Latex Equation Compiler Code

/***************************************************************************
                          operands.cpp  -  description
                             -------------------
    begin                : Wed Jun 26 2002
    copyright            : (C) 2002 by Jan Rheinlaender
    email                : jrheinlaender@users.sourceforge.net
 ***************************************************************************/

/***************************************************************************
 *                                                                         *
 *   This program is free software; you can redistribute it and/or modify  *
 *   it under the terms of the GNU General Public License as published by  *
 *   the Free Software Foundation; either version 2 of the License, or     *
 *   (at your option) any later version.                                   *
 *                                                                         *
 ***************************************************************************/

//#include "../config/config.h" // *** added in 1.3.1
#include <sstream>
#include "operands.h"
#include "printing.h"
#include "msgdriver.h" // *** added in 1.3.1
#include "equation.h" // *** added in 1.2
#include "ncsymbol.h" // *** added in 1.4.3

exrec::exrec (const expression &exp, const operands &op1, const operands &op2)
    : e(exp), o1(op1), o2(op2), hits(0) {};

exrec::~exrec() {
  MSG_INFO(0) << hits << " hits for " << e << endline;
} // ~exrec()

ex mul_ops(const ex &op1, const ex &op2) {
  return (op1 * op2);
} //mul_ops()

ex add_ops(const ex &op1, const ex &op2) {
  return (op1 + op2);
} //add_ops()

operands::operands(const int ops_type) throw(std::invalid_argument) {
  // *** added matrices in 1.0, integrals in 1.3.1
  if ((ops_type != GINAC_ADD) && (ops_type != GINAC_MUL))
    throw std::invalid_argument("operands::operands(): Type must be ADD or MUL");
  symbols = constants = units = functions = integrals = adds = muls = powers = matrices = others = coefficient = ops_type;
  oper = ((ops_type == GINAC_ADD) ? &add_ops : &mul_ops);
  type = ops_type;
} //operands()

operands::~operands() {}

void operands::split_ex(const expression &e, operands &o1, operands &o2) throw(std::runtime_error) {
  // Split the ex into different types of operands (symbols, functions etc.)
  // *** changed ex& to expression& in 0.9
  // *** removed ex_to<> in argument of include() in 1.0
  // *** added caching of split_ex() results in 1.0
  MSG_INFO(3) << "Splitting expression " << e <<
    ", number of operands: " << e.nops() << endline;

  unsigned hash = e.gethash();
  if ((remember_split[hash] != NULL) && (remember_split[hash]->e.is_equal(e))) {
    o1 = remember_split[hash]->o1;
    o2 = remember_split[hash]->o2;
    remember_split[hash]->hits++;
    MSG_INFO(3) << "split_ex: Cache hit for " << e << endline;
    return;
  }

  if (is_a<mul>(e))
    for (const_iterator i = e.begin(); i != e.end(); i++) {
      // *** changed to const_iterator in 0.7
      if (is_negpower(*i))
        o2.include(pow(*i, -1));
      else if (is_a<numeric>(*i)) // *** changed in 1.2, separating numerator and denominator make no sense
        o1.include(*i);
      else
        o1.include(*i);
    }
  else if (is_a<add>(e))
    for (const_iterator i = e.begin(); i != e.end(); i++) {
      // *** changed to const_iterator in 0.7
      if (is_negex(*i))
        o2.include(-*i);
      else
        o1.include(*i);
    }
  else if (is_negpower(e))
    o2.include(pow(e, -1));
  else if (is_a<power>(e))
    o1.include(e);
  else if (is_a<numeric>(e)) // *** changed in 1.2, separating numerator and denominator make no sense
    o1.include(e);
  else if (is_a<constant>(e)) // Pi etc.
    o1.include(e); // *** added in 1.2
  else if (is_a<function>(e))
    o1.include(e); // *** added in 0.6
  else if (is_a<func>(e))
    o1.include(e); // *** added in 0.6
  else if (is_a<integral>(e))
    o1.include(e); // *** added in 1.3.1
  else if (is_a<matrix>(e))
    o1.include(e); // *** added in 1.0
  else if (e.nops() == 0)
    o1.include(e);
  else // *** changed in 0.6 because throwing an exception makes no sense
    msg::error(0) << "Internal error: Unexpected expression type in split_ex()" << endline;

  if (msg::info().checkprio(4)) {
    std::ostringstream os;
    o1.print(os);
    o2.print(os);
    msg::info() << os.str();
  }

