smib Files

In this version :
 - some bugs corrected 
 - lsmib is back (lost in last version)
 - new function integration : "generic" form of exp and log
   (cf. smib-0.46/documentation/application/Performance/tutorial-v2 end of section "* II.ii.4.b * antiderivative")

V 0.44 :
 - new factorization function (fact(A,x))
 - new simplification function (simp(A,x))
 - new function integration

V 0.44 :
 - smib & embarrassingly parallel computation 

V 0.43 :
 - Makefile installs components to /usr/local/
 - LaTeX file generator :
   - better latexify function 
   - better documentation 
   - bug correction 

V 0.42 :
 - LaTeX file generator :
   - table of contents 
   - table of figures 
   - better latexify function 

V 0.41 : 
 - LaTeX file generator : 
   - better latexify function 
   - some new examples 

V 0.40 : 
 - LaTeX file generator 
 - antider : some new integrals handled using new simplification procedure 
   - integral function : 
     - exponential 
     - logarithm 
     - sinus 
     - cosinus 
     
V 0.39 : 
 - Functions of matrix : Kronecker sum & product, some applications dealing with commutator or anticommutator 
 - antider : some new integrals handled 
 - Laplace transform (& inverse) : basic version 

V 0.38 :
 - Variational calculus : Euler-Lagrange operator
 - Functions of matrix : exponential, logarithm
 - System of ordinary linear differential equations  
 - antider : some new integrals handled (if versionint=5 it may give interesting result or infinite loop)

V 0.37 :
 - odesolve : automatic computation of particular solution, when it is possible.
 - antider : some new integrals handled
 - Sylvester matrix and new computation for resultant
 - PDE simulation : bug correction
 - limit : bug correction

V 0.36 :
 - PDE simulation using SDE and Feynman-Kac formula : 1D & 2D
 - Graph : number of connected components
 - Weyl sum : some plottings
 - Bugs correction

V 0.35 :
 - partial differential equation simulation using stochastic differential equation and Feynman-Kac formula

V 0.34 :
  - Differential operators in orthogonal system of coordinates
  - Gosper algorithm : antidifference
  - antiderivative : new version
  - bugs correction

V 0.33 :
  - propositional logic : operators, truth table, tautology, antilogy
  - 60 seconds in a minute, why ?
  - on nonassociativity and Jacobi identity

V 0.32 :
 - What can we do with euclidean division of polynomial :
   * GCD 
   * polynomial equations
   * modular inversion
   * chinese remainder theorem
 - Factorization, field of rational function.

V 0.31 :
 - stochastic differential equation in higher dimension
 - partial differential equation simulation using stochastic differential equation
 - some improvement in documentation.

V 0.30 :
 - spectral theory of undirected graphs : 
   * adjacency matrix
   * degree matrix 
   * laplacian matrix 
   * number of triangles 
   * number of connected components
 - electromagnetic tensor and its properties
 - odesolve : second order if a particular solution is known

V 0.29 :
 - odesolve : ordinary differential equation solver (for first order - using dsolve-, and second order if coefficients are constant)
 - dsolve uses antider instead of integral (calling a smib program in the smib kernel (in C language))
 - Syracuze conjecture (dynamic allocation of arrays)
 - Mertens function & Redheffer matrix 

V 0.28 :
 - some optimizations in generalized stochastic differential equation
 - Mertens fonction
 - new documentation

V 0.27 :
 - quantum mechanic using smib

V 0.26 :
 - quaternions
 - bug corrections

V 0.25 :
 - antiderivative v2 : new version of defint too
 - perfect number & harmonic mean of divisors
 - bug corrections

V 0.24 :
 - rational fonction & decomposition
 - antiderivative
 - bug corrections

V 0.23 :
 - Some polynomial algebra :
   * Bezout identity (extended greater divisor)
   * squarefree factorization
   * resultant
   * discriminant

V 0.22 :
 - law of large numbers & central limit theorem
 - some simplifications in hyperbolic trigonometry
 - almost all warnings suppressed (using -Wno-write-strings option)

V 0.21 :
 - generalized stochastic differential equation (not only with brownian motion): mean and variance computation
 - Stratonovitch stochastic integral with brownian motion
 - bug correction.

V 0.20 :
 - stochastic differential equation : mean and variance computation
 - non-linear least squares approximation.

V 0.19 :
 - Lagrange interpolation using Newton polynomials
 - sample applied to quantile and median.

V 0.18 :
 - complex analysis : complex path, complex path integral, complex path index, number of singularities
 - bug fix: simplification of expressions, numerical evaluation.

V 0.17 :
 - derivation of samples (integer & fractional)
 - bug correction.

V 0.16 :
 - Numerical application to special functions : Bessel functions, Hankel functions & Airy functions
 - Some new example applied to differential geometry, probability & statistic.  

V 0.15 :
 - tensor calculus finally documented
 
V 0.14 :
- numerical analysis :
  - fractionnal derivative
  - new version of Euler scheme : ODE and coupled ODEs are treated by one program
- probability & statistic :
  - gaussian random nuber
  - new version of brownian motion
- bugs correction.


V 0.13 :
- numerical analysis :
  - first order differential equation
  - system of two first order differential equations
  (using Euler scheme).

- probability & statistic :
  - quantile & median
  - stochastic differential equation (Euler-Murayama & Milstein schemes)

- new documentation.


V 0.12 :
- probality & statistic :
  - expected value
  - variance
  - standard deviation
  - skewness
  - kurtosis
  - least square line

- differential geometry :
  - planar curves
  - 3D curves
  - theory of surfaces using Gauss approach

- improvement :
  - simplify (if A=(x-1)*(x+1)/(x-1), simplify(A) returns : 1 + x)
  - numint (if simpsonint = 1, Simpson scheme is used, else Gauss scheme is used), for probability, it is a good idea to set simsonint to 1.