly:
+writing $D_i=\prod_{j=1}^m H_j^{\lfloor ij/n\rfloor}$ we have
+\[
+\begin{array}{ccl}
+S_i & = &\displaystyle UV^m\left(\frac{w_i}{V^{m-1}}\right)^{'}
+=UV^m\left(\frac{z^{i-1}}{D_{i-1}V^{m-1}}\right)^{'}\\
+&&\\
+&=&\displaystyle UV^m\left(\frac{i-1}{n}\frac{H^{'}}{H}-
+\frac{{D_{i-1}}^{'}}{D_{i-1}}
+-(m-1)\frac{V^{'}}{V}\right)\left(\frac{z^{i-1}}{D_{i-1}V^{m-1}}\right)\\
+&&\\
+&=&\displaystyle U\left(V\left(\frac{i-1}{n}\frac{H^{'}}{H}
+-\frac{{D_{i-1}}^{'}}{D_{i-1}}\right)-(m-1)V^{'}\right)w_i
+\end{array}
+\]
+so the unique solution of (8) in $K(x)$ is
+\begin{equation}
+f_i=\frac{A_i}{U\left(V\left(\frac{i-1}{n}\frac{H^{'}}{H}-
+\frac{{D_{i-1}}^{'}}{D_{i-1}}\right)-(m-1)V^{'}\right)}
+\quad{\rm for\ }1 \le i \le n
+\end{equation}
+and it can be shown that the denominator of each $f_i$ is coprime with
+$V$ when $m \ge 2$.
+
+\noindent
+{\bf Example 3} {\sl Consider
+\[
+\int\frac{(2x^8+1)\sqrt{(x^8+1)}}{x^{17}+2x^9+x}~dx
+\]
+The integrand is
+\[
+f=\frac{(2x^8+1)y}{x^{17}+2x^9+x} \in E
+=\mathbb{Q}(x)[y]/(y^2-x^8-1)
+\]
+so $H=x^8+1$ which is squarefree, implying that the integral basis
+(11) is $(w_1,w_2)=(1,y)$. The squarefree factorization of
+$x^{17}+2x^9+x$ is $x(x^8+1)^2$ so $U=x$, $V=x^8+1$, $m=2$, and the
+solution (12) of (8) is
+\[
+f_1=0,\quad
+f_2=\frac{2x^8+1}{x\left((x^8+1)\frac{1}{2}\frac{8x^7}{x^8+1}
+-8x^7\right)}=-\frac{(2x^8+1)/4}{x^8}
+\]
+We have $Q=x^8$, so $V-Q=1$, $A=1$, $R=-1$ and $RQf_2=V/2-1/4$,
+implying that
+\[
+B=-\frac{y}{4}\quad {\rm and}\quad h=f-\left(\frac{B}{V}\right)^{'}
+=\frac{y}{x(x^8+1)}
+\]
+solve (7), i.e.
+\[
+\int\frac{(2x^8+1)\sqrt{(x^8+1)}}{x^{17}+2x^9+x}~dx=
+-\frac{\sqrt{x^8+1}}{4(x^8+1)}
++\int\frac{\sqrt{x^8+1}}{x(x^8+1)}~dx
+\]
+and the remaining integrand has a squarefree denominator.}
+
+\subsection{Liouville's Theorem}
+Up to this point, the algorithms we have presented never fail, yet it
+can happen that an algebraic function does not have an elementary
+integral, for example
+\[
+\int{\frac{x~dx}{\sqrt{1-x^3}}}
+\]
+which is not an elementary function of $x$. So we need a way to
+recognize such functions before completing the integration
+algorithm. Liouville was the first to state and prove a precise
+theorem from Laplace's observation that we can restrict the elementary
+integration problem by allowing only new logarithms to appear linearly
+in the integral, all the other terms appearing in the integral being
+already in the integrand.
+
+{\bf Theorem 4 (Liouville \cite{8,9})} {\sl
+Let $E$ be an algebraic extension of the rational function field
+$K(x)$, and $f \in E$. If $f$ has an elementary integral, then there
+exist $v \in E$, constants $c_1,\ldots,c_n \in \overline{K}$ and
+$u_1,\ldots,u_k \in E(c_1,\ldots,c_k)^{*}$ such that}
+\begin{equation}
+f=v^{'}+c_1\frac{u_1^{'}}{u_1}+\cdots+c_k\frac{u_k^{'}}{u_k}
+\end{equation}
+The above is a restriction to algebraic functions of the strong
+Liouville Theorem, whose proof can be found in \cite{4,14}. An elegant
+and elementary algebraic proof of a slightly weaker version can be
+found in \cite{17}. As a consequence, we can look for an integral of
+the form (4), Liouville's Theorem guaranteeing that there is no
+elementary integral if we cannot find one in that form. Note that the
+above theorem does not say that every integral must have the above
+form, and in fact that form is not always the most convenient one, for
+example,
+\[
+\int{\frac{dx}{1+x^2}}=arctan(x)=\frac{\sqrt{-1}}{2}
+\log\left(\frac{\sqrt{-1}+x}{\sqrt{-1}-x}\right)
+\]
+
+\subsection{The integral part}
+Following the Hermite reduction, we can assume that we have a basis
+$w=(w_1,\ldots,w_n)$ of $E$ over $K(x)$ made of integral elements such
+that our integrand is of the form $f=\sum_{i=1}^n A_iw_i/D$ where
+$D \in K[x]$ is squarefree. Given Liouville's Theorem, we now have to
+solve equation (13) for $v$, $u_1,\ldots,u_k$ and the constants
+$c_1,\ldots,c_k$. Since $D$ is squarefree, it can be shown that
+$v \in {\bf O}_{K[x]}$ for any solution, and in fact $v$
+corresponds to the polynomial part of the integral of rational
+functions. It is however more difficult to compute than the integral
+of polynomials, so Trager \cite{20} gave a change of variable that
+guarantees that either $v^{'}=0$ or $f$ has no elementary integral. In
+order to describe it, we need to define the analogue for algebraic
+functions of having a nontrivial polynomial part: we say that
+$\alpha \in E$ is {\sl integral at infinity} if there is a polynomial
+$p=\sum_{i=1}^m a_iy^i \in K[x][y]$ such that $p(x,\alpha)=0$ and
+$deg(a_m) \ge deg(a_i)$ for each $i$. Note that a rational function
+$A/D \in K(x)$ is integral at infinity if and only if
+$deg(A) \le deg(D)$ since it is a zero of $Dy-A$. When $\alpha-E$ is
+not integral at infinity, we say that it has a {\sl pole at
+infinity}. Let
+\[
+{\bf O}_\infty = \{\alpha \in E {\rm\ such\ that\ }\alpha
+{\rm\ is\ integral\ at\ infinity}\}
+\]
+A set $(b_1,\ldots,b_n) \in E^n$ is called {\sl normal at infinity} if
+there are $r_1,\ldots,r_n \in K(x)$ such that every
+$\alpha \in {\bf O}_\infty$ can be written as
+$\alpha = \sum_{i=1}^n B_ir_ib_i/C$ where $C,B_1,\ldots,B_n \in K[x]$
+and $deg(C) \ge deg(B_i)$ for each $i$. We say that the differential
+$\alpha ~dx$ is integral at infinity if
+$\alpha x^{1+1/r} \in {\bf O}_\infty$ where $r$ is the smallest
+ramification index at infinity. Trager \cite{20} described an
+algorithm that converts an arbitrary integral basis $w_1,\ldots,w_n$
+into one that is also normal at infinity, so the first part of his
+integration algorithm is as follows:
+\begin{enumerate}
+\item Pick any basis $b=(b_1,\ldots,b_n)$ of $E$ over $K(x)$ that is
+composed of integral elements.
+\item Pick an integer $N \in \mathbb{Z}$ that is not zero of the
+denominator of $f$ with respect to $b$, nor of the discriminant of $E$
+over $K(x)$, and perform the change of variable $x=N+1/z$,
+$dx=-dz/z^2$ on the integrand.
+\item Compute an integral basis $w$ for $E$ over $K(z)$ and make it
+normal at infinity
+\item Perform the Hermite reduction on $f$ using $w$, this yields
+$g,h \in E$ such that $\int{f~dz}=g+\int{h~dz}$ and $h$ has a
+squarefree denominator with respect to $w$.
+\item If $hz^2$ has a pole at infinity, then $\int{f~dz}$ and
+$\int{h~dz}$ are not elementary functions
+\item Otherwise, $\int{h~dz}$ is elementary if and only if there are
+constants $c_1,\ldots,c_k \in \overline{K}$ and
+$u_1,\ldots,u_k \in E(c_1,\ldots,c_k)^{*}$ such that
+\end{enumerate}
+\begin{equation}
+h=\frac{c_1}{u_1}\frac{du_1}{dz}+\cdots+\frac{c_k}{u_k}\frac{du_k}{dz}
+\end{equation}
+The condition that $N$ is not a zero of the denominator of $f$ with
+respect to $b$ implies that the $f~dz$ is integral at infinity after
+the change of variable, and Trager proved that if $h~dz$ is not
+integral at infinity after the Hermite reduction, then $\int{h~dz}$
+and $\int{f~dz}$ are not elementary functions. The condition that $N$
+is not a zero of the discriminant of $E$ over $K(x)$ implies that the
+ramification indices at infinity are all equal to 1 after the change
+of variable, hence that $h~dz$ is integral at infinity if and only if
+$hz^2 \in {\bf O}_\infty$. That second condition on $N$ can be
+disregarded, in which case we must replace $hz^2$ in step 5 by
+$hz^{1+1/r}$ where $r$ is the smallest ramification index at
+infinity. Note that $hz^2 \in {\bf O}_\infty$ implies that
+$hz^{1+1/r} \in {\bf O}_\infty$, but not conversely. Finally, we
+remark that for simple radical extensions, the integral basis (11) is
+already normal at infinity.
+
+Alternatively, we can use lazy Hermite reduction in the above
+algorithm: in step 3, we pick any basis made of integral elements,
+then perform the lazy Hermite reduction in step 4. If $h \in K(z)$
+after the Hermite reduction, then we can complete the integral without
+computing an integral basis. Otherwise, we compute an integral basis
+and make it normal at infinity between steps 4 and 5. This lazy
+variant can compute $\int{f~dx}$ whenever it is an element of $E$
+without computing an integral basis.
+
+\subsection{The logarithmic part}
+Following the previous sections, we are left with solving equation
+(14) for the constants $c_1,\ldots,c_k$ and for $u_1,\ldots,u_k$. We
+must make at this point the following additional assumptions:
+\begin{itemize}
+\item we have an integral primitive element for $E$ over $K(z)$, {\sl
+i.e.} $y \in {\bf O}_{K[z]}$ such that $E=K(z)(y)$,
+\item $[E : K(z)]=[E : \overline{K}(z)]$, {\sl i.e.} the minimal
+polynomial for $y$ over $K[z]$ is absolutely reducible, and
+\item we have an integral basis $w=(w_1,\ldots,w_n)$ for $E$ over
+$K(z)$, and $w$ is normal at infinity
+\end{itemize}
+A primitive element can be computed by considering linear combinations
+of the generators of $E$ over $K(x)$ with random coefficients in
+$K(x)$, and Trager \cite{20} describes an absolute factorization
+algorithm, so the above assumptions can be ensured, although those
+steps can be computationally very expensive, except in the case of
+simple radical extensions. Before describing the second part of
+Trager's integration algorithm, we need to define some concepts from
+the theory of algebraic curves. Given a finite algebraic extension
+$E=K(z)(y)$ of $K(z)$, a {\sl place} $P$ of $E$ is a proper local
+subring of $E$ containing $K$, and a {\sl divisor} is a formal sum
+$\sum{n_PP}$ with finite support, where the $n_P$'s are integers and
+the $P$'s are places. Let $P$ be a place, then its maximal ideal
+$\mu_P$ is principal, so let $p\in E$ be a generator of $\mu_P$. The
+{\sl order at} $P$ is the function
+$\nu_P : E^{*} \rightarrow \mathbb{Z}$ which maps $f \in E^{*}$ to the
+largest $k \in \mathbb{Z}$ such that $f \in p^kP$. Given
+$f \in E^{*}$, the {\sl divisor of} $f$ is $(f) = \sum{\nu_P(f)P}$
+where the sum is taken over all the places. It has finite support
+since $\nu_P(f) \ne 0$ if and only if $P$ is a pole or zero of
+$f$. Finally, we way that a divisor $\delta = \sum{n_PP}$ is
+{\sl principal} if $\delta=(f)$ for some $f \in E^{*}$. Note that if
+$\delta$ is principal, the $\sum{n_P}=0$, but the converse is not
+generally true, except if $E=K(z)$. Trager's algorithm proceeds
+essentially by constructing candidate divisors for the $u_i$'s of
+(14):
+\begin{itemize}
+\item Let $\sum_{i=1}^n A_iw_i$ be the numerator of $h$ with respect
+to $w$, and $D$ be its (squarefree) denominator
+\item Write $\sum_{i=1}^n A_iw_i=G/H$, where $G \in K[z,y]$ and
+$H \in K[z]$
+\item Let $f \in K[z,y]$ be the (monic) minimum polynomial for $y$
+over $K(z)$, $t$ be a new indeterminante and compute
+\[
+R(t)={\rm resultant_z\ }\left({\rm\ pp_t }\left({\rm\ resultant_y\ }\left(
+G-tH\frac{dD}{dz},F\right)\right),D\right) \in K[t]
+\]
+\item Let $\alpha_1,\ldots,\alpha_s \in \overline{K}$ be the distinct
+nonzero roots of $R$, $(q_1,\ldots,q_k)$ be a basis for the vector
+space that they generate over $\mathbb{Q}$, write
+$\alpha_i=r_{i1}q_1+\cdots+r_{ik}q_k$ for each $i$, where
+$r_{ij} \in \mathbb{Q}$ and let $m > 0$ be a common denominator for
+all the $r_{ij}$'s
+\item For $1 \le j \le k$, let
+$\delta_j=\sum_{i=1}^s mr_{ij}\sum_l r_lP_l$ where $r_l$ is the
+ramification index of $P_l$ and $P_l$ runs over all the places at
+which $h~dz$ has residue $r_i\alpha_i$
+\item If there are nonzero integers $n_1,\ldots,n_k$ such that
+$n_j\delta_j$ is principal for each $j$, then let
+\[
+u=h-\frac{1}{m}\sum_{j=1}^k\frac{q_j}{n_ju_j}\frac{du_j}{dz}
+\]
+where $u_j \in E(\alpha_1,\ldots,\alpha_s)^{*}$ is such that
+$n_j\delta_j=(u_j)$. If $u=0$, then
+$\int{h~dz}=\sum_{j=1}^k q_j\log(u_j)/(mn_j)$, otherwise if either
+$u \ne 0$ or there is no such integer $n_j$ for at least one $j$,
+then $h~dz$ has no elementary integral.
