3 * Implementation of GiNaC's indices. */
6 * GiNaC Copyright (C) 1999-2008 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
30 #include "relational.h"
31 #include "operators.h"
37 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(idx, basic,
38 print_func<print_context>(&idx::do_print).
39 print_func<print_latex>(&idx::do_print_latex).
40 print_func<print_csrc>(&idx::do_print_csrc).
41 print_func<print_tree>(&idx::do_print_tree))
43 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(varidx, idx,
44 print_func<print_context>(&varidx::do_print).
45 print_func<print_latex>(&varidx::do_print_latex).
46 print_func<print_tree>(&varidx::do_print_tree))
48 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(spinidx, varidx,
49 print_func<print_context>(&spinidx::do_print).
50 print_func<print_latex>(&spinidx::do_print_latex).
51 print_func<print_tree>(&spinidx::do_print_tree))
54 // default constructor
59 varidx::varidx() : covariant(false)
63 spinidx::spinidx() : dotted(false)
71 idx::idx(const ex & v, const ex & d) : value(v), dim(d)
74 if (!dim.info(info_flags::posint))
75 throw(std::invalid_argument("dimension of space must be a positive integer"));
78 varidx::varidx(const ex & v, const ex & d, bool cov) : inherited(v, d), covariant(cov)
82 spinidx::spinidx(const ex & v, const ex & d, bool cov, bool dot) : inherited(v, d, cov), dotted(dot)
90 idx::idx(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
92 n.find_ex("value", value, sym_lst);
93 n.find_ex("dim", dim, sym_lst);
96 varidx::varidx(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
98 n.find_bool("covariant", covariant);
101 spinidx::spinidx(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
103 n.find_bool("dotted", dotted);
106 void idx::archive(archive_node &n) const
108 inherited::archive(n);
109 n.add_ex("value", value);
110 n.add_ex("dim", dim);
113 void varidx::archive(archive_node &n) const
115 inherited::archive(n);
116 n.add_bool("covariant", covariant);
119 void spinidx::archive(archive_node &n) const
121 inherited::archive(n);
122 n.add_bool("dotted", dotted);
125 DEFAULT_UNARCHIVE(idx)
126 DEFAULT_UNARCHIVE(varidx)
127 DEFAULT_UNARCHIVE(spinidx)
130 // functions overriding virtual functions from base classes
133 void idx::print_index(const print_context & c, unsigned level) const
135 bool need_parens = !(is_exactly_a<numeric>(value) || is_a<symbol>(value));
141 if (c.options & print_options::print_index_dimensions) {
148 void idx::do_print(const print_context & c, unsigned level) const
151 print_index(c, level);
154 void idx::do_print_latex(const print_latex & c, unsigned level) const
157 print_index(c, level);
161 void idx::do_print_csrc(const print_csrc & c, unsigned level) const
164 if (value.info(info_flags::integer))
165 c.s << ex_to<numeric>(value).to_int();
171 void idx::do_print_tree(const print_tree & c, unsigned level) const
173 c.s << std::string(level, ' ') << class_name() << " @" << this
174 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
176 value.print(c, level + c.delta_indent);
177 dim.print(c, level + c.delta_indent);
180 void varidx::do_print(const print_context & c, unsigned level) const
186 print_index(c, level);
189 void varidx::do_print_tree(const print_tree & c, unsigned level) const
191 c.s << std::string(level, ' ') << class_name() << " @" << this
192 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
193 << (covariant ? ", covariant" : ", contravariant")
195 value.print(c, level + c.delta_indent);
196 dim.print(c, level + c.delta_indent);
199 void spinidx::do_print(const print_context & c, unsigned level) const
207 print_index(c, level);
210 void spinidx::do_print_latex(const print_latex & c, unsigned level) const
216 print_index(c, level);
220 void spinidx::do_print_tree(const print_tree & c, unsigned level) const
222 c.s << std::string(level, ' ') << class_name() << " @" << this
223 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
224 << (covariant ? ", covariant" : ", contravariant")
225 << (dotted ? ", dotted" : ", undotted")
227 value.print(c, level + c.delta_indent);
228 dim.print(c, level + c.delta_indent);
231 bool idx::info(unsigned inf) const
