* Some internal reorganization WRT flyweight handling and initialization,
[ginac.git] / ginac / color.cpp
1 /** @file color.cpp
2  *
3  *  Implementation of GiNaC's color (SU(3) Lie algebra) objects. */
4
5 /*
6  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
7  *
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.
12  *
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.
17  *
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
21  */
22
23 #include <algorithm>
24 #include <stdexcept>
25
26 #include "color.h"
27 #include "idx.h"
28 #include "ncmul.h"
29 #include "symmetry.h"
30 #include "numeric.h"
31 #include "mul.h"
32 #include "power.h" // for sqrt()
33 #include "symbol.h"
34 #include "print.h"
35 #include "archive.h"
36 #include "debugmsg.h"
37 #include "utils.h"
38
39 namespace GiNaC {
40
41 GINAC_IMPLEMENT_REGISTERED_CLASS(color, indexed)
42 GINAC_IMPLEMENT_REGISTERED_CLASS(su3one, tensor)
43 GINAC_IMPLEMENT_REGISTERED_CLASS(su3t, tensor)
44 GINAC_IMPLEMENT_REGISTERED_CLASS(su3f, tensor)
45 GINAC_IMPLEMENT_REGISTERED_CLASS(su3d, tensor)
46
47 //////////
48 // default constructor, destructor, copy constructor assignment operator and helpers
49 //////////
50
51 color::color() : representation_label(0)
52 {
53         debugmsg("color default constructor", LOGLEVEL_CONSTRUCT);
54         tinfo_key = TINFO_color;
55 }
56
57 void color::copy(const color & other)
58 {
59         inherited::copy(other);
60         representation_label = other.representation_label;
61 }
62
63 DEFAULT_DESTROY(color)
64 DEFAULT_CTORS(su3one)
65 DEFAULT_CTORS(su3t)
66 DEFAULT_CTORS(su3f)
67 DEFAULT_CTORS(su3d)
68
69 //////////
70 // other constructors
71 //////////
72
73 /** Construct object without any color index. This constructor is for
74  *  internal use only. Use the color_ONE() function instead.
75  *  @see color_ONE */
76 color::color(const ex & b, unsigned char rl) : inherited(b), representation_label(rl)
77 {
78         debugmsg("color constructor from ex,unsigned char", LOGLEVEL_CONSTRUCT);
79         tinfo_key = TINFO_color;
80 }
81
82 /** Construct object with one color index. This constructor is for internal
83  *  use only. Use the color_T() function instead.
84  *  @see color_T */
85 color::color(const ex & b, const ex & i1, unsigned char rl) : inherited(b, i1), representation_label(rl)
86 {
87         debugmsg("color constructor from ex,ex,unsigned char", LOGLEVEL_CONSTRUCT);
88         tinfo_key = TINFO_color;
89 }
90
91 color::color(unsigned char rl, const exvector & v, bool discardable) : inherited(sy_none(), v, discardable), representation_label(rl)
92 {
93         debugmsg("color constructor from unsigned char,exvector", LOGLEVEL_CONSTRUCT);
94         tinfo_key = TINFO_color;
95 }
96
97 color::color(unsigned char rl, exvector * vp) : inherited(sy_none(), vp), representation_label(rl)
98 {
99         debugmsg("color constructor from unsigned char,exvector *", LOGLEVEL_CONSTRUCT);
100         tinfo_key = TINFO_color;
101 }
102
103 //////////
104 // archiving
105 //////////
106
107 color::color(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
108 {
109         debugmsg("color constructor from archive_node", LOGLEVEL_CONSTRUCT);
110         unsigned rl;
111         n.find_unsigned("label", rl);
112         representation_label = rl;
113 }
114
115 void color::archive(archive_node &n) const
116 {
117         inherited::archive(n);
118         n.add_unsigned("label", representation_label);
119 }
120
121 DEFAULT_UNARCHIVE(color)
122 DEFAULT_ARCHIVING(su3one)
123 DEFAULT_ARCHIVING(su3t)
124 DEFAULT_ARCHIVING(su3f)
125 DEFAULT_ARCHIVING(su3d)
126
127 //////////
128 // functions overriding virtual functions from base classes
129 //////////
130
131 int color::compare_same_type(const basic & other) const
132 {
133         GINAC_ASSERT(is_a<color>(other));
134         const color &o = static_cast<const color &>(other);
