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"
31 #include "operators.h"
38 GINAC_IMPLEMENT_REGISTERED_CLASS(idx, basic)
39 GINAC_IMPLEMENT_REGISTERED_CLASS(varidx, idx)
40 GINAC_IMPLEMENT_REGISTERED_CLASS(spinidx, varidx)
43 // default constructor
46 idx::idx() : inherited(TINFO_idx) {}
48 varidx::varidx() : covariant(false)
50 tinfo_key = TINFO_varidx;
53 spinidx::spinidx() : dotted(false)
55 tinfo_key = TINFO_spinidx;
62 idx::idx(const ex & v, const ex & d) : inherited(TINFO_idx), value(v), dim(d)
65 if (!dim.info(info_flags::posint))
66 throw(std::invalid_argument("dimension of space must be a positive integer"));
69 varidx::varidx(const ex & v, const ex & d, bool cov) : inherited(v, d), covariant(cov)
71 tinfo_key = TINFO_varidx;
74 spinidx::spinidx(const ex & v, const ex & d, bool cov, bool dot) : inherited(v, d, cov), dotted(dot)
76 tinfo_key = TINFO_spinidx;
83 idx::idx(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
85 n.find_ex("value", value, sym_lst);
86 n.find_ex("dim", dim, sym_lst);
89 varidx::varidx(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
91 n.find_bool("covariant", covariant);
94 spinidx::spinidx(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
96 n.find_bool("dotted", dotted);
99 void idx::archive(archive_node &n) const
101 inherited::archive(n);
102 n.add_ex("value", value);
103 n.add_ex("dim", dim);
106 void varidx::archive(archive_node &n) const
108 inherited::archive(n);
109 n.add_bool("covariant", covariant);
112 void spinidx::archive(archive_node &n) const
114 inherited::archive(n);
115 n.add_bool("dotted", dotted);
118 DEFAULT_UNARCHIVE(idx)
119 DEFAULT_UNARCHIVE(varidx)
120 DEFAULT_UNARCHIVE(spinidx)
123 // functions overriding virtual functions from base classes
126 void idx::print(const print_context & c, unsigned level) const
128 if (is_a<print_tree>(c)) {
130 c.s << std::string(level, ' ') << class_name()
131 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
133 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
134 value.print(c, level + delta_indent);
135 dim.print(c, level + delta_indent);
139 if (is_a<print_latex>(c))
143 bool need_parens = !(is_exactly_a<numeric>(value) || is_a<symbol>(value));
149 if (c.options & print_options::print_index_dimensions) {
154 if (is_a<print_latex>(c))
159 void varidx::print(const print_context & c, unsigned level) const
161 if (is_a<print_tree>(c)) {
163 c.s << std::string(level, ' ') << class_name()
164 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
165 << (covariant ? ", covariant" : ", contravariant")
167 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
168 value.print(c, level + delta_indent);
169 dim.print(c, level + delta_indent);
172 if (is_a<print_latex>(c))
180 bool need_parens = !(is_exactly_a<numeric>(value) || is_a<symbol>(value));
186 if (c.options & print_options::print_index_dimensions) {
191 if (is_a<print_latex>(c))
196 void spinidx::print(const print_context & c, unsigned level) const
198 if (is_a<print_tree>(c)) {
200 c.s << std::string(level, ' ') << class_name()
201 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
202 << (covariant ? ", covariant" : ", contravariant")
203 << (dotted ? ", dotted" : ", undotted")
205 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
206 value.print(c, level + delta_indent);
207 dim.print(c, level + delta_indent);
211 bool is_tex = is_a<print_latex>(c);
229 bool need_parens = !(is_exactly_a<numeric>(value) || is_a<symbol>(value));