234 case info_flags::idx:
235 case info_flags::has_indices:
238 return inherited::info(inf);
241 size_t idx::nops() const
243 // don't count the dimension as that is not really a sub-expression
247 ex idx::op(size_t i) const
249 GINAC_ASSERT(i == 0);
253 ex idx::map(map_function & f) const
255 const ex &mapped_value = f(value);
256 if (are_ex_trivially_equal(value, mapped_value))
259 idx *copy = duplicate();
260 copy->setflag(status_flags::dynallocated);
261 copy->clearflag(status_flags::hash_calculated);
262 copy->value = mapped_value;
267 /** Returns order relation between two indices of the same type. The order
268 * must be such that dummy indices lie next to each other. */
269 int idx::compare_same_type(const basic & other) const
271 GINAC_ASSERT(is_a<idx>(other));
272 const idx &o = static_cast<const idx &>(other);
274 int cmpval = value.compare(o.value);
277 return dim.compare(o.dim);
280 bool idx::match_same_type(const basic & other) const
282 GINAC_ASSERT(is_a<idx>(other));
283 const idx &o = static_cast<const idx &>(other);
285 return dim.is_equal(o.dim);
288 int varidx::compare_same_type(const basic & other) const
290 GINAC_ASSERT(is_a<varidx>(other));
291 const varidx &o = static_cast<const varidx &>(other);
293 int cmpval = inherited::compare_same_type(other);
297 // Check variance last so dummy indices will end up next to each other
298 if (covariant != o.covariant)
299 return covariant ? -1 : 1;
304 bool varidx::match_same_type(const basic & other) const
306 GINAC_ASSERT(is_a<varidx>(other));
307 const varidx &o = static_cast<const varidx &>(other);
309 if (covariant != o.covariant)
312 return inherited::match_same_type(other);
315 int spinidx::compare_same_type(const basic & other) const
317 GINAC_ASSERT(is_a<spinidx>(other));
318 const spinidx &o = static_cast<const spinidx &>(other);
320 // Check dottedness first so dummy indices will end up next to each other
321 if (dotted != o.dotted)
322 return dotted ? -1 : 1;
324 int cmpval = inherited::compare_same_type(other);
331 bool spinidx::match_same_type(const basic & other) const
333 GINAC_ASSERT(is_a<spinidx>(other));
334 const spinidx &o = static_cast<const spinidx &>(other);
336 if (dotted != o.dotted)
338 return inherited::match_same_type(other);
341 unsigned idx::calchash() const
343 // NOTE: The code in simplify_indexed() assumes that canonically
344 // ordered sequences of indices have the two members of dummy index
345 // pairs lying next to each other. The hash values for indices must
346 // be devised accordingly. The easiest (only?) way to guarantee the
347 // desired ordering is to make indices with the same value have equal
348 // hash keys. That is, the hash values must not depend on the index
349 // dimensions or other attributes (variance etc.).
350 // The compare_same_type() methods will take care of the rest.
351 const void* this_tinfo = (const void*)(typeid(*this).name());
352 unsigned v = golden_ratio_hash((p_int)this_tinfo);
354 v ^= value.gethash();
356 // Store calculated hash value only if object is already evaluated
357 if (flags & status_flags::evaluated) {
358 setflag(status_flags::hash_calculated);
365 /** By default, basic::evalf would evaluate the index value but we don't want
366 * a.1 to become a.(1.0). */
367 ex idx::evalf(int level) const
372 ex idx::subs(const exmap & m, unsigned options) const
374 // First look for index substitutions
375 exmap::const_iterator it = m.find(*this);
378 // Substitution index->index
379 if (is_a<idx>(it->second) || (options & subs_options::really_subs_idx))
382 // Otherwise substitute value
383 idx *i_copy = duplicate();
384 i_copy->value = it->second;
385 i_copy->clearflag(status_flags::hash_calculated);
386 return i_copy->setflag(status_flags::dynallocated);
389 // None, substitute objects in value (not in dimension)
390 const ex &subsed_value = value.subs(m, options);
391 if (are_ex_trivially_equal(value, subsed_value))
394 idx *i_copy = duplicate();
395 i_copy->value = subsed_value;
396 i_copy->clearflag(status_flags::hash_calculated);
397 return i_copy->setflag(status_flags::dynallocated);
400 /** Implementation of ex::diff() for an index always returns 0.