+\end{itemize}
+Note that this algorithm expresses the integral, when it is
+elementary, with the smallest possible number of logarithms. Steps 3
+to 6 requires computing in the splitting field $K_0$ of $R$ over $K$,
+but it can be proven that, as in the case of rational functions, $K_0$
+is the minimal algebraic extension of $K$ necessary to express the
+integral in the form (4). Trager \cite{20} describes a representation
+of divisors as fractional ideals and gives algorithms for the
+arithmetic of divisors and for testing whether a given divisor is
+principal. In order to determine whether there exists an integer $N$
+such that $N\delta$ is principal, we need to reduce the algebraic
+extension to one over a finite field $\mathbb{F}_{p^q}$ for some
+``good'' prime $p \in \mathbb{Z}$. Over $\mathbb{F}_{p^q}$, it is
+known that for every divisor $\delta=\sum{n_PP}$ such that
+$\sum{n_P}=0$, $M\delta$ is principal for some integer
+$1 \le M \le (1+\sqrt{p^q})^{2g}$, where $g$ is the genus of the curve
+\cite{22}, so we compute such an $M$ by testing $M=1,2,3,\ldots$ until
+we find it. It can then be shown that for almost all primes $p$, if
+$M\delta$ is not principal in characteristic 0, the $N\delta$ is not
+principal for any integer $N \ne 0$. Since we can test whether the
+prime $p$ is ``good'' by testing whether the image in
+$\mathbb{F}_{p^q}$ of the discriminant of the discriminant of the
+minimal polynomial for $y$ over $K[z]$ is 0, this yields a complete
+algorithm. In the special case of hyperelliptic extensions, {\sl i.e.}
+simple radical extensions of degree 2, Bertrand \cite{1} describes a
+simpler representation of divisors for which the arithmetic and
+principality tests are more efficient than the general methods.
+
+\noindent
+{\bf Example 4} {\sl
+Continuing example 3, we were left with the integrand
+\[
+\frac{\sqrt{x^8+1}}{x(x^8+1)}=\frac{w_2}{x(x^8+1)} \in E
+=\mathbb{Q}(x)[y]/(y^2-x^8-1)
+\]
+where $(w_1,w_2)=(1,y)$ is an integral basis normal at infinity, and
+the denominator $D=x(x^8+1)$ of the integrand is squarefree. Its
+numerator is $w_2=y$, so the resultant of step 3 is
+\[
+resultant_x(pp_t(resultant_y(y-t(9x^8+1),y^2-x^8-1)),x(x^8+1))=
+ct^{16}(t^2-1)
+\]
+where $c$ is a large nonzero integer. Its nonzero roots are $\pm 1$,
+and the integrand has residue 1 at the place $P$ corresponding to the
+point $(x,y)=(0,1)$ and $-1$ at the place $Q$ corresponding to the
+point $(x,y)=(0,-1)$, so the divisor $\delta_1$ of step 5 is
+$\delta_1=P-Q$. It turns out that $\delta_1$, $2\delta_1$, and
+$3\delta_1$ are not principal, but that
+\[
+4\delta_1=\left(\frac{x^4}{1+y}\right)\quad{\rm\ and\ }\quad
+\frac{w_2}{x(x^8+1)}
+-\frac{1}{4}\frac{(x^4/(1+y))^{'}}{x^4/(1+y)}=0
+\]
+which implies that
+\[
+\int{\frac{\sqrt{x^8+1}}{x(x^8+1)}}~dx
+=\frac{1}{4}\log\left(\frac{x^4}{1+\sqrt{x^8+1}}\right)
+\]}
+
+\noindent
+{\bf Example 5} {\sl
+Consider
+\[
+\int{\frac{x~dx}{\sqrt{1-x^3}}}
+\]
+The integrand is
+\[
+f=\frac{xy}{1-x^3} \in E =
+\mathbb{Q}(x)[y]/(y^2+x^3-1)
+\]
+where $(w_1,w_2)=(1,y)$ is an integral basis normal at infinity, and
+the denominaotr $D=1-x^3$ of the integrand is squarefree. Its
+numerator is $xw_2=xy$, so the resultant of step 3 is
+\[
+resultant_x(pp_t(resultant_y(xy+3tx^2,y^2+x^3-1)),1-x^3)=729t^6
+\]
+whose only root is 0. Since $f \ne 0$, we conclude from step 6 that
+$\int{f~dx}$ is not an elementary function.}
+
+\noindent
+{\bf Example 6} {\sl
+\[
+\int{\frac{dx}{x\sqrt{1-x^3}}}
+\]
+The integrand is
+\[
+f=\frac{y}{x-x^4} \in E =
+\mathbb{Q}(x)[y]/(y^2+x^3-1)
+\]
+where $(w_1,w_2)=(1,y)$ is an integral basis normal at infinity, and
+the denominator $D=x-x^4$ of the integrand is squarefree. Its
+numerator is $w_2=y$, so the resultant of step 3 is
+\[
+resultant_x(pp_t(resultant_y(y+t(4x^3-1),y^2+x^3-1)),x-x^4)=729t^6(t^2-1)
+\]
+Its nonzero roots are $\pm 1$, and the integrand has residue 1 at the
+place $P$ corrseponding to the point $(x,y)=(0,1)$ and $-1$ at the
+place $Q$ corresponding to the point $(x,y)=(0,-1)$ so the divisor
+$\delta_1$ of step 5 is $\delta_1=P-Q$. It turns out that $\delta_1$
+and $2\delta_1$ are not principal, but that
+\[
+3\delta_1=\left(\frac{y-1}{y+1}\right)\quad{\rm and}\quad
+\frac{y}{x-x^4}-\frac{1}{3}\frac{((y-1)/(y+1))^{'}}{(y-1)/(y+1)}=0
+\]
+which implies that
+\[
+\int{\frac{dx}{x\sqrt{1-x^3}}}
+=\frac{1}{3}\log\left(\frac{\sqrt{1-x^3}-1}{\sqrt{1-x^3}+1}\right)
+\]}
+
+\section{Elementary Functions}
+Let $f$ be an arbitrary elementary function. In order to generalize
+the algorithms of the previous sections, we need to build an algebraic
+model in which $f$ behaves in some sense like a rational or algebraic
+function. For that purpose, we need to formally define differential
+fields and elementary functions.
+
+\subsection{Differential algebra}
+A {\sl differential field} $(K,')$ is a {\sl differential extension}
+of $(K,')$ with a given map $a \rightarrow a'$ from $K$ into $K$,
+satisfying $(a+b)'=a'+b'$ and $(ab)'=a'b+ab'$. Such a map is called a
+{\sl derivation} on $K$. An element $a \in K$ which satisfies $a'=0$
+is called a {\sl constant}, and the set
+Const($K$)$=\{a \in K {\rm\ such\ that\ }a'=0\}$ of all the constants
+of $K$ is a subfield of $K$.
+
+A differential field $(E,')$ is a {\sl differential equation} of
+$(K,')$ if $K \subseteq E$ and the derivation on $E$ extends the one
+on $K$. In that case, an element $t \in E$ is a {\sl monomial} over
+$K$ if $t$ is transcendental over $K$ and $t' \in K[t]$, which implies
+that both $K[t]$ and $K(t)$ are closed under '. An element $t \in E$
+is {\sl elementary over} $K$ if either
+\begin{itemize}
+\item $t'=b'/b$ for some $b \in K^{*}$, in which case we say that $t$
+is a {\sl logarithm} over $K$, and write $t=log(b)$, or
+\item $t'=b't$ for some $b \in K^{*}$, in which case we say that $t$
+is an {\sl exponential} over $K$, and write $t=...
