GiNaC/ginac/add.cpp

/** @file add.cpp
 *
 *  Implementation of GiNaC's sums of expressions. */

/*
 *  GiNaC Copyright (C) 1999 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 */

#include <iostream>
#include <stdexcept>

#include "add.h"
#include "mul.h"
#include "debugmsg.h"
#include "utils.h"

#ifndef NO_GINAC_NAMESPACE
namespace GiNaC {
#endif // ndef NO_GINAC_NAMESPACE

//////////
// default constructor, destructor, copy constructor assignment operator and helpers
//////////

// public

add::add()
{
    debugmsg("add default constructor",LOGLEVEL_CONSTRUCT);
    tinfo_key = TINFO_add;
}

add::~add()
{
    debugmsg("add destructor",LOGLEVEL_DESTRUCT);
    destroy(0);
}

add::add(add const & other)
{
    debugmsg("add copy constructor",LOGLEVEL_CONSTRUCT);
    copy(other);
}

add const & add::operator=(add const & other)
{
    debugmsg("add operator=",LOGLEVEL_ASSIGNMENT);
    if (this != &other) {
        destroy(1);
        copy(other);
    }
    return *this;
}

// protected

void add::copy(add const & other)
{
    expairseq::copy(other);
}

void add::destroy(bool call_parent)
{
    if (call_parent) expairseq::destroy(call_parent);
}

//////////
// other constructors
//////////

// public

add::add(ex const & lh, ex const & rh)
{
    debugmsg("add constructor from ex,ex",LOGLEVEL_CONSTRUCT);
    tinfo_key = TINFO_add;
    overall_coeff=_ex0();
    construct_from_2_ex(lh,rh);
    GINAC_ASSERT(is_canonical());
}

add::add(exvector const & v)
{
    debugmsg("add constructor from exvector",LOGLEVEL_CONSTRUCT);
    tinfo_key = TINFO_add;
    overall_coeff=_ex0();
    construct_from_exvector(v);
    GINAC_ASSERT(is_canonical());
}

/*
add::add(epvector const & v, bool do_not_canonicalize)
{
    debugmsg("add constructor from epvector,bool",LOGLEVEL_CONSTRUCT);
    tinfo_key = TINFO_add;
    if (do_not_canonicalize) {
        seq=v;
#ifdef EXPAIRSEQ_USE_HASHTAB
        combine_same_terms(); // to build hashtab
#endif // def EXPAIRSEQ_USE_HASHTAB
    } else {
        construct_from_epvector(v);
    }
    GINAC_ASSERT(is_canonical());
}
*/

add::add(epvector const & v)
{
    debugmsg("add constructor from epvector",LOGLEVEL_CONSTRUCT);
    tinfo_key = TINFO_add;
    overall_coeff=_ex0();
    construct_from_epvector(v);
    GINAC_ASSERT(is_canonical());
}

add::add(epvector const & v, ex const & oc)
{
    debugmsg("add constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
    tinfo_key = TINFO_add;
    overall_coeff=oc;
    construct_from_epvector(v);
    GINAC_ASSERT(is_canonical());
}

add::add(epvector * vp, ex const & oc)
{
    debugmsg("add constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
    tinfo_key = TINFO_add;
    GINAC_ASSERT(vp!=0);
    overall_coeff=oc;
    construct_from_epvector(*vp);
    delete vp;
    GINAC_ASSERT(is_canonical());
}

//////////
// functions overriding virtual functions from bases classes
//////////

// public

basic * add::duplicate() const
{
    debugmsg("add duplicate",LOGLEVEL_DUPLICATE);
    return new add(*this);
}

/*void add::print(ostream & os, unsigned upper_precedence) const
{
    debugmsg("add print",LOGLEVEL_PRINT);
    if (precedence<=upper_precedence) os << "(";
    numeric coeff;
    bool first=true;
    for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
        coeff = ex_to_numeric(cit->coeff);
        if (!first) {
            if (coeff.csgn()==-1) os << '-'; else os << '+';
        } else {
            if (coeff.csgn()==-1) os << '-';
            first=false;
        }
        if (!coeff.is_equal(_num1()) &&
            !coeff.is_equal(_num_1())) {
            if (coeff.is_rational()) {
                if (coeff.is_negative())
                    os << -coeff;
                else
                    os << coeff;
            } else {
                if (coeff.csgn()==-1)
                    (-coeff).print(os, precedence);
                else
                    coeff.print(os, precedence);
            }
            os << '*';
        }
        os << cit->rest;
    }
    // print the overall numeric coefficient, if present:
    if (!overall_coeff.is_zero()) {
        if (overall_coeff.info(info_flags::positive)) os << '+';
        os << overall_coeff;
    }
    if (precedence<=upper_precedence) os << ")";
}*/

