add.cpp

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/*
 *  GiNaC Copyright (C) 1999-2011 Johannes Gutenberg University Mainz, Germany
 *
 *  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.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program; if not, write to the Free Software
 *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 */

#include "add.h"
#include "mul.h"
#include "archive.h"
#include "operators.h"
#include "matrix.h"
#include "utils.h"
#include "clifford.h"
#include "ncmul.h"
#include "compiler.h"

#include <iostream>
#include <limits>
#include <stdexcept>
#include <string>

namespace GiNaC {

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(add, expairseq,
  print_func<print_context>(&add::do_print).
  print_func<print_latex>(&add::do_print_latex).
  print_func<print_csrc>(&add::do_print_csrc).
  print_func<print_tree>(&add::do_print_tree).
  print_func<print_python_repr>(&add::do_print_python_repr))


// default constructor

add::add()
{
}

// other constructors

// public

add::add(const ex & lh, const ex & rh)
{
    overall_coeff = _ex0;
    construct_from_2_ex(lh,rh);
    GINAC_ASSERT(is_canonical());
}

add::add(const exvector & v)
{
    overall_coeff = _ex0;
    construct_from_exvector(v);
    GINAC_ASSERT(is_canonical());
}

add::add(const epvector & v)
{
    overall_coeff = _ex0;
    construct_from_epvector(v);
    GINAC_ASSERT(is_canonical());
}

add::add(const epvector & v, const ex & oc)
{
    overall_coeff = oc;
    construct_from_epvector(v);
    GINAC_ASSERT(is_canonical());
}

add::add(std::auto_ptr<epvector> vp, const ex & oc)
{
    GINAC_ASSERT(vp.get()!=0);
    overall_coeff = oc;
    construct_from_epvector(*vp);
    GINAC_ASSERT(is_canonical());
}

// archiving

GINAC_BIND_UNARCHIVER(add);

// functions overriding virtual functions from base classes

// public

void add::print_add(const print_context & c, const char *openbrace, const char *closebrace, const char *mul_sym, unsigned level) const
{
    if (precedence() <= level)
        c.s << openbrace << '(';

    numeric coeff;
    bool first = true;

    // First print the overall numeric coefficient, if present
    if (!overall_coeff.is_zero()) {
        overall_coeff.print(c, 0);
        first = false;
    }

    // Then proceed with the remaining factors
    epvector::const_iterator it = seq.begin(), itend = seq.end();
    while (it != itend) {
        coeff = ex_to<numeric>(it->coeff);
        if (!first) {
            if (coeff.csgn() == -1) c.s << '-'; else c.s << '+';
        } else {
            if (coeff.csgn() == -1) c.s << '-';
            first = false;
        }
        if (!coeff.is_equal(*_num1_p) &&
            !coeff.is_equal(*_num_1_p)) {
            if (coeff.is_rational()) {
                if (coeff.is_negative())
                    (-coeff).print(c);
                else
                    coeff.print(c);
            } else {
                if (coeff.csgn() == -1)
                    (-coeff).print(c, precedence());
                else
                    coeff.print(c, precedence());
            }
            c.s << mul_sym;
        }
        it->rest.print(c, precedence());
        ++it;
    }

    if (precedence() <= level)
        c.s << ')' << closebrace;
}

void add::do_print(const print_context & c, unsigned level) const
{
    print_add(c, "", "", "*", level);
}

void add::do_print_latex(const print_latex & c, unsigned level) const
{
    print_add(c, "{", "}", " ", level);
}

void add::do_print_csrc(const print_csrc & c, unsigned level) const
{
    if (precedence() <= level)
        c.s << "(";
    
    // Print arguments, separated by "+" or "-"
    epvector::const_iterator it = seq.begin(), itend = seq.end();
    char separator = ' ';
    while (it != itend) {
        
        // If the coefficient is negative, separator is "-"
        if (it->coeff.is_equal(_ex_1) || 
            ex_to<numeric>(it->coeff).numer().is_equal(*_num_1_p))
            separator = '-';
        c.s << separator;
        if (it->coeff.is_equal(_ex1) || it->coeff.is_equal(_ex_1)) {
            it->rest.print(c, precedence());
        } else if (ex_to<numeric>(it->coeff).numer().is_equal(*_num1_p) ||
                 ex_to<numeric>(it->coeff).numer().is_equal(*_num_1_p))
        {
            it->rest.print(c, precedence());
            c.s << '/';
            ex_to<numeric>(it->coeff).denom().print(c, precedence());
        } else {
            it->coeff.print(c, precedence());
            c.s << '*';
            it->rest.print(c, precedence());
        }
        
