3 * Implementation of GiNaC's indices. */
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
30 #include "relational.h"
37 GINAC_IMPLEMENT_REGISTERED_CLASS(idx, basic)
38 GINAC_IMPLEMENT_REGISTERED_CLASS(varidx, idx)
39 GINAC_IMPLEMENT_REGISTERED_CLASS(spinidx, varidx)
42 // default ctor, dtor, copy ctor, assignment operator and helpers
45 idx::idx() : inherited(TINFO_idx) {}
47 varidx::varidx() : covariant(false)
49 tinfo_key = TINFO_varidx;
52 spinidx::spinidx() : dotted(false)
54 tinfo_key = TINFO_spinidx;
57 void idx::copy(const idx & other)
59 inherited::copy(other);
64 void varidx::copy(const varidx & other)
66 inherited::copy(other);
67 covariant = other.covariant;
70 void spinidx::copy(const spinidx & other)
72 inherited::copy(other);
73 dotted = other.dotted;
77 DEFAULT_DESTROY(varidx)
78 DEFAULT_DESTROY(spinidx)
84 idx::idx(const ex & v, const ex & d) : inherited(TINFO_idx), value(v), dim(d)
87 if (!dim.info(info_flags::posint))
88 throw(std::invalid_argument("dimension of space must be a positive integer"));
91 varidx::varidx(const ex & v, const ex & d, bool cov) : inherited(v, d), covariant(cov)
93 tinfo_key = TINFO_varidx;
96 spinidx::spinidx(const ex & v, const ex & d, bool cov, bool dot) : inherited(v, d, cov), dotted(dot)
98 tinfo_key = TINFO_spinidx;
105 idx::idx(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
107 n.find_ex("value", value, sym_lst);
108 n.find_ex("dim", dim, sym_lst);
111 varidx::varidx(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
113 n.find_bool("covariant", covariant);
116 spinidx::spinidx(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
118 n.find_bool("dotted", dotted);
121 void idx::archive(archive_node &n) const
123 inherited::archive(n);
124 n.add_ex("value", value);
125 n.add_ex("dim", dim);
128 void varidx::archive(archive_node &n) const
130 inherited::archive(n);
131 n.add_bool("covariant", covariant);
134 void spinidx::archive(archive_node &n) const
136 inherited::archive(n);
137 n.add_bool("dotted", dotted);
140 DEFAULT_UNARCHIVE(idx)
141 DEFAULT_UNARCHIVE(varidx)
142 DEFAULT_UNARCHIVE(spinidx)
145 // functions overriding virtual functions from base classes
148 void idx::print(const print_context & c, unsigned level) const
150 if (is_of_type(c, print_tree)) {
152 c.s << std::string(level, ' ') << class_name()
153 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
155 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
156 value.print(c, level + delta_indent);
157 dim.print(c, level + delta_indent);
161 if (is_a<print_latex>(c))
165 bool need_parens = !(is_exactly_a<numeric>(value) || is_a<symbol>(value));
171 if (is_a<print_latex>(c))
176 void varidx::print(const print_context & c, unsigned level) const
178 if (is_of_type(c, print_tree)) {
180 c.s << std::string(level, ' ') << class_name()
181 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
182 << (covariant ? ", covariant" : ", contravariant")
184 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
185 value.print(c, level + delta_indent);
186 dim.print(c, level + delta_indent);
189 if (is_a<print_latex>(c))
197 bool need_parens = !(is_exactly_a<numeric>(value) || is_a<symbol>(value));
203 if (is_a<print_latex>(c))
208 void spinidx::print(const print_context & c, unsigned level) const
210 if (is_of_type(c, print_tree)) {
212 c.s << std::string(level, ' ') << class_name()
213 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
214 << (covariant ? ", covariant" : ", contravariant")
