3 * Implementation of GiNaC's sums of expressions. */
6 * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
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.
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.
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
29 #include "operators.h"
35 GINAC_IMPLEMENT_REGISTERED_CLASS(add, expairseq)
38 // default constructor
43 tinfo_key = TINFO_add;
52 add::add(const ex & lh, const ex & rh)
54 tinfo_key = TINFO_add;
56 construct_from_2_ex(lh,rh);
57 GINAC_ASSERT(is_canonical());
60 add::add(const exvector & v)
62 tinfo_key = TINFO_add;
64 construct_from_exvector(v);
65 GINAC_ASSERT(is_canonical());
68 add::add(const epvector & v)
70 tinfo_key = TINFO_add;
72 construct_from_epvector(v);
73 GINAC_ASSERT(is_canonical());
76 add::add(const epvector & v, const ex & oc)
78 tinfo_key = TINFO_add;
80 construct_from_epvector(v);
81 GINAC_ASSERT(is_canonical());
84 add::add(epvector * vp, const ex & oc)
86 tinfo_key = TINFO_add;
89 construct_from_epvector(*vp);
91 GINAC_ASSERT(is_canonical());
98 DEFAULT_ARCHIVING(add)
101 // functions overriding virtual functions from base classes
106 void add::print(const print_context & c, unsigned level) const
108 if (is_a<print_tree>(c)) {
110 inherited::print(c, level);
112 } else if (is_a<print_csrc>(c)) {
114 if (precedence() <= level)
117 // Print arguments, separated by "+"
118 epvector::const_iterator it = seq.begin(), itend = seq.end();
119 while (it != itend) {
121 // If the coefficient is -1, it is replaced by a single minus sign
122 if (it->coeff.is_equal(_ex1)) {
123 it->rest.print(c, precedence());
124 } else if (it->coeff.is_equal(_ex_1)) {
126 it->rest.print(c, precedence());
127 } else if (ex_to<numeric>(it->coeff).numer().is_equal(_num1)) {
128 it->rest.print(c, precedence());
130 ex_to<numeric>(it->coeff).denom().print(c, precedence());
131 } else if (ex_to<numeric>(it->coeff).numer().is_equal(_num_1)) {
133 it->rest.print(c, precedence());
135 ex_to<numeric>(it->coeff).denom().print(c, precedence());
137 it->coeff.print(c, precedence());
139 it->rest.print(c, precedence());
142 // Separator is "+", except if the following expression would have a leading minus sign or the sign is sitting in parenthesis (as in a ctor)
145 && (is_a<print_csrc_cl_N>(c) || !it->coeff.info(info_flags::real) // sign inside ctor arguments
146 || !(it->coeff.info(info_flags::negative) || (it->coeff.is_equal(_num1) && is_exactly_a<numeric>(it->rest) && it->rest.info(info_flags::negative)))))
150 if (!overall_coeff.is_zero()) {
151 if (overall_coeff.info(info_flags::positive)
152 || is_a<print_csrc_cl_N>(c) || !overall_coeff.info(info_flags::real)) // sign inside ctor argument
154 overall_coeff.print(c, precedence());
157 if (precedence() <= level)
160 } else if (is_a<print_python_repr>(c)) {
162 c.s << class_name() << '(';
164 for (size_t i=1; i<nops(); ++i) {
172 if (precedence() <= level) {
173 if (is_a<print_latex>(c))
182 // First print the overall numeric coefficient, if present
183 if (!overall_coeff.is_zero()) {
184 if (!is_a<print_tree>(c))
185 overall_coeff.print(c, 0);
187 overall_coeff.print(c, precedence());
191 // Then proceed with the remaining factors
192 epvector::const_iterator it = seq.begin(), itend = seq.end();
193 while (it != itend) {
194 coeff = ex_to<numeric>(it->coeff);
196 if (coeff.csgn() == -1) c.s << '-'; else c.s << '+';
198 if (coeff.csgn() == -1) c.s << '-';
201 if (!coeff.is_equal(_num1) &&
202 !coeff.is_equal(_num_1)) {
203 if (coeff.is_rational()) {
204 if (coeff.is_negative())
209 if (coeff.csgn() == -1)
210 (-coeff).print(c, precedence());
212 coeff.print(c, precedence());
214 if (is_a<print_latex>(c))