135
136         if (representation_label != o.representation_label) {
137                 // different representation label
138                 return representation_label < o.representation_label ? -1 : 1;
139         }
140
141         return inherited::compare_same_type(other);
142 }
143
144 bool color::match_same_type(const basic & other) const
145 {
146         GINAC_ASSERT(is_a<color>(other));
147         const color &o = static_cast<const color &>(other);
148
149         return representation_label == o.representation_label;
150 }
151
152 DEFAULT_COMPARE(su3one)
153 DEFAULT_COMPARE(su3t)
154 DEFAULT_COMPARE(su3f)
155 DEFAULT_COMPARE(su3d)
156
157 DEFAULT_PRINT_LATEX(su3one, "ONE", "\\mathbb{1}")
158 DEFAULT_PRINT(su3t, "T")
159 DEFAULT_PRINT(su3f, "f")
160 DEFAULT_PRINT(su3d, "d")
161
162 /** Perform automatic simplification on noncommutative product of color
163  *  objects. This removes superfluous ONEs. */
164 ex color::simplify_ncmul(const exvector & v) const
165 {
166         exvector s;
167         s.reserve(v.size());
168
169         // Remove superfluous ONEs
170         exvector::const_iterator it = v.begin(), itend = v.end();
171         while (it != itend) {
172                 if (!is_ex_of_type(it->op(0), su3one))
173                         s.push_back(*it);
174                 it++;
175         }
176
177         if (s.empty())
178                 return color(su3one(), representation_label);
179         else
180                 return simplified_ncmul(s);
181 }
182
183 ex color::thisexprseq(const exvector & v) const
184 {
185         return color(representation_label, v);
186 }
187
188 ex color::thisexprseq(exvector * vp) const
189 {
190         return color(representation_label, vp);
191 }
192
193 /** Given a vector iv3 of three indices and a vector iv2 of two indices that
194  *  is a subset of iv3, return the (free) index that is in iv3 but not in
195  *  iv2 and the sign introduced by permuting that index to the front.
196  *
197  *  @param iv3 Vector of 3 indices
198  *  @param iv2 Vector of 2 indices, must be a subset of iv3
199  *  @param sig Returs sign introduced by index permutation
200  *  @return the free index (the one that is in iv3 but not in iv2) */
201 static ex permute_free_index_to_front(const exvector & iv3, const exvector & iv2, int & sig)
202 {
203         GINAC_ASSERT(iv3.size() == 3);
204         GINAC_ASSERT(iv2.size() == 2);
205
206         sig = 1;
207
208 #define TEST_PERMUTATION(A,B,C,P) \
209         if (iv3[B].is_equal(iv2[0]) && iv3[C].is_equal(iv2[1])) { \
210                 sig = P; \
211                 return iv3[A]; \
212         }
213         
214         TEST_PERMUTATION(0,1,2,  1);
215         TEST_PERMUTATION(0,2,1, -1);
216         TEST_PERMUTATION(1,0,2, -1);
217         TEST_PERMUTATION(1,2,0,  1);
218         TEST_PERMUTATION(2,0,1,  1);
219         TEST_PERMUTATION(2,1,0, -1);
220
221         throw(std::logic_error("permute_free_index_to_front(): no valid permutation found"));
222 }
223
224 /** Automatic symbolic evaluation of indexed symmetric structure constant. */
225 ex su3d::eval_indexed(const basic & i) const
226 {
227         GINAC_ASSERT(is_a<indexed>(i));
228         GINAC_ASSERT(i.nops() == 4);
229         GINAC_ASSERT(is_a<su3d>(i.op(0)));
230
231         // Convolutions are zero
232         if (!(static_cast<const indexed &>(i).get_dummy_indices().empty()))
233                 return _ex0;
234
235         // Numeric evaluation
236         if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
237
238                 // Sort indices
239                 int v[3];
240                 for (unsigned j=0; j<3; j++)
241                         v[j] = ex_to<numeric>(ex_to<idx>(i.op(j + 1)).get_value()).to_int();
242                 if (v[0] > v[1]) std::swap(v[0], v[1]);
243                 if (v[0] > v[2]) std::swap(v[0], v[2]);
