3 * Implementation of GiNaC's indices. */
6 * GiNaC Copyright (C) 1999-2004 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
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_tree>(&idx::do_print_tree))
42 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(varidx, idx,
43 print_func<print_context>(&varidx::do_print).
44 print_func<print_latex>(&varidx::do_print_latex).
45 print_func<print_tree>(&varidx::do_print_tree))
47 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(spinidx, varidx,
48 print_func<print_context>(&spinidx::do_print).
49 print_func<print_latex>(&spinidx::do_print_latex).
50 print_func<print_tree>(&spinidx::do_print_tree))
53 // default constructor
56 idx::idx() : inherited(TINFO_idx) {}
58 varidx::varidx() : covariant(false)
60 tinfo_key = TINFO_varidx;
63 spinidx::spinidx() : dotted(false)
65 tinfo_key = TINFO_spinidx;
72 idx::idx(const ex & v, const ex & d) : inherited(TINFO_idx), value(v), dim(d)
75 if (!dim.info(info_flags::posint))
76 throw(std::invalid_argument("dimension of space must be a positive integer"));
79 varidx::varidx(const ex & v, const ex & d, bool cov) : inherited(v, d), covariant(cov)
81 tinfo_key = TINFO_varidx;
84 spinidx::spinidx(const ex & v, const ex & d, bool cov, bool dot) : inherited(v, d, cov), dotted(dot)
86 tinfo_key = TINFO_spinidx;
93 idx::idx(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
95 n.find_ex("value", value, sym_lst);
96 n.find_ex("dim", dim, sym_lst);
99 varidx::varidx(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
101 n.find_bool("covariant", covariant);
104 spinidx::spinidx(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
106 n.find_bool("dotted", dotted);
109 void idx::archive(archive_node &n) const
111 inherited::archive(n);
112 n.add_ex("value", value);
113 n.add_ex("dim", dim);
116 void varidx::archive(archive_node &n) const
118 inherited::archive(n);
119 n.add_bool("covariant", covariant);
122 void spinidx::archive(archive_node &n) const
124 inherited::archive(n);
125 n.add_bool("dotted", dotted);
128 DEFAULT_UNARCHIVE(idx)
129 DEFAULT_UNARCHIVE(varidx)
130 DEFAULT_UNARCHIVE(spinidx)
133 // functions overriding virtual functions from base classes
136 void idx::print_index(const print_context & c, unsigned level) const
138 bool need_parens = !(is_exactly_a<numeric>(value) || is_a<symbol>(value));
144 if (c.options & print_options::print_index_dimensions) {
151 void idx::do_print(const print_context & c, unsigned level) const
154 print_index(c, level);
157 void idx::do_print_latex(const print_latex & c, unsigned level) const
160 print_index(c, level);
164 void idx::do_print_tree(const print_tree & c, unsigned level) const
166 c.s << std::string(level, ' ') << class_name() << " @" << this
167 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
169 value.print(c, level + c.delta_indent);
170 dim.print(c, level + c.delta_indent);
173 void varidx::do_print(const print_context & c, unsigned level) const
179 print_index(c, level);
182 void varidx::do_print_tree(const print_tree & c, unsigned level) const
184 c.s << std::string(level, ' ') << class_name() << " @" << this
185 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
186 << (covariant ? ", covariant" : ", contravariant")
188 value.print(c, level + c.delta_indent);
189 dim.print(c, level + c.delta_indent);
192 void spinidx::do_print(const print_context & c, unsigned level) const
200 print_index(c, level);
203 void spinidx::do_print_latex(const print_latex & c, unsigned level) const
209 print_index(c, level);
213 void spinidx::do_print_tree(const print_tree & c, unsigned level) const
215 c.s << std::string(level, ' ') << class_name() << " @" << this
216 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
217 << (covariant ? ", covariant" : ", contravariant")
218 << (dotted ? ", dotted" : ", undotted")
220 value.print(c, level + c.delta_indent);
221 dim.print(c, level + c.delta_indent);
224 bool idx::info(unsigned inf) const
226 if (inf == info_flags::idx)