  // *** added in 1.0
  remember_split[hash] = new exrec(e, o1, o2);
  MSG_INFO(3) << "split_ex: Cached result for " << e << endline;
} // split_ex()

void operands::include(const ex &what) {
  // Find the type of what and include it in the receiver
       if (is_a<symbol>(what) || is_a<ncsymbol>(what)) symbols = oper(symbols, what);
  else if (is_a<constant>(what)) constants = oper(constants, what); // *** added in 1.2
  else if (is_a<Unit>(what)) units = oper(units, what);
  else if (is_a<func>(what)) functions = oper(functions, what); // *** added in 0.5
  else if (is_a<function>(what)) functions = oper(functions, what);
  else if (is_a<integral>(what)) integrals = oper(integrals, what); // *** added in 1.3.1
  else if (is_a<add>(what)) adds = oper(adds, what);
  else if (is_a<mul>(what)) muls = oper(muls, what);
  else if (is_a<matrix>(what)) matrices = oper(matrices, what); // *** added in 1.0
  else if (is_a<power>(what)) {
    power pow = ex_to<power>(what);
    ex base = get_basis(pow); // *** changed to get_.. in 1.2
    ex exponent = get_exp(pow);
    if (is_a<numeric>(exponent) && (is_a<Unit>(base))) {
      units = oper(units, what);
    } else if (is_a<numeric>(exponent) && (is_a<symbol>(base) || is_a<ncsymbol>(base))) { // *** added in 1.2
      symbols = oper(symbols, what);
    } else if (is_a<numeric>(exponent) && (is_a<constant>(base))) { // *** added in 1.2
      constants = oper(constants, what);
    } else {
      powers = oper(powers, what);
    }
  } else if (is_a<numeric>(what)) {
      if (what == I)
        others = oper(others, I);
      else if (what == -I) {
        coefficient = ex_to<numeric>(oper(coefficient, -1));
        others = oper(others, I);
      } else
        coefficient = ex_to<numeric>(oper(coefficient, what));
 } else others = oper(others, what);

  MSG_INFO(6) << "Included expression " << what << endline;
} //operands::include()

void operands::exclude(const ex &what) { // *** added in 1.2
  // Find the type of what and include it in the receiver
       if (is_a<symbol>(what) || is_a<ncsymbol>(what)) symbols = oper(symbols, 1 / what);
  else if (is_a<constant>(what)) constants = oper(constants, 1 / what);
  else if (is_a<Unit>(what)) units = oper(units, 1 / what);
  else if (is_a<func>(what)) functions = oper(functions, 1 / what); // *** added in 0.5
  else if (is_a<function>(what)) functions = oper(functions, 1 / what);
  else if (is_a<integral>(what)) integrals = oper(integrals, 1 / what); // *** added in 1.3.1
  else if (is_a<add>(what)) adds = oper(adds, 1 / what);
  else if (is_a<mul>(what)) muls = oper(muls, 1 / what);
  else if (is_a<matrix>(what)) matrices = oper(matrices, 1 / what); // *** added in 1.0
  else if (is_a<power>(what)) {
    power pow = ex_to<power>(what);
    ex base = get_basis(pow); // *** changed to get_.. in 1.2
    ex exponent = get_exp(pow);
    if (is_a<numeric>(exponent) && (is_a<Unit>(base))) {
      units = oper(units, 1 / what);
    } else if (is_a<numeric>(exponent) && (is_a<symbol>(base) || is_a<ncsymbol>(base))) {
      symbols = oper(symbols, 1 / what);
    } else if (is_a<numeric>(exponent) && (is_a<constant>(base))) {
      constants = oper(constants, 1 / what);
    } else {
      powers = oper(powers, 1 / what);
    }
  } else if (is_a<numeric>(what))
    coefficient = ex_to<numeric>(oper(coefficient, 1 / what));
  else others = oper(others, 1 / what);
} //operands::exclude()