244                 if (v[1] > v[2]) std::swap(v[1], v[2]);
245
246 #define CMPINDICES(A,B,C) ((v[0] == (A)) && (v[1] == (B)) && (v[2] == (C)))
247
248                 // Check for non-zero elements
249                 if (CMPINDICES(1,4,6) || CMPINDICES(1,5,7) || CMPINDICES(2,5,6)
250                  || CMPINDICES(3,4,4) || CMPINDICES(3,5,5))
251                         return _ex1_2;
252                 else if (CMPINDICES(2,4,7) || CMPINDICES(3,6,6) || CMPINDICES(3,7,7))
253                         return _ex_1_2;
254                 else if (CMPINDICES(1,1,8) || CMPINDICES(2,2,8) || CMPINDICES(3,3,8))
255                         return sqrt(_ex3)*_ex1_3;
256                 else if (CMPINDICES(8,8,8))
257                         return sqrt(_ex3)*_ex_1_3;
258                 else if (CMPINDICES(4,4,8) || CMPINDICES(5,5,8)
259                       || CMPINDICES(6,6,8) || CMPINDICES(7,7,8))
260                         return sqrt(_ex3)/_ex_6;
261                 else
262                         return _ex0;
263         }
264
265         // No further simplifications
266         return i.hold();
267 }
268
269 /** Automatic symbolic evaluation of indexed antisymmetric structure constant. */
270 ex su3f::eval_indexed(const basic & i) const
271 {
272         GINAC_ASSERT(is_a<indexed>(i));
273         GINAC_ASSERT(i.nops() == 4);
274         GINAC_ASSERT(is_a<su3f>(i.op(0)));
275
276         // Numeric evaluation
277         if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
278
279                 // Sort indices, remember permutation sign
280                 int v[3];
281                 for (unsigned j=0; j<3; j++)
282                         v[j] = ex_to<numeric>(ex_to<idx>(i.op(j + 1)).get_value()).to_int();
283                 int sign = 1;
284                 if (v[0] > v[1]) { std::swap(v[0], v[1]); sign = -sign; }
285                 if (v[0] > v[2]) { std::swap(v[0], v[2]); sign = -sign; }
286                 if (v[1] > v[2]) { std::swap(v[1], v[2]); sign = -sign; }
287
288                 // Check for non-zero elements
289                 if (CMPINDICES(1,2,3))
290                         return sign;
291                 else if (CMPINDICES(1,4,7) || CMPINDICES(2,4,6)
292                       || CMPINDICES(2,5,7) || CMPINDICES(3,4,5))
293                         return _ex1_2 * sign;
294                 else if (CMPINDICES(1,5,6) || CMPINDICES(3,6,7))
295                         return _ex_1_2 * sign;
296                 else if (CMPINDICES(4,5,8) || CMPINDICES(6,7,8))
297                         return sqrt(_ex3)/2 * sign;
298                 else
299                         return _ex0;
300         }
301
302         // No further simplifications
303         return i.hold();
304 }
305
306
307 /** Contraction of generator with something else. */
308 bool su3t::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
309 {
310         GINAC_ASSERT(is_a<indexed>(*self));
311         GINAC_ASSERT(is_a<indexed>(*other));
312         GINAC_ASSERT(self->nops() == 2);
313         GINAC_ASSERT(is_a<su3t>(self->op(0)));
314         unsigned char rl = ex_to<color>(*self).get_representation_label();
315
316         if (is_ex_exactly_of_type(other->op(0), su3t)) {
317
318                 // T.a T.a = 4/3 ONE
319                 if (other - self == 1) {
320                         *self = numeric(4, 3);
321                         *other = color_ONE(rl);
322                         return true;
323
324                 // T.a T.b T.a = -1/6 T.b
325                 } else if (other - self == 2
326                         && is_ex_of_type(self[1], color)) {
327                         *self = numeric(-1, 6);
328                         *other = _ex1;
329                         return true;
330
331                 // T.a S T.a = 1/2 Tr(S) - 1/6 S
332                 } else {
333                         exvector::iterator it = self + 1;