[truncated message content] |
|
From: <gi...@ax...> - 2008-09-13 05:20:57
|
books/Makefile.pamphlet | 23 +-
books/bookvol10.1.pamphlet | 2090 +++++++
books/bookvol10.2.pamphlet | 8210 ++++++++++++++++++++++++
books/bookvol10.3.pamphlet | 246 +
books/bookvol10.4.pamphlet | 245 +
books/bookvol10.pamphlet | 8677 +-------------------------
books/ps/v102agg.ps | 350 ++
books/ps/v102associationlistaggregate.ps | 727 +++
books/ps/v102bagaggregate.ps | 452 ++
books/ps/v102binaryrecursiveaggregate.ps | 503 ++
books/ps/v102collection.ps | 452 ++
books/ps/v102dequeueaggregate.ps | 523 ++
books/ps/v102dictionary.ps | 625 ++
books/ps/v102dictionaryoperations.ps | 676 ++
books/ps/v102doublylinkedaggregate.ps | 503 ++
books/ps/v102eltab.ps | 299 +
books/ps/v102eltableaggregate.ps | 350 ++
books/ps/v102extensiblelinearaggregate.ps | 574 ++
books/ps/v102finitelinearaggregate.ps | 574 ++
books/ps/v102homogeneousaggregate.ps | 503 ++
books/ps/v102indexedaggregate.ps | 574 ++
books/ps/v102keyeddictionary.ps | 676 ++
books/ps/v102koerce.ps | 299 +
books/ps/v102konvert.ps | 299 +
books/ps/v102linearaggregate.ps | 625 ++
books/ps/v102listaggregate.ps | 697 +++
books/ps/v102multidictionary.ps | 625 ++
books/ps/v102onedimensionalarrayaggregate.ps | 503 ++
books/ps/v102priorityqueueaggregate.ps | 503 ++
books/ps/v102queueaggregate.ps | 503 ++
books/ps/v102recursiveaggregate.ps | 452 ++
books/ps/v102retractableto.ps | 299 +
books/ps/v102stackaggregate.ps | 503 ++
books/ps/v102streamaggregate.ps | 646 ++
books/ps/v102stringaggregate.ps | 605 ++
books/ps/v102tableaggregate.ps | 903 +++
books/ps/v102type.ps | 299 +
books/ps/v102unaryrecursiveaggregate.ps | 503 ++
books/ps/v10agg.ps | 350 --
books/ps/v10associationlistaggregate.ps | 778 ---
books/ps/v10bagaggregate.ps | 452 --
books/ps/v10binaryrecursiveaggregate.ps | 503 --
books/ps/v10collection.ps | 452 --
books/ps/v10dequeueaggregate.ps | 523 --
books/ps/v10dictionary.ps | 625 --
books/ps/v10dictionaryoperations.ps | 676 --
books/ps/v10doublylinkedaggregate.ps | 503 --
books/ps/v10eltab.ps | 299 -
books/ps/v10eltableaggregate.ps | 350 --
books/ps/v10extensiblelinearaggregate.ps | 574 --
books/ps/v10finitelinearaggregate.ps | 574 --
books/ps/v10homogeneousaggregate.ps | 401 --
books/ps/v10indexedaggregate.ps | 574 --
books/ps/v10keyeddictionary.ps | 676 --
books/ps/v10koerce.ps | 299 -
books/ps/v10konvert.ps | 299 -
books/ps/v10linearaggregate.ps | 625 --
books/ps/v10listaggregate.ps | 697 ---
books/ps/v10multidictionary.ps | 625 --
books/ps/v10onedimensionalarrayaggregate.ps | 503 --
books/ps/v10priorityqueueaggregate.ps | 503 --
books/ps/v10queueaggregate.ps | 503 --
books/ps/v10recursiveaggregate.ps | 452 --
books/ps/v10retractableto.ps | 299 -
books/ps/v10stackaggregate.ps | 503 --
books/ps/v10streamaggregate.ps | 646 --
books/ps/v10stringaggregate.ps | 605 --
books/ps/v10tableaggregate.ps | 903 ---
books/ps/v10type.ps | 299 -
books/ps/v10unaryrecursiveaggregate.ps | 503 --
changelog | 10 +
src/Makefile.pamphlet | 12 +-
72 files changed, 27455 insertions(+), 25257 deletions(-)
New commits:
commit 315cde6ee41f4143519084d4f1dca25916104dc5
Author: Tim Daly <da...@ax...>
Date: Thu Jul 24 11:06:23 2008 -0400
20080912 tpd books/Makefile add bookvol10 subvolumes
20080912 tpd books/bookvol10.4 added
20080912 tpd books/bookvol10.3 added
20080912 tpd books/bookvol10.2 added
20080912 tpd books/bookvol10.1 added
20080912 tpd books/bookvol10 split
20080912 tpd books/ps/v102keyeddictionary.ps updated
20080912 tpd books/ps/v102homogeneousaggregate.ps updated
20080912 tpd books/ps/v102homogeneousaggregate.ps updated
20080912 tpd books/ps/v10* renamed to books/ps/v102*
|
|
From: <da...@us...> - 2008-09-12 01:26:06
|
Revision: 971
http://axiom.svn.sourceforge.net/axiom/?rev=971&view=rev
Author: daly
Date: 2008-09-12 01:26:14 +0000 (Fri, 12 Sep 2008)
Log Message:
-----------
20080911 tpd src/algebra/Makefile remove coerce.spad
20080911 tpd books/ps/v10unaryrecursiveaggregate.ps add image
20080911 tpd books/ps/v10type.ps add image
20080911 tpd books/ps/v10tableaggregate.ps add image
20080911 tpd books/ps/v10stringaggregate.ps add image
20080911 tpd books/ps/v10streamaggregate.ps add image
20080911 tpd books/ps/v10stackaggregate.ps add image
20080911 tpd books/ps/v10retractableto.ps add image
20080911 tpd books/ps/v10recursiveaggregate.ps add image
20080911 tpd books/ps/v10queueaggregate.ps add image
20080911 tpd books/ps/v10priorityqueueaggregate.ps add image
20080911 tpd books/ps/v10onedimensionalarrayaggregate.ps add image
20080911 tpd books/ps/v10multidictionary.ps add image
20080911 tpd books/ps/v10listaggregate.ps add image
20080911 tpd books/ps/v10linearaggregate.ps add image
20080911 tpd books/ps/v10konvert.ps add image
20080911 tpd books/ps/v10koerce.ps add image
20080911 tpd books/ps/v10keyeddictionary.ps add image
20080911 tpd books/ps/v10indexedaggregate.ps add image
20080911 tpd books/ps/v10homogeneousaggregate.ps add image
20080911 tpd books/ps/v10finitelinearaggregate.ps add image
20080911 tpd books/ps/v10extensiblelinearaggregate.ps add image
20080911 tpd books/ps/v10eltableaggregate.ps add image
20080911 tpd books/ps/v10eltab.ps add image
20080911 tpd books/ps/v10doublylinkedaggregate.ps add image
20080911 tpd books/ps/v10dictionaryoperations.ps add image
20080911 tpd books/ps/v10dictionary.ps add image
20080911 tpd books/ps/v10dequeueaggregate.ps add image
20080911 tpd books/ps/v10collection.ps add image
20080911 tpd books/ps/v10binaryrecursiveaggregate.ps add image
20080911 tpd books/ps/v10bagaggregate.ps add image
20080911 tpd books/ps/v10associationlistaggregate.ps add image
20080911 tpd books/ps/v10agg.ps add image
20080911 tpd src/algebra/coerce.spad merge into bookvol10
20080911 tpd books/bookvol10 document aggcat, coerce layers
Modified Paths:
--------------
trunk/axiom/books/bookvol10.pamphlet
trunk/axiom/changelog
trunk/axiom/src/algebra/Makefile.pamphlet
Added Paths:
-----------
trunk/axiom/books/ps/v10agg.ps
trunk/axiom/books/ps/v10associationlistaggregate.ps
trunk/axiom/books/ps/v10bagaggregate.ps
trunk/axiom/books/ps/v10binaryrecursiveaggregate.ps
trunk/axiom/books/ps/v10collection.ps
trunk/axiom/books/ps/v10dequeueaggregate.ps
trunk/axiom/books/ps/v10dictionary.ps
trunk/axiom/books/ps/v10dictionaryoperations.ps
trunk/axiom/books/ps/v10doublylinkedaggregate.ps
trunk/axiom/books/ps/v10eltab.ps
trunk/axiom/books/ps/v10eltableaggregate.ps
trunk/axiom/books/ps/v10extensiblelinearaggregate.ps
trunk/axiom/books/ps/v10finitelinearaggregate.ps
trunk/axiom/books/ps/v10homogeneousaggregate.ps
trunk/axiom/books/ps/v10indexedaggregate.ps
trunk/axiom/books/ps/v10keyeddictionary.ps
trunk/axiom/books/ps/v10koerce.ps
trunk/axiom/books/ps/v10konvert.ps
trunk/axiom/books/ps/v10linearaggregate.ps
trunk/axiom/books/ps/v10listaggregate.ps
trunk/axiom/books/ps/v10multidictionary.ps
trunk/axiom/books/ps/v10onedimensionalarrayaggregate.ps
trunk/axiom/books/ps/v10priorityqueueaggregate.ps
trunk/axiom/books/ps/v10queueaggregate.ps
trunk/axiom/books/ps/v10recursiveaggregate.ps
trunk/axiom/books/ps/v10retractableto.ps
trunk/axiom/books/ps/v10stackaggregate.ps
trunk/axiom/books/ps/v10streamaggregate.ps
trunk/axiom/books/ps/v10stringaggregate.ps
trunk/axiom/books/ps/v10tableaggregate.ps
trunk/axiom/books/ps/v10type.ps
trunk/axiom/books/ps/v10unaryrecursiveaggregate.ps
Removed Paths:
-------------
trunk/axiom/src/algebra/coerce.spad.pamphlet
Modified: trunk/axiom/books/bookvol10.pamphlet
===================================================================
--- trunk/axiom/books/bookvol10.pamphlet 2008-09-11 18:35:17 UTC (rev 970)
+++ trunk/axiom/books/bookvol10.pamphlet 2008-09-12 01:26:14 UTC (rev 971)
@@ -8,13 +8,29 @@
%%
%% pagehead consolidates standard page indexing
%%
-\newcommand{\pagehead}[3]{% e.g. \pagehead{page}{file.ht}{title}
-\subsection{#3}%
-\label{#1}
-\index{pages!#1!#2}%
-\index{#1!#2!pages}%
-\index{#2!pages!#1}}
+\newcommand{\pagehead}[2]{% e.g. \pagehead{name}{abb}
+\section{#1}
+\label{#1}%
+\label{#2}%
+\index{{#1}}%
+\index{{#2}}}%
%%
+%% pagepic adds an image and an index entry
+%%
+\newcommand{\pagepic}[2]{% e.g. \pagepic{pathandfile}{abb}
+\includegraphics{#1}%
+\index{images!#2}}
+%%
+%% pageto is a forward link to a referenced page
+%%
+\newcommand{\pageto}[2]{% e.g. \pageto{abb}{name}
+\ \\${\bf\Rightarrow{}}${``#1''} (#2) \ref{#1} on page~\pageref{#1}}
+%%
+%% pageback is a backward link to a referencing page
+%%
+\newcommand{\pagefrom}[2]{% e.g. \pagefrom{name}{abb}
+\ \\${\bf\Leftarrow{}}${``#1''} (#2) \ref{#1} on page~\pageref{#1}}
+%%
% special meanings for math characters
\providecommand{\N}{\mbox{\bbold N}}
\providecommand{\Natural}{\mbox{\bbold N}}
@@ -1982,8 +1998,289 @@
case. Again, the details are quite technical and can be found in
\cite{2,12,13}.
-\chapter{Categories Layers}
-\section{category AGG Aggregate}
+\chapter{Category Layer 1}
+\pagehead{Category}{CATEGORY}
+This is the root of the category hierarchy and is not represented by code.
+
+See:\\
+\pageto{Eltable}{ELTAB}
+\pageto{CoercibleTo}{KOERCE}
+\pageto{ConvertibleTo}{KONVERT}
+\pageto{RetractableTo}{RETRACT}
+\pageto{Type}{TYPE}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{CoercibleTo}{KOERCE}
+\pagepic{ps/v10koerce.ps}{KOERCE}
+
+See:\\
+\pagefrom{Category}{CATEGORY}
+<<category KOERCE CoercibleTo>>=
+)abbrev category KOERCE CoercibleTo
+++ Category for coerce
+++ Author: Manuel Bronstein
+++ Date Created: ???
+++ Date Last Updated: 14 May 1991
+++ Description:
+++ A is coercible to B means any element of A can automatically be
+++ converted into an element of B by the interpreter.
+CoercibleTo(S:Type): Category == with
+ coerce: % -> S
+ ++ coerce(a) transforms a into an element of S.
+
+@
+<<KOERCE.dotabb>>=
+"KOERCE" [color=lightblue,href="books/bookvol10.pamphlet"];
+"KOERCE" -> "CATEGORY"
+
+@
+<<KOERCE.dotfull>>=
+"CoercibleTo(a:Type)" [color=lightblue,href="books/bookvol10.pamphlet"];
+"CoercibleTo(a:Type)" -> "Category"
+
+"CoercibleTo(OutputForm)" [color=seagreen,href="books/bookvol10.pamphlet"];
+"CoercibleTo(OutputForm)" ->
+ "CoercibleTo(a:Type)"
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{ConvertibleTo}{KONVERT}
+\pagepic{ps/v10konvert.ps}{KONVERT}
+
+See:\\
+\pagefrom{Category}{CATEGORY}
+<<category KONVERT ConvertibleTo>>=
+)abbrev category KONVERT ConvertibleTo
+++ Category for convert
+++ Author: Manuel Bronstein
+++ Date Created: ???
+++ Date Last Updated: 14 May 1991
+++ Description:
+++ A is convertible to B means any element of A
+++ can be converted into an element of B,
+++ but not automatically by the interpreter.
+ConvertibleTo(S:Type): Category == with
+ convert: % -> S
+ ++ convert(a) transforms a into an element of S.
+
+@
+<<KONVERT.dotabb>>=
+"KONVERT" [color=lightblue,href="books/bookvol10.pamphlet"];
+"KONVERT" -> "CATEGORY"
+
+@
+<<KONVERT.dotfull>>=
+"ConvertibleTo(a:Type)"
+ [color=lightblue,href="books/bookvol10.pamphlet"];
+"ConvertibleTo(a:Type)" -> "Category"
+
+"ConvertibleTo(DoubleFloat)"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"ConvertibleTo(DoubleFloat)" -> "ConvertibleTo(a:Type)"
+
+"ConvertibleTo(Float)"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"ConvertibleTo(Float)" -> "ConvertibleTo(a:Type)"
+
+"ConvertibleTo(InputForm)"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"ConvertibleTo(InputForm)" -> "ConvertibleTo(a:Type)"
+
+"ConvertibleTo(Integer)"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"ConvertibleTo(Integer)" -> "ConvertibleTo(a:Type)"
+
+"ConvertibleTo(Pattern(Integer))"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"ConvertibleTo(Pattern(Integer))" -> "ConvertibleTo(a:Type)"
+
+"ConvertibleTo(Pattern(Float))"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"ConvertibleTo(Pattern(Float))" -> "ConvertibleTo(a:Type)"
+
+"ConvertibleTo(Complex(Float))"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"ConvertibleTo(Complex(Float))" -> "ConvertibleTo(a:Type)"
+
+"ConvertibleTo(Complex(DoubleFloat))"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"ConvertibleTo(Complex(DoubleFloat))" -> "ConvertibleTo(a:Type)"
+
+"ConvertibleTo(String)"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"ConvertibleTo(String)" -> "ConvertibleTo(a:Type)"
+
+"ConvertibleTo(Symbol)"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"ConvertibleTo(Symbol)" -> "ConvertibleTo(a:Type)"
+
+"ConvertibleTo(SExpression)"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"ConvertibleTo(SExpression)" -> "ConvertibleTo(a:Type)"
+
+"ConvertibleTo(Pattern(Base))"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"ConvertibleTo(Pattern(Base))" -> "ConvertibleTo(a:Type)"
+
+"ConvertibleTo(List(Integer))"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"ConvertibleTo(List(Integer))" -> "ConvertibleTo(a:Type)"
+
+"ConvertibleTo(List(Character))"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"ConvertibleTo(List(Character))" -> "ConvertibleTo(a:Type)"
+
+"ConvertibleTo(UnivariatePolynomialCategory(CommutativeRing))"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"ConvertibleTo(UnivariatePolynomialCategory(CommutativeRing))" ->
+ "ConvertibleTo(a:Type)"
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{Eltable}{ELTAB}
+\pagepic{ps/v10eltab.ps}{ELTAB}
+
+See:\\
+\pagefrom{Category}{CATEGORY}
+<<category ELTAB Eltable>>=
+)abbrev category ELTAB Eltable
+++ Author: Michael Monagan; revised by Manuel Bronstein and Manuel Bronstein
+++ Date Created: August 87 through August 88
+++ Date Last Updated: April 1991
+++ Basic Operations:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++ An eltable over domains D and I is a structure which can be viewed
+++ as a function from D to I.