void operands::exclude_all(const ex &what) {
  if ((is_a<mul>(what) && (type == GINAC_MUL)) || (is_a<add>(what) && (type == GINAC_ADD))) {
    for (const_iterator i = what.begin(); i != what.end(); i++) {
      exclude(*i);
    }
  } else {
    exclude(what);
  }
} // operands::exclude_all()

bool checkmatrix(const matrix &m) { // *** added in 1.0
  for (unsigned i = 0; i < m.nops(); i++) {
    if (is_a<matrix>(m.op(i))) {
      if (!checkmatrix(ex_to<matrix>(m.op(i))))
        return false;
    } else {
      if (!m.op(i).info(info_flags::numeric))
        return false;
    }
  }
  return true;
} // checkmatrix()

// TODO: Store the result of these queries for the next time!

const bool operands::is_quantity() const {
  // *** added integrals in 1.3.1
  return ((check_symbols(type)) && (constants == type) && (functions == type) && (integrals == type) && (adds == type) &&
          (muls == type) && (powers == type) && (others == type) && check_matrices(type));
} // operands::is_quantity()

const bool operands::is_number() const {
  return (this->is_quantity() && (units == type));
  } // operands::is_number()

const bool operands::is_trivial() const {
  return (this->is_number() && (abs(coefficient) == type));
  } // operands::is_trivial()

const bool operands::is_symbol() const { // *** added in 1.2, added integrals in 1.3.1
  return ((coefficient == type) && (!check_symbols(type)) && (constants == type) && (functions == type) && (adds == type) &&
          (muls == type) && (powers == type) && (check_matrices(type)) && (others == type) && (integrals == type));
} // operands::is_symbol()

const bool operands::is_add() const {
  return (type == GINAC_ADD);
} // operands::is_add()

const bool operands::is_mul() const {
  return (type == GINAC_MUL);
} // operands::is_mul()

void checksplit(const bool toplevel, const int opnum, std::ostream &os) {
  if (toplevel) {
    if (opnum == optstack::options->get(o_eqsplit).integer) {
      MSG_INFO(1) << "Splitting equation at operand " << opnum << endline;
      MSG_INFO(2) << "Interjected text: " << *optstack::options->get(o_eqsplittext).str << endline;
      if (optstack::options->get(o_eqalign).align == onlyleft) {
        os << "\\\\" << std::endl;
        if (*optstack::options->get(o_eqsplittext).str == "") {
          os << "&\\quad\\,\\,";
        } else {
          os << *optstack::options->get(o_eqsplittext).str;
        }
      } else if (optstack::options->get(o_eqalign).align == both) {
        os << "\\nonumber\\\\" << std::endl;
        if (*optstack::options->get(o_eqsplittext).str == "") {
          os << "&&";
        } else {
          os << *optstack::options->get(o_eqsplittext).str;
        }
      } else {
        os << "\\\\" << std::endl << *optstack::options->get(o_eqsplittext).str;
      }
    }
  }
} // operands::checksplit()

const bool operands::check_matrices(const unsigned type) const {
  if (matrices.info(info_flags::numeric)) {
    return (matrices == type);
  } else {
    return (false);
  }
}

const bool operands::check_symbols(const unsigned type) const {
  if (symbols.info(info_flags::numeric)) {
    return (symbols == type);
  } else {
    return (false);
  }
}