403 ex idx::derivative(const symbol & s) const
409 // new virtual functions
412 bool idx::is_dummy_pair_same_type(const basic & other) const
414 const idx &o = static_cast<const idx &>(other);
416 // Only pure symbols form dummy pairs, "2n+1" doesn't
417 if (!is_a<symbol>(value))
420 // Value must be equal, of course
421 if (!value.is_equal(o.value))
424 // Dimensions need not be equal but must be comparable (so we can
425 // determine the minimum dimension of contractions)
426 if (dim.is_equal(o.dim))
429 return is_exactly_a<numeric>(dim) || is_exactly_a<numeric>(o.dim);
432 bool varidx::is_dummy_pair_same_type(const basic & other) const
434 const varidx &o = static_cast<const varidx &>(other);
436 // Variance must be opposite
437 if (covariant == o.covariant)
440 return inherited::is_dummy_pair_same_type(other);
443 bool spinidx::is_dummy_pair_same_type(const basic & other) const
445 const spinidx &o = static_cast<const spinidx &>(other);
447 // Dottedness must be the same
448 if (dotted != o.dotted)
451 return inherited::is_dummy_pair_same_type(other);
456 // non-virtual functions
459 ex idx::replace_dim(const ex & new_dim) const
461 idx *i_copy = duplicate();
462 i_copy->dim = new_dim;
463 i_copy->clearflag(status_flags::hash_calculated);
464 return i_copy->setflag(status_flags::dynallocated);
467 ex idx::minimal_dim(const idx & other) const
469 return GiNaC::minimal_dim(dim, other.dim);
472 ex varidx::toggle_variance() const
474 varidx *i_copy = duplicate();
475 i_copy->covariant = !i_copy->covariant;
476 i_copy->clearflag(status_flags::hash_calculated);
477 return i_copy->setflag(status_flags::dynallocated);
480 ex spinidx::toggle_dot() const
482 spinidx *i_copy = duplicate();
483 i_copy->dotted = !i_copy->dotted;
484 i_copy->clearflag(status_flags::hash_calculated);
485 return i_copy->setflag(status_flags::dynallocated);
488 ex spinidx::toggle_variance_dot() const
490 spinidx *i_copy = duplicate();
491 i_copy->covariant = !i_copy->covariant;
492 i_copy->dotted = !i_copy->dotted;
493 i_copy->clearflag(status_flags::hash_calculated);
494 return i_copy->setflag(status_flags::dynallocated);
501 bool is_dummy_pair(const idx & i1, const idx & i2)
503 // The indices must be of exactly the same type
504 if (typeid(i1) != typeid(i2))
507 // Same type, let the indices decide whether they are paired
508 return i1.is_dummy_pair_same_type(i2);
511 bool is_dummy_pair(const ex & e1, const ex & e2)
513 // The expressions must be indices
514 if (!is_a<idx>(e1) || !is_a<idx>(e2))
517 return is_dummy_pair(ex_to<idx>(e1), ex_to<idx>(e2));
520 void find_free_and_dummy(exvector::const_iterator it, exvector::const_iterator itend, exvector & out_free, exvector & out_dummy)
525 // No indices? Then do nothing
529 // Only one index? Then it is a free one if it's not numeric
530 if (itend - it == 1) {
531 if (ex_to<idx>(*it).is_symbolic())
532 out_free.push_back(*it);
536 // Sort index vector. This will cause dummy indices come to lie next
537 // to each other (because the sort order is defined to guarantee this).
538 exvector v(it, itend);
539 shaker_sort(v.begin(), v.end(), ex_is_less(), ex_swap());
541 // Find dummy pairs and free indices
542 it = v.begin(); itend = v.end();
543 exvector::const_iterator last = it++;
544 while (it != itend) {
545 if (is_dummy_pair(*it, *last)) {
546 out_dummy.push_back(*last);
551 if (!it->is_equal(*last) && ex_to<idx>(*last).is_symbolic())
552 out_free.push_back(*last);
556 if (ex_to<idx>(*last).is_symbolic())
557 out_free.push_back(*last);
560 ex minimal_dim(const ex & dim1, const ex & dim2)
562 if (dim1.is_equal(dim2) || dim1 < dim2 || (is_exactly_a<numeric>(dim1) && !is_a<numeric>(dim2)))
564 else if (dim1 > dim2 || (!is_a<numeric>(dim1) && is_exactly_a<numeric>(dim2)))
567 std::ostringstream s;
568 s << "minimal_dim(): index dimensions " << dim1 << " and " << dim2 << " cannot be ordered";
569 throw (std::runtime_error(s.str()));