3 * Implementation of GiNaC's indices. */
6 * GiNaC Copyright (C) 1999-2002 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
35 GINAC_IMPLEMENT_REGISTERED_CLASS(idx, basic)
36 GINAC_IMPLEMENT_REGISTERED_CLASS(varidx, idx)
37 GINAC_IMPLEMENT_REGISTERED_CLASS(spinidx, varidx)
40 // default ctor, dtor, copy ctor, assignment operator and helpers
43 idx::idx() : inherited(TINFO_idx) {}
45 varidx::varidx() : covariant(false)
47 tinfo_key = TINFO_varidx;
50 spinidx::spinidx() : dotted(false)
52 tinfo_key = TINFO_spinidx;
55 void idx::copy(const idx & other)
57 inherited::copy(other);
62 void varidx::copy(const varidx & other)
64 inherited::copy(other);
65 covariant = other.covariant;
68 void spinidx::copy(const spinidx & other)
70 inherited::copy(other);
71 dotted = other.dotted;
75 DEFAULT_DESTROY(varidx)
76 DEFAULT_DESTROY(spinidx)
82 idx::idx(const ex & v, const ex & d) : inherited(TINFO_idx), value(v), dim(d)
85 if (!dim.info(info_flags::posint))
86 throw(std::invalid_argument("dimension of space must be a positive integer"));
89 varidx::varidx(const ex & v, const ex & d, bool cov) : inherited(v, d), covariant(cov)
91 tinfo_key = TINFO_varidx;
94 spinidx::spinidx(const ex & v, const ex & d, bool cov, bool dot) : inherited(v, d, cov), dotted(dot)
96 tinfo_key = TINFO_spinidx;
103 idx::idx(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
105 n.find_ex("value", value, sym_lst);
106 n.find_ex("dim", dim, sym_lst);
109 varidx::varidx(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
111 n.find_bool("covariant", covariant);
114 spinidx::spinidx(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
116 n.find_bool("dotted", dotted);
119 void idx::archive(archive_node &n) const
121 inherited::archive(n);
122 n.add_ex("value", value);
123 n.add_ex("dim", dim);
126 void varidx::archive(archive_node &n) const
128 inherited::archive(n);
129 n.add_bool("covariant", covariant);
132 void spinidx::archive(archive_node &n) const
134 inherited::archive(n);
135 n.add_bool("dotted", dotted);
138 DEFAULT_UNARCHIVE(idx)
139 DEFAULT_UNARCHIVE(varidx)
140 DEFAULT_UNARCHIVE(spinidx)
143 // functions overriding virtual functions from base classes
146 void idx::print(const print_context & c, unsigned level) const
148 if (is_of_type(c, print_tree)) {
150 c.s << std::string(level, ' ') << class_name()
151 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
153 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
154 value.print(c, level + delta_indent);
155 dim.print(c, level + delta_indent);
159 if (is_a<print_latex>(c))
163 bool need_parens = !(is_ex_exactly_of_type(value, numeric) || is_ex_of_type(value, symbol));
169 if (is_a<print_latex>(c))
174 void varidx::print(const print_context & c, unsigned level) const
176 if (is_of_type(c, print_tree)) {
178 c.s << std::string(level, ' ') << class_name()
179 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
180 << (covariant ? ", covariant" : ", contravariant")
182 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
183 value.print(c, level + delta_indent);
184 dim.print(c, level + delta_indent);
187 if (is_a<print_latex>(c)) {
198 bool need_parens = !(is_ex_exactly_of_type(value, numeric) || is_ex_of_type(value, symbol));
204 if (is_a<print_latex>(c))
209 void spinidx::print(const print_context & c, unsigned level) const
211 if (is_of_type(c, print_tree)) {
213 c.s << std::string(level, ' ') << class_name()
214 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
215 << (covariant ? ", covariant" : ", contravariant")
216 << (dotted ? ", dotted" : ", undotted")
218 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
219 value.print(c, level + delta_indent);
220 dim.print(c, level + delta_indent);
224 bool is_tex = is_of_type(c, print_latex);
242 bool need_parens = !(is_ex_exactly_of_type(value, numeric) || is_ex_of_type(value, symbol));
248 if (is_tex && dotted)
255 bool idx::info(unsigned inf) const
257 if (inf == info_flags::idx)
259 return inherited::info(inf);
262 unsigned idx::nops() const
264 // don't count the dimension as that is not really a sub-expression
268 ex & idx::let_op(int i)
270 GINAC_ASSERT(i == 0);
274 /** Returns order relation between two indices of the same type. The order
275 * must be such that dummy indices lie next to each other. */
276 int idx::compare_same_type(const basic & other) const
278 GINAC_ASSERT(is_a<idx>(other));
279 const idx &o = static_cast<const idx &>(other);
281 int cmpval = value.compare(o.value);
284 return dim.compare(o.dim);
287 bool idx::match_same_type(const basic & other) const
289 GINAC_ASSERT(is_a<idx>(other));
290 const idx &o = static_cast<const idx &>(other);
292 return dim.is_equal(o.dim);
295 int varidx::compare_same_type(const basic & other) const
297 GINAC_ASSERT(is_a<varidx>(other));
298 const varidx &o = static_cast<const varidx &>(other);
300 int cmpval = inherited::compare_same_type(other);
304 // Check variance last so dummy indices will end up next to each other
305 if (covariant != o.covariant)
306 return covariant ? -1 : 1;
310 bool varidx::match_same_type(const basic & other) const