void print_ltx_ops (const ex &e, const std::string &sym, std::ostream &os, const bool toplevel, int &opnum) {
  // *** replaced first with opnum in 1.2
  if (opnum > 0) {
    os << sym;
    checksplit(toplevel, opnum, os); // *** added in 1.2
  }

  if (is_a<symbol>(e))
    print_ltx(ex_to<symbol>(e), os);
  else if (is_a<ncsymbol>(e))
    print_ltx(ex_to<ncsymbol>(e), os);
  else if (is_a<power>(e))
    print_ltx(ex_to<power>(e), os);
  else if (is_a<Unit>(e))
    print_ltx(ex_to<Unit>(e), os);
  else if (is_a<func>(e))
    print_ltx(ex_to<func>(e), os); // *** added in 0.5
  else if (is_a<function>(e))
    print_ltx(ex_to<function>(e), os);
  else if (is_a<integral>(e))
    print_ltx(ex_to<integral>(e), os); // *** added in 1.3.1
  else if (is_a<matrix>(e)) {
    print_ltx(ex_to<matrix>(e), os); // *** added in 1.0
  } else if (is_a<add>(e)) {
    for (const_iterator i = e.begin(); i != e.end(); i++) {
      // *** changed to const_iterator in 0.7
      if (i != e.begin()) checksplit(toplevel, opnum, os);
      if (is_a<Unit>(*i)) {
        os << "\\unit{1}{"; // *** added in 1.2, toplevel has a new meaning now
        print_ltx(ex_to<Unit>(*i), os);
        os << "}";
      } else
        print_ltx(*i, os);
      if ((i != e.end()-1) && !is_negex(*(i+1)))
          os << sym;
      opnum++;
    }
    return; // Don't increment opnum again!
  } else if (is_a<mul>(e)) {
    for (const_iterator i = e.end(); i != e.begin();) { // *** changed to const_iterator in 0.7
      if (i != e.end()) checksplit(toplevel, opnum, os);
      i--;
      if (is_a<add>(*i)) {
        os << "\\left(";
        print_ltx(ex_to<add>(*i), os, false, 0);
        os << "\\right)";
      } else {
        print_ltx(*i, os);
      }
      if (i != e.begin()) os << sym;
      opnum++;
      //std::cout << "Incremented opnum after printing " << *i << ", value: " << opnum << std::endl;
    }
    return;
  } else
    os << latex << e << dflt; // *** changed print to << in 0.8
  opnum++;
} // print_ltx_ops()

void operands::print_ltx_mul(std::ostream &os, const bool toplevel, const int ops) const throw(std::invalid_argument) {
  if (!type == GINAC_MUL)
    throw std::invalid_argument("Receiver must be of type GINAC_MUL");

  if (msg::info().checkprio(5)) {
    msg::info() << "Printing Latex mul ";
    std::ostringstream os;
    this->print(os);
    msg::info() << os.str();
  }
  // Print the coefficient
  //bool first = true; // *** changed in 1.2
  int opnum = ops;
  if (!is_equal_one(coefficient) || is_trivial()) { // *** changed to is_equal_one() in 1.0
    //std::cout << "Printing coefficient " << coefficient << std::endl;
    if (coefficient.is_real())
      print_ltx(coefficient, os);
    else {
      os << "\\left(";
      print_ltx(coefficient, os);
      os << "\\right)";
    }
    opnum++;
  }

  const std::string separator = "\\,"; // *** added in 1.0

  // Print powers of numerics *** added in 1.2
  ex restpowers = 1;
  if (is_a<mul>(powers)) {
    for (const_iterator i = powers.begin(); i != powers.end(); i++) {
      if (is_a<numeric>(get_basis(ex_to<power>(*i))) && is_a<numeric>(get_exp(ex_to<power>(*i)))) {
        print_ltx_ops(*i, separator, os, toplevel, opnum);
      } else {
        restpowers = restpowers * *i;
      }
    }
  } else if (powers != 1) {
    if (is_a<numeric>(get_basis(ex_to<power>(powers))) && is_a<numeric>(get_exp(ex_to<power>(powers)))) {
        print_ltx_ops(powers, separator, os, toplevel, opnum);
    } else {
      restpowers = powers;
    }
  }