219 it->rest.print(c, precedence());
223 if (precedence() <= level) {
224 if (is_a<print_latex>(c))
232 bool add::info(unsigned inf) const
235 case info_flags::polynomial:
236 case info_flags::integer_polynomial:
237 case info_flags::cinteger_polynomial:
238 case info_flags::rational_polynomial:
239 case info_flags::crational_polynomial:
240 case info_flags::rational_function: {
241 epvector::const_iterator i = seq.begin(), end = seq.end();
243 if (!(recombine_pair_to_ex(*i).info(inf)))
247 return overall_coeff.info(inf);
249 case info_flags::algebraic: {
250 epvector::const_iterator i = seq.begin(), end = seq.end();
252 if ((recombine_pair_to_ex(*i).info(inf)))
259 return inherited::info(inf);
262 int add::degree(const ex & s) const
265 if (!overall_coeff.is_zero())
268 // Find maximum of degrees of individual terms
269 epvector::const_iterator i = seq.begin(), end = seq.end();
271 int cur_deg = i->rest.degree(s);
279 int add::ldegree(const ex & s) const
282 if (!overall_coeff.is_zero())
285 // Find minimum of degrees of individual terms
286 epvector::const_iterator i = seq.begin(), end = seq.end();
288 int cur_deg = i->rest.ldegree(s);
296 ex add::coeff(const ex & s, int n) const
298 epvector *coeffseq = new epvector();
300 // Calculate sum of coefficients in each term
301 epvector::const_iterator i = seq.begin(), end = seq.end();
303 ex restcoeff = i->rest.coeff(s, n);
304 if (!restcoeff.is_zero())
305 coeffseq->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
309 return (new add(coeffseq, n==0 ? overall_coeff : _ex0))->setflag(status_flags::dynallocated);
312 /** Perform automatic term rewriting rules in this class. In the following
313 * x stands for a symbolic variables of type ex and c stands for such
314 * an expression that contain a plain number.
318 * @param level cut-off in recursive evaluation */
319 ex add::eval(int level) const
321 epvector *evaled_seqp = evalchildren(level);
323 // do more evaluation later
324 return (new add(evaled_seqp, overall_coeff))->
325 setflag(status_flags::dynallocated);
328 #ifdef DO_GINAC_ASSERT
329 epvector::const_iterator i = seq.begin(), end = seq.end();
331 GINAC_ASSERT(!is_exactly_a<add>(i->rest));
332 if (is_exactly_a<numeric>(i->rest))
334 GINAC_ASSERT(!is_exactly_a<numeric>(i->rest));
337 #endif // def DO_GINAC_ASSERT
339 if (flags & status_flags::evaluated) {
340 GINAC_ASSERT(seq.size()>0);
341 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_zero());
345 int seq_size = seq.size();
348 return overall_coeff;
349 } else if (seq_size == 1 && overall_coeff.is_zero()) {
351 return recombine_pair_to_ex(*(seq.begin()));
352 } else if (!overall_coeff.is_zero() && seq[0].rest.return_type() != return_types::commutative) {
353 throw (std::logic_error("add::eval(): sum of non-commutative objects has non-zero numeric term"));
358 ex add::evalm() const
360 // Evaluate children first and add up all matrices. Stop if there's one
361 // term that is not a matrix.
362 epvector *s = new epvector;
363 s->reserve(seq.size());
365 bool all_matrices = true;
366 bool first_term = true;
369 epvector::const_iterator it = seq.begin(), itend = seq.end();
370 while (it != itend) {
371 const ex &m = recombine_pair_to_ex(*it).evalm();
372 s->push_back(split_ex_to_pair(m));
373 if (is_a<matrix>(m)) {
375 sum = ex_to<matrix>(m);
378 sum = sum.add(ex_to<matrix>(m));
380 all_matrices = false;
386 return sum + overall_coeff;
388 return (new add(s, overall_coeff))->setflag(status_flags::dynallocated);
391 ex add::eval_ncmul(const exvector & v) const
394 return inherited::eval_ncmul(v);
396 return seq.begin()->rest.eval_ncmul(v);
401 /** Implementation of ex::diff() for a sum. It differentiates each term.