        ++it;
        separator = '+';
    }
    
    if (!overall_coeff.is_zero()) {
        if (overall_coeff.info(info_flags::positive)
         || is_a<print_csrc_cl_N>(c) || !overall_coeff.info(info_flags::real))  // sign inside ctor argument
            c.s << '+';
        overall_coeff.print(c, precedence());
    }
        
    if (precedence() <= level)
        c.s << ")";
}

void add::do_print_python_repr(const print_python_repr & c, unsigned level) const
{
    c.s << class_name() << '(';
    op(0).print(c);
    for (size_t i=1; i<nops(); ++i) {
        c.s << ',';
        op(i).print(c);
    }
    c.s << ')';
}

bool add::info(unsigned inf) const
{
    switch (inf) {
        case info_flags::polynomial:
        case info_flags::integer_polynomial:
        case info_flags::cinteger_polynomial:
        case info_flags::rational_polynomial:
        case info_flags::real:
        case info_flags::rational:
        case info_flags::integer:
        case info_flags::crational:
        case info_flags::cinteger:
        case info_flags::positive:
        case info_flags::nonnegative:
        case info_flags::posint:
        case info_flags::nonnegint:
        case info_flags::even:
        case info_flags::crational_polynomial:
        case info_flags::rational_function: {
            epvector::const_iterator i = seq.begin(), end = seq.end();
            while (i != end) {
                if (!(recombine_pair_to_ex(*i).info(inf)))
                    return false;
                ++i;
            }
            if (overall_coeff.is_zero() && (inf == info_flags::positive || inf == info_flags::posint))
                return true;
            return overall_coeff.info(inf);
        }
        case info_flags::algebraic: {
            epvector::const_iterator i = seq.begin(), end = seq.end();
            while (i != end) {
                if ((recombine_pair_to_ex(*i).info(inf)))
                    return true;
                ++i;
            }
            return false;
        }
    }
    return inherited::info(inf);
}

bool add::is_polynomial(const ex & var) const
{
    for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
        if (!(i->rest).is_polynomial(var)) {
            return false;
        }
    }
    return true;
}

int add::degree(const ex & s) const
{
    int deg = std::numeric_limits<int>::min();
    if (!overall_coeff.is_zero())
        deg = 0;
    
    // Find maximum of degrees of individual terms
    epvector::const_iterator i = seq.begin(), end = seq.end();
    while (i != end) {
        int cur_deg = i->rest.degree(s);
        if (cur_deg > deg)
            deg = cur_deg;
        ++i;
    }
    return deg;
}

int add::ldegree(const ex & s) const
{
    int deg = std::numeric_limits<int>::max();
    if (!overall_coeff.is_zero())
        deg = 0;
    
    // Find minimum of degrees of individual terms
    epvector::const_iterator i = seq.begin(), end = seq.end();
    while (i != end) {
        int cur_deg = i->rest.ldegree(s);
        if (cur_deg < deg)
            deg = cur_deg;
        ++i;
    }
    return deg;
}

ex add::coeff(const ex & s, int n) const
{
    std::auto_ptr<epvector> coeffseq(new epvector);
    std::auto_ptr<epvector> coeffseq_cliff(new epvector);
    int rl = clifford_max_label(s);
    bool do_clifford = (rl != -1);
    bool nonscalar = false;

    // Calculate sum of coefficients in each term
    epvector::const_iterator i = seq.begin(), end = seq.end();
    while (i != end) {
        ex restcoeff = i->rest.coeff(s, n);
        if (!restcoeff.is_zero()) {
            if (do_clifford) {
                if (clifford_max_label(restcoeff) == -1) {
                    coeffseq_cliff->push_back(combine_ex_with_coeff_to_pair(ncmul(restcoeff, dirac_ONE(rl)), i->coeff));
                } else {
                    coeffseq_cliff->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
                    nonscalar = true;
                }
            }
            coeffseq->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
        }
        ++i;
    }

    return (new add(nonscalar ? coeffseq_cliff : coeffseq,
                    n==0 ? overall_coeff : _ex0))->setflag(status_flags::dynallocated);
}

ex add::eval(int level) const
{
    std::auto_ptr<epvector> evaled_seqp = evalchildren(level);
    if (evaled_seqp.get()) {
        // do more evaluation later
        return (new add(evaled_seqp, overall_coeff))->
               setflag(status_flags::dynallocated);
    }
    