+++ Examples of eltable structures range from data structures, e.g. those
+++ of type \spadtype{List}, to algebraic structures like \spadtype{Polynomial}.
+Eltable(S:SetCategory, Index:Type): Category == with
+ elt : (%, S) -> Index
+ ++ elt(u,i) (also written: u . i) returns the element of u indexed by i.
+ ++ Error: if i is not an index of u.
+
+@
+<<ELTAB.dotabb>>=
+"ELTAB" [color=lightblue,href="books/bookvol10.pamphlet"];
+"ELTAB" -> "CATEGORY"
+
+@
+<<ELTAB.dotfull>>=
+"Eltable(a:SetCategory,b:Type)"
+ [color=lightblue,href="books/bookvol10.pamphlet"];
+"Eltable(a:SetCategory,b:Type)" -> "Category"
+
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{RetractableTo}{RETRACT}
+\pagepic{ps/v10retractableto.ps}{RETRACT}
+
+See:\\
+\pagefrom{Category}{CATEGORY}
+<<category RETRACT RetractableTo>>=
+)abbrev category RETRACT RetractableTo
+++ Category for retract
+++ Author: ???
+++ Date Created: ???
+++ Date Last Updated: 14 May 1991
+++ Description:
+++ A is retractable to B means that some elementsif A can be converted
+++ into elements of B and any element of B can be converted into an
+++ element of A.
+RetractableTo(S: Type): Category == with
+ coerce: S -> %
+ ++ coerce(a) transforms a into an element of %.
+ retractIfCan: % -> Union(S,"failed")
+ ++ retractIfCan(a) transforms a into an element of S if possible.
+ ++ Returns "failed" if a cannot be made into an element of S.
+ retract: % -> S
+ ++ retract(a) transforms a into an element of S if possible.
+ ++ Error: if a cannot be made into an element of S.
+ add
+ retract(s) ==
+ (u:=retractIfCan s) case "failed" => error "not retractable"
+ u
+
+@
+<<RETRACT.dotabb>>=
+"RETRACT" [color=lightblue,href="books/bookvol10.pamphlet"];
+"RETRACT" -> "CATEGORY"
+
+@
+<<RETRACT.dotfull>>=
+"RetractableTo(a:Type)"
+ [color=lightblue,href="books/bookvol10.pamphlet"];
+"RetractableTo(a:Type)" -> "Category"
+
+"RetractableTo(SetCategory)"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"RetractableTo(SetCategory)" -> "RetractableTo(a:Type)"
+
+"RetractableTo(Symbol)"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"RetractableTo(Symbol)" -> "RetractableTo(a:Type)"
+
+"RetractableTo(Integer)"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"RetractableTo(Integer)" -> "RetractableTo(a:Type)"
+
+"RetractableTo(NonNegativeInteger)"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"RetractableTo(NonNegativeInteger)" -> "RetractableTo(a:Type)"
+
+"RetractableTo(Fraction(Integer))"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"RetractableTo(Fraction(Integer))" -> "RetractableTo(a:Type)"
+
+"RetractableTo(Float)"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"RetractableTo(Float)" -> "RetractableTo(a:Type)"
+
+"RetractableTo(Kernel(ExpressionSpace))"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"RetractableTo(Kernel(ExpressionSpace))" -> "RetractableTo(a:Type)"
+
+"RetractableTo(CommutativeRing)"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"RetractableTo(CommutativeRing)" -> "RetractableTo(a:Type)"
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{Type}{TYPE}
+\pagepic{ps/v10type.ps}{TYPE}
+
+See:\\
+\pageto{Aggregate}{AGG}
+\pagefrom{Category}{CATEGORY}
+<<category TYPE Type>>=
+)abbrev category TYPE Type
+++ The new fundamental Type (keeping Object for 1.5 as well)
+++ Author: Richard Jenks
+++ Date Created: 14 May 1992
+++ Date Last Updated: 14 May 1992
+++ Description: The fundamental Type;
+Type(): Category == with nil
+
+@
+<<TYPE.dotabb>>=
+"TYPE" [color=lightblue,href="books/bookvol10.pamphlet"];
+"TYPE" -> "CATEGORY"
+
+@
+<<TYPE.dotfull>>=
+"Type()" [color=lightblue,href="books/bookvol10.pamphlet"];
+"Type()" -> "Category"
+
+@
+\chapter{Category Layer 2}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{Aggregate}{AGG}
+\pagepic{ps/v10agg.ps}{AGG}
+
+See:\\
+\pageto{HomogeneousAggregate}{HOAGG}
+\pagefrom{Type}{TYPE}
<<category AGG Aggregate>>=
)abbrev category AGG Aggregate
++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
@@ -2047,9 +2344,17 @@
"Aggregate()" -> "Type()"
@
-\section{category ALAGG AssociationListAggregate}
-<<category ALAGG AssociationListAggregate>>=
-)abbrev category ALAGG AssociationListAggregate
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{EltableAggregate}{ELTAGG}
+%\pagepic{ps/v10eltableaggregate.ps}{ELTAGG}
+\includegraphics[scale=0.75]{ps/v10eltableaggregate.ps}
+\index{images!STAGG}
+
+See:\\
+\pageto{IndexedAggregate}{IXAGG}
+\pagefrom{Eltable}{ELTAB}
+<<category ELTAGG EltableAggregate>>=
+)abbrev category ELTAGG EltableAggregate
++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
++ Date Created: August 87 through August 88
++ Date Last Updated: April 1991
@@ -2060,105 +2365,71 @@
++ Keywords:
++ References:
++ Description:
-++ An association list is a list of key entry pairs which may be viewed
-++ as a table. It is a poor mans version of a table:
-++ searching for a key is a linear operation.
-AssociationListAggregate(Key:SetCategory,Entry:SetCategory): Category ==
- Join(TableAggregate(Key, Entry), ListAggregate Record(key:Key,entry:Entry)) with
- assoc: (Key, %) -> Union(Record(key:Key,entry:Entry), "failed")
- ++ assoc(k,u) returns the element x in association list u stored
- ++ with key k, or "failed" if u has no key k.
+++ An eltable aggregate is one which can be viewed as a function.
+++ For example, the list \axiom{[1,7,4]} can applied to 0,1, and 2 respectively
+++ will return the integers 1,7, and 4; thus this list may be viewed
+++ as mapping 0 to 1, 1 to 7 and 2 to 4. In general, an aggregate
+++ can map members of a domain {\em Dom} to an image domain {\em Im}.
+EltableAggregate(Dom:SetCategory, Im:Type): Category ==
+-- This is separated from Eltable
+-- and series won't have to support qelt's and setelt's.
+ Eltable(Dom, Im) with
+ elt : (%, Dom, Im) -> Im
+ ++ elt(u, x, y) applies u to x if x is in the domain of u,
+ ++ and returns y otherwise.
+ ++ For example, if u is a polynomial in \axiom{x} over the rationals,
+ ++ \axiom{elt(u,n,0)} may define the coefficient of \axiom{x}
+ ++ to the power n, returning 0 when n is out of range.
+ qelt: (%, Dom) -> Im
+ ++ qelt(u, x) applies \axiom{u} to \axiom{x} without checking whether
+ ++ \axiom{x} is in the domain of \axiom{u}. If \axiom{x} is not in the
+ ++ domain of \axiom{u} a memory-access violation may occur. If a check
+ ++ on whether \axiom{x} is in the domain of \axiom{u} is required, use
+ ++ the function \axiom{elt}.
+ if % has shallowlyMutable then
+ setelt : (%, Dom, Im) -> Im
+ ++ setelt(u,x,y) sets the image of x to be y under u,
+ ++ assuming x is in the domain of u.
+ ++ Error: if x is not in the domain of u.
+ -- this function will soon be renamed as setelt!.
+ qsetelt_!: (%, Dom, Im) -> Im
+ ++ qsetelt!(u,x,y) sets the image of \axiom{x} to be \axiom{y} under
+ ++ \axiom{u}, without checking that \axiom{x} is in the domain of
+ ++ \axiom{u}.
+ ++ If such a check is required use the function \axiom{setelt}.
+ add
+ qelt(a, x) == elt(a, x)
+ if % has shallowlyMutable then
+ qsetelt_!(a, x, y) == (a.x := y)
@
-<<ALAGG.dotabb>>=
-"ALAGG" [color=lightblue,href="books/bookvol10.pamphlet"];
-"ALAGG" -> "TBAGG"
-"ALAGG" -> "LSAGG"
+<<ELTAGG.dotabb>>=
+"ELTAGG" [color=lightblue,href="books/bookvol10.pamphlet"];
+"ELTAGG" -> "ELTAB"
@
-<<ALAGG.dotfull>>=
-"AssociationListAggregate(a:SetCategory,b:SetCategory)"
+<<ELTAGG.dotfull>>=
+"EltableAggregate(a:SetCategory,b:Type)"
[color=lightblue,href="books/bookvol10.pamphlet"];
-"AssociationListAggregate(a:SetCategory,b:SetCategory)" ->
- "TableAggregate(a:SetCategory,b:SetCategory)"
-"AssociationListAggregate(a:SetCategory,b:SetCategory)" ->
- "ListAggregate(Record(a:SetCategory,b:SetCategory))"
+"EltableAggregate(a:SetCategory,b:Type)" -> "Eltable(a:SetCategory,b:Type)"
@
-\section{ALAGG.lsp BOOTSTRAP}
-{\bf ALAGG} depends on a chain of files. We need to break this cycle to build
-the algebra. So we keep a cached copy of the translated {\bf ALAGG}
-category which we can write into the {\bf MID} directory. We compile
-the lisp code and copy the {\bf ALAGG.o} file to the {\bf OUT} directory.
-This is eventually forcibly replaced by a recompiled version.
+\chapter{Category Layer 3}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{HomogeneousAggregate}{HOAGG}
+\pagepic{ps/v10homogeneousaggregate.ps}{HOAGG}
-Note that this code is not included in the generated catdef.spad file.