void add::print(ostream & os, unsigned upper_precedence) const
{
    debugmsg("add print",LOGLEVEL_PRINT);
    if (precedence<=upper_precedence) os << "(";
    numeric coeff;
    bool first = true;
    // first print the overall numeric coefficient, if present:
    if (!overall_coeff.is_zero()) {
        os << overall_coeff;
        first = false;
    }
    // then proceed with the remaining factors:
    for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
        coeff = ex_to_numeric(cit->coeff);
        if (!first) {
            if (coeff.csgn()==-1) os << '-'; else os << '+';
        } else {
            if (coeff.csgn()==-1) os << '-';
            first = false;
        }
        if (!coeff.is_equal(_num1()) &&
            !coeff.is_equal(_num_1())) {
            if (coeff.is_rational()) {
                if (coeff.is_negative())
                    os << -coeff;
                else
                    os << coeff;
            } else {
                if (coeff.csgn()==-1)
                    (-coeff).print(os, precedence);
                else
                    coeff.print(os, precedence);
            }
            os << '*';
        }
        os << cit->rest;
    }
    if (precedence<=upper_precedence) os << ")";
}

void add::printraw(ostream & os) const
{
    debugmsg("add printraw",LOGLEVEL_PRINT);

    os << "+(";
    for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
        os << "(";
        (*it).rest.bp->printraw(os);
        os << ",";
        (*it).coeff.bp->printraw(os);        
        os << "),";
    }
    os << ",hash=" << hashvalue << ",flags=" << flags;
    os << ")";
}

void add::printcsrc(ostream & os, unsigned type, unsigned upper_precedence) const
{
    debugmsg("add print csrc", LOGLEVEL_PRINT);
    if (precedence <= upper_precedence)
        os << "(";

    // Print arguments, separated by "+"
    epvector::const_iterator it = seq.begin();
    epvector::const_iterator itend = seq.end();
    while (it != itend) {

        // If the coefficient is -1, it is replaced by a single minus sign
        if (it->coeff.compare(_num1()) == 0) {
            it->rest.bp->printcsrc(os, type, precedence);
        } else if (it->coeff.compare(_num_1()) == 0) {
            os << "-";
            it->rest.bp->printcsrc(os, type, precedence);
        } else if (ex_to_numeric(it->coeff).numer().compare(_num1()) == 0) {
            it->rest.bp->printcsrc(os, type, precedence);
            os << "/";
            ex_to_numeric(it->coeff).denom().printcsrc(os, type, precedence);
        } else if (ex_to_numeric(it->coeff).numer().compare(_num_1()) == 0) {
            os << "-";
            it->rest.bp->printcsrc(os, type, precedence);
            os << "/";
            ex_to_numeric(it->coeff).denom().printcsrc(os, type, precedence);
        } else {
            it->coeff.bp->printcsrc(os, type, precedence);
            os << "*";
            it->rest.bp->printcsrc(os, type, precedence);
        }

        // Separator is "+", except if the following expression would have a leading minus sign
        it++;
        if (it != itend && !(it->coeff.compare(_num0()) < 0 || (it->coeff.compare(_num1()) == 0 && is_ex_exactly_of_type(it->rest, numeric) && it->rest.compare(_num0()) < 0)))
            os << "+";
    }
    
    if (!overall_coeff.is_equal(_ex0())) {
        if (overall_coeff.info(info_flags::positive)) os << '+';
        overall_coeff.bp->printcsrc(os,type,precedence);
    }
    
    if (precedence <= upper_precedence)
        os << ")";
}

bool add::info(unsigned inf) const
{
    // TODO: optimize
    if (inf==info_flags::polynomial ||
        inf==info_flags::integer_polynomial ||
        inf==info_flags::cinteger_polynomial ||
        inf==info_flags::rational_polynomial ||
        inf==info_flags::crational_polynomial ||
        inf==info_flags::rational_function) {
        for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
            if (!(recombine_pair_to_ex(*it).info(inf)))
                return false;
        }
        return overall_coeff.info(inf);
    } else {
        return expairseq::info(inf);
    }
}

int add::degree(symbol const & s) const
{
    int deg=INT_MIN;
    if (!overall_coeff.is_equal(_ex0())) {
        deg=0;
    }
    int cur_deg;
    for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
        cur_deg=(*cit).rest.degree(s);
        if (cur_deg>deg) deg=cur_deg;
    }
    return deg;
}