  // Functions must be printed last to avoid ambiguities like tan xa -> tan (x*a) or tan (x) * a ?
  // TODO: Print constants right after that!
  if (units != 1) // *** moved here in 1.2
    print_ltx_ops(units, separator, os, toplevel, opnum);
  if (constants != 1)
    print_ltx_ops(constants, separator, os, toplevel, opnum);
  if (!check_symbols(1))
    print_ltx_ops(symbols, separator, os, toplevel, opnum);
  if (restpowers != 1)
    print_ltx_ops(restpowers, separator, os, toplevel, opnum);
  if (adds != 1) { // *** changed in 0.6 to avoid unnecessary brackets
    if (opnum > 0) os << separator;

    if (is_a<mul>(adds)) { // There are several adds in this mul
      opnum++; // suppress op_symbol here!
      print_ltx_ops(adds, separator, os, toplevel, opnum);
      opnum--; // correct operator count
    } else {
      if ((opnum == 0) && (others == 1) && (functions == 1) &&
          (muls == 1) && (integrals == 1) &&  check_matrices(1)) {
        // *** added in 0.6, added muls in 0.9, added matrices in 1.0, integrals in 1.3.1
        // *** removed units in 1.2
        // In other words, if there is only this one add in the mul
        print_ltx(ex_to<add>(adds), os, toplevel, opnum);
      } else {
        os << "\\left(";
        print_ltx(ex_to<add>(adds), os, false, 0);
        os << "\\right) ";
      }
      checksplit(toplevel, opnum, os);
    }
  }
  // Warning: The preceding code depends on these statements following AFTER it!
  if (muls != 1) { // *** added in 0.9
    print_ltx(ex_to<mul>(muls), os, toplevel, opnum);
    opnum += muls.nops();
  }
  if (!check_matrices(1)) {// *** added in 1.0
    // Matrices cannot be compared to a numeric! Because of non-commutativity.
    print_ltx_ops(matrices, separator, os, toplevel, opnum);
  }
  if (others != 1)
    print_ltx_ops(others, separator, os, toplevel, opnum);
  if (functions != 1)
    print_ltx_ops(functions, separator, os, toplevel, opnum);
  if (integrals != 1) // *** added in 1.3.1
    print_ltx_ops(integrals, separator, os, toplevel, opnum);
  os << ' ';
} // operands::print_ltx_mul()

void operands::print_ltx_add(const operands &neg, std::ostream &os, const bool toplevel, const int ops) const throw(std::invalid_argument) {
  // *** added opnum in 1.2, replaces first
  if (!type == GINAC_ADD)
    throw std::invalid_argument("Receiver must be of type GINAC_ADD");

  // *** added integrals in 1.3.1
  bool coefficient_later = false, units_later = false, symbols_later = false, constants_later = false, muls_later = false,
    powers_later = false, adds_later = false, matrices_later = false, others_later = false, functions_later = false, integrals_later = false;
  int opnum = ops; // *** added in 1.2

  checksplit(toplevel, opnum, os); // *** added in 1.2

  if (!coefficient.is_zero()) {
    print_ltx(coefficient, os);
    opnum++;
  }
  if (!neg.get_coefficient().is_zero()) {
    if (opnum == 0) { // *** added code to always print something with a posivite sign first in 1.2
      coefficient_later = true;
    } else {
      os << "-";
      checksplit(toplevel, opnum, os);
      print_ltx(neg.get_coefficient(), os);
      opnum++;
    }
  }

