GiNaC/ginac/add.cpp

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

/*
 *  GiNaC Copyright (C) 1999-2000 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 "archive.h"
#include "debugmsg.h"
#include "utils.h"

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

GINAC_IMPLEMENT_REGISTERED_CLASS(add, expairseq)

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

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

// protected

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

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

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

// public

add::add(const ex & lh, const ex & 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(const exvector & 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(const epvector & 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(const epvector & 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(const epvector & v, const ex & 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, const ex & 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());
}

//////////
// archiving
//////////

/** Construct object from archive_node. */
add::add(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
{
    debugmsg("add constructor from archive_node", LOGLEVEL_CONSTRUCT);
}

/** Unarchive the object. */
ex add::unarchive(const archive_node &n, const lst &sym_lst)
{
    return (new add(n, sym_lst))->setflag(status_flags::dynallocated);
}

/** Archive the object. */
void add::archive(archive_node &n) const
{
    inherited::archive(n);
}

//////////
// 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;
    // 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 inherited::info(inf);
    }
}

int add::degree(const symbol & 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(const symbol & 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(const symbol & s, int 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(const exvector & v) const
{
    if (seq.size()==0) {
        return inherited::simplify_ncmul(v);
    }
    return (*seq.begin()).rest.simplify_ncmul(v);
}    

// protected

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

bool add::is_equal_same_type(const basic & other) const
{
    return inherited::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(const epvector & v, const ex & oc) const
{
    return (new add(v,oc))->setflag(status_flags::dynallocated);
}