235 if (is_tex && dotted)
242 bool idx::info(unsigned inf) const
244 if (inf == info_flags::idx)
246 return inherited::info(inf);
249 size_t idx::nops() const
251 // don't count the dimension as that is not really a sub-expression
255 ex idx::op(size_t i) const
257 GINAC_ASSERT(i == 0);
261 ex idx::map(map_function & f) const
263 idx *copy = duplicate();
264 copy->setflag(status_flags::dynallocated);
265 copy->clearflag(status_flags::hash_calculated);
266 copy->value = f(value);
270 /** Returns order relation between two indices of the same type. The order
271 * must be such that dummy indices lie next to each other. */
272 int idx::compare_same_type(const basic & other) const
274 GINAC_ASSERT(is_a<idx>(other));
275 const idx &o = static_cast<const idx &>(other);
277 int cmpval = value.compare(o.value);
280 return dim.compare(o.dim);
283 bool idx::match_same_type(const basic & other) const
285 GINAC_ASSERT(is_a<idx>(other));
286 const idx &o = static_cast<const idx &>(other);
288 return dim.is_equal(o.dim);
291 int varidx::compare_same_type(const basic & other) const
293 GINAC_ASSERT(is_a<varidx>(other));
294 const varidx &o = static_cast<const varidx &>(other);
296 int cmpval = inherited::compare_same_type(other);
300 // Check variance last so dummy indices will end up next to each other
301 if (covariant != o.covariant)
302 return covariant ? -1 : 1;
307 bool varidx::match_same_type(const basic & other) const
309 GINAC_ASSERT(is_a<varidx>(other));
310 const varidx &o = static_cast<const varidx &>(other);
312 if (covariant != o.covariant)
315 return inherited::match_same_type(other);
318 int spinidx::compare_same_type(const basic & other) const
320 GINAC_ASSERT(is_a<spinidx>(other));
321 const spinidx &o = static_cast<const spinidx &>(other);
323 // Check dottedness first so dummy indices will end up next to each other
324 if (dotted != o.dotted)
325 return dotted ? -1 : 1;
327 int cmpval = inherited::compare_same_type(other);
334 bool spinidx::match_same_type(const basic & other) const
336 GINAC_ASSERT(is_a<spinidx>(other));
337 const spinidx &o = static_cast<const spinidx &>(other);
339 if (dotted != o.dotted)
341 return inherited::match_same_type(other);
344 unsigned idx::calchash() const
346 unsigned v = golden_ratio_hash(tinfo());
348 v ^= value.gethash();
352 // Store calculated hash value only if object is already evaluated
353 if (flags & status_flags::evaluated) {
354 setflag(status_flags::hash_calculated);
361 /** By default, basic::evalf would evaluate the index value but we don't want
362 * a.1 to become a.(1.0). */
363 ex idx::evalf(int level) const
368 ex idx::subs(const exmap & m, unsigned options) const
370 // First look for index substitutions
371 exmap::const_iterator it = m.find(*this);
374 // Substitution index->index
375 if (is_a<idx>(it->second))
378 // Otherwise substitute value
379 idx *i_copy = duplicate();
380 i_copy->value = it->second;
381 i_copy->clearflag(status_flags::hash_calculated);
382 return i_copy->setflag(status_flags::dynallocated);
385 // None, substitute objects in value (not in dimension)
386 const ex &subsed_value = value.subs(m, options);
387 if (are_ex_trivially_equal(value, subsed_value))
390 idx *i_copy = duplicate();
391 i_copy->value = subsed_value;
392 i_copy->clearflag(status_flags::hash_calculated);
393 return i_copy->setflag(status_flags::dynallocated);
396 /** Implementation of ex::diff() for an index always returns 0.