215 << (dotted ? ", dotted" : ", undotted")
217 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
218 value.print(c, level + delta_indent);
219 dim.print(c, level + delta_indent);
223 bool is_tex = is_of_type(c, print_latex);
241 bool need_parens = !(is_exactly_a<numeric>(value) || is_a<symbol>(value));
247 if (is_tex && dotted)
254 bool idx::info(unsigned inf) const
256 if (inf == info_flags::idx)
258 return inherited::info(inf);
261 unsigned idx::nops() const
263 // don't count the dimension as that is not really a sub-expression
267 ex & idx::let_op(int i)
269 GINAC_ASSERT(i == 0);
273 /** Returns order relation between two indices of the same type. The order
274 * must be such that dummy indices lie next to each other. */
275 int idx::compare_same_type(const basic & other) const
277 GINAC_ASSERT(is_a<idx>(other));
278 const idx &o = static_cast<const idx &>(other);
280 int cmpval = value.compare(o.value);
283 return dim.compare(o.dim);
286 bool idx::match_same_type(const basic & other) const
288 GINAC_ASSERT(is_a<idx>(other));
289 const idx &o = static_cast<const idx &>(other);
291 return dim.is_equal(o.dim);
294 int varidx::compare_same_type(const basic & other) const
296 GINAC_ASSERT(is_a<varidx>(other));
297 const varidx &o = static_cast<const varidx &>(other);
299 int cmpval = inherited::compare_same_type(other);
303 // Check variance last so dummy indices will end up next to each other
304 if (covariant != o.covariant)
305 return covariant ? -1 : 1;
309 bool varidx::match_same_type(const basic & other) const
311 GINAC_ASSERT(is_a<varidx>(other));
312 const varidx &o = static_cast<const varidx &>(other);
314 if (covariant != o.covariant)
316 return inherited::match_same_type(other);
319 int spinidx::compare_same_type(const basic & other) const
321 GINAC_ASSERT(is_a<spinidx>(other));
322 const spinidx &o = static_cast<const spinidx &>(other);
324 // Check dottedness first so dummy indices will end up next to each other
325 if (dotted != o.dotted)
326 return dotted ? -1 : 1;
328 int cmpval = inherited::compare_same_type(other);
335 bool spinidx::match_same_type(const basic & other) const
337 GINAC_ASSERT(is_a<spinidx>(other));
338 const spinidx &o = static_cast<const spinidx &>(other);
340 if (dotted != o.dotted)
342 return inherited::match_same_type(other);
345 /** By default, basic::evalf would evaluate the index value but we don't want
346 * a.1 to become a.(1.0). */
347 ex idx::evalf(int level) const
352 ex idx::subs(const lst & ls, const lst & lr, bool no_pattern) const
354 GINAC_ASSERT(ls.nops() == lr.nops());
356 // First look for index substitutions
357 for (unsigned i=0; i<ls.nops(); i++) {
358 if (is_equal(ex_to<basic>(ls.op(i)))) {
360 // Substitution index->index
361 if (is_a<idx>(lr.op(i)))
364 // Otherwise substitute value
365 idx *i_copy = static_cast<idx *>(duplicate());
366 i_copy->value = lr.op(i);
367 i_copy->clearflag(status_flags::hash_calculated);
368 return i_copy->setflag(status_flags::dynallocated);
372 // None, substitute objects in value (not in dimension)
373 const ex &subsed_value = value.subs(ls, lr, no_pattern);
374 if (are_ex_trivially_equal(value, subsed_value))
377 idx *i_copy = static_cast<idx *>(duplicate());
378 i_copy->value = subsed_value;
379 i_copy->clearflag(status_flags::hash_calculated);
380 return i_copy->setflag(status_flags::dynallocated);
383 /** Implementation of ex::diff() for an index always returns 0.