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

expair add::split_ex_to_pair(const ex & e) const
{
    if (is_ex_exactly_of_type(e,mul)) {
        const mul & 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(const ex & e,
                                          const ex & c) const
{
    GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
    if (is_ex_exactly_of_type(e,mul)) {
        const mul & 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(const expair & p,
                                            const ex & 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(const expair & 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;
const type_info & 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	kreckel	1.12	* GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
7	cbauer	1.2	*
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	1.13	#include "archive.h"
29	cbauer	1.5	#include "debugmsg.h"
30	kreckel	1.10	#include "utils.h"
31	cbauer	1.5
32	frink	1.7	#ifndef NO_GINAC_NAMESPACE
33	cbauer	1.5	namespace GiNaC {
34	frink	1.7	#endif // ndef NO_GINAC_NAMESPACE
35	cbauer	1.1
36	cbauer	1.13	GINAC_IMPLEMENT_REGISTERED_CLASS(add, expairseq)
37
38	cbauer	1.1	//////////
39			// default constructor, destructor, copy constructor assignment operator and helpers
40			//////////
41
42			// public
43
44			add::add()
45			{
46			debugmsg("add default constructor",LOGLEVEL_CONSTRUCT);
47	cbauer	1.3	tinfo_key = TINFO_add;
48	cbauer	1.1	}
49
50			add::~add()
51			{
52			debugmsg("add destructor",LOGLEVEL_DESTRUCT);
53			destroy(0);
54			}
55
56	cbauer	1.14	add::add(const add & other)
57	cbauer	1.1	{
58			debugmsg("add copy constructor",LOGLEVEL_CONSTRUCT);
59			copy(other);
60			}
61
62	cbauer	1.14	const add & add::operator=(const add & other)
63	cbauer	1.1	{
64			debugmsg("add operator=",LOGLEVEL_ASSIGNMENT);
65			if (this != &other) {
66			destroy(1);
67			copy(other);
68			}
69			return *this;
70			}
71
72			// protected
73
74	cbauer	1.14	void add::copy(const add & other)
75	cbauer	1.1	{
76	cbauer	1.13	inherited::copy(other);
77	cbauer	1.1	}
78
79			void add::destroy(bool call_parent)
80			{
81	cbauer	1.13	if (call_parent) inherited::destroy(call_parent);
82	cbauer	1.1	}
83
84			//////////
85			// other constructors
86			//////////
87
88			// public
89
90	cbauer	1.14	add::add(const ex & lh, const ex & rh)
91	cbauer	1.1	{
92			debugmsg("add constructor from ex,ex",LOGLEVEL_CONSTRUCT);
93	cbauer	1.3	tinfo_key = TINFO_add;
94	kreckel	1.10	overall_coeff=_ex0();
95	cbauer	1.1	construct_from_2_ex(lh,rh);
96	cbauer	1.6	GINAC_ASSERT(is_canonical());
97	cbauer	1.1	}
98
99	cbauer	1.14	add::add(const exvector & v)
100	cbauer	1.1	{
101			debugmsg("add constructor from exvector",LOGLEVEL_CONSTRUCT);
102	cbauer	1.3	tinfo_key = TINFO_add;
103	kreckel	1.10	overall_coeff=_ex0();
104	cbauer	1.1	construct_from_exvector(v);
105	cbauer	1.6	GINAC_ASSERT(is_canonical());
106	cbauer	1.1	}
107
108			/*
109	cbauer	1.14	add::add(const epvector & v, bool do_not_canonicalize)
110	cbauer	1.1	{
111			debugmsg("add constructor from epvector,bool",LOGLEVEL_CONSTRUCT);
112	cbauer	1.3	tinfo_key = TINFO_add;
113	cbauer	1.1	if (do_not_canonicalize) {
114			seq=v;
115			#ifdef EXPAIRSEQ_USE_HASHTAB
116			combine_same_terms(); // to build hashtab
117			#endif // def EXPAIRSEQ_USE_HASHTAB
118			} else {
119			construct_from_epvector(v);
120			}
121	cbauer	1.6	GINAC_ASSERT(is_canonical());
122	cbauer	1.1	}
123			*/
124
125	cbauer	1.14	add::add(const epvector & v)
126	cbauer	1.1	{
127			debugmsg("add constructor from epvector",LOGLEVEL_CONSTRUCT);
128	cbauer	1.3	tinfo_key = TINFO_add;
129	kreckel	1.10	overall_coeff=_ex0();
130	cbauer	1.1	construct_from_epvector(v);
131	cbauer	1.6	GINAC_ASSERT(is_canonical());
132	cbauer	1.1	}
133
134	cbauer	1.14	add::add(const epvector & v, const ex & oc)
135	cbauer	1.1	{
136			debugmsg("add constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
137	cbauer	1.3	tinfo_key = TINFO_add;
138	cbauer	1.1	overall_coeff=oc;
139			construct_from_epvector(v);
140	cbauer	1.6	GINAC_ASSERT(is_canonical());
141	cbauer	1.1	}
142
143	cbauer	1.14	add::add(epvector * vp, const ex & oc)
144	cbauer	1.1	{
145			debugmsg("add constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
146	cbauer	1.3	tinfo_key = TINFO_add;
147	cbauer	1.6	GINAC_ASSERT(vp!=0);
148	cbauer	1.1	overall_coeff=oc;