-
-<<ALAGG.lsp BOOTSTRAP>>=
-
-(|/VERSIONCHECK| 2)
-
-(SETQ |AssociationListAggregate;CAT| (QUOTE NIL))
-
-(SETQ |AssociationListAggregate;AL| (QUOTE NIL))
-
-(DEFUN |AssociationListAggregate|
- (|&REST| #1=#:G88404 |&AUX| #2=#:G88402)
- (DSETQ #2# #1#)
- (LET (#3=#:G88403)
- (COND
- ((SETQ #3# (|assoc| (|devaluateList| #2#) |AssociationListAggregate;AL|))
- (CDR #3#))
- (T
- (SETQ |AssociationListAggregate;AL|
- (|cons5|
- (CONS
- (|devaluateList| #2#)
- (SETQ #3# (APPLY (FUNCTION |AssociationListAggregate;|) #2#)))
- |AssociationListAggregate;AL|)) #3#))))
-
-(DEFUN |AssociationListAggregate;| (|t#1| |t#2|)
- (PROG (#1=#:G88401)
- (RETURN
- (PROG1
- (LETT #1#
- (|sublisV|
- (PAIR
- (QUOTE (|t#1| |t#2|)) (LIST (|devaluate| |t#1|) (|devaluate| |t#2|)))
- (|sublisV|
- (PAIR
- (QUOTE (#2=#:G88400))
- (LIST (QUOTE (|Record| (|:| |key| |t#1|) (|:| |entry| |t#2|)))))
- (COND
- (|AssociationListAggregate;CAT|)
- ((QUOTE T)
- (LETT |AssociationListAggregate;CAT|
- (|Join|
- (|TableAggregate| (QUOTE |t#1|) (QUOTE |t#2|))
- (|ListAggregate| (QUOTE #2#))
- (|mkCategory|
- (QUOTE |domain|)
- (QUOTE
- (((|assoc|
- ((|Union|
- (|Record| (|:| |key| |t#1|) (|:| |entry| |t#2|)) "failed")
- |t#1| |$|))
- T)))
- NIL (QUOTE NIL) NIL))
- . #3=(|AssociationListAggregate|))))))
- . #3#)
- (SETELT #1# 0
- (LIST
- (QUOTE |AssociationListAggregate|)
- (|devaluate| |t#1|)
- (|devaluate| |t#2|)))))))
-@
-\section{category A1AGG OneDimensionalArrayAggregate}
-<<category A1AGG OneDimensionalArrayAggregate>>=
-)abbrev category A1AGG OneDimensionalArrayAggregate
+See:\\
+\pageto{BagAggregate}{BGAGG}
+\pageto{Collection}{CLAGG}
+\pageto{IndexedAggregate}{IXAGG}
+\pageto{RecursiveAggregate}{RCAGG}
+\pagefrom{Aggregate}{AGG}
+<<category HOAGG HomogeneousAggregate>>=
+)abbrev category HOAGG HomogeneousAggregate
++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
++ Date Created: August 87 through August 88
-++ Date Last Updated: April 1991
+++ Date Last Updated: April 1991, May 1995
++ Basic Operations:
++ Related Constructors:
++ Also See:
@@ -2166,264 +2437,93 @@
++ Keywords:
++ References:
++ Description:
-++ One-dimensional-array aggregates serves as models for one-dimensional arrays.
-++ Categorically, these aggregates are finite linear aggregates
-++ with the \spadatt{shallowlyMutable} property, that is, any component of
-++ the array may be changed without affecting the
-++ identity of the overall array.
-++ Array data structures are typically represented by a fixed area in storage and
-++ therefore cannot efficiently grow or shrink on demand as can list structures
-++ (see however \spadtype{FlexibleArray} for a data structure which
-++ is a cross between a list and an array).
-++ Iteration over, and access to, elements of arrays is extremely fast
-++ (and often can be optimized to open-code).
-++ Insertion and deletion however is generally slow since an entirely new
-++ data structure must be created for the result.
-OneDimensionalArrayAggregate(S:Type): Category ==
- FiniteLinearAggregate S with shallowlyMutable
+++ A homogeneous aggregate is an aggregate of elements all of the
+++ same type.
+++ In the current system, all aggregates are homogeneous.
+++ Two attributes characterize classes of aggregates.
+++ Aggregates from domains with attribute \spadatt{finiteAggregate}
+++ have a finite number of members.
+++ Those with attribute \spadatt{shallowlyMutable} allow an element
+++ to be modified or updated without changing its overall value.
+HomogeneousAggregate(S:Type): Category == Aggregate with
+ if S has SetCategory then SetCategory
+ if S has SetCategory then
+ if S has Evalable S then Evalable S
+ map : (S->S,%) -> %
+ ++ map(f,u) returns a copy of u with each element x replaced by f(x).
+ ++ For collections, \axiom{map(f,u) = [f(x) for x in u]}.
+ if % has shallowlyMutable then
+ map_!: (S->S,%) -> %
+ ++ map!(f,u) destructively replaces each element x of u
+ ++ by \axiom{f(x)}.
+ if % has finiteAggregate then
+ any?: (S->Boolean,%) -> Boolean
+ ++ any?(p,u) tests if \axiom{p(x)} is true for any element x of u.
+ ++ Note: for collections,
+ ++ \axiom{any?(p,u) = reduce(or,map(f,u),false,true)}.
+ every?: (S->Boolean,%) -> Boolean
+ ++ every?(f,u) tests if p(x) is true for all elements x of u.
+ ++ Note: for collections,
+ ++ \axiom{every?(p,u) = reduce(and,map(f,u),true,false)}.
+ count: (S->Boolean,%) -> NonNegativeInteger
+ ++ count(p,u) returns the number of elements x in u
+ ++ such that \axiom{p(x)} is true. For collections,
+ ++ \axiom{count(p,u) = reduce(+,[1 for x in u | p(x)],0)}.
+ parts: % -> List S
+ ++ parts(u) returns a list of the consecutive elements of u.
+ ++ For collections, \axiom{parts([x,y,...,z]) = (x,y,...,z)}.
+ members: % -> List S
+ ++ members(u) returns a list of the consecutive elements of u.
+ ++ For collections, \axiom{parts([x,y,...,z]) = (x,y,...,z)}.
+ if S has SetCategory then
+ count: (S,%) -> NonNegativeInteger
+ ++ count(x,u) returns the number of occurrences of x in u. For
+ ++ collections, \axiom{count(x,u) = reduce(+,[x=y for y in u],0)}.
+ member?: (S,%) -> Boolean
+ ++ member?(x,u) tests if x is a member of u.
+ ++ For collections,
+ ++ \axiom{member?(x,u) = reduce(or,[x=y for y in u],false)}.
add
- parts x == [qelt(x, i) for i in minIndex x .. maxIndex x]
- sort_!(f, a) == quickSort(f, a)$FiniteLinearAggregateSort(S, %)
+ if S has Evalable S then
+ eval(u:%,l:List Equation S):% == map(eval(#1,l),u)
+ if % has finiteAggregate then
+ #c == # parts c
+ any?(f, c) == _or/[f x for x in parts c]
+ every?(f, c) == _and/[f x for x in parts c]
+ count(f:S -> Boolean, c:%) == _+/[1 for x in parts c | f x]
+ members x == parts x
+ if S has SetCategory then
+ count(s:S, x:%) == count(s = #1, x)
+ member?(e, c) == any?(e = #1,c)
+ x = y ==
+ size?(x, #y) and _and/[a = b for a in parts x for b in parts y]
+ coerce(x:%):OutputForm ==
+ bracket
+ commaSeparate [a::OutputForm for a in parts x]$List(OutputForm)
- any?(f, a) ==
- for i in minIndex a .. maxIndex a repeat
- f qelt(a, i) => return true
- false
-
- every?(f, a) ==
- for i in minIndex a .. maxIndex a repeat
- not(f qelt(a, i)) => return false
- true
-
- position(f:S -> Boolean, a:%) ==
- for i in minIndex a .. maxIndex a repeat
- f qelt(a, i) => return i
- minIndex(a) - 1
-
- find(f, a) ==
- for i in minIndex a .. maxIndex a repeat
- f qelt(a, i) => return qelt(a, i)
- "failed"
-
- count(f:S->Boolean, a:%) ==
- n:NonNegativeInteger := 0
- for i in minIndex a .. maxIndex a repeat
- if f(qelt(a, i)) then n := n+1
- n
-
- map_!(f, a) ==
- for i in minIndex a .. maxIndex a repeat
- qsetelt_!(a, i, f qelt(a, i))
- a
-
- setelt(a:%, s:UniversalSegment(Integer), x:S) ==
- l := lo s; h := if hasHi s then hi s else maxIndex a
- l < minIndex a or h > maxIndex a => error "index out of range"
- for k in l..h repeat qsetelt_!(a, k, x)
- x
-
- reduce(f, a) ==
- empty? a => error "cannot reduce an empty aggregate"
- r := qelt(a, m := minIndex a)
- for k in m+1 .. maxIndex a repeat r := f(r, qelt(a, k))
- r
-
- reduce(f, a, identity) ==
- for k in minIndex a .. maxIndex a repeat
- identity := f(identity, qelt(a, k))
- identity
-
- if S has SetCategory then
- reduce(f, a, identity,absorber) ==
- for k in minIndex a .. maxIndex a while identity ^= absorber
- repeat identity := f(identity, qelt(a, k))
- identity
-
--- this is necessary since new has disappeared.
- stupidnew: (NonNegativeInteger, %, %) -> %
- stupidget: List % -> S
--- a and b are not both empty if n > 0
- stupidnew(n, a, b) ==
- zero? n => empty()
- new(n, (empty? a => qelt(b, minIndex b); qelt(a, minIndex a)))
--- at least one element of l must be non-empty
- stupidget l ==
- for a in l repeat
- not empty? a => return first a
- error "Should not happen"
-
- map(f, a, b) ==
- m := max(minIndex a, minIndex b)
- n := min(maxIndex a, maxIndex b)
- l := max(0, n - m + 1)::NonNegativeInteger
- c := stupidnew(l, a, b)
- for i in minIndex(c).. for j in m..n repeat
- qsetelt_!(c, i, f(qelt(a, j), qelt(b, j)))
- c
-
--- map(f, a, b, x) ==
--- m := min(minIndex a, minIndex b)
--- n := max(maxIndex a, maxIndex b)
--- l := (n - m + 1)::NonNegativeInteger
--- c := new l
--- for i in minIndex(c).. for j in m..n repeat
--- qsetelt_!(c, i, f(a(j, x), b(j, x)))
--- c
-
- merge(f, a, b) ==
- r := stupidnew(#a + #b, a, b)
- i := minIndex a
- m := maxIndex a
- j := minIndex b
- n := maxIndex b
- for k in minIndex(r).. while i <= m and j <= n repeat
- if f(qelt(a, i), qelt(b, j)) then
- qsetelt_!(r, k, qelt(a, i))
- i := i+1
- else
- qsetelt_!(r, k, qelt(b, j))
- j := j+1
- for k in k.. for i in i..m repeat qsetelt_!(r, k, elt(a, i))
- for k in k.. for j in j..n repeat qsetelt_!(r, k, elt(b, j))
- r
-
- elt(a:%, s:UniversalSegment(Integer)) ==
- l := lo s
- h := if hasHi s then hi s else maxIndex a
- l < minIndex a or h > maxIndex a => error "index out of range"
- r := stupidnew(max(0, h - l + 1)::NonNegativeInteger, a, a)
- for k in minIndex r.. for i in l..h repeat
- qsetelt_!(r, k, qelt(a, i))
- r
-
- insert(a:%, b:%, i:Integer) ==
- m := minIndex b
- n := maxIndex b
- i < m or i > n => error "index out of range"
- y := stupidnew(#a + #b, a, b)
- for k in minIndex y.. for j in m..i-1 repeat
- qsetelt_!(y, k, qelt(b, j))
- for k in k.. for j in minIndex a .. maxIndex a repeat
- qsetelt_!(y, k, qelt(a, j))
- for k in k.. for j in i..n repeat qsetelt_!(y, k, qelt(b, j))
- y
-
- copy x ==
- y := stupidnew(#x, x, x)
- for i in minIndex x .. maxIndex x for j in minIndex y .. repeat
- qsetelt_!(y, j, qelt(x, i))
- y
-
- copyInto_!(y, x, s) ==
- s < minIndex y or s + #x > maxIndex y + 1 =>
- error "index out of range"
- for i in minIndex x .. maxIndex x for j in s.. repeat
- qsetelt_!(y, j, qelt(x, i))
- y
-
- construct l ==
--- a := new(#l)
- empty? l => empty()
- a := new(#l, first l)
- for i in minIndex(a).. for x in l repeat qsetelt_!(a, i, x)
- a
-
- delete(a:%, s:UniversalSegment(Integer)) ==
- l := lo s; h := if hasHi s then hi s else maxIndex a
- l < minIndex a or h > maxIndex a => error "index out of range"
- h < l => copy a
- r := stupidnew((#a - h + l - 1)::NonNegativeInteger, a, a)
- for k in minIndex(r).. for i in minIndex a..l-1 repeat
- qsetelt_!(r, k, qelt(a, i))
- for k in k.. for i in h+1 .. maxIndex a repeat
- qsetelt_!(r, k, qelt(a, i))
- r
-
- delete(x:%, i:Integer) ==
- i < minIndex x or i > maxIndex x => error "index out of range"
- y := stupidnew((#x - 1)::NonNegativeInteger, x, x)
- for i in minIndex(y).. for j in minIndex x..i-1 repeat
- qsetelt_!(y, i, qelt(x, j))
- for i in i .. for j in i+1 .. maxIndex x repeat
- qsetelt_!(y, i, qelt(x, j))
- y
-
- reverse_! x ==
- m := minIndex x
- n := maxIndex x
- for i in 0..((n-m) quo 2) repeat swap_!(x, m+i, n-i)
- x
-
- concat l ==
- empty? l => empty()
- n := _+/[#a for a in l]
- i := minIndex(r := new(n, stupidget l))
- for a in l repeat
- copyInto_!(r, a, i)
- i := i + #a
- r
-
- sorted?(f, a) ==
- for i in minIndex(a)..maxIndex(a)-1 repeat
- not f(qelt(a, i), qelt(a, i + 1)) => return false
- true
-
- concat(x:%, y:%) ==
- z := stupidnew(#x + #y, x, y)
- copyInto_!(z, x, i := minIndex z)
- copyInto_!(z, y, i + #x)
- z
-
- if S has SetCategory then
- x = y ==
- #x ^= #y => false
- for i in minIndex x .. maxIndex x repeat
- not(qelt(x, i) = qelt(y, i)) => return false
- true
-
- coerce(r:%):OutputForm ==
- bracket commaSeparate
- [qelt(r, k)::OutputForm for k in minIndex r .. maxIndex r]
-
- position(x:S, t:%, s:Integer) ==
- n := maxIndex t
- s < minIndex t or s > n => error "index out of range"
- for k in s..n repeat
- qelt(t, k) = x => return k
- minIndex(t) - 1
-
- if S has OrderedSet then
- a < b ==
- for i in minIndex a .. maxIndex a
- for j in minIndex b .. maxIndex b repeat
- qelt(a, i) ^= qelt(b, j) => return a.i < b.j
- #a < #b
-
-
@
-<<A1AGG.dotabb>>=
-"A1AGG" [color=lightblue,style=filled];
-"A1AGG" -> "FLAGG"
+<<HOAGG.dotabb>>=
+"HOAGG" [color=lightblue,href="books/bookvol10.pamphlet"];
+"HOAGG" -> "AGG"
@
-<<A1AGG.dotfull>>=
-"OneDimensionalArrayAggregate(a:Type)"
+<<HOAGG.dotfull>>=
+"HomogeneousAggregate(a:Type)"
[color=lightblue,href="books/bookvol10.pamphlet"];
-"OneDimensionalArrayAggregate(a:Type)" ->
- "FiniteLinearAggregate(a:Type)"
+"HomogeneousAggregate(a:Type)" -> "Aggregate()"
-"OneDimensionalArrayAggregate(Character)"
- [color=seagreen,href="books/bookvol10.pamphlet"];
-"OneDimensionalArrayAggregate(Character)" ->
- "OneDimensionalArrayAggregate(a:Type)"
+@
+\chapter{Category Layer 4}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{BagAggregate}{BGAGG}
+\pagepic{ps/v10bagaggregate.ps}{BGAGG}
-"OneDimensionalArrayAggregate(Boolean)"
- [color=seagreen,href="books/bookvol10.pamphlet"];
-"OneDimensionalArrayAggregate(Boolean)" ->
- "OneDimensionalArrayAggregate(a:Type)"
-
-@
-\section{category BGAGG BagAggregate}
+See:\\
+\pageto{DictionaryOperations}{DIOPS}
+\pageto{PriorityQueueAggregate}{PRQAGG}
+\pageto{QueueAggregate}{QUAGG}
+\pageto{StackAggregate}{SKAGG}
+\pagefrom{HomogeneousAggregate}{HOAGG}
<<category BGAGG BagAggregate>>=
)abbrev category BGAGG BagAggregate
++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
@@ -2436,13 +2536,14 @@
++ Keywords:
++ References:
++ Description:
-++ A bag aggregate is an aggregate for which one can insert and extract objects,
-++ and where the order in which objects are inserted determines the order
-++ of extraction.
