3 * Implementation of GiNaC's non-commutative products of expressions. */
6 * GiNaC Copyright (C) 1999-2005 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
37 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(ncmul, exprseq,
38 print_func<print_context>(&ncmul::do_print).
39 print_func<print_tree>(&ncmul::do_print_tree).
40 print_func<print_csrc>(&ncmul::do_print_csrc).
41 print_func<print_python_repr>(&ncmul::do_print_csrc))
45 // default constructor
50 tinfo_key = TINFO_ncmul;
59 ncmul::ncmul(const ex & lh, const ex & rh) : inherited(lh,rh)
61 tinfo_key = TINFO_ncmul;
64 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3) : inherited(f1,f2,f3)
66 tinfo_key = TINFO_ncmul;
69 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
70 const ex & f4) : inherited(f1,f2,f3,f4)
72 tinfo_key = TINFO_ncmul;
75 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
76 const ex & f4, const ex & f5) : inherited(f1,f2,f3,f4,f5)
78 tinfo_key = TINFO_ncmul;
81 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
82 const ex & f4, const ex & f5, const ex & f6) : inherited(f1,f2,f3,f4,f5,f6)
84 tinfo_key = TINFO_ncmul;
87 ncmul::ncmul(const exvector & v, bool discardable) : inherited(v,discardable)
89 tinfo_key = TINFO_ncmul;
92 ncmul::ncmul(std::auto_ptr<exvector> vp) : inherited(vp)
94 tinfo_key = TINFO_ncmul;
101 DEFAULT_ARCHIVING(ncmul)
104 // functions overriding virtual functions from base classes
109 void ncmul::do_print(const print_context & c, unsigned level) const
111 printseq(c, '(', '*', ')', precedence(), level);
114 void ncmul::do_print_csrc(const print_context & c, unsigned level) const
117 printseq(c, '(', ',', ')', precedence(), precedence());
120 bool ncmul::info(unsigned inf) const
122 return inherited::info(inf);
125 typedef std::vector<int> intvector;
127 ex ncmul::expand(unsigned options) const
129 // First, expand the children
130 std::auto_ptr<exvector> vp = expandchildren(options);
131 const exvector &expanded_seq = vp.get() ? *vp : this->seq;
133 // Now, look for all the factors that are sums and remember their
134 // position and number of terms.
135 intvector positions_of_adds(expanded_seq.size());
136 intvector number_of_add_operands(expanded_seq.size());
138 size_t number_of_adds = 0;
139 size_t number_of_expanded_terms = 1;
141 size_t current_position = 0;
142 exvector::const_iterator last = expanded_seq.end();
143 for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
144 if (is_exactly_a<add>(*cit)) {
145 positions_of_adds[number_of_adds] = current_position;
146 size_t num_ops = cit->nops();
147 number_of_add_operands[number_of_adds] = num_ops;
148 number_of_expanded_terms *= num_ops;
154 // If there are no sums, we are done
155 if (number_of_adds == 0) {
157 return (new ncmul(vp))->
158 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
163 // Now, form all possible products of the terms of the sums with the
164 // remaining factors, and add them together
166 distrseq.reserve(number_of_expanded_terms);
168 intvector k(number_of_adds);
171 exvector term = expanded_seq;
172 for (size_t i=0; i<number_of_adds; i++)
173 term[positions_of_adds[i]] = expanded_seq[positions_of_adds[i]].op(k[i]);
174 distrseq.push_back((new ncmul(term, true))->
175 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
178 int l = number_of_adds-1;
179 while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
187 return (new add(distrseq))->
188 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
191 int ncmul::degree(const ex & s) const
193 if (is_equal(ex_to<basic>(s)))
196 // Sum up degrees of factors
198 exvector::const_iterator i = seq.begin(), end = seq.end();
200 deg_sum += i->degree(s);
206 int ncmul::ldegree(const ex & s) const
208 if (is_equal(ex_to<basic>(s)))
211 // Sum up degrees of factors
213 exvector::const_iterator i = seq.begin(), end = seq.end();
215 deg_sum += i->degree(s);
221 ex ncmul::coeff(const ex & s, int n) const
223 if (is_equal(ex_to<basic>(s)))
224 return n==1 ? _ex1 : _ex0;
227 coeffseq.reserve(seq.size());
230 // product of individual coeffs
231 // if a non-zero power of s is found, the resulting product will be 0
232 exvector::const_iterator it=seq.begin();
233 while (it!=seq.end()) {
234 coeffseq.push_back((*it).coeff(s,n));
237 return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
240 exvector::const_iterator i = seq.begin(), end = seq.end();
241 bool coeff_found = false;
243 ex c = i->coeff(s,n);
245 coeffseq.push_back(*i);
247 coeffseq.push_back(c);
253 if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
258 size_t ncmul::count_factors(const ex & e) const
260 if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
261 (is_exactly_a<ncmul>(e))) {
263 for (size_t i=0; i<e.nops(); i++)
264 factors += count_factors(e.op(i));
271 void ncmul::append_factors(exvector & v, const ex & e) const
273 if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
274 (is_exactly_a<ncmul>(e))) {
275 for (size_t i=0; i<e.nops(); i++)
276 append_factors(v, e.op(i));
281 typedef std::vector<unsigned> unsignedvector;
282 typedef std::vector<exvector> exvectorvector;
284 /** Perform automatic term rewriting rules in this class. In the following
285 * x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
286 * stand for such expressions that contain a plain number.