386 ex idx::derivative(const symbol & s) const
392 // new virtual functions
395 bool idx::is_dummy_pair_same_type(const basic & other) const
397 const idx &o = static_cast<const idx &>(other);
399 // Only pure symbols form dummy pairs, numeric indices and expressions
401 if (!is_a<symbol>(value))
404 // Value must be equal, of course
405 if (!value.is_equal(o.value))
408 // Dimensions need not be equal but must be comparable (so we can
409 // determine the minimum dimension of contractions)
410 if (dim.is_equal(o.dim))
413 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)));
416 bool varidx::is_dummy_pair_same_type(const basic & other) const
418 const varidx &o = static_cast<const varidx &>(other);
420 // Variance must be opposite
421 if (covariant == o.covariant)
424 return inherited::is_dummy_pair_same_type(other);
427 bool spinidx::is_dummy_pair_same_type(const basic & other) const
429 const spinidx &o = static_cast<const spinidx &>(other);
431 // Dottedness must be the same
432 if (dotted != o.dotted)
435 return inherited::is_dummy_pair_same_type(other);
440 // non-virtual functions
443 ex idx::replace_dim(const ex & new_dim) const
445 idx *i_copy = static_cast<idx *>(duplicate());
446 i_copy->dim = new_dim;
447 i_copy->clearflag(status_flags::hash_calculated);
448 return i_copy->setflag(status_flags::dynallocated);
451 ex idx::minimal_dim(const idx & other) const
453 return GiNaC::minimal_dim(dim, other.dim);
456 ex varidx::toggle_variance(void) const
458 varidx *i_copy = static_cast<varidx *>(duplicate());
459 i_copy->covariant = !i_copy->covariant;
460 i_copy->clearflag(status_flags::hash_calculated);
461 return i_copy->setflag(status_flags::dynallocated);
464 ex spinidx::toggle_dot(void) const
466 spinidx *i_copy = static_cast<spinidx *>(duplicate());
467 i_copy->dotted = !i_copy->dotted;
468 i_copy->clearflag(status_flags::hash_calculated);
469 return i_copy->setflag(status_flags::dynallocated);
472 ex spinidx::toggle_variance_dot(void) const
474 spinidx *i_copy = static_cast<spinidx *>(duplicate());
475 i_copy->covariant = !i_copy->covariant;
476 i_copy->dotted = !i_copy->dotted;
477 i_copy->clearflag(status_flags::hash_calculated);
478 return i_copy->setflag(status_flags::dynallocated);
485 bool is_dummy_pair(const idx & i1, const idx & i2)
487 // The indices must be of exactly the same type
488 if (i1.tinfo() != i2.tinfo())
491 // Same type, let the indices decide whether they are paired
492 return i1.is_dummy_pair_same_type(i2);
495 bool is_dummy_pair(const ex & e1, const ex & e2)
497 // The expressions must be indices
498 if (!is_a<idx>(e1) || !is_a<idx>(e2))
501 return is_dummy_pair(ex_to<idx>(e1), ex_to<idx>(e2));
504 void find_free_and_dummy(exvector::const_iterator it, exvector::const_iterator itend, exvector & out_free, exvector & out_dummy)
509 // No indices? Then do nothing
513 // Only one index? Then it is a free one if it's not numeric
514 if (itend - it == 1) {
515 if (ex_to<idx>(*it).is_symbolic())
516 out_free.push_back(*it);
520 // Sort index vector. This will cause dummy indices come to lie next
521 // to each other (because the sort order is defined to guarantee this).
522 exvector v(it, itend);
523 shaker_sort(v.begin(), v.end(), ex_is_less(), ex_swap());
525 // Find dummy pairs and free indices
526 it = v.begin(); itend = v.end();
527 exvector::const_iterator last = it++;
528 while (it != itend) {
529 if (is_dummy_pair(*it, *last)) {
530 out_dummy.push_back(*last);
535 if (!it->is_equal(*last) && ex_to<idx>(*last).is_symbolic())
536 out_free.push_back(*last);
540 if (ex_to<idx>(*last).is_symbolic())
541 out_free.push_back(*last);
544 ex minimal_dim(const ex & dim1, const ex & dim2)
546 if (dim1.is_equal(dim2) || dim1 < dim2 || (is_exactly_a<numeric>(dim1) && is_a<symbol>(dim2)))
548 else if (dim1 > dim2 || (is_a<symbol>(dim1) && is_exactly_a<numeric>(dim2)))
551 std::ostringstream s;
552 s << "minimal_dim(): index dimensions " << dim1 << " and " << dim2 << " cannot be ordered";
553 throw (std::runtime_error(s.str()));