149			construct_from_epvector(*vp);
150			delete vp;
151	cbauer	1.6	GINAC_ASSERT(is_canonical());
152	cbauer	1.1	}
153
154			//////////
155	cbauer	1.13	// archiving
156			//////////
157
158			/** Construct object from archive_node. */
159			add::add(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
160			{
161			debugmsg("add constructor from archive_node", LOGLEVEL_CONSTRUCT);
162			}
163
164			/** Unarchive the object. */
165			ex add::unarchive(const archive_node &n, const lst &sym_lst)
166			{
167			return (new add(n, sym_lst))->setflag(status_flags::dynallocated);
168			}
169
170			/** Archive the object. */
171			void add::archive(archive_node &n) const
172			{
173			inherited::archive(n);
174			}
175
176			//////////
177	cbauer	1.1	// functions overriding virtual functions from bases classes
178			//////////
179
180			// public
181
182			basic * add::duplicate() const
183			{
184			debugmsg("add duplicate",LOGLEVEL_DUPLICATE);
185			return new add(*this);
186			}
187
188	kreckel	1.11	void add::print(ostream & os, unsigned upper_precedence) const
189			{
190			debugmsg("add print",LOGLEVEL_PRINT);
191			if (precedence<=upper_precedence) os << "(";
192			numeric coeff;
193			bool first = true;
194			// first print the overall numeric coefficient, if present:
195			if (!overall_coeff.is_zero()) {
196			os << overall_coeff;
197			first = false;
198			}
199			// then proceed with the remaining factors:
200			for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
201			coeff = ex_to_numeric(cit->coeff);
202			if (!first) {
203			if (coeff.csgn()==-1) os << '-'; else os << '+';
204			} else {
205			if (coeff.csgn()==-1) os << '-';
206			first = false;
207			}
208			if (!coeff.is_equal(_num1()) &&
209			!coeff.is_equal(_num_1())) {
210			if (coeff.is_rational()) {
211			if (coeff.is_negative())
212			os << -coeff;
213			else
214			os << coeff;
215			} else {
216			if (coeff.csgn()==-1)
217			(-coeff).print(os, precedence);
218			else
219			coeff.print(os, precedence);
220			}
221			os << '*';
222			}
223			os << cit->rest;
224	kreckel	1.9	}
225			if (precedence<=upper_precedence) os << ")";
226			}
227
228			void add::printraw(ostream & os) const
229			{
230			debugmsg("add printraw",LOGLEVEL_PRINT);
231
232			os << "+(";
233			for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
234			os << "(";
235			(*it).rest.bp->printraw(os);
236			os << ",";
237			(*it).coeff.bp->printraw(os);
238			os << "),";
239			}
240			os << ",hash=" << hashvalue << ",flags=" << flags;
241			os << ")";
242			}
243
244			void add::printcsrc(ostream & os, unsigned type, unsigned upper_precedence) const
245			{
246			debugmsg("add print csrc", LOGLEVEL_PRINT);
247			if (precedence <= upper_precedence)
248			os << "(";
249
250			// Print arguments, separated by "+"
251			epvector::const_iterator it = seq.begin();
252			epvector::const_iterator itend = seq.end();
253			while (it != itend) {
254
255			// If the coefficient is -1, it is replaced by a single minus sign
256	kreckel	1.10	if (it->coeff.compare(_num1()) == 0) {
257	kreckel	1.9	it->rest.bp->printcsrc(os, type, precedence);
258	kreckel	1.10	} else if (it->coeff.compare(_num_1()) == 0) {
259	kreckel	1.9	os << "-";
260			it->rest.bp->printcsrc(os, type, precedence);
261	kreckel	1.10	} else if (ex_to_numeric(it->coeff).numer().compare(_num1()) == 0) {
262	kreckel	1.9	it->rest.bp->printcsrc(os, type, precedence);
263			os << "/";
264			ex_to_numeric(it->coeff).denom().printcsrc(os, type, precedence);
265	kreckel	1.10	} else if (ex_to_numeric(it->coeff).numer().compare(_num_1()) == 0) {
266	kreckel	1.9	os << "-";
267			it->rest.bp->printcsrc(os, type, precedence);
268			os << "/";
269			ex_to_numeric(it->coeff).denom().printcsrc(os, type, precedence);
270			} else {
271			it->coeff.bp->printcsrc(os, type, precedence);
272			os << "*";
273			it->rest.bp->printcsrc(os, type, precedence);
274			}
275
276			// Separator is "+", except if the following expression would have a leading minus sign
277			it++;
278	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)))
279	kreckel	1.9	os << "+";
280			}
281
282	kreckel	1.10	if (!overall_coeff.is_equal(_ex0())) {
283	kreckel	1.9	if (overall_coeff.info(info_flags::positive)) os << '+';
284			overall_coeff.bp->printcsrc(os,type,precedence);
285			}
286
287			if (precedence <= upper_precedence)
288			os << ")";
289			}
290