228 return inherited::info(inf);
231 size_t idx::nops() const
233 // don't count the dimension as that is not really a sub-expression
237 ex idx::op(size_t i) const
239 GINAC_ASSERT(i == 0);
243 ex idx::map(map_function & f) const
245 const ex &mapped_value = f(value);
246 if (are_ex_trivially_equal(value, mapped_value))
249 idx *copy = duplicate();
250 copy->setflag(status_flags::dynallocated);
251 copy->clearflag(status_flags::hash_calculated);
252 copy->value = mapped_value;
257 /** Returns order relation between two indices of the same type. The order
258 * must be such that dummy indices lie next to each other. */
259 int idx::compare_same_type(const basic & other) const
261 GINAC_ASSERT(is_a<idx>(other));
262 const idx &o = static_cast<const idx &>(other);
264 int cmpval = value.compare(o.value);
267 return dim.compare(o.dim);
270 bool idx::match_same_type(const basic & other) const
272 GINAC_ASSERT(is_a<idx>(other));
273 const idx &o = static_cast<const idx &>(other);
275 return dim.is_equal(o.dim);
278 int varidx::compare_same_type(const basic & other) const
280 GINAC_ASSERT(is_a<varidx>(other));
281 const varidx &o = static_cast<const varidx &>(other);
283 int cmpval = inherited::compare_same_type(other);
287 // Check variance last so dummy indices will end up next to each other
288 if (covariant != o.covariant)
289 return covariant ? -1 : 1;
294 bool varidx::match_same_type(const basic & other) const
296 GINAC_ASSERT(is_a<varidx>(other));
297 const varidx &o = static_cast<const varidx &>(other);
299 if (covariant != o.covariant)
302 return inherited::match_same_type(other);
305 int spinidx::compare_same_type(const basic & other) const
307 GINAC_ASSERT(is_a<spinidx>(other));
308 const spinidx &o = static_cast<const spinidx &>(other);
310 // Check dottedness first so dummy indices will end up next to each other
311 if (dotted != o.dotted)
312 return dotted ? -1 : 1;
314 int cmpval = inherited::compare_same_type(other);
321 bool spinidx::match_same_type(const basic & other) const
323 GINAC_ASSERT(is_a<spinidx>(other));
324 const spinidx &o = static_cast<const spinidx &>(other);
326 if (dotted != o.dotted)
328 return inherited::match_same_type(other);
331 unsigned idx::calchash() const
333 // NOTE: The code in simplify_indexed() assumes that canonically
334 // ordered sequences of indices have the two members of dummy index
335 // pairs lying next to each other. The hash values for indices must
336 // be devised accordingly. The easiest (only?) way to guarantee the
337 // desired ordering is to make indices with the same value have equal
338 // hash keys. That is, the hash values must not depend on the index
339 // dimensions or other attributes (variance etc.).
340 // The compare_same_type() methods will take care of the rest.
341 unsigned v = golden_ratio_hash(tinfo());
343 v ^= value.gethash();
345 // Store calculated hash value only if object is already evaluated
346 if (flags & status_flags::evaluated) {
347 setflag(status_flags::hash_calculated);
354 /** By default, basic::evalf would evaluate the index value but we don't want
355 * a.1 to become a.(1.0). */
356 ex idx::evalf(int level) const
361 ex idx::subs(const exmap & m, unsigned options) const
363 // First look for index substitutions
364 exmap::const_iterator it = m.find(*this);
367 // Substitution index->index
368 if (is_a<idx>(it->second))
371 // Otherwise substitute value
372 idx *i_copy = duplicate();
373 i_copy->value = it->second;
374 i_copy->clearflag(status_flags::hash_calculated);
375 return i_copy->setflag(status_flags::dynallocated);
378 // None, substitute objects in value (not in dimension)
379 const ex &subsed_value = value.subs(m, options);
380 if (are_ex_trivially_equal(value, subsed_value))
383 idx *i_copy = duplicate();
384 i_copy->value = subsed_value;
385 i_copy->clearflag(status_flags::hash_calculated);
386 return i_copy->setflag(status_flags::dynallocated);
389 /** Implementation of ex::diff() for an index always returns 0.