  std::string addsym = "+"; // *** added in 1.0
  std::string subsym = "-";
  if (units != 0) { // *** moved here in 1.2
    os << "\\unit{1}{"; // *** changed in 1.2, toplevel has a new meaning now
    print_ltx_ops(units, addsym, os, toplevel, opnum); // *** changed first to opnum in 1.2
    os << "}";
  }
  if (neg.get_units() != 0) { // *** moved here in 1.2
    if (opnum == 0) { // *** changed first to  opnum == 0
      units_later = true;
    } else {
      os << "\\unit{1}{"; // *** added in 1.2 instead of first = false
      print_ltx_ops(neg.get_units(), subsym, os, toplevel, opnum);
      os << "}";
    }
  }
  if (constants != 0)
    print_ltx_ops(constants, addsym, os, toplevel, opnum);
  if (neg.get_constants() != 0) {
    if (opnum == 0) {
      constants_later = true;
    } else {
      print_ltx_ops(neg.get_constants(), subsym, os, toplevel, opnum);
    }
  }
  if (!check_symbols(0))
    print_ltx_ops(symbols, addsym, os, toplevel, opnum);
  if (!neg.check_symbols(0)) {
    if (opnum == 0) {
      symbols_later = true;
    } else {
      print_ltx_ops(neg.get_symbols(), subsym, os, toplevel, opnum);
    }
  }
  if (powers != 0)
    print_ltx_ops(powers, addsym, os, toplevel, opnum);
  if (neg.get_powers() != 0) {
    if (opnum == 0) {
      powers_later = true;
    } else {
      print_ltx_ops(neg.get_powers(), subsym, os, toplevel, opnum);
    }
  }
  if (muls != 0) {
    if (is_a<add>(muls)) { // There are several muls in this add
      print_ltx_ops(muls, addsym, os, toplevel, opnum);
    } else { // There is only one mul
      if (opnum > 0) {
        os << addsym;
        checksplit(toplevel, opnum, os);
      }
      print_ltx(ex_to<mul>(muls), os, false, 0);
      opnum++;
    }
  }
  if (neg.get_muls() != 0) {
    if (opnum == 0) {
      muls_later = true;
    } else {
      if (is_a<add>(neg.get_muls())) {
        print_ltx_ops(neg.get_muls(), subsym, os, toplevel, opnum);
      } else {
        checksplit(toplevel, opnum, os);
        print_ltx(ex_to<mul>(-neg.get_muls()), os, false, 0);
        opnum++;
      }
    }
  }
  if (adds != 0) { // *** added in 0.9
    print_ltx(ex_to<add>(adds), os, toplevel, opnum);
    opnum += adds.nops();
  }
  if (neg.get_adds() != 0) { // *** added in 0.9
    if (opnum == 0) {
      adds_later = true;
    } else {
      print_ltx(ex_to<add>(neg.get_adds()), os, toplevel, opnum);
      opnum += adds.nops();
    }
  }
  if (!check_matrices(0)) // *** added in 1.0
    print_ltx_ops(matrices, addsym, os, toplevel, opnum);
  ex negmatrices = neg.get_matrices();
  if (is_a<matrix>(negmatrices) || is_a<add>(negmatrices)) { // *** added in 1.0
    if (opnum == 0) {
      matrices_later = true;
    } else {
      print_ltx_ops(neg.get_matrices(), subsym, os, toplevel, opnum);
    }
  }
  if (others != 0)
    print_ltx_ops(others, addsym, os, toplevel, opnum);
  if (neg.get_others()!= 0) {
    if (opnum == 0) {
      others_later = true;
    } else {
      print_ltx_ops(neg.get_others(), subsym, os, toplevel, opnum);
    }
  }
  if (functions != 0)
    print_ltx_ops(functions, addsym, os, toplevel, opnum);
  if (neg.get_functions() != 0) {
    if (opnum == 0) {
      functions_later = true;
    } else {
      print_ltx_ops(neg.get_functions(), subsym, os, toplevel, opnum);
    }
  }
  if (integrals != 0) // *** added in 1.3.1
    print_ltx_ops(integrals, addsym, os, toplevel, opnum);
  if (neg.get_integrals() != 0) {
    if (opnum == 0) {
      integrals_later = true;
    } else {
      print_ltx_ops(neg.get_integrals(), subsym, os, toplevel, opnum);
    }
  } 