int add::ldegree(symbol const & s) const
{
    int deg=INT_MAX;
    if (!overall_coeff.is_equal(_ex0())) {
        deg=0;
    }
    int cur_deg;
    for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
        cur_deg=(*cit).rest.ldegree(s);
        if (cur_deg<deg) deg=cur_deg;
    }
    return deg;
}

ex add::coeff(symbol const & s, int const n) const
{
    epvector coeffseq;
    coeffseq.reserve(seq.size());

    epvector::const_iterator it=seq.begin();
    while (it!=seq.end()) {
        coeffseq.push_back(combine_ex_with_coeff_to_pair((*it).rest.coeff(s,n),
                                                         (*it).coeff));
        ++it;
    }
    if (n==0) {
        return (new add(coeffseq,overall_coeff))->setflag(status_flags::dynallocated);
    }
    return (new add(coeffseq))->setflag(status_flags::dynallocated);
}

ex add::eval(int level) const
{
    // simplifications: +(;c) -> c
    //                  +(x;1) -> x

    debugmsg("add eval",LOGLEVEL_MEMBER_FUNCTION);

    epvector * evaled_seqp=evalchildren(level);
    if (evaled_seqp!=0) {
        // do more evaluation later
        return (new add(evaled_seqp,overall_coeff))->
                   setflag(status_flags::dynallocated);
    }

#ifdef DO_GINAC_ASSERT
    for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
        GINAC_ASSERT(!is_ex_exactly_of_type((*cit).rest,add));
        if (is_ex_exactly_of_type((*cit).rest,numeric)) {
            dbgprint();
        }
        GINAC_ASSERT(!is_ex_exactly_of_type((*cit).rest,numeric));
    }
#endif // def DO_GINAC_ASSERT

    if (flags & status_flags::evaluated) {
        GINAC_ASSERT(seq.size()>0);
        GINAC_ASSERT((seq.size()>1)||!overall_coeff.is_equal(_ex0()));
        return *this;
    }

    int seq_size=seq.size();
    if (seq_size==0) {
        // +(;c) -> c
        return overall_coeff;
    } else if ((seq_size==1)&&overall_coeff.is_equal(_ex0())) {
        // +(x;0) -> x
        return recombine_pair_to_ex(*(seq.begin()));
    }
    return this->hold();
}

exvector add::get_indices(void) const
{
    // FIXME: all terms in the sum should have the same indices (compatible
    // tensors) however this is not checked, since there is no function yet
    // which compares indices (idxvector can be unsorted)
    if (seq.size()==0) {
        return exvector();
    }
    return (seq.begin())->rest.get_indices();
}    

ex add::simplify_ncmul(exvector const & v) const
{
    if (seq.size()==0) {
        return expairseq::simplify_ncmul(v);
    }
    return (*seq.begin()).rest.simplify_ncmul(v);
}    

// protected

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

bool add::is_equal_same_type(basic const & other) const
{
    return expairseq::is_equal_same_type(other);
}

unsigned add::return_type(void) const
{
    if (seq.size()==0) {
        return return_types::commutative;
    }
    return (*seq.begin()).rest.return_type();
}
   
unsigned add::return_type_tinfo(void) const
{
    if (seq.size()==0) {
        return tinfo_key;
    }
    return (*seq.begin()).rest.return_type_tinfo();
}

ex add::thisexpairseq(epvector const & v, ex const & oc) const
{
    return (new add(v,oc))->setflag(status_flags::dynallocated);
}

ex add::thisexpairseq(epvector * vp, ex const & oc) const
{
    return (new add(vp,oc))->setflag(status_flags::dynallocated);
}

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

expair add::combine_ex_with_coeff_to_pair(ex const & e,
                                          ex const & c) const
{
    GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
    if (is_ex_exactly_of_type(e,mul)) {
        mul const & mulref=ex_to_mul(e);
        ex numfactor=mulref.overall_coeff;
        //mul * mulcopyp=static_cast<mul *>(mulref.duplicate());
        mul * mulcopyp=new mul(mulref);
        mulcopyp->overall_coeff=_ex1();
        mulcopyp->clearflag(status_flags::evaluated);
        mulcopyp->clearflag(status_flags::hash_calculated);
        if (are_ex_trivially_equal(c,_ex1())) {
            return expair(mulcopyp->setflag(status_flags::dynallocated),numfactor);
        } else if (are_ex_trivially_equal(numfactor,_ex1())) {
            return expair(mulcopyp->setflag(status_flags::dynallocated),c);
        }
        return expair(mulcopyp->setflag(status_flags::dynallocated),
                          ex_to_numeric(numfactor).mul_dyn(ex_to_numeric(c)));
    } else if (is_ex_exactly_of_type(e,numeric)) {
        if (are_ex_trivially_equal(c,_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(expair const & p,
                                            ex const & c) const
{
    GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
    GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));