392 ex idx::derivative(const symbol & s) const
398 // new virtual functions
401 bool idx::is_dummy_pair_same_type(const basic & other) const
403 const idx &o = static_cast<const idx &>(other);
405 // Only pure symbols form dummy pairs, "2n+1" doesn't
406 if (!is_a<symbol>(value))
409 // Value must be equal, of course
410 if (!value.is_equal(o.value))
413 // Dimensions need not be equal but must be comparable (so we can
414 // determine the minimum dimension of contractions)
415 if (dim.is_equal(o.dim))
418 return (dim < o.dim || dim > o.dim || (is_exactly_a<numeric>(dim) && is_a<symbol>(o.dim)) || (is_a<symbol>(dim) && is_exactly_a<numeric>(o.dim)));
421 bool varidx::is_dummy_pair_same_type(const basic & other) const
423 const varidx &o = static_cast<const varidx &>(other);
425 // Variance must be opposite
426 if (covariant == o.covariant)
429 return inherited::is_dummy_pair_same_type(other);
432 bool spinidx::is_dummy_pair_same_type(const basic & other) const
434 const spinidx &o = static_cast<const spinidx &>(other);
436 // Dottedness must be the same
437 if (dotted != o.dotted)
440 return inherited::is_dummy_pair_same_type(other);
445 // non-virtual functions
448 ex idx::replace_dim(const ex & new_dim) const
450 idx *i_copy = duplicate();
451 i_copy->dim = new_dim;
452 i_copy->clearflag(status_flags::hash_calculated);
453 return i_copy->setflag(status_flags::dynallocated);
456 ex idx::minimal_dim(const idx & other) const
458 return GiNaC::minimal_dim(dim, other.dim);
461 ex varidx::toggle_variance() const
463 varidx *i_copy = duplicate();
464 i_copy->covariant = !i_copy->covariant;
465 i_copy->clearflag(status_flags::hash_calculated);
466 return i_copy->setflag(status_flags::dynallocated);
469 ex spinidx::toggle_dot() const
471 spinidx *i_copy = duplicate();
472 i_copy->dotted = !i_copy->dotted;
473 i_copy->clearflag(status_flags::hash_calculated);
474 return i_copy->setflag(status_flags::dynallocated);
477 ex spinidx::toggle_variance_dot() const
479 spinidx *i_copy = duplicate();
480 i_copy->covariant = !i_copy->covariant;
481 i_copy->dotted = !i_copy->dotted;
482 i_copy->clearflag(status_flags::hash_calculated);
483 return i_copy->setflag(status_flags::dynallocated);
490 bool is_dummy_pair(const idx & i1, const idx & i2)
492 // The indices must be of exactly the same type
493 if (i1.tinfo() != i2.tinfo())
496 // Same type, let the indices decide whether they are paired
497 return i1.is_dummy_pair_same_type(i2);
500 bool is_dummy_pair(const ex & e1, const ex & e2)
502 // The expressions must be indices
503 if (!is_a<idx>(e1) || !is_a<idx>(e2))
506 return is_dummy_pair(ex_to<idx>(e1), ex_to<idx>(e2));
509 void find_free_and_dummy(exvector::const_iterator it, exvector::const_iterator itend, exvector & out_free, exvector & out_dummy)
514 // No indices? Then do nothing
518 // Only one index? Then it is a free one if it's not numeric
519 if (itend - it == 1) {
520 if (ex_to<idx>(*it).is_symbolic())
521 out_free.push_back(*it);
525 // Sort index vector. This will cause dummy indices come to lie next
526 // to each other (because the sort order is defined to guarantee this).
527 exvector v(it, itend);
528 shaker_sort(v.begin(), v.end(), ex_is_less(), ex_swap());
530 // Find dummy pairs and free indices
531 it = v.begin(); itend = v.end();
532 exvector::const_iterator last = it++;
533 while (it != itend) {
534 if (is_dummy_pair(*it, *last)) {
535 out_dummy.push_back(*last);
540 if (!it->is_equal(*last) && ex_to<idx>(*last).is_symbolic())
541 out_free.push_back(*last);
545 if (ex_to<idx>(*last).is_symbolic())
546 out_free.push_back(*last);
549 ex minimal_dim(const ex & dim1, const ex & dim2)
551 if (dim1.is_equal(dim2) || dim1 < dim2 || (is_exactly_a<numeric>(dim1) && is_a<symbol>(dim2)))
553 else if (dim1 > dim2 || (is_a<symbol>(dim1) && is_exactly_a<numeric>(dim2)))
556 std::ostringstream s;
557 s << "minimal_dim(): index dimensions " << dim1 << " and " << dim2 << " cannot be ordered";
558 throw (std::runtime_error(s.str()));