287 * - ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) -> ncmul(...,x1,x2,...,x3,x4,...) (associativity)
290 * - ncmul(...,c1,...,c2,...) -> *(c1,c2,ncmul(...)) (pull out commutative elements)
291 * - ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2)) (collect elements of same type)
292 * - ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
294 * @param level cut-off in recursive evaluation */
295 ex ncmul::eval(int level) const
297 // The following additional rule would be nice, but produces a recursion,
298 // which must be trapped by introducing a flag that the sub-ncmuls()
299 // are already evaluated (maybe later...)
300 // ncmul(x1,x2,...,X,y1,y2,...) ->
301 // ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
302 // (X noncommutative_composite)
304 if ((level==1) && (flags & status_flags::evaluated)) {
308 exvector evaledseq=evalchildren(level);
310 // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
311 // ncmul(...,x1,x2,...,x3,x4,...) (associativity)
313 exvector::const_iterator cit = evaledseq.begin(), citend = evaledseq.end();
314 while (cit != citend)
315 factors += count_factors(*cit++);
318 assocseq.reserve(factors);
319 cit = evaledseq.begin();
320 while (cit != citend)
321 append_factors(assocseq, *cit++);
324 if (assocseq.size()==1) return *(seq.begin());
327 if (assocseq.empty()) return _ex1;
329 // determine return types
330 unsignedvector rettypes;
331 rettypes.reserve(assocseq.size());
333 size_t count_commutative=0;
334 size_t count_noncommutative=0;
335 size_t count_noncommutative_composite=0;
336 cit = assocseq.begin(); citend = assocseq.end();
337 while (cit != citend) {
338 switch (rettypes[i] = cit->return_type()) {
339 case return_types::commutative:
342 case return_types::noncommutative:
343 count_noncommutative++;
345 case return_types::noncommutative_composite:
346 count_noncommutative_composite++;
349 throw(std::logic_error("ncmul::eval(): invalid return type"));
353 GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
355 // ncmul(...,c1,...,c2,...) ->
356 // *(c1,c2,ncmul(...)) (pull out commutative elements)
357 if (count_commutative!=0) {
358 exvector commutativeseq;
359 commutativeseq.reserve(count_commutative+1);
360 exvector noncommutativeseq;
361 noncommutativeseq.reserve(assocseq.size()-count_commutative);
362 size_t num = assocseq.size();
363 for (size_t i=0; i<num; ++i) {
364 if (rettypes[i]==return_types::commutative)
365 commutativeseq.push_back(assocseq[i]);
367 noncommutativeseq.push_back(assocseq[i]);
369 commutativeseq.push_back((new ncmul(noncommutativeseq,1))->setflag(status_flags::dynallocated));
370 return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
373 // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
374 // (collect elements of same type)
376 if (count_noncommutative_composite==0) {
377 // there are neither commutative nor noncommutative_composite
378 // elements in assocseq
379 GINAC_ASSERT(count_commutative==0);
381 size_t assoc_num = assocseq.size();
383 unsignedvector rttinfos;
384 evv.reserve(assoc_num);
385 rttinfos.reserve(assoc_num);
387 cit = assocseq.begin(), citend = assocseq.end();
388 while (cit != citend) {
389 unsigned ti = cit->return_type_tinfo();
390 size_t rtt_num = rttinfos.size();
391 // search type in vector of known types
392 for (i=0; i<rtt_num; ++i) {
393 if (ti == rttinfos[i]) {
394 evv[i].push_back(*cit);
400 rttinfos.push_back(ti);
401 evv.push_back(exvector());
402 (evv.end()-1)->reserve(assoc_num);
403 (evv.end()-1)->push_back(*cit);
408 size_t evv_num = evv.size();
409 #ifdef DO_GINAC_ASSERT
410 GINAC_ASSERT(evv_num == rttinfos.size());
411 GINAC_ASSERT(evv_num > 0);
413 for (i=0; i<evv_num; ++i)
415 GINAC_ASSERT(s == assoc_num);
416 #endif // def DO_GINAC_ASSERT
418 // if all elements are of same type, simplify the string
420 return evv[0][0].eval_ncmul(evv[0]);
423 splitseq.reserve(evv_num);
424 for (i=0; i<evv_num; ++i)
425 splitseq.push_back((new ncmul(evv[i]))->setflag(status_flags::dynallocated));
427 return (new mul(splitseq))->setflag(status_flags::dynallocated);
430 return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
431 status_flags::evaluated);