    if (is_ex_exactly_of_type(p.rest,numeric)) {
        GINAC_ASSERT(ex_to_numeric(p.coeff).is_equal(_num1())); // 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(expair const & p) const
{
    //if (p.coeff.compare(_ex1())==0) {
    //if (are_ex_trivially_equal(p.coeff,_ex1())) {
    if (ex_to_numeric(p.coeff).is_equal(_num1())) {
        return p.rest;
    } else {
        return p.rest*p.coeff;
    }
}

ex add::expand(unsigned options) const
{
    epvector * vp=expandchildren(options);
    if (vp==0) {
        return *this;
    }
    return (new add(vp,overall_coeff))->setflag(status_flags::expanded    |
                                                status_flags::dynallocated );
}

//////////
// new virtual functions which can be overridden by derived classes
//////////

// none

//////////
// non-virtual functions in this class
//////////

// none

//////////
// static member variables
//////////

// protected

unsigned add::precedence=40;

//////////
// global constants
//////////

const add some_add;
type_info const & typeid_add=typeid(some_add);

#ifndef NO_GINAC_NAMESPACE
} // namespace GiNaC
#endif // ndef NO_GINAC_NAMESPACE
1	cbauer	1.1	/** @file add.cpp
2			*
3	cbauer	1.4	* Implementation of GiNaC's sums of expressions. */
4
5			/*
6	cbauer	1.2	* GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
7			*
8			* This program is free software; you can redistribute it and/or modify
9			* it under the terms of the GNU General Public License as published by
10			* the Free Software Foundation; either version 2 of the License, or
11			* (at your option) any later version.
12			*
13			* This program is distributed in the hope that it will be useful,
14			* but WITHOUT ANY WARRANTY; without even the implied warranty of
15			* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16			* GNU General Public License for more details.
17			*
18			* You should have received a copy of the GNU General Public License
19			* along with this program; if not, write to the Free Software
20			* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
21			*/
22	cbauer	1.1
23			#include <iostream>
24			#include <stdexcept>
25
26	cbauer	1.3	#include "add.h"
27			#include "mul.h"
28	cbauer	1.5	#include "debugmsg.h"
29	kreckel	1.10	#include "utils.h"
30	cbauer	1.5
31	frink	1.7	#ifndef NO_GINAC_NAMESPACE
32	cbauer	1.5	namespace GiNaC {
33	frink	1.7	#endif // ndef NO_GINAC_NAMESPACE
34	cbauer	1.1
35			//////////
36			// default constructor, destructor, copy constructor assignment operator and helpers
37			//////////
38
39			// public
40
41			add::add()
42			{
43			debugmsg("add default constructor",LOGLEVEL_CONSTRUCT);
44	cbauer	1.3	tinfo_key = TINFO_add;
45	cbauer	1.1	}
46
47			add::~add()
48			{
49			debugmsg("add destructor",LOGLEVEL_DESTRUCT);
50			destroy(0);
51			}
52
53			add::add(add const & other)
54			{
55			debugmsg("add copy constructor",LOGLEVEL_CONSTRUCT);
56			copy(other);
57			}
58
59			add const & add::operator=(add const & other)
60			{
61			debugmsg("add operator=",LOGLEVEL_ASSIGNMENT);
62			if (this != &other) {
63			destroy(1);
64			copy(other);
65			}
66			return *this;
67			}
68
69			// protected
70
71			void add::copy(add const & other)
72			{
73			expairseq::copy(other);
74			}
75
76			void add::destroy(bool call_parent)
77			{
78			if (call_parent) expairseq::destroy(call_parent);
79			}
80
81			//////////
82			// other constructors
83			//////////
84
85			// public
86
87			add::add(ex const & lh, ex const & rh)
88			{
89			debugmsg("add constructor from ex,ex",LOGLEVEL_CONSTRUCT);
90	cbauer	1.3	tinfo_key = TINFO_add;
91	kreckel	1.10	overall_coeff=_ex0();
92	cbauer	1.1	construct_from_2_ex(lh,rh);
93	cbauer	1.6	GINAC_ASSERT(is_canonical());
94	cbauer	1.1	}
95
96			add::add(exvector const & v)
97			{