399 ex idx::derivative(const symbol & s) const
405 // new virtual functions
408 bool idx::is_dummy_pair_same_type(const basic & other) const
410 const idx &o = static_cast<const idx &>(other);
412 // Only pure symbols form dummy pairs, "2n+1" doesn't
413 if (!is_a<symbol>(value))
416 // Value must be equal, of course
417 if (!value.is_equal(o.value))
420 // Dimensions need not be equal but must be comparable (so we can
421 // determine the minimum dimension of contractions)
422 if (dim.is_equal(o.dim))
425 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)));
428 bool varidx::is_dummy_pair_same_type(const basic & other) const
430 const varidx &o = static_cast<const varidx &>(other);
432 // Variance must be opposite
433 if (covariant == o.covariant)
436 return inherited::is_dummy_pair_same_type(other);
439 bool spinidx::is_dummy_pair_same_type(const basic & other) const
441 const spinidx &o = static_cast<const spinidx &>(other);
443 // Dottedness must be the same
444 if (dotted != o.dotted)
447 return inherited::is_dummy_pair_same_type(other);
452 // non-virtual functions
455 ex idx::replace_dim(const ex & new_dim) const
457 idx *i_copy = duplicate();
458 i_copy->dim = new_dim;
459 i_copy->clearflag(status_flags::hash_calculated);
460 return i_copy->setflag(status_flags::dynallocated);
463 ex idx::minimal_dim(const idx & other) const
465 return GiNaC::minimal_dim(dim, other.dim);
468 ex varidx::toggle_variance() const
470 varidx *i_copy = duplicate();
471 i_copy->covariant = !i_copy->covariant;
472 i_copy->clearflag(status_flags::hash_calculated);
473 return i_copy->setflag(status_flags::dynallocated);
476 ex spinidx::toggle_dot() const
478 spinidx *i_copy = duplicate();
479 i_copy->dotted = !i_copy->dotted;
480 i_copy->clearflag(status_flags::hash_calculated);
481 return i_copy->setflag(status_flags::dynallocated);
484 ex spinidx::toggle_variance_dot() const
486 spinidx *i_copy = duplicate();
487 i_copy->covariant = !i_copy->covariant;
488 i_copy->dotted = !i_copy->dotted;
489 i_copy->clearflag(status_flags::hash_calculated);
490 return i_copy->setflag(status_flags::dynallocated);
497 bool is_dummy_pair(const idx & i1, const idx & i2)
499 // The indices must be of exactly the same type
500 if (i1.tinfo() != i2.tinfo())
503 // Same type, let the indices decide whether they are paired
504 return i1.is_dummy_pair_same_type(i2);
507 bool is_dummy_pair(const ex & e1, const ex & e2)
509 // The expressions must be indices
510 if (!is_a<idx>(e1) || !is_a<idx>(e2))
513 return is_dummy_pair(ex_to<idx>(e1), ex_to<idx>(e2));
516 void find_free_and_dummy(exvector::const_iterator it, exvector::const_iterator itend, exvector & out_free, exvector & out_dummy)
521 // No indices? Then do nothing
525 // Only one index? Then it is a free one if it's not numeric
526 if (itend - it == 1) {
527 if (ex_to<idx>(*it).is_symbolic())
528 out_free.push_back(*it);
532 // Sort index vector. This will cause dummy indices come to lie next
533 // to each other (because the sort order is defined to guarantee this).
534 exvector v(it, itend);
535 shaker_sort(v.begin(), v.end(), ex_is_less(), ex_swap());
537 // Find dummy pairs and free indices
538 it = v.begin(); itend = v.end();
539 exvector::const_iterator last = it++;
540 while (it != itend) {
541 if (is_dummy_pair(*it, *last)) {
542 out_dummy.push_back(*last);
547 if (!it->is_equal(*last) && ex_to<idx>(*last).is_symbolic())
548 out_free.push_back(*last);
552 if (ex_to<idx>(*last).is_symbolic())
553 out_free.push_back(*last);
556 ex minimal_dim(const ex & dim1, const ex & dim2)
558 if (dim1.is_equal(dim2) || dim1 < dim2 || (is_exactly_a<numeric>(dim1) && is_a<symbol>(dim2)))
560 else if (dim1 > dim2 || (is_a<symbol>(dim1) && is_exactly_a<numeric>(dim2)))
563 std::ostringstream s;
564 s << "minimal_dim(): index dimensions " << dim1 << " and " << dim2 << " cannot be ordered";
565 throw (std::runtime_error(s.str()));