334                         while (it != other) {
335                                 if (!is_ex_of_type(*it, color)) {
336                                         return false;
337                                 }
338                                 it++;
339                         }
340
341                         it = self + 1;
342                         ex S = _ex1;
343                         while (it != other) {
344                                 S *= *it;
345                                 *it++ = _ex1;
346                         }
347
348                         *self = color_trace(S, rl) * color_ONE(rl) / 2 - S / 6;
349                         *other = _ex1;
350                         return true;
351                 }
352         }
353
354         return false;
355 }
356
357 /** Contraction of an indexed symmetric structure constant with something else. */
358 bool su3d::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
359 {
360         GINAC_ASSERT(is_a<indexed>(*self));
361         GINAC_ASSERT(is_a<indexed>(*other));
362         GINAC_ASSERT(self->nops() == 4);
363         GINAC_ASSERT(is_a<su3d>(self->op(0)));
364
365         if (is_ex_exactly_of_type(other->op(0), su3d)) {
366
367                 // Find the dummy indices of the contraction
368                 exvector self_indices = ex_to<indexed>(*self).get_indices();
369                 exvector other_indices = ex_to<indexed>(*other).get_indices();
370                 exvector all_indices = self_indices;
371                 all_indices.insert(all_indices.end(), other_indices.begin(), other_indices.end());
372                 exvector free_indices, dummy_indices;
373                 find_free_and_dummy(all_indices, free_indices, dummy_indices);
374
375                 // d.abc d.abc = 40/3
376                 if (dummy_indices.size() == 3) {
377                         *self = numeric(40, 3);
378                         *other = _ex1;
379                         return true;
380
381                 // d.akl d.bkl = 5/3 delta.ab
382                 } else if (dummy_indices.size() == 2) {
383                         exvector a;
384                         std::back_insert_iterator<exvector> ita(a);
385                         ita = set_difference(self_indices.begin(), self_indices.end(), dummy_indices.begin(), dummy_indices.end(), ita, ex_is_less());
386                         ita = set_difference(other_indices.begin(), other_indices.end(), dummy_indices.begin(), dummy_indices.end(), ita, ex_is_less());
387                         GINAC_ASSERT(a.size() == 2);
388                         *self = numeric(5, 3) * delta_tensor(a[0], a[1]);
389                         *other = _ex1;
390                         return true;
391                 }
392
393         } else if (is_ex_exactly_of_type(other->op(0), su3t)) {
394
395                 // d.abc T.b T.c = 5/6 T.a
396                 if (other+1 != v.end()
397                  && is_ex_exactly_of_type(other[1].op(0), su3t)
398                  && ex_to<indexed>(*self).has_dummy_index_for(other[1].op(1))) {
399
400                         exvector self_indices = ex_to<indexed>(*self).get_indices();
401                         exvector dummy_indices;
402                         dummy_indices.push_back(other[0].op(1));
403                         dummy_indices.push_back(other[1].op(1));
404                         int sig;
405                         ex a = permute_free_index_to_front(self_indices, dummy_indices, sig);
406                         *self = numeric(5, 6);
407                         other[0] = color_T(a, ex_to<color>(other[0]).get_representation_label());
408                         other[1] = _ex1;
409                         return true;
410                 }
411         }
412
413         return false;
414 }
415
416 /** Contraction of an indexed antisymmetric structure constant with something else. */