98			debugmsg("add constructor from exvector",LOGLEVEL_CONSTRUCT);
99	cbauer	1.3	tinfo_key = TINFO_add;
100	kreckel	1.10	overall_coeff=_ex0();
101	cbauer	1.1	construct_from_exvector(v);
102	cbauer	1.6	GINAC_ASSERT(is_canonical());
103	cbauer	1.1	}
104
105			/*
106			add::add(epvector const & v, bool do_not_canonicalize)
107			{
108			debugmsg("add constructor from epvector,bool",LOGLEVEL_CONSTRUCT);
109	cbauer	1.3	tinfo_key = TINFO_add;
110	cbauer	1.1	if (do_not_canonicalize) {
111			seq=v;
112			#ifdef EXPAIRSEQ_USE_HASHTAB
113			combine_same_terms(); // to build hashtab
114			#endif // def EXPAIRSEQ_USE_HASHTAB
115			} else {
116			construct_from_epvector(v);
117			}
118	cbauer	1.6	GINAC_ASSERT(is_canonical());
119	cbauer	1.1	}
120			*/
121
122			add::add(epvector const & v)
123			{
124			debugmsg("add constructor from epvector",LOGLEVEL_CONSTRUCT);
125	cbauer	1.3	tinfo_key = TINFO_add;
126	kreckel	1.10	overall_coeff=_ex0();
127	cbauer	1.1	construct_from_epvector(v);
128	cbauer	1.6	GINAC_ASSERT(is_canonical());
129	cbauer	1.1	}
130
131			add::add(epvector const & v, ex const & oc)
132			{
133			debugmsg("add constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
134	cbauer	1.3	tinfo_key = TINFO_add;
135	cbauer	1.1	overall_coeff=oc;
136			construct_from_epvector(v);
137	cbauer	1.6	GINAC_ASSERT(is_canonical());
138	cbauer	1.1	}
139
140			add::add(epvector * vp, ex const & oc)
141			{
142			debugmsg("add constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
143	cbauer	1.3	tinfo_key = TINFO_add;
144	cbauer	1.6	GINAC_ASSERT(vp!=0);
145	cbauer	1.1	overall_coeff=oc;
146			construct_from_epvector(*vp);
147			delete vp;
148	cbauer	1.6	GINAC_ASSERT(is_canonical());
149	cbauer	1.1	}
150
151			//////////
152			// functions overriding virtual functions from bases classes
153			//////////
154
155			// public
156
157			basic * add::duplicate() const
158			{
159			debugmsg("add duplicate",LOGLEVEL_DUPLICATE);
160			return new add(*this);
161			}
162
163	kreckel	1.11	/*void add::print(ostream & os, unsigned upper_precedence) const
164	kreckel	1.9	{
165			debugmsg("add print",LOGLEVEL_PRINT);
166			if (precedence<=upper_precedence) os << "(";
167			numeric coeff;
168			bool first=true;
169			for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
170			coeff = ex_to_numeric(cit->coeff);
171			if (!first) {
172			if (coeff.csgn()==-1) os << '-'; else os << '+';
173			} else {
174			if (coeff.csgn()==-1) os << '-';
175			first=false;
176			}
177	kreckel	1.10	if (!coeff.is_equal(_num1()) &&
178			!coeff.is_equal(_num_1())) {
179	kreckel	1.11	if (coeff.is_rational()) {
180			if (coeff.is_negative())
181			os << -coeff;
182			else
183			os << coeff;
184			} else {
185			if (coeff.csgn()==-1)
186			(-coeff).print(os, precedence);
187			else
188			coeff.print(os, precedence);
189			}
190	kreckel	1.9	os << '*';
191			}
192			os << cit->rest;
193			}
194			// print the overall numeric coefficient, if present:
195			if (!overall_coeff.is_zero()) {
196			if (overall_coeff.info(info_flags::positive)) os << '+';
197			os << overall_coeff;
198	kreckel	1.11	}
199			if (precedence<=upper_precedence) os << ")";
200			}*/
201
202			void add::print(ostream & os, unsigned upper_precedence) const
203			{
204			debugmsg("add print",LOGLEVEL_PRINT);
205			if (precedence<=upper_precedence) os << "(";
206			numeric coeff;
207			bool first = true;
208			// first print the overall numeric coefficient, if present:
209			if (!overall_coeff.is_zero()) {
210			os << overall_coeff;
211			first = false;
212			}
213			// then proceed with the remaining factors:
214			for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
215			coeff = ex_to_numeric(cit->coeff);
216			if (!first) {
217			if (coeff.csgn()==-1) os << '-'; else os << '+';
218			} else {
219			if (coeff.csgn()==-1) os << '-';