#ifdef DO_GINAC_ASSERT
    epvector::const_iterator i = seq.begin(), end = seq.end();
    while (i != end) {
        GINAC_ASSERT(!is_exactly_a<add>(i->rest));
        ++i;
    }
#endif // def DO_GINAC_ASSERT
    
    if (flags & status_flags::evaluated) {
        GINAC_ASSERT(seq.size()>0);
        GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_zero());
        return *this;
    }
    
    int seq_size = seq.size();
    if (seq_size == 0) {
        // +(;c) -> c
        return overall_coeff;
    } else if (seq_size == 1 && overall_coeff.is_zero()) {
        // +(x;0) -> x
        return recombine_pair_to_ex(*(seq.begin()));
    } else if (!overall_coeff.is_zero() && seq[0].rest.return_type() != return_types::commutative) {
        throw (std::logic_error("add::eval(): sum of non-commutative objects has non-zero numeric term"));
    }
    
    // if any terms in the sum still are purely numeric, then they are more
    // appropriately collected into the overall coefficient
    epvector::const_iterator last = seq.end();
    epvector::const_iterator j = seq.begin();
    int terms_to_collect = 0;
    while (j != last) {
        if (unlikely(is_a<numeric>(j->rest)))
            ++terms_to_collect;
        ++j;
    }
    if (terms_to_collect) {
        std::auto_ptr<epvector> s(new epvector);
        s->reserve(seq_size - terms_to_collect);
        numeric oc = *_num1_p;
        j = seq.begin();
        while (j != last) {
            if (unlikely(is_a<numeric>(j->rest)))
                oc = oc.mul(ex_to<numeric>(j->rest)).mul(ex_to<numeric>(j->coeff));
            else
                s->push_back(*j);
            ++j;
        }
        return (new add(s, ex_to<numeric>(overall_coeff).add_dyn(oc)))
                ->setflag(status_flags::dynallocated);
    }
    
    return this->hold();
}

ex add::evalm() const
{
    // Evaluate children first and add up all matrices. Stop if there's one
    // term that is not a matrix.
    std::auto_ptr<epvector> s(new epvector);
    s->reserve(seq.size());

    bool all_matrices = true;
    bool first_term = true;
    matrix sum;

    epvector::const_iterator it = seq.begin(), itend = seq.end();
    while (it != itend) {
        const ex &m = recombine_pair_to_ex(*it).evalm();
        s->push_back(split_ex_to_pair(m));
        if (is_a<matrix>(m)) {
            if (first_term) {
                sum = ex_to<matrix>(m);
                first_term = false;
            } else
                sum = sum.add(ex_to<matrix>(m));
        } else
            all_matrices = false;
        ++it;
    }

    if (all_matrices)
        return sum + overall_coeff;
    else
        return (new add(s, overall_coeff))->setflag(status_flags::dynallocated);
}

ex add::conjugate() const
{
    exvector *v = 0;
    for (size_t i=0; i<nops(); ++i) {
        if (v) {
            v->push_back(op(i).conjugate());
            continue;
        }
        ex term = op(i);
        ex ccterm = term.conjugate();
        if (are_ex_trivially_equal(term, ccterm))
            continue;
        v = new exvector;
        v->reserve(nops());
        for (size_t j=0; j<i; ++j)
            v->push_back(op(j));
        v->push_back(ccterm);
    }
    if (v) {
        ex result = add(*v);
        delete v;
        return result;
    }
    return *this;
}

ex add::real_part() const
{
    epvector v;
    v.reserve(seq.size());
    for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i)
        if ((i->coeff).info(info_flags::real)) {
            ex rp = (i->rest).real_part();
            if (!rp.is_zero())
                v.push_back(expair(rp, i->coeff));
        } else {
            ex rp=recombine_pair_to_ex(*i).real_part();
            if (!rp.is_zero())
                v.push_back(split_ex_to_pair(rp));
        }
    return (new add(v, overall_coeff.real_part()))
        -> setflag(status_flags::dynallocated);
}

ex add::imag_part() const
{
    epvector v;
    v.reserve(seq.size());
    for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i)
        if ((i->coeff).info(info_flags::real)) {
            ex ip = (i->rest).imag_part();
            if (!ip.is_zero())
                v.push_back(expair(ip, i->coeff));
        } else {
            ex ip=recombine_pair_to_ex(*i).imag_part();
            if (!ip.is_zero())
                v.push_back(split_ex_to_pair(ip));
        }
    return (new add(v, overall_coeff.imag_part()))
        -> setflag(status_flags::dynallocated);
}

ex add::eval_ncmul(const exvector & v) const
{
    if (seq.empty())
        return inherited::eval_ncmul(v);
    else
        return seq.begin()->rest.eval_ncmul(v);
}    