417 bool su3f::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
418 {
419         GINAC_ASSERT(is_a<indexed>(*self));
420         GINAC_ASSERT(is_a<indexed>(*other));
421         GINAC_ASSERT(self->nops() == 4);
422         GINAC_ASSERT(is_a<su3f>(self->op(0)));
423
424         if (is_ex_exactly_of_type(other->op(0), su3f)) { // f*d is handled by su3d class
425
426                 // Find the dummy indices of the contraction
427                 exvector dummy_indices;
428                 dummy_indices = ex_to<indexed>(*self).get_dummy_indices(ex_to<indexed>(*other));
429
430                 // f.abc f.abc = 24
431                 if (dummy_indices.size() == 3) {
432                         *self = 24;
433                         *other = _ex1;
434                         return true;
435
436                 // f.akl f.bkl = 3 delta.ab
437                 } else if (dummy_indices.size() == 2) {
438                         int sign1, sign2;
439                         ex a = permute_free_index_to_front(ex_to<indexed>(*self).get_indices(), dummy_indices, sign1);
440                         ex b = permute_free_index_to_front(ex_to<indexed>(*other).get_indices(), dummy_indices, sign2);
441                         *self = sign1 * sign2 * 3 * delta_tensor(a, b);
442                         *other = _ex1;
443                         return true;
444                 }
445
446         } else if (is_ex_exactly_of_type(other->op(0), su3t)) {
447
448                 // f.abc T.b T.c = 3/2 I T.a
449                 if (other+1 != v.end()
450                  && is_ex_exactly_of_type(other[1].op(0), su3t)
451                  && ex_to<indexed>(*self).has_dummy_index_for(other[1].op(1))) {
452
453                         exvector self_indices = ex_to<indexed>(*self).get_indices();
454                         exvector dummy_indices;
455                         dummy_indices.push_back(other[0].op(1));
456                         dummy_indices.push_back(other[1].op(1));
457                         int sig;
458                         ex a = permute_free_index_to_front(self_indices, dummy_indices, sig);
459                         *self = numeric(3, 2) * sig * I;
460                         other[0] = color_T(a, ex_to<color>(other[0]).get_representation_label());
461                         other[1] = _ex1;
462                         return true;
463                 }
464         }
465
466         return false;
467 }
468
469 //////////
470 // global functions
471 //////////
472
473 ex color_ONE(unsigned char rl)
474 {
475         return color(su3one(), rl);
476 }
477
478 ex color_T(const ex & a, unsigned char rl)
479 {
480         if (!is_ex_of_type(a, idx))
481                 throw(std::invalid_argument("indices of color_T must be of type idx"));
482         if (!ex_to<idx>(a).get_dim().is_equal(8))
483                 throw(std::invalid_argument("index dimension for color_T must be 8"));
484
485         return color(su3t(), a, rl);
486 }
487
488 ex color_f(const ex & a, const ex & b, const ex & c)
489 {
490         if (!is_ex_of_type(a, idx) || !is_ex_of_type(b, idx) || !is_ex_of_type(c, idx))
491                 throw(std::invalid_argument("indices of color_f must be of type idx"));
492         if (!ex_to<idx>(a).get_dim().is_equal(8) || !ex_to<idx>(b).get_dim().is_equal(8) || !ex_to<idx>(c).get_dim().is_equal(8))
493                 throw(std::invalid_argument("index dimension for color_f must be 8"));
494
495         return indexed(su3f(), sy_anti(), a, b, c);
496 }
497
498 ex color_d(const ex & a, const ex & b, const ex & c)
499 {
500         if (!is_ex_of_type(a, idx) || !is_ex_of_type(b, idx) || !is_ex_of_type(c, idx))
501                 throw(std::invalid_argument("indices of color_d must be of type idx"));
502         if (!ex_to<idx>(a).get_dim().is_equal(8) || !ex_to<idx>(b).get_dim().is_equal(8) || !ex_to<idx>(c).get_dim().is_equal(8))