220			first = false;
221			}
222			if (!coeff.is_equal(_num1()) &&
223			!coeff.is_equal(_num_1())) {
224			if (coeff.is_rational()) {
225			if (coeff.is_negative())
226			os << -coeff;
227			else
228			os << coeff;
229			} else {
230			if (coeff.csgn()==-1)
231			(-coeff).print(os, precedence);
232			else
233			coeff.print(os, precedence);
234			}
235			os << '*';
236			}
237			os << cit->rest;
238	kreckel	1.9	}
239			if (precedence<=upper_precedence) os << ")";
240			}
241
242			void add::printraw(ostream & os) const
243			{
244			debugmsg("add printraw",LOGLEVEL_PRINT);
245
246			os << "+(";
247			for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
248			os << "(";
249			(*it).rest.bp->printraw(os);
250			os << ",";
251			(*it).coeff.bp->printraw(os);
252			os << "),";
253			}
254			os << ",hash=" << hashvalue << ",flags=" << flags;
255			os << ")";
256			}
257
258			void add::printcsrc(ostream & os, unsigned type, unsigned upper_precedence) const
259			{
260			debugmsg("add print csrc", LOGLEVEL_PRINT);
261			if (precedence <= upper_precedence)
262			os << "(";
263
264			// Print arguments, separated by "+"
265			epvector::const_iterator it = seq.begin();
266			epvector::const_iterator itend = seq.end();
267			while (it != itend) {
268
269			// If the coefficient is -1, it is replaced by a single minus sign
270	kreckel	1.10	if (it->coeff.compare(_num1()) == 0) {
271	kreckel	1.9	it->rest.bp->printcsrc(os, type, precedence);
272	kreckel	1.10	} else if (it->coeff.compare(_num_1()) == 0) {
273	kreckel	1.9	os << "-";
274			it->rest.bp->printcsrc(os, type, precedence);
275	kreckel	1.10	} else if (ex_to_numeric(it->coeff).numer().compare(_num1()) == 0) {
276	kreckel	1.9	it->rest.bp->printcsrc(os, type, precedence);
277			os << "/";
278			ex_to_numeric(it->coeff).denom().printcsrc(os, type, precedence);
279	kreckel	1.10	} else if (ex_to_numeric(it->coeff).numer().compare(_num_1()) == 0) {
280	kreckel	1.9	os << "-";
281			it->rest.bp->printcsrc(os, type, precedence);
282			os << "/";
283			ex_to_numeric(it->coeff).denom().printcsrc(os, type, precedence);
284			} else {
285			it->coeff.bp->printcsrc(os, type, precedence);
286			os << "*";
287			it->rest.bp->printcsrc(os, type, precedence);
288			}
289
290			// Separator is "+", except if the following expression would have a leading minus sign
291			it++;
292	kreckel	1.10	if (it != itend && !(it->coeff.compare(_num0()) < 0 \|\| (it->coeff.compare(_num1()) == 0 && is_ex_exactly_of_type(it->rest, numeric) && it->rest.compare(_num0()) < 0)))
293	kreckel	1.9	os << "+";
294			}
295
296	kreckel	1.10	if (!overall_coeff.is_equal(_ex0())) {
297	kreckel	1.9	if (overall_coeff.info(info_flags::positive)) os << '+';
298			overall_coeff.bp->printcsrc(os,type,precedence);
299			}
300
301			if (precedence <= upper_precedence)
302			os << ")";
303			}
304
305	cbauer	1.1	bool add::info(unsigned inf) const
306			{
307			// TODO: optimize
308	kreckel	1.9	if (inf==info_flags::polynomial \|\|
309			inf==info_flags::integer_polynomial \|\|
310			inf==info_flags::cinteger_polynomial \|\|
311			inf==info_flags::rational_polynomial \|\|
312			inf==info_flags::crational_polynomial \|\|
313			inf==info_flags::rational_function) {
314	cbauer	1.1	for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
315			if (!(recombine_pair_to_ex(*it).info(inf)))
316			return false;
317			}
318	kreckel	1.9	return overall_coeff.info(inf);
319	cbauer	1.1	} else {
320			return expairseq::info(inf);
321			}
322			}
323
324			int add::degree(symbol const & s) const
325			{
326			int deg=INT_MIN;
327	kreckel	1.10	if (!overall_coeff.is_equal(_ex0())) {
328	cbauer	1.1	deg=0;
329			}
330			int cur_deg;
331			for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
332			cur_deg=(*cit).rest.degree(s);