403 ex add::derivative(const symbol & y) const
405 epvector *s = new epvector();
406 s->reserve(seq.size());
408 // Only differentiate the "rest" parts of the expairs. This is faster
409 // than the default implementation in basic::derivative() although
410 // if performs the same function (differentiate each term).
411 epvector::const_iterator i = seq.begin(), end = seq.end();
413 s->push_back(combine_ex_with_coeff_to_pair(i->rest.diff(y), i->coeff));
416 return (new add(s, _ex0))->setflag(status_flags::dynallocated);
419 int add::compare_same_type(const basic & other) const
421 return inherited::compare_same_type(other);
424 unsigned add::return_type() const
427 return return_types::commutative;
429 return seq.begin()->rest.return_type();
432 unsigned add::return_type_tinfo() const
437 return seq.begin()->rest.return_type_tinfo();
440 ex add::thisexpairseq(const epvector & v, const ex & oc) const
442 return (new add(v,oc))->setflag(status_flags::dynallocated);
445 ex add::thisexpairseq(epvector * vp, const ex & oc) const
447 return (new add(vp,oc))->setflag(status_flags::dynallocated);
450 expair add::split_ex_to_pair(const ex & e) const
452 if (is_exactly_a<mul>(e)) {
453 const mul &mulref(ex_to<mul>(e));
454 const ex &numfactor = mulref.overall_coeff;
455 mul *mulcopyp = new mul(mulref);
456 mulcopyp->overall_coeff = _ex1;
457 mulcopyp->clearflag(status_flags::evaluated);
458 mulcopyp->clearflag(status_flags::hash_calculated);
459 mulcopyp->setflag(status_flags::dynallocated);
460 return expair(*mulcopyp,numfactor);
462 return expair(e,_ex1);
465 expair add::combine_ex_with_coeff_to_pair(const ex & e,
468 GINAC_ASSERT(is_exactly_a<numeric>(c));
469 if (is_exactly_a<mul>(e)) {
470 const mul &mulref(ex_to<mul>(e));
471 const ex &numfactor = mulref.overall_coeff;
472 mul *mulcopyp = new mul(mulref);
473 mulcopyp->overall_coeff = _ex1;
474 mulcopyp->clearflag(status_flags::evaluated);
475 mulcopyp->clearflag(status_flags::hash_calculated);
476 mulcopyp->setflag(status_flags::dynallocated);
477 if (c.is_equal(_ex1))
478 return expair(*mulcopyp, numfactor);
479 else if (numfactor.is_equal(_ex1))
480 return expair(*mulcopyp, c);
482 return expair(*mulcopyp, ex_to<numeric>(numfactor).mul_dyn(ex_to<numeric>(c)));
483 } else if (is_exactly_a<numeric>(e)) {
484 if (c.is_equal(_ex1))
485 return expair(e, _ex1);
486 return expair(ex_to<numeric>(e).mul_dyn(ex_to<numeric>(c)), _ex1);
491 expair add::combine_pair_with_coeff_to_pair(const expair & p,
494 GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
495 GINAC_ASSERT(is_exactly_a<numeric>(c));
497 if (is_exactly_a<numeric>(p.rest)) {
498 GINAC_ASSERT(ex_to<numeric>(p.coeff).is_equal(_num1)); // should be normalized
499 return expair(ex_to<numeric>(p.rest).mul_dyn(ex_to<numeric>(c)),_ex1);
502 return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
505 ex add::recombine_pair_to_ex(const expair & p) const
507 if (ex_to<numeric>(p.coeff).is_equal(_num1))
510 return (new mul(p.rest,p.coeff))->setflag(status_flags::dynallocated);
513 ex add::expand(unsigned options) const
515 epvector *vp = expandchildren(options);
517 // the terms have not changed, so it is safe to declare this expanded
518 return (options == 0) ? setflag(status_flags::expanded) : *this;
521 return (new add(vp, overall_coeff))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));