  if (coefficient_later) {
    if (opnum != 0) checksplit(toplevel, opnum, os);
    os << subsym;
    print_ltx(neg.get_coefficient(), os);
    opnum++;
  } else if (opnum == 0) {
    os << subsym;
  }
  if (units_later) { // TODO: Does this ever occur? *** removed unit{1}{... in 1.2
    //os << "\\unit{1}{"; // *** changed in 1.2, toplevel has a new meaning now
    print_ltx_ops(neg.get_units(), subsym, os, toplevel, opnum);
    //os << "}";
  }
  if (constants_later)
    print_ltx_ops(neg.get_constants(), subsym, os, toplevel, opnum);
  if (symbols_later)
    print_ltx_ops(neg.get_symbols(), subsym, os, toplevel, opnum);
  if (muls_later) {
    if (is_a<add>(neg.get_muls())) {
      print_ltx_ops(neg.get_muls(), subsym, os, toplevel, opnum);
    } else {
      if (opnum != 0) {
        checksplit(toplevel, opnum, os);
        os << subsym;
      }
      print_ltx(ex_to<mul>(neg.get_muls()), os);
      opnum++;
    }
  }
  if (powers_later)
    print_ltx_ops(neg.get_powers(), subsym, os, toplevel, opnum);
  if (adds_later) { // *** changed neg to -neg in 1.2
    print_ltx(ex_to<add>(-neg.get_adds()), os, toplevel, opnum);
    opnum += adds.nops();
  }
  if (matrices_later)
    print_ltx_ops(neg.get_matrices(), subsym, os, toplevel, opnum);
  if (others_later)
    print_ltx_ops(neg.get_others(), subsym, os, toplevel, opnum);
  if (functions_later)
    print_ltx_ops(neg.get_functions(), subsym, os, toplevel, opnum);
  if (integrals_later) // *** added in 1.3.1
    print_ltx_ops(neg.get_integrals(), subsym, os, toplevel, opnum);
  os << " ";
} // print_ltx_add()

void operands::print(std::ostream &os) const {
  os << "Symbols: " << symbols << std::endl;
  os << "Constants: " << constants << std::endl;
  os << "Units: " << units << std::endl;
  os << "Functions: " << functions << std::endl;
  os << "Adds: " << adds << std::endl;
  os << "Muls: " << muls << std::endl;
  os << "Powers: " << powers << std::endl;
  os << "Numerics: " << ex(coefficient) << std::endl;
  os << "Matrices: " << matrices << std::endl; // *** added in 1.3.0
  os << "Integrals: " << integrals << std::endl; // *** added in 1.3.1
  os << "Others: " << others << std::endl;
  os << "Quantity: " << (is_quantity() ? "true" : "false") << std::endl;
  os << "Number: " << (is_number() ? "true" : "false")  << std::endl;
  os << "Trivial: " << (is_trivial() ? "true" : "false")  << std::endl;
} //operands::print()

/*void operands::print(message &ms) const {
  ms << "Symbols: " << symbols << endline;  
  ms << "Constants: " << constants << endline;
  ms << "Units: " << units << endline;
  ms << "Functions: " << functions << endline;
  ms << "Adds: " << adds << endline;
  ms << "Muls: " << muls << endline;
  ms << "Powers: " << powers << endline;
  ms << "Numerics: " << ex(coefficient) << endline;
  ms << "Matrices: " << matrices << endline; // *** added in 1.3.0
  ms << "Integrals: " << integrals << endline; // *** added in 1.3.1
  ms << "Others: " << others << endline;
  ms << "Quantity: " << (is_quantity() ? "true" : "false") << endline;
  ms << "Number: " << (is_number() ? "true" : "false")  << endline;   
  ms << "Trivial: " << (is_trivial() ? "true" : "false")  << endline;
} //operands::print()
*/