// protected

ex add::derivative(const symbol & y) const
{
    std::auto_ptr<epvector> s(new epvector);
    s->reserve(seq.size());
    
    // Only differentiate the "rest" parts of the expairs. This is faster
    // than the default implementation in basic::derivative() although
    // if performs the same function (differentiate each term).
    epvector::const_iterator i = seq.begin(), end = seq.end();
    while (i != end) {
        s->push_back(combine_ex_with_coeff_to_pair(i->rest.diff(y), i->coeff));
        ++i;
    }
    return (new add(s, _ex0))->setflag(status_flags::dynallocated);
}

int add::compare_same_type(const basic & other) const
{
    return inherited::compare_same_type(other);
}

unsigned add::return_type() const
{
    if (seq.empty())
        return return_types::commutative;
    else
        return seq.begin()->rest.return_type();
}

return_type_t add::return_type_tinfo() const
{
    if (seq.empty())
        return make_return_type_t<add>();
    else
        return seq.begin()->rest.return_type_tinfo();
}

// Note: do_index_renaming is ignored because it makes no sense for an add.
ex add::thisexpairseq(const epvector & v, const ex & oc, bool do_index_renaming) const
{
    return (new add(v,oc))->setflag(status_flags::dynallocated);
}

// Note: do_index_renaming is ignored because it makes no sense for an add.
ex add::thisexpairseq(std::auto_ptr<epvector> vp, const ex & oc, bool do_index_renaming) const
{
    return (new add(vp,oc))->setflag(status_flags::dynallocated);
}

expair add::split_ex_to_pair(const ex & e) const
{
    if (is_exactly_a<mul>(e)) {
        const mul &mulref(ex_to<mul>(e));
        const ex &numfactor = mulref.overall_coeff;
        mul *mulcopyp = new mul(mulref);
        mulcopyp->overall_coeff = _ex1;
        mulcopyp->clearflag(status_flags::evaluated);
        mulcopyp->clearflag(status_flags::hash_calculated);
        mulcopyp->setflag(status_flags::dynallocated);
        return expair(*mulcopyp,numfactor);
    }
    return expair(e,_ex1);
}

expair add::combine_ex_with_coeff_to_pair(const ex & e,
                                          const ex & c) const
{
    GINAC_ASSERT(is_exactly_a<numeric>(c));
    if (is_exactly_a<mul>(e)) {
        const mul &mulref(ex_to<mul>(e));
        const ex &numfactor = mulref.overall_coeff;
        mul *mulcopyp = new mul(mulref);
        mulcopyp->overall_coeff = _ex1;
        mulcopyp->clearflag(status_flags::evaluated);
        mulcopyp->clearflag(status_flags::hash_calculated);
        mulcopyp->setflag(status_flags::dynallocated);
        if (c.is_equal(_ex1))
            return expair(*mulcopyp, numfactor);
        else if (numfactor.is_equal(_ex1))
            return expair(*mulcopyp, c);
        else
            return expair(*mulcopyp, ex_to<numeric>(numfactor).mul_dyn(ex_to<numeric>(c)));
    } else if (is_exactly_a<numeric>(e)) {
        if (c.is_equal(_ex1))
            return expair(e, _ex1);
        return expair(ex_to<numeric>(e).mul_dyn(ex_to<numeric>(c)), _ex1);
    }
    return expair(e, c);
}

expair add::combine_pair_with_coeff_to_pair(const expair & p,
                                            const ex & c) const
{
    GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
    GINAC_ASSERT(is_exactly_a<numeric>(c));

    if (is_exactly_a<numeric>(p.rest)) {
        GINAC_ASSERT(ex_to<numeric>(p.coeff).is_equal(*_num1_p)); // should be normalized
        return expair(ex_to<numeric>(p.rest).mul_dyn(ex_to<numeric>(c)),_ex1);
    }

    return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
}

ex add::recombine_pair_to_ex(const expair & p) const
{
    if (ex_to<numeric>(p.coeff).is_equal(*_num1_p))
        return p.rest;
    else
        return (new mul(p.rest,p.coeff))->setflag(status_flags::dynallocated);
}

ex add::expand(unsigned options) const
{
    std::auto_ptr<epvector> vp = expandchildren(options);
    if (vp.get() == 0) {
        // the terms have not changed, so it is safe to declare this expanded
        return (options == 0) ? setflag(status_flags::expanded) : *this;
    }

    return (new add(vp, overall_coeff))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
}

} // namespace GiNaC