+++ A bag aggregate is an aggregate for which one can insert and extract
+++ objects, and where the order in which objects are inserted determines
+++ the order of extraction.
++ Examples of bags are stacks, queues, and dequeues.
BagAggregate(S:Type): Category == HomogeneousAggregate S with
shallowlyMutable
- ++ shallowlyMutable means that elements of bags may be destructively changed.
+ ++ shallowlyMutable means that elements of bags may be
+ ++ destructively changed.
bag: List S -> %
++ bag([x,y,...,z]) creates a bag with elements x,y,...,z.
extract_!: % -> S
@@ -2471,196 +2572,14 @@
"BagAggregate(a:SetCategory)" -> "BagAggregate(a:Type)"
@
-\section{category BRAGG BinaryRecursiveAggregate}
-<<category BRAGG BinaryRecursiveAggregate>>=
-)abbrev category BRAGG BinaryRecursiveAggregate
-++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
-++ Date Created: August 87 through August 88
-++ Date Last Updated: April 1991
-++ Basic Operations:
-++ Related Constructors:
-++ Also See:
-++ AMS Classifications:
-++ Keywords:
-++ References:
-++ Description:
-++ A binary-recursive aggregate has 0, 1 or 2 children and
-++ serves as a model for a binary tree or a doubly-linked aggregate structure
-BinaryRecursiveAggregate(S:Type):Category == RecursiveAggregate S with
- -- needs preorder, inorder and postorder iterators
- left: % -> %
- ++ left(u) returns the left child.
- elt: (%,"left") -> %
- ++ elt(u,"left") (also written: \axiom{a . left}) is
- ++ equivalent to \axiom{left(a)}.
- right: % -> %
- ++ right(a) returns the right child.
- elt: (%,"right") -> %
- ++ elt(a,"right") (also written: \axiom{a . right})
- ++ is equivalent to \axiom{right(a)}.
- if % has shallowlyMutable then
- setelt: (%,"left",%) -> %
- ++ setelt(a,"left",b) (also written \axiom{a . left := b}) is equivalent
- ++ to \axiom{setleft!(a,b)}.
- setleft_!: (%,%) -> %
- ++ setleft!(a,b) sets the left child of \axiom{a} to be b.
- setelt: (%,"right",%) -> %
- ++ setelt(a,"right",b) (also written \axiom{b . right := b})
- ++ is equivalent to \axiom{setright!(a,b)}.
- setright_!: (%,%) -> %
- ++ setright!(a,x) sets the right child of t to be x.
- add
- cycleMax ==> 1000
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{Collection}{CLAGG}
+\pagepic{ps/v10collection.ps}{CLAGG}
- elt(x,"left") == left x
- elt(x,"right") == right x
- leaf? x == empty? x or empty? left x and empty? right x
- leaves t ==
- empty? t => empty()$List(S)
- leaf? t => [value t]
- concat(leaves left t,leaves right t)
- nodes x ==
- l := empty()$List(%)
- empty? x => l
- concat(nodes left x,concat([x],nodes right x))
- children x ==
- l := empty()$List(%)
- empty? x => l
- empty? left x => [right x]
- empty? right x => [left x]
- [left x, right x]
- if % has SetAggregate(S) and S has SetCategory then
- node?(u,v) ==
- empty? v => false
- u = v => true
- for y in children v repeat node?(u,y) => return true
- false
- x = y ==
- empty?(x) => empty?(y)
- empty?(y) => false
- value x = value y and left x = left y and right x = right y
- if % has finiteAggregate then
- member?(x,u) ==
- empty? u => false
- x = value u => true
- member?(x,left u) or member?(x,right u)
-
- if S has SetCategory then
- coerce(t:%): OutputForm ==
- empty? t => "[]"::OutputForm
- v := value(t):: OutputForm
- empty? left t =>
- empty? right t => v
- r := coerce(right t)@OutputForm
- bracket ["."::OutputForm, v, r]
- l := coerce(left t)@OutputForm
- r :=
- empty? right t => "."::OutputForm
- coerce(right t)@OutputForm
- bracket [l, v, r]
-
- if % has finiteAggregate then
- aggCount: (%,NonNegativeInteger) -> NonNegativeInteger
- #x == aggCount(x,0)
- aggCount(x,k) ==
- empty? x => 0
- k := k + 1
- k = cycleMax and cyclic? x => error "cyclic tree"
- for y in children x repeat k := aggCount(y,k)
- k
-
- isCycle?: (%, List %) -> Boolean
- eqMember?: (%, List %) -> Boolean
- cyclic? x == not empty? x and isCycle?(x,empty()$(List %))
- isCycle?(x,acc) ==
- empty? x => false
- eqMember?(x,acc) => true
- for y in children x | not empty? y repeat
- isCycle?(y,acc) => return true
- false
- eqMember?(y,l) ==
- for x in l repeat eq?(x,y) => return true
- false
- if % has shallowlyMutable then
- setelt(x,"left",b) == setleft_!(x,b)
- setelt(x,"right",b) == setright_!(x,b)
-
-@
-<<BRAGG.dotabb>>=
-"BRAGG" [color=lightblue,href="books/bookvol10.pamphlet"];
-"BRAGG" -> "RCAGG"
-
-@
-<<BRAGG.dotfull>>=
-"BinaryRecursiveAggregate(a:Type)"
- [color=lightblue,href="books/bookvol10.pamphlet"];
-"BinaryRecursiveAggregate(a:Type)" -> "RecursiveAggregate(a:Type)"
-
-@
-\section{category BTAGG BitAggregate}
-<<category BTAGG BitAggregate>>=
-)abbrev category BTAGG BitAggregate
-++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
-++ Date Created: August 87 through August 88
-++ Date Last Updated: April 1991
-++ Basic Operations:
-++ Related Constructors:
-++ Also See:
-++ AMS Classifications:
-++ Keywords:
-++ References:
-++ Description:
-++ The bit aggregate category models aggregates representing large
-++ quantities of Boolean data.
-BitAggregate(): Category ==
- Join(OrderedSet, Logic, OneDimensionalArrayAggregate Boolean) with
- "not": % -> %
- ++ not(b) returns the logical {\em not} of bit aggregate
- ++ \axiom{b}.
- "^" : % -> %
- ++ ^ b returns the logical {\em not} of bit aggregate
- ++ \axiom{b}.
- nand : (%, %) -> %
- ++ nand(a,b) returns the logical {\em nand} of bit aggregates \axiom{a}
- ++ and \axiom{b}.
- nor : (%, %) -> %
- ++ nor(a,b) returns the logical {\em nor} of bit aggregates \axiom{a} and
- ++ \axiom{b}.
- _and : (%, %) -> %
- ++ a and b returns the logical {\em and} of bit aggregates \axiom{a} and
- ++ \axiom{b}.
- _or : (%, %) -> %
- ++ a or b returns the logical {\em or} of bit aggregates \axiom{a} and
- ++ \axiom{b}.
- xor : (%, %) -> %
- ++ xor(a,b) returns the logical {\em exclusive-or} of bit aggregates
- ++ \axiom{a} and \axiom{b}.
-
- add
- not v == map(_not, v)
- _^ v == map(_not, v)
- _~(v) == map(_~, v)
- _/_\(v, u) == map(_/_\, v, u)
- _\_/(v, u) == map(_\_/, v, u)
- nand(v, u) == map(nand, v, u)
- nor(v, u) == map(nor, v, u)
-
-@
-<<BTAGG.dotabb>>=
-"BTAGG" [color=lightblue,href="books/bookvol10.pamphlet"];
-"BTAGG" -> "ORDSET"
-"BTAGG" -> "LOGIC"
-"BTAGG" -> "A1AGG"
-
-@
-<<BTAGG.dotfull>>=
-"BitAggregate()" [color=lightblue,href="books/bookvol10.pamphlet"];
-"BitAggregate()" -> "OrderedSet()"
-"BitAggregate()" -> "Logic()"
-"BitAggregate()" -> "OneDimensionalArrayAggregate(Boolean)"
-
-@
-\section{category CLAGG Collection}
+See:\\
+\pageto{DictionaryOperations}{DIOPS}
+\pageto{LinearAggregate}{LNAGG}
+\pagefrom{HomogeneousAggregate}{HOAGG}
<<category CLAGG Collection>>=
)abbrev category CLAGG Collection
++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
@@ -2682,8 +2601,9 @@
++ \spadfun{flexibleArray} for \spadtype{FlexibleArray}, and so on.
Collection(S:Type): Category == HomogeneousAggregate(S) with
construct: List S -> %
- ++ \axiom{construct(x,y,...,z)} returns the collection of elements \axiom{x,y,...,z}
- ++ ordered as given. Equivalently written as \axiom{[x,y,...,z]$D}, where
+ ++ \axiom{construct(x,y,...,z)} returns the collection of elements
+ ++ \axiom{x,y,...,z} ordered as given. Equivalently written as
+ ++ \axiom{[x,y,...,z]$D}, where
++ D is the domain. D may be omitted for those of type List.
find: (S->Boolean, %) -> Union(S, "failed")
++ find(p,u) returns the first x in u such that \axiom{p(x)} is true, and
@@ -2727,7 +2647,8 @@
++ elements \axiom{y = x} removed.
++ Note: \axiom{remove(y,c) == [x for x in c | x ^= y]}.
removeDuplicates: % -> %
- ++ removeDuplicates(u) returns a copy of u with all duplicates removed.