333			if (cur_deg>deg) deg=cur_deg;
334			}
335			return deg;
336			}
337
338			int add::ldegree(symbol const & s) const
339			{
340			int deg=INT_MAX;
341	kreckel	1.10	if (!overall_coeff.is_equal(_ex0())) {
342	cbauer	1.1	deg=0;
343			}
344			int cur_deg;
345			for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
346			cur_deg=(*cit).rest.ldegree(s);
347			if (cur_deg<deg) deg=cur_deg;
348			}
349			return deg;
350			}
351
352			ex add::coeff(symbol const & s, int const n) const
353			{
354			epvector coeffseq;
355			coeffseq.reserve(seq.size());
356
357			epvector::const_iterator it=seq.begin();
358			while (it!=seq.end()) {
359			coeffseq.push_back(combine_ex_with_coeff_to_pair((*it).rest.coeff(s,n),
360			(*it).coeff));
361			++it;
362			}
363			if (n==0) {
364			return (new add(coeffseq,overall_coeff))->setflag(status_flags::dynallocated);
365			}
366			return (new add(coeffseq))->setflag(status_flags::dynallocated);
367			}
368
369			ex add::eval(int level) const
370			{
371			// simplifications: +(;c) -> c
372			// +(x;1) -> x
373
374			debugmsg("add eval",LOGLEVEL_MEMBER_FUNCTION);
375
376			epvector * evaled_seqp=evalchildren(level);
377			if (evaled_seqp!=0) {
378			// do more evaluation later
379			return (new add(evaled_seqp,overall_coeff))->
380			setflag(status_flags::dynallocated);
381			}
382
383	cbauer	1.6	#ifdef DO_GINAC_ASSERT
384	cbauer	1.1	for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
385	cbauer	1.6	GINAC_ASSERT(!is_ex_exactly_of_type((*cit).rest,add));
386	cbauer	1.1	if (is_ex_exactly_of_type((*cit).rest,numeric)) {
387			dbgprint();
388			}
389	cbauer	1.6	GINAC_ASSERT(!is_ex_exactly_of_type((*cit).rest,numeric));
390	cbauer	1.1	}
391	cbauer	1.6	#endif // def DO_GINAC_ASSERT
392	cbauer	1.1
393			if (flags & status_flags::evaluated) {
394	cbauer	1.6	GINAC_ASSERT(seq.size()>0);
395	kreckel	1.10	GINAC_ASSERT((seq.size()>1)\|\|!overall_coeff.is_equal(_ex0()));
396	cbauer	1.1	return *this;
397			}
398
399			int seq_size=seq.size();
400			if (seq_size==0) {
401			// +(;c) -> c
402			return overall_coeff;
403	kreckel	1.10	} else if ((seq_size==1)&&overall_coeff.is_equal(_ex0())) {
404	cbauer	1.1	// +(x;0) -> x
405			return recombine_pair_to_ex(*(seq.begin()));
406			}
407			return this->hold();
408			}
409
410			exvector add::get_indices(void) const
411			{
412	cbauer	1.5	// FIXME: all terms in the sum should have the same indices (compatible
413			// tensors) however this is not checked, since there is no function yet
414			// which compares indices (idxvector can be unsorted)
415	cbauer	1.1	if (seq.size()==0) {
416			return exvector();
417			}
418			return (seq.begin())->rest.get_indices();
419			}
420
421			ex add::simplify_ncmul(exvector const & v) const
422			{
423			if (seq.size()==0) {
424			return expairseq::simplify_ncmul(v);
425			}
426			return (*seq.begin()).rest.simplify_ncmul(v);
427			}
428
429			// protected
430
431			int add::compare_same_type(basic const & other) const
432			{
433			return expairseq::compare_same_type(other);
434			}
435
436			bool add::is_equal_same_type(basic const & other) const
437			{
438			return expairseq::is_equal_same_type(other);
439			}
440
441			unsigned add::return_type(void) const
442			{
443			if (seq.size()==0) {
444			return return_types::commutative;
445			}
446			return (*seq.begin()).rest.return_type();
447			}
448
449			unsigned add::return_type_tinfo(void) const
450			{
451			if (seq.size()==0) {
452			return tinfo_key;
453			}
454			return (*seq.begin()).rest.return_type_tinfo();
455			}
456
457			ex add::thisexpairseq(epvector const & v, ex const & oc) const
458			{
459			return (new add(v,oc))->setflag(status_flags::dynallocated);
460			}
461
462			ex add::thisexpairseq(epvector * vp, ex const & oc) const
463			{
464			return (new add(vp,oc))->setflag(status_flags::dynallocated);