434 ex ncmul::evalm() const
436 // Evaluate children first
437 std::auto_ptr<exvector> s(new exvector);
438 s->reserve(seq.size());
439 exvector::const_iterator it = seq.begin(), itend = seq.end();
440 while (it != itend) {
441 s->push_back(it->evalm());
445 // If there are only matrices, simply multiply them
446 it = s->begin(); itend = s->end();
447 if (is_a<matrix>(*it)) {
448 matrix prod(ex_to<matrix>(*it));
450 while (it != itend) {
451 if (!is_a<matrix>(*it))
453 prod = prod.mul(ex_to<matrix>(*it));
460 return (new ncmul(s))->setflag(status_flags::dynallocated);
463 ex ncmul::thiscontainer(const exvector & v) const
465 return (new ncmul(v))->setflag(status_flags::dynallocated);
468 ex ncmul::thiscontainer(std::auto_ptr<exvector> vp) const
470 return (new ncmul(vp))->setflag(status_flags::dynallocated);
473 ex ncmul::conjugate() const
475 if (return_type() != return_types::noncommutative) {
476 return exprseq::conjugate();
479 if ((return_type_tinfo() & 0xffffff00U) != TINFO_clifford) {
480 return exprseq::conjugate();
485 for (const_iterator i=end(); i!=begin();) {
487 ev.push_back(i->conjugate());
489 return (new ncmul(ev, true))->setflag(status_flags::dynallocated).eval();
494 /** Implementation of ex::diff() for a non-commutative product. It applies
497 ex ncmul::derivative(const symbol & s) const
499 size_t num = seq.size();
503 // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
504 exvector ncmulseq = seq;
505 for (size_t i=0; i<num; ++i) {
506 ex e = seq[i].diff(s);
508 addseq.push_back((new ncmul(ncmulseq))->setflag(status_flags::dynallocated));
511 return (new add(addseq))->setflag(status_flags::dynallocated);
514 int ncmul::compare_same_type(const basic & other) const
516 return inherited::compare_same_type(other);
519 unsigned ncmul::return_type() const
522 return return_types::commutative;
524 bool all_commutative = true;
525 exvector::const_iterator noncommutative_element; // point to first found nc element
527 exvector::const_iterator i = seq.begin(), end = seq.end();
529 unsigned rt = i->return_type();
530 if (rt == return_types::noncommutative_composite)
531 return rt; // one ncc -> mul also ncc
532 if ((rt == return_types::noncommutative) && (all_commutative)) {
533 // first nc element found, remember position
534 noncommutative_element = i;
535 all_commutative = false;
537 if ((rt == return_types::noncommutative) && (!all_commutative)) {
538 // another nc element found, compare type_infos
539 if (noncommutative_element->return_type_tinfo() != i->return_type_tinfo()) {
540 // diffent types -> mul is ncc
541 return return_types::noncommutative_composite;
546 // all factors checked
547 GINAC_ASSERT(!all_commutative); // not all factors should commutate, because this is a ncmul();
548 return all_commutative ? return_types::commutative : return_types::noncommutative;
551 unsigned ncmul::return_type_tinfo() const
556 // return type_info of first noncommutative element
557 exvector::const_iterator i = seq.begin(), end = seq.end();
559 if (i->return_type() == return_types::noncommutative)
560 return i->return_type_tinfo();
564 // no noncommutative element found, should not happen
569 // new virtual functions which can be overridden by derived classes
575 // non-virtual functions in this class
578 std::auto_ptr<exvector> ncmul::expandchildren(unsigned options) const
580 const_iterator cit = this->seq.begin(), end = this->seq.end();
582 const ex & expanded_ex = cit->expand(options);
583 if (!are_ex_trivially_equal(*cit, expanded_ex)) {
585 // copy first part of seq which hasn't changed
586 std::auto_ptr<exvector> s(new exvector(this->seq.begin(), cit));
587 reserve(*s, this->seq.size());
589 // insert changed element
590 s->push_back(expanded_ex);
595 s->push_back(cit->expand(options));
605 return std::auto_ptr<exvector>(0); // nothing has changed
608 const exvector & ncmul::get_factors() const
617 ex reeval_ncmul(const exvector & v)
619 return (new ncmul(v))->setflag(status_flags::dynallocated);
622 ex hold_ncmul(const exvector & v)
626 else if (v.size() == 1)
629 return (new ncmul(v))->setflag(status_flags::dynallocated |
630 status_flags::evaluated);