+ ++ removeDuplicates(u) returns a copy of u with all duplicates
+ ++ removed.
if S has ConvertibleTo InputForm then ConvertibleTo InputForm
add
if % has finiteAggregate then
@@ -2760,74 +2681,224 @@
"Collection(a:SetCategory)" [color=seagreen,href="books/bookvol10.pamphlet"];
"Collection(a:SetCategory)" -> "Collection(a:Type)"
-@
-\section{CLAGG.lsp BOOTSTRAP}
-{\bf CLAGG} depends on a chain of files. We need to break this cycle to build
-the algebra. So we keep a cached copy of the translated {\bf CLAGG}
-category which we can write into the {\bf MID} directory. We compile
-the lisp code and copy the {\bf CLAGG.o} file to the {\bf OUT} directory.
-This is eventually forcibly replaced by a recompiled version.
-Note that this code is not included in the generated catdef.spad file.
-
-<<CLAGG.lsp BOOTSTRAP>>=
-
-(|/VERSIONCHECK| 2)
-
-(SETQ |Collection;CAT| (QUOTE NIL))
-
-(SETQ |Collection;AL| (QUOTE NIL))
-
-(DEFUN |Collection| (#1=#:G82618) (LET (#2=#:G82619) (COND ((SETQ #2# (|assoc| (|devaluate| #1#) |Collection;AL|)) (CDR #2#)) (T (SETQ |Collection;AL| (|cons5| (CONS (|devaluate| #1#) (SETQ #2# (|Collection;| #1#))) |Collection;AL|)) #2#))))
-
-(DEFUN |Collection;| (|t#1|) (PROG (#1=#:G82617) (RETURN (PROG1 (LETT #1# (|sublisV| (PAIR (QUOTE (|t#1|)) (LIST (|devaluate| |t#1|))) (COND (|Collection;CAT|) ((QUOTE T) (LETT |Collection;CAT| (|Join| (|HomogeneousAggregate| (QUOTE |t#1|)) (|mkCategory| (QUOTE |domain|) (QUOTE (((|construct| (|$| (|List| |t#1|))) T) ((|find| ((|Union| |t#1| "failed") (|Mapping| (|Boolean|) |t#1|) |$|)) T) ((|reduce| (|t#1| (|Mapping| |t#1| |t#1| |t#1|) |$|)) (|has| |$| (ATTRIBUTE |finiteAggregate|))) ((|reduce| (|t#1| (|Mapping| |t#1| |t#1| |t#1|) |$| |t#1|)) (|has| |$| (ATTRIBUTE |finiteAggregate|))) ((|remove| (|$| (|Mapping| (|Boolean|) |t#1|) |$|)) (|has| |$| (ATTRIBUTE |finiteAggregate|))) ((|select| (|$| (|Mapping| (|Boolean|) |t#1|) |$|)) (|has| |$| (ATTRIBUTE |finiteAggregate|))) ((|reduce| (|t#1| (|Mapping| |t#1| |t#1| |t#1|) |$| |t#1| |t#1|)) (AND (|has| |t#1| (|SetCategory|)) (|has| |$| (ATTRIBUTE |finiteAggregate|)))) ((|remove| (|$| |t#1| |$|)) (AND (|has| |t#1| (|SetCategory|)) (|has| |$| (ATTRIBUTE |finiteAggregate|)))) ((|removeDuplicates| (|$| |$|)) (AND (|has| |t#1| (|SetCategory|)) (|has| |$| (ATTRIBUTE |finiteAggregate|)))))) (QUOTE (((|ConvertibleTo| (|InputForm|)) (|has| |t#1| (|ConvertibleTo| (|InputForm|)))))) (QUOTE ((|List| |t#1|))) NIL)) . #2=(|Collection|))))) . #2#) (SETELT #1# 0 (LIST (QUOTE |Collection|) (|devaluate| |t#1|)))))))
@
-\section{CLAGG-.lsp BOOTSTRAP}
-{\bf CLAGG-} depends on {\bf CLAGG}. We need to break this cycle to build
-the algebra. So we keep a cached copy of the translated {\bf CLAGG-}
-category which we can write into the {\bf MID} directory. We compile
-the lisp code and copy the {\bf CLAGG-.o} file to the {\bf OUT} directory.
-This is eventually forcibly replaced by a recompiled version.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{IndexedAggregate}{IXAGG}
+\pagepic{ps/v10indexedaggregate.ps}{IXAGG}
-Note that this code is not included in the generated catdef.spad file.
+See:\\
+\pageto{LinearAggregate}{LNAGG}
+\pageto{TableAggregate}{TBAGG}
+\pagefrom{EltableAggregate}{ELTAGG}
+\pagefrom{HomogeneousAggregate}{HOAGG}
+<<category IXAGG IndexedAggregate>>=
+)abbrev category IXAGG IndexedAggregate
+++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
+++ Date Created: August 87 through August 88
+++ Date Last Updated: April 1991
+++ Basic Operations:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++ An indexed aggregate is a many-to-one mapping of indices to entries.
+++ For example, a one-dimensional-array is an indexed aggregate where
+++ the index is an integer. Also, a table is an indexed aggregate
+++ where the indices and entries may have any type.
+IndexedAggregate(Index: SetCategory, Entry: Type): Category ==
+ Join(HomogeneousAggregate(Entry), EltableAggregate(Index, Entry)) with
+ entries: % -> List Entry
+ ++ entries(u) returns a list of all the entries of aggregate u
+ ++ in no assumed order.
+ -- to become entries: % -> Entry* and entries: % -> Iterator(Entry,Entry)
+ index?: (Index,%) -> Boolean
+ ++ index?(i,u) tests if i is an index of aggregate u.
+ indices: % -> List Index
+ ++ indices(u) returns a list of indices of aggregate u in no
+ ++ particular order. to become indices:
+ -- % -> Index* and indices: % -> Iterator(Index,Index).
+-- map: ((Entry,Entry)->Entry,%,%,Entry) -> %
+-- ++ exists c = map(f,a,b,x), i:Index where
+-- ++ c.i = f(a(i,x),b(i,x)) | index?(i,a) or index?(i,b)
+ if Entry has SetCategory and % has finiteAggregate then
+ entry?: (Entry,%) -> Boolean
+ ++ entry?(x,u) tests if x equals \axiom{u . i} for some index i.
+ if Index has OrderedSet then
+ maxIndex: % -> Index
+ ++ maxIndex(u) returns the maximum index i of aggregate u.
+ ++ Note: in general,
+ ++ \axiom{maxIndex(u) = reduce(max,[i for i in indices u])};
+ ++ if u is a list, \axiom{maxIndex(u) = #u}.
+ minIndex: % -> Index
+ ++ minIndex(u) returns the minimum index i of aggregate u.
+ ++ Note: in general,
+ ++ \axiom{minIndex(a) = reduce(min,[i for i in indices a])};
+ ++ for lists, \axiom{minIndex(a) = 1}.
+ first : % -> Entry
+ ++ first(u) returns the first element x of u.
+ ++ Note: for collections, \axiom{first([x,y,...,z]) = x}.
+ ++ Error: if u is empty.
-<<CLAGG-.lsp BOOTSTRAP>>=
+ if % has shallowlyMutable then
+ fill_!: (%,Entry) -> %
+ ++ fill!(u,x) replaces each entry in aggregate u by x.
+ ++ The modified u is returned as value.
+ swap_!: (%,Index,Index) -> Void
+ ++ swap!(u,i,j) interchanges elements i and j of aggregate u.
+ ++ No meaningful value is returned.
+ add
+ elt(a, i, x) == (index?(i, a) => qelt(a, i); x)
-(|/VERSIONCHECK| 2)
+ if % has finiteAggregate then
+ entries x == parts x
+ if Entry has SetCategory then
+ entry?(x, a) == member?(x, a)
-(DEFUN |CLAGG-;#;ANni;1| (|c| |$|) (LENGTH (SPADCALL |c| (QREFELT |$| 9))))
+ if Index has OrderedSet then
+ maxIndex a == "max"/indices(a)
+ minIndex a == "min"/indices(a)
+ first a == a minIndex a
-(DEFUN |CLAGG-;count;MANni;2| (|f| |c| |$|) (PROG (|x| #1=#:G82637 #2=#:G82634 #3=#:G82632 #4=#:G82633) (RETURN (SEQ (PROGN (LETT #4# NIL |CLAGG-;count;MANni;2|) (SEQ (LETT |x| NIL |CLAGG-;count;MANni;2|) (LETT #1# (SPADCALL |c| (QREFELT |$| 9)) |CLAGG-;count;MANni;2|) G190 (COND ((OR (ATOM #1#) (PROGN (LETT |x| (CAR #1#) |CLAGG-;count;MANni;2|) NIL)) (GO G191))) (SEQ (EXIT (COND ((SPADCALL |x| |f|) (PROGN (LETT #2# 1 |CLAGG-;count;MANni;2|) (COND (#4# (LETT #3# (|+| #3# #2#) |CLAGG-;count;MANni;2|)) ((QUOTE T) (PROGN (LETT #3# #2# |CLAGG-;count;MANni;2|) (LETT #4# (QUOTE T) |CLAGG-;count;MANni;2|))))))))) (LETT #1# (CDR #1#) |CLAGG-;count;MANni;2|) (GO G190) G191 (EXIT NIL)) (COND (#4# #3#) ((QUOTE T) 0)))))))
+ if % has shallowlyMutable then
+ map(f, a) == map_!(f, copy a)
-(DEFUN |CLAGG-;any?;MAB;3| (|f| |c| |$|) (PROG (|x| #1=#:G82642 #2=#:G82640 #3=#:G82638 #4=#:G82639) (RETURN (SEQ (PROGN (LETT #4# NIL |CLAGG-;any?;MAB;3|) (SEQ (LETT |x| NIL |CLAGG-;any?;MAB;3|) (LETT #1# (SPADCALL |c| (QREFELT |$| 9)) |CLAGG-;any?;MAB;3|) G190 (COND ((OR (ATOM #1#) (PROGN (LETT |x| (CAR #1#) |CLAGG-;any?;MAB;3|) NIL)) (GO G191))) (SEQ (EXIT (PROGN (LETT #2# (SPADCALL |x| |f|) |CLAGG-;any?;MAB;3|) (COND (#4# (LETT #3# (COND (#3# (QUOTE T)) ((QUOTE T) #2#)) |CLAGG-;any?;MAB;3|)) ((QUOTE T) (PROGN (LETT #3# #2# |CLAGG-;any?;MAB;3|) (LETT #4# (QUOTE T) |CLAGG-;any?;MAB;3|))))))) (LETT #1# (CDR #1#) |CLAGG-;any?;MAB;3|) (GO G190) G191 (EXIT NIL)) (COND (#4# #3#) ((QUOTE T) (QUOTE NIL))))))))
+ map_!(f, a) ==
+ for i in indices a repeat qsetelt_!(a, i, f qelt(a, i))
+ a
-(DEFUN |CLAGG-;every?;MAB;4| (|f| |c| |$|) (PROG (|x| #1=#:G82647 #2=#:G82645 #3=#:G82643 #4=#:G82644) (RETURN (SEQ (PROGN (LETT #4# NIL |CLAGG-;every?;MAB;4|) (SEQ (LETT |x| NIL |CLAGG-;every?;MAB;4|) (LETT #1# (SPADCALL |c| (QREFELT |$| 9)) |CLAGG-;every?;MAB;4|) G190 (COND ((OR (ATOM #1#) (PROGN (LETT |x| (CAR #1#) |CLAGG-;every?;MAB;4|) NIL)) (GO G191))) (SEQ (EXIT (PROGN (LETT #2# (SPADCALL |x| |f|) |CLAGG-;every?;MAB;4|) (COND (#4# (LETT #3# (COND (#3# #2#) ((QUOTE T) (QUOTE NIL))) |CLAGG-;every?;MAB;4|)) ((QUOTE T) (PROGN (LETT #3# #2# |CLAGG-;every?;MAB;4|) (LETT #4# (QUOTE T) |CLAGG-;every?;MAB;4|))))))) (LETT #1# (CDR #1#) |CLAGG-;every?;MAB;4|) (GO G190) G191 (EXIT NIL)) (COND (#4# #3#) ((QUOTE T) (QUOTE T))))))))
+ fill_!(a, x) ==
+ for i in indices a repeat qsetelt_!(a, i, x)
+ a
-(DEFUN |CLAGG-;find;MAU;5| (|f| |c| |$|) (SPADCALL |f| (SPADCALL |c| (QREFELT |$| 9)) (QREFELT |$| 18)))
+ swap_!(a, i, j) ==
+ t := a.i
+ qsetelt_!(a, i, a.j)
+ qsetelt_!(a, j, t)
+ void
-(DEFUN |CLAGG-;reduce;MAS;6| (|f| |x| |$|) (SPADCALL |f| (SPADCALL |x| (QREFELT |$| 9)) (QREFELT |$| 21)))
+@
+<<IXAGG.dotabb>>=
+"IXAGG" [color=lightblue,href="books/bookvol10.pamphlet"];
+"IXAGG" -> "HOAGG"
+"IXAGG" -> "ELTAGG"
-(DEFUN |CLAGG-;reduce;MA2S;7| (|f| |x| |s| |$|) (SPADCALL |f| (SPADCALL |x| (QREFELT |$| 9)) |s| (QREFELT |$| 23)))
+@
+<<IXAGG.dotfull>>=
+"IndexedAggregate(a:SetCategory,b:Type)"
+ [color=lightblue,href="books/bookvol10.pamphlet"];
+"IndexedAggregate(a:SetCategory,b:Type)" ->
+ "HomogeneousAggregate(a:Type)"
+"IndexedAggregate(a:SetCategory,b:Type)" ->
+ "EltableAggregate(a:SetCategory,b:Type)"
-(DEFUN |CLAGG-;remove;M2A;8| (|f| |x| |$|) (SPADCALL (SPADCALL |f| (SPADCALL |x| (QREFELT |$| 9)) (QREFELT |$| 25)) (QREFELT |$| 26)))
+"IndexedAggregate(a:SetCategory,b:SetCategory)"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"IndexedAggregate(a:SetCategory,b:SetCategory)" ->
+ "IndexedAggregate(a:SetCategory,b:Type)"
-(DEFUN |CLAGG-;select;M2A;9| (|f| |x| |$|) (SPADCALL (SPADCALL |f| (SPADCALL |x| (QREFELT |$| 9)) (QREFELT |$| 28)) (QREFELT |$| 26)))
+"IndexedAggregate(b:Integer,a:Type)"
+ [color=seagreen,href="books/bookvol10.pamphlet"];
+"IndexedAggregate(b:Integer,a:Type)" ->
+ "IndexedAggregate(a:SetCategory,b:Type)"
-(DEFUN |CLAGG-;remove;S2A;10| (|s| |x| |$|) (SPADCALL (CONS (FUNCTION |CLAGG-;remove;S2A;10!0|) (VECTOR |$| |s|)) |x| (QREFELT |$| 31)))
+@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{RecursiveAggregate}{RCAGG}
+\pagepic{ps/v10recursiveaggregate.ps}{RCAGG}
-(DEFUN |CLAGG-;remove;S2A;10!0| (|#1| |$$|) (SPADCALL |#1| (QREFELT |$$| 1) (QREFELT (QREFELT |$$| 0) 30)))
+See:\\
+\pageto{BinaryRecursiveAggregate}{BRAGG}
+\pageto{DoublyLinkedAggregate}{DLAGG}
+\pageto{StreamAggregate}{STAGG}
+\pageto{UnaryRecursiveAggregate}{URAGG}
+\pagefrom{HomogeneousAggregate}{HOAGG}
+<<category RCAGG RecursiveAggregate>>=
+)abbrev category RCAGG RecursiveAggregate
+++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
+++ Date Created: August 87 through August 88
+++ Date Last Updated: April 1991
+++ Basic Operations:
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++ A recursive aggregate over a type S is a model for a
+++ a directed graph containing values of type S.