291	cbauer	1.1	bool add::info(unsigned inf) const
292			{
293			// TODO: optimize
294	kreckel	1.9	if (inf==info_flags::polynomial \|\|
295			inf==info_flags::integer_polynomial \|\|
296			inf==info_flags::cinteger_polynomial \|\|
297			inf==info_flags::rational_polynomial \|\|
298			inf==info_flags::crational_polynomial \|\|
299			inf==info_flags::rational_function) {
300	cbauer	1.1	for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
301			if (!(recombine_pair_to_ex(*it).info(inf)))
302			return false;
303			}
304	kreckel	1.9	return overall_coeff.info(inf);
305	cbauer	1.1	} else {
306	cbauer	1.13	return inherited::info(inf);
307	cbauer	1.1	}
308			}
309
310	cbauer	1.14	int add::degree(const symbol & s) const
311	cbauer	1.1	{
312			int deg=INT_MIN;
313	kreckel	1.10	if (!overall_coeff.is_equal(_ex0())) {
314	cbauer	1.1	deg=0;
315			}
316			int cur_deg;
317			for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
318			cur_deg=(*cit).rest.degree(s);
319			if (cur_deg>deg) deg=cur_deg;
320			}
321			return deg;
322			}
323
324	cbauer	1.14	int add::ldegree(const symbol & s) const
325	cbauer	1.1	{
326			int deg=INT_MAX;
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.ldegree(s);
333			if (cur_deg<deg) deg=cur_deg;
334			}
335			return deg;
336			}
337
338	cbauer	1.14	ex add::coeff(const symbol & s, int n) const
339	cbauer	1.1	{
340			epvector coeffseq;
341			coeffseq.reserve(seq.size());
342
343			epvector::const_iterator it=seq.begin();
344			while (it!=seq.end()) {
345			coeffseq.push_back(combine_ex_with_coeff_to_pair((*it).rest.coeff(s,n),
346			(*it).coeff));
347			++it;
348			}
349			if (n==0) {
350			return (new add(coeffseq,overall_coeff))->setflag(status_flags::dynallocated);
351			}
352			return (new add(coeffseq))->setflag(status_flags::dynallocated);
353			}
354
355			ex add::eval(int level) const
356			{
357			// simplifications: +(;c) -> c
358			// +(x;1) -> x
359
360			debugmsg("add eval",LOGLEVEL_MEMBER_FUNCTION);
361
362			epvector * evaled_seqp=evalchildren(level);
363			if (evaled_seqp!=0) {
364			// do more evaluation later
365			return (new add(evaled_seqp,overall_coeff))->
366			setflag(status_flags::dynallocated);
367			}
368
369	cbauer	1.6	#ifdef DO_GINAC_ASSERT
370	cbauer	1.1	for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
371	cbauer	1.6	GINAC_ASSERT(!is_ex_exactly_of_type((*cit).rest,add));
372	cbauer	1.1	if (is_ex_exactly_of_type((*cit).rest,numeric)) {
373			dbgprint();
374			}
375	cbauer	1.6	GINAC_ASSERT(!is_ex_exactly_of_type((*cit).rest,numeric));
376	cbauer	1.1	}
377	cbauer	1.6	#endif // def DO_GINAC_ASSERT
378	cbauer	1.1
379			if (flags & status_flags::evaluated) {
380	cbauer	1.6	GINAC_ASSERT(seq.size()>0);
381	kreckel	1.10	GINAC_ASSERT((seq.size()>1)\|\|!overall_coeff.is_equal(_ex0()));
382	cbauer	1.1	return *this;
383			}
384
385			int seq_size=seq.size();
386			if (seq_size==0) {
387			// +(;c) -> c
388			return overall_coeff;
389	kreckel	1.10	} else if ((seq_size==1)&&overall_coeff.is_equal(_ex0())) {
390	cbauer	1.1	// +(x;0) -> x
391			return recombine_pair_to_ex(*(seq.begin()));
392			}
393			return this->hold();
394			}
395
396			exvector add::get_indices(void) const
397			{
398	cbauer	1.5	// FIXME: all terms in the sum should have the same indices (compatible
399			// tensors) however this is not checked, since there is no function yet
400			// which compares indices (idxvector can be unsorted)
401	cbauer	1.1	if (seq.size()==0) {
402			return exvector();
403			}
404			return (seq.begin())->rest.get_indices();
405			}
406
407	cbauer	1.14	ex add::simplify_ncmul(const exvector & v) const
408	cbauer	1.1	{
409			if (seq.size()==0) {
410	cbauer	1.13	return inherited::simplify_ncmul(v);
411	cbauer	1.1	}
412			return (*seq.begin()).rest.simplify_ncmul(v);
413			}
414
415			// protected
416
417	cbauer	1.14	int add::compare_same_type(const basic & other) const
418	cbauer	1.1	{
419	cbauer	1.13	return inherited::compare_same_type(other);
420	cbauer	1.1	}
421
422	cbauer	1.14	bool add::is_equal_same_type(const basic & other) const
423	cbauer	1.1	{
424	cbauer	1.13	return inherited::is_equal_same_type(other);
425	cbauer	1.1	}
426
427			unsigned add::return_type(void) const
428			{
429			if (seq.size()==0) {
430			return return_types::commutative;
431			}
432			return (*seq.begin()).rest.return_type();
433			}
434
435			unsigned add::return_type_tinfo(void) const