503                 throw(std::invalid_argument("index dimension for color_d must be 8"));
504
505         return indexed(su3d(), sy_symm(), a, b, c);
506 }
507
508 ex color_h(const ex & a, const ex & b, const ex & c)
509 {
510         return color_d(a, b, c) + I * color_f(a, b, c);
511 }
512
513 /** Check whether a given tinfo key (as returned by return_type_tinfo()
514  *  is that of a color object with the specified representation label. */
515 static bool is_color_tinfo(unsigned ti, unsigned char rl)
516 {
517         return ti == (TINFO_color + rl);
518 }
519
520 ex color_trace(const ex & e, unsigned char rl)
521 {
522         if (is_ex_of_type(e, color)) {
523
524                 if (ex_to<color>(e).get_representation_label() == rl
525                  && is_ex_of_type(e.op(0), su3one))
526                         return _ex3;
527                 else
528                         return _ex0;
529
530         } else if (is_ex_exactly_of_type(e, mul)) {
531
532                 // Trace of product: pull out non-color factors
533                 ex prod = _ex1;
534                 for (unsigned i=0; i<e.nops(); i++) {
535                         const ex &o = e.op(i);
536                         if (is_color_tinfo(o.return_type_tinfo(), rl))
537                                 prod *= color_trace(o, rl);
538                         else
539                                 prod *= o;
540                 }
541                 return prod;
542
543         } else if (is_ex_exactly_of_type(e, ncmul)) {
544
545                 if (!is_color_tinfo(e.return_type_tinfo(), rl))
546                         return _ex0;
547
548                 // Expand product, if necessary
549                 ex e_expanded = e.expand();
550                 if (!is_ex_of_type(e_expanded, ncmul))
551                         return color_trace(e_expanded, rl);
552
553                 unsigned num = e.nops();
554
555                 if (num == 2) {
556
557                         // Tr T_a T_b = 1/2 delta_a_b
558                         return delta_tensor(e.op(0).op(1), e.op(1).op(1)) / 2;
559
560                 } else if (num == 3) {
561
562                         // Tr T_a T_b T_c = 1/4 h_a_b_c
563                         return color_h(e.op(0).op(1), e.op(1).op(1), e.op(2).op(1)) / 4;
564
565                 } else {
566
567                         // Traces of 4 or more generators are computed recursively:
568                         // Tr T_a1 .. T_an =
569                         //     1/6 delta_a(n-1)_an Tr T_a1 .. T_a(n-2)
570                         //   + 1/2 h_a(n-1)_an_k Tr T_a1 .. T_a(n-2) T_k
571                         const ex &last_index = e.op(num - 1).op(1);
572                         const ex &next_to_last_index = e.op(num - 2).op(1);
573                         idx summation_index((new symbol)->setflag(status_flags::dynallocated), 8);
574
575                         exvector v1;
576                         v1.reserve(num - 2);
577                         for (unsigned i=0; i<num-2; i++)
578                                 v1.push_back(e.op(i));
579
580                         exvector v2 = v1;
581                         v2.push_back(color_T(summation_index, rl));
582
583                         return delta_tensor(next_to_last_index, last_index) * color_trace(ncmul(v1), rl) / 6
584                                + color_h(next_to_last_index, last_index, summation_index) * color_trace(ncmul(v2), rl) / 2;
585                 }
586
587         } else if (e.nops() > 0) {
588
589                 // Trace maps to all other container classes (this includes sums)
590                 pointer_to_map_function_1arg<unsigned char> fcn(color_trace, rl);
591                 return e.map(fcn);
592
593         } else
594                 return _ex0;
595 }
596
597 } // namespace GiNaC