+++ Recursively, a recursive aggregate is a {\em node}
+++ consisting of a \spadfun{value} from S and 0 or more \spadfun{children}
+++ which are recursive aggregates.
+++ A node with no children is called a \spadfun{leaf} node.
+++ A recursive aggregate may be cyclic for which some operations as noted
+++ may go into an infinite loop.
+RecursiveAggregate(S:Type): Category == HomogeneousAggregate(S) with
+ children: % -> List %
+ ++ children(u) returns a list of the children of aggregate u.
+ -- should be % -> %* and also needs children: % -> Iterator(S,S)
+ nodes: % -> List %
+ ++ nodes(u) returns a list of all of the nodes of aggregate u.
+ -- to become % -> %* and also nodes: % -> Iterator(S,S)
+ leaf?: % -> Boolean
+ ++ leaf?(u) tests if u is a terminal node.
+ value: % -> S
+ ++ value(u) returns the value of the node u.
+ elt: (%,"value") -> S
+ ++ elt(u,"value") (also written: \axiom{a. value}) is
+ ++ equivalent to \axiom{value(a)}.
+ cyclic?: % -> Boolean
+ ++ cyclic?(u) tests if u has a cycle.
+ leaves: % -> List S
+ ++ leaves(t) returns the list of values in obtained by visiting the
+ ++ nodes of tree \axiom{t} in left-to-right order.
+ distance: (%,%) -> Integer
+ ++ distance(u,v) returns the path length (an integer) from node u to v.
+ if S has SetCategory then
+ child?: (%,%) -> Boolean
+ ++ child?(u,v) tests if node u is a child of node v.
+ node?: (%,%) -> Boolean
+ ++ node?(u,v) tests if node u is contained in node v
+ ++ (either as a child, a child of a child, etc.).
+ if % has shallowlyMutable then
+ setchildren_!: (%,List %)->%
+ ++ setchildren!(u,v) replaces the current children of node u
+ ++ with the members of v in left-to-right order.
+ setelt: (%,"value",S) -> S
+ ++ setelt(a,"value",x) (also written \axiom{a . value := x})
+ ++ is equivalent to \axiom{setvalue!(a,x)}
+ setvalue_!: (%,S) -> S
+ ++ setvalue!(u,x) sets the value of node u to x.
+ add
+ elt(x,"value") == value x
+ if % has shallowlyMutable then
+ setelt(x,"value",y) == setvalue_!(x,y)
+ if S has SetCategory then
+ child?(x,l) == member?(x,children(l))
-(DEFUN |CLAGG-;reduce;MA3S;11| (|f| |x| |s1| |s2| |$|) (SPADCALL |f| (SPADCALL |x| (QREFELT |$| 9)) |s1| |s2| (QREFELT |$| 33)))
+@
+<<RCAGG.dotabb>>=
+"RCAGG" [color=lightblue,href="books/bookvol10.pamphlet"];
+"RCAGG" -> "HOAGG"
-(DEFUN |CLAGG-;removeDuplicates;2A;12| (|x| |$|) (SPADCALL (SPADCALL (SPADCALL |x| (QREFELT |$| 9)) (QREFELT |$| 35)) (QREFELT |$| 26)))
+@
+<<RCAGG.dotfull>>=
+"RecursiveAggregate(a:Type)"
+ [color=lightblue,href="books/bookvol10.pamphlet"];
+"RecursiveAggregate(a:Type)" -> "HomogeneousAggregate(a:Type)"
-(DEFUN |Collection&| (|#1| |#2|) (PROG (|DV$1| |DV$2| |dv$| |$| |pv$|) (RETURN (PROGN (LETT |DV$1| (|devaluate| |#1|) . #1=(|Collection&|)) (LETT |DV$2| (|devaluate| |#2|) . #1#) (LETT |dv$| (LIST (QUOTE |Collection&|) |DV$1| |DV$2|) . #1#) (LETT |$| (GETREFV 37) . #1#) (QSETREFV |$| 0 |dv$|) (QSETREFV |$| 3 (LETT |pv$| (|buildPredVector| 0 0 (LIST (|HasCategory| |#2| (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| |#2| (QUOTE (|SetCategory|))) (|HasAttribute| |#1| (QUOTE |finiteAggregate|)))) . #1#)) (|stuffDomainSlots| |$|) (QSETREFV |$| 6 |#1|) (QSETREFV |$| 7 |#2|) (COND ((|testBitVector| |pv$| 3) (PROGN (QSETREFV |$| 11 (CONS (|dispatchFunction| |CLAGG-;#;ANni;1|) |$|)) (QSETREFV |$| 13 (CONS (|dispatchFunction| |CLAGG-;count;MANni;2|) |$|)) (QSETREFV |$| 15 (CONS (|dispatchFunction| |CLAGG-;any?;MAB;3|) |$|)) (QSETREFV |$| 16 (CONS (|dispatchFunction| |CLAGG-;every?;MAB;4|) |$|)) (QSETREFV |$| 19 (CONS (|dispatchFunction| |CLAGG-;find;MAU;5|) |$|)) (QSETREFV |$| 22 (CONS (|dispatchFunction| |CLAGG-;reduce;MAS;6|) |$|)) (QSETREFV |$| 24 (CONS (|dispatchFunction| |CLAGG-;reduce;MA2S;7|) |$|)) (QSETREFV |$| 27 (CONS (|dispatchFunction| |CLAGG-;remove;M2A;8|) |$|)) (QSETREFV |$| 29 (CONS (|dispatchFunction| |CLAGG-;select;M2A;9|) |$|)) (COND ((|testBitVector| |pv$| 2) (PROGN (QSETREFV |$| 32 (CONS (|dispatchFunction| |CLAGG-;remove;S2A;10|) |$|)) (QSETREFV |$| 34 (CONS (|dispatchFunction| |CLAGG-;reduce;MA3S;11|) |$|)) (QSETREFV |$| 36 (CONS (|dispatchFunction| |CLAGG-;removeDuplicates;2A;12|) |$|)))))))) |$|))))
+@
+\chapter{Category Layer 5}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagehead{BinaryRecursiveAggregate}{BRAGG}
+\pagepic{ps/v10binaryrecursiveaggregate.ps}{BRAGG}
-(MAKEPROP (QUOTE |Collection&|) (QUOTE |infovec|) (LIST (QUOTE #(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|local| |#2|) (|List| 7) (0 . |parts|) (|NonNegativeInteger|) (5 . |#|) (|Mapping| 14 7) (10 . |count|) (|Boolean|) (16 . |any?|) (22 . |every?|) (|Union| 7 (QUOTE "failed")) (28 . |find|) (34 . |find|) (|Mapping| 7 7 7) (40 . |reduce|) (46 . |reduce|) (52 . |reduce|) (59 . |reduce|) (66 . |remove|) (72 . |construct|) (77 . |remove|) (83 . |select|) (89 . |select|) (95 . |=|) (101 . |remove|) (107 . |remove|) (113 . |reduce|) (121 . |reduce|) (129 . |removeDuplicates|) (134 . |removeDuplicates|))) (QUOTE #(|select| 139 |removeDuplicates| 145 |remove| 150 |reduce| 162 |find| 183 |every?| 189 |count| 195 |any?| 201 |#| 207)) (QUOTE NIL) (CONS (|makeByteWordVec2| 1 (QUOTE NIL)) (CONS (QUOTE #()) (CONS (QUOTE #()) (|makeByteWordVec2| 36 (QUOTE (1 6 8 0 9 1 0 10 0 11 2 0 10 12 0 13 2 0 14 12 0 15 2 0 14 12 0 16 2 8 17 12 0 18 2 0 17 12 0 19 2 8 7 20 0 21 2 0 7 20 0 22 3 8 7 20 0 7 23 3 0 7 20 0 7 24 2 8 0 12 0 25 1 6 0 8 26 2 0 0 12 0 27 2 8 0 12 0 28 2 0 0 12 0 29 2 7 14 0 0 30 2 6 0 12 0 31 2 0 0 7 0 32 4 8 7 20 0 7 7 33 4 0 7 20 0 7 7 34 1 8 0 0 35 1 0 0 0 36 2 0 0 12 0 29 1 0 0 0 36 2 0 0 7 0 32 2 0 0 12 0 27 4 0 7 20 0 7 7 34 3 0 7 20 0 7 24 2 0 7 20 0 22 2 0 17 12 0 19 2 0 14 12 0 16 2 0 10 12 0 13 2 0 14 12 0 15 1 0 10 0 11)))))) (QUOTE |lookupComplete|)))
-@
-\section{category DIAGG Dictionary}
-<<category DIAGG Dictionary>>=
-)abbrev category DIAGG Dictionary
+See:\\
+\pagefrom{RecursiveAggregate}{RCAGG}
+<<category BRAGG BinaryRecursiveAggregate>>=
+)abbrev category BRAGG BinaryRecursiveAggregate
++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
++ Date Created: August 87 through August 88
++ Date Last Updated: April 1991
@@ -2838,54 +2909,128 @@
++ Keywords:
++ References:
++ Description:
-++ A dictionary is an aggregate in which entries can be inserted,
-++ searched for and removed. Duplicates are thrown away on insertion.
-++ This category models the usual notion of dictionary which involves
-++ large amounts of data where copying is impractical.
-++ Principal operations are thus destructive (non-copying) ones.
-Dictionary(S:SetCategory): Category ==
- DictionaryOperations S add
- dictionary l ==
- d := dictionary()
- for x in l repeat insert_!(x, d)
- d
+++ A binary-recursive aggregate has 0, 1 or 2 children and
+++ serves as a model for a binary tree or a doubly-linked aggregate structure
+BinaryRecursiveAggregate(S:Type):Category == RecursiveAggregate S with
+ -- needs preorder, inorder and postorder iterators
+ left: % -> %
+ ++ left(u) returns the left child.
+ elt: (%,"left") -> %
+ ++ elt(u,"left") (also written: \axiom{a . ...
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