436			{
437			if (seq.size()==0) {
438			return tinfo_key;
439			}
440			return (*seq.begin()).rest.return_type_tinfo();
441			}
442
443	cbauer	1.14	ex add::thisexpairseq(const epvector & v, const ex & oc) const
444	cbauer	1.1	{
445			return (new add(v,oc))->setflag(status_flags::dynallocated);
446			}
447
448	cbauer	1.14	ex add::thisexpairseq(epvector * vp, const ex & oc) const
449	cbauer	1.1	{
450			return (new add(vp,oc))->setflag(status_flags::dynallocated);
451			}
452
453	cbauer	1.14	expair add::split_ex_to_pair(const ex & e) const
454	cbauer	1.1	{
455			if (is_ex_exactly_of_type(e,mul)) {
456	cbauer	1.14	const mul & mulref=ex_to_mul(e);
457	cbauer	1.1	ex numfactor=mulref.overall_coeff;
458			// mul * mulcopyp=static_cast<mul *>(mulref.duplicate());
459			mul * mulcopyp=new mul(mulref);
460	kreckel	1.10	mulcopyp->overall_coeff=_ex1();
461	cbauer	1.1	mulcopyp->clearflag(status_flags::evaluated);
462			mulcopyp->clearflag(status_flags::hash_calculated);
463			return expair(mulcopyp->setflag(status_flags::dynallocated),numfactor);
464			}
465	kreckel	1.10	return expair(e,_ex1());
466	cbauer	1.1	}
467
468	cbauer	1.14	expair add::combine_ex_with_coeff_to_pair(const ex & e,
469			const ex & c) const
470	cbauer	1.1	{
471	cbauer	1.6	GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
472	cbauer	1.1	if (is_ex_exactly_of_type(e,mul)) {
473	cbauer	1.14	const mul & mulref=ex_to_mul(e);
474	cbauer	1.1	ex numfactor=mulref.overall_coeff;
475			//mul * mulcopyp=static_cast<mul *>(mulref.duplicate());
476			mul * mulcopyp=new mul(mulref);
477	kreckel	1.10	mulcopyp->overall_coeff=_ex1();
478	cbauer	1.1	mulcopyp->clearflag(status_flags::evaluated);
479			mulcopyp->clearflag(status_flags::hash_calculated);
480	kreckel	1.10	if (are_ex_trivially_equal(c,_ex1())) {
481	cbauer	1.1	return expair(mulcopyp->setflag(status_flags::dynallocated),numfactor);
482	kreckel	1.10	} else if (are_ex_trivially_equal(numfactor,_ex1())) {
483	cbauer	1.1	return expair(mulcopyp->setflag(status_flags::dynallocated),c);
484			}
485			return expair(mulcopyp->setflag(status_flags::dynallocated),
486			ex_to_numeric(numfactor).mul_dyn(ex_to_numeric(c)));
487			} else if (is_ex_exactly_of_type(e,numeric)) {
488	kreckel	1.10	if (are_ex_trivially_equal(c,_ex1())) {
489			return expair(e,_ex1());
490	cbauer	1.1	}
491	kreckel	1.10	return expair(ex_to_numeric(e).mul_dyn(ex_to_numeric(c)),_ex1());
492	cbauer	1.1	}
493			return expair(e,c);
494			}
495
496	cbauer	1.14	expair add::combine_pair_with_coeff_to_pair(const expair & p,
497			const ex & c) const
498	cbauer	1.1	{
499	cbauer	1.6	GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
500			GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
501	cbauer	1.1
502			if (is_ex_exactly_of_type(p.rest,numeric)) {
503	kreckel	1.10	GINAC_ASSERT(ex_to_numeric(p.coeff).is_equal(_num1())); // should be normalized
504			return expair(ex_to_numeric(p.rest).mul_dyn(ex_to_numeric(c)),_ex1());
505	cbauer	1.1	}
506
507			return expair(p.rest,ex_to_numeric(p.coeff).mul_dyn(ex_to_numeric(c)));
508			}
509
510	cbauer	1.14	ex add::recombine_pair_to_ex(const expair & p) const
511	cbauer	1.1	{
512	kreckel	1.10	//if (p.coeff.compare(_ex1())==0) {
513			//if (are_ex_trivially_equal(p.coeff,_ex1())) {
514			if (ex_to_numeric(p.coeff).is_equal(_num1())) {
515	cbauer	1.1	return p.rest;
516			} else {
517			return p.rest*p.coeff;
518			}
519			}
520
521			ex add::expand(unsigned options) const
522			{
523			epvector * vp=expandchildren(options);
524			if (vp==0) {
525			return *this;
526			}
527			return (new add(vp,overall_coeff))->setflag(status_flags::expanded \|
528			status_flags::dynallocated );
529			}
530
531			//////////
532			// new virtual functions which can be overridden by derived classes
533			//////////
534
535			// none
536
537			//////////
538			// non-virtual functions in this class
539			//////////
540
541			// none
542
543			//////////
544			// static member variables
545			//////////
546
547			// protected
548
549			unsigned add::precedence=40;
550
551			//////////
552			// global constants
553			//////////
554
555			const add some_add;
556	cbauer	1.14	const type_info & typeid_add=typeid(some_add);
557	cbauer	1.1
558	frink	1.7	#ifndef NO_GINAC_NAMESPACE
559	cbauer	1.5	} // namespace GiNaC
560	frink	1.7	#endif // ndef NO_GINAC_NAMESPACE
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