312 GINAC_ASSERT(is_a<varidx>(other));
313 const varidx &o = static_cast<const varidx &>(other);
315 if (covariant != o.covariant)
317 return inherited::match_same_type(other);
320 int spinidx::compare_same_type(const basic & other) const
322 GINAC_ASSERT(is_a<spinidx>(other));
323 const spinidx &o = static_cast<const spinidx &>(other);
325 // Check dottedness first so dummy indices will end up next to each other
326 if (dotted != o.dotted)
327 return dotted ? -1 : 1;
329 int cmpval = inherited::compare_same_type(other);
336 bool spinidx::match_same_type(const basic & other) const
338 GINAC_ASSERT(is_a<spinidx>(other));
339 const spinidx &o = static_cast<const spinidx &>(other);
341 if (dotted != o.dotted)
343 return inherited::match_same_type(other);
346 /** By default, basic::evalf would evaluate the index value but we don't want
347 * a.1 to become a.(1.0). */
348 ex idx::evalf(int level) const
353 ex idx::subs(const lst & ls, const lst & lr, bool no_pattern) const
355 GINAC_ASSERT(ls.nops() == lr.nops());
357 // First look for index substitutions
358 for (unsigned i=0; i<ls.nops(); i++) {
359 if (is_equal(ex_to<basic>(ls.op(i)))) {
361 // Substitution index->index
362 if (is_ex_of_type(lr.op(i), idx))
365 // Otherwise substitute value
366 idx *i_copy = static_cast<idx *>(duplicate());
367 i_copy->value = lr.op(i);
368 i_copy->clearflag(status_flags::hash_calculated);
369 return i_copy->setflag(status_flags::dynallocated);
373 // None, substitute objects in value (not in dimension)
374 const ex &subsed_value = value.subs(ls, lr, no_pattern);
375 if (are_ex_trivially_equal(value, subsed_value))
378 idx *i_copy = static_cast<idx *>(duplicate());
379 i_copy->value = subsed_value;
380 i_copy->clearflag(status_flags::hash_calculated);
381 return i_copy->setflag(status_flags::dynallocated);
384 /** Implementation of ex::diff() for an index always returns 0.
387 ex idx::derivative(const symbol & s) const
393 // new virtual functions
396 bool idx::is_dummy_pair_same_type(const basic & other) const
398 const idx &o = static_cast<const idx &>(other);
400 // Only pure symbols form dummy pairs, "2n+1" doesn't
401 if (!is_ex_of_type(value, symbol))
404 // Value must be equal, of course
405 if (!value.is_equal(o.value))
408 // Also the dimension
409 return dim.is_equal(o.dim);
412 bool varidx::is_dummy_pair_same_type(const basic & other) const
414 const varidx &o = static_cast<const varidx &>(other);
416 // Variance must be opposite
417 if (covariant == o.covariant)
420 return inherited::is_dummy_pair_same_type(other);
423 bool spinidx::is_dummy_pair_same_type(const basic & other) const
425 const spinidx &o = static_cast<const spinidx &>(other);
427 // Dottedness must be the same
428 if (dotted != o.dotted)
431 return inherited::is_dummy_pair_same_type(other);
436 // non-virtual functions
439 ex varidx::toggle_variance(void) const
441 varidx *i_copy = static_cast<varidx *>(duplicate());
442 i_copy->covariant = !i_copy->covariant;
443 i_copy->clearflag(status_flags::hash_calculated);
444 return i_copy->setflag(status_flags::dynallocated);
447 ex spinidx::toggle_dot(void) const
449 spinidx *i_copy = static_cast<spinidx *>(duplicate());
450 i_copy->dotted = !i_copy->dotted;
451 i_copy->clearflag(status_flags::hash_calculated);
452 return i_copy->setflag(status_flags::dynallocated);
455 ex spinidx::toggle_variance_dot(void) const
457 spinidx *i_copy = static_cast<spinidx *>(duplicate());
458 i_copy->covariant = !i_copy->covariant;
459 i_copy->dotted = !i_copy->dotted;
460 i_copy->clearflag(status_flags::hash_calculated);
461 return i_copy->setflag(status_flags::dynallocated);
468 bool is_dummy_pair(const idx & i1, const idx & i2)
470 // The indices must be of exactly the same type
471 if (i1.tinfo() != i2.tinfo())
474 // Same type, let the indices decide whether they are paired
475 return i1.is_dummy_pair_same_type(i2);
478 bool is_dummy_pair(const ex & e1, const ex & e2)
480 // The expressions must be indices
481 if (!is_ex_of_type(e1, idx) || !is_ex_of_type(e2, idx))
484 return is_dummy_pair(ex_to<idx>(e1), ex_to<idx>(e2));
487 void find_free_and_dummy(exvector::const_iterator it, exvector::const_iterator itend, exvector & out_free, exvector & out_dummy)
492 // No indices? Then do nothing
496 // Only one index? Then it is a free one if it's not numeric
497 if (itend - it == 1) {
498 if (ex_to<idx>(*it).is_symbolic())
499 out_free.push_back(*it);
503 // Sort index vector. This will cause dummy indices come to lie next
504 // to each other (because the sort order is defined to guarantee this).
505 exvector v(it, itend);
506 shaker_sort(v.begin(), v.end(), ex_is_less(), ex_swap());
508 // Find dummy pairs and free indices
509 it = v.begin(); itend = v.end();
510 exvector::const_iterator last = it++;
511 while (it != itend) {
512 if (is_dummy_pair(*it, *last)) {
513 out_dummy.push_back(*last);
518 if (!it->is_equal(*last) && ex_to<idx>(*last).is_symbolic())
519 out_free.push_back(*last);
523 if (ex_to<idx>(*last).is_symbolic())
524 out_free.push_back(*last);