465			}
466
467			expair add::split_ex_to_pair(ex const & e) const
468			{
469			if (is_ex_exactly_of_type(e,mul)) {
470			mul const & mulref=ex_to_mul(e);
471			ex numfactor=mulref.overall_coeff;
472			// mul * mulcopyp=static_cast<mul *>(mulref.duplicate());
473			mul * mulcopyp=new mul(mulref);
474	kreckel	1.10	mulcopyp->overall_coeff=_ex1();
475	cbauer	1.1	mulcopyp->clearflag(status_flags::evaluated);
476			mulcopyp->clearflag(status_flags::hash_calculated);
477			return expair(mulcopyp->setflag(status_flags::dynallocated),numfactor);
478			}
479	kreckel	1.10	return expair(e,_ex1());
480	cbauer	1.1	}
481
482			expair add::combine_ex_with_coeff_to_pair(ex const & e,
483			ex const & c) const
484			{
485	cbauer	1.6	GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
486	cbauer	1.1	if (is_ex_exactly_of_type(e,mul)) {
487			mul const & mulref=ex_to_mul(e);
488			ex numfactor=mulref.overall_coeff;
489			//mul * mulcopyp=static_cast<mul *>(mulref.duplicate());
490			mul * mulcopyp=new mul(mulref);
491	kreckel	1.10	mulcopyp->overall_coeff=_ex1();
492	cbauer	1.1	mulcopyp->clearflag(status_flags::evaluated);
493			mulcopyp->clearflag(status_flags::hash_calculated);
494	kreckel	1.10	if (are_ex_trivially_equal(c,_ex1())) {
495	cbauer	1.1	return expair(mulcopyp->setflag(status_flags::dynallocated),numfactor);
496	kreckel	1.10	} else if (are_ex_trivially_equal(numfactor,_ex1())) {
497	cbauer	1.1	return expair(mulcopyp->setflag(status_flags::dynallocated),c);
498			}
499			return expair(mulcopyp->setflag(status_flags::dynallocated),
500			ex_to_numeric(numfactor).mul_dyn(ex_to_numeric(c)));
501			} else if (is_ex_exactly_of_type(e,numeric)) {
502	kreckel	1.10	if (are_ex_trivially_equal(c,_ex1())) {
503			return expair(e,_ex1());
504	cbauer	1.1	}
505	kreckel	1.10	return expair(ex_to_numeric(e).mul_dyn(ex_to_numeric(c)),_ex1());
506	cbauer	1.1	}
507			return expair(e,c);
508			}
509
510			expair add::combine_pair_with_coeff_to_pair(expair const & p,
511			ex const & c) const
512			{
513	cbauer	1.6	GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
514			GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
515	cbauer	1.1
516			if (is_ex_exactly_of_type(p.rest,numeric)) {
517	kreckel	1.10	GINAC_ASSERT(ex_to_numeric(p.coeff).is_equal(_num1())); // should be normalized
518			return expair(ex_to_numeric(p.rest).mul_dyn(ex_to_numeric(c)),_ex1());
519	cbauer	1.1	}
520
521			return expair(p.rest,ex_to_numeric(p.coeff).mul_dyn(ex_to_numeric(c)));
522			}
523
524			ex add::recombine_pair_to_ex(expair const & p) const
525			{
526	kreckel	1.10	//if (p.coeff.compare(_ex1())==0) {
527			//if (are_ex_trivially_equal(p.coeff,_ex1())) {
528			if (ex_to_numeric(p.coeff).is_equal(_num1())) {
529	cbauer	1.1	return p.rest;
530			} else {
531			return p.rest*p.coeff;
532			}
533			}
534
535			ex add::expand(unsigned options) const
536			{
537			epvector * vp=expandchildren(options);
538			if (vp==0) {
539			return *this;
540			}
541			return (new add(vp,overall_coeff))->setflag(status_flags::expanded \|
542			status_flags::dynallocated );
543			}
544
545			//////////
546			// new virtual functions which can be overridden by derived classes
547			//////////
548
549			// none
550
551			//////////
552			// non-virtual functions in this class
553			//////////
554
555			// none
556
557			//////////
558			// static member variables
559			//////////
560
561			// protected
562
563			unsigned add::precedence=40;
564
565			//////////
566			// global constants
567			//////////
568
569			const add some_add;
570			type_info const & typeid_add=typeid(some_add);
571
572	frink	1.7	#ifndef NO_GINAC_NAMESPACE
573	cbauer	1.5	} // namespace GiNaC
574	frink	1.7	#endif // ndef NO_GINAC_NAMESPACE
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