Finalize 1.7.8 release.
[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) 1999-2019 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., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
21  */
22
23 #include "color.h"
24 #include "idx.h"
25 #include "ncmul.h"
26 #include "symmetry.h"
27 #include "operators.h"
28 #include "numeric.h"
29 #include "mul.h"
30 #include "power.h" // for sqrt()
31 #include "symbol.h"
32 #include "archive.h"
33 #include "utils.h"
34
35 #include <iostream>
36 #include <stdexcept>
37
38 namespace GiNaC {
39
40 GINAC_IMPLEMENT_REGISTERED_CLASS(color, indexed)
41
42 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3one, tensor,
43   print_func<print_dflt>(&su3one::do_print).
44   print_func<print_latex>(&su3one::do_print_latex))
45
46 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3t, tensor,
47   print_func<print_dflt>(&su3t::do_print).
48   print_func<print_latex>(&su3t::do_print))
49
50 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3f, tensor,
51   print_func<print_dflt>(&su3f::do_print).
52   print_func<print_latex>(&su3f::do_print))
53
54 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3d, tensor,
55   print_func<print_dflt>(&su3d::do_print).
56   print_func<print_latex>(&su3d::do_print))
57
58 //////////
59 // default constructors
60 //////////
61
62 color::color() : representation_label(0)
63 {
64 }
65
66 DEFAULT_CTOR(su3one)
67 DEFAULT_CTOR(su3t)
68 DEFAULT_CTOR(su3f)
69 DEFAULT_CTOR(su3d)
70
71 //////////
72 // other constructors
73 //////////
74
75 /** Construct object without any color index. This constructor is for
76  *  internal use only. Use the color_ONE() function instead.
77  *  @see color_ONE */
78 color::color(const ex & b, unsigned char rl) : inherited(b), representation_label(rl)
79 {
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 }
88
89 color::color(unsigned char rl, const exvector & v) : inherited(not_symmetric(), v), representation_label(rl)
90 {
91 }
92
93 color::color(unsigned char rl, exvector && v) : inherited(not_symmetric(), std::move(v)), representation_label(rl)
94 {
95 }
96
97 return_type_t color::return_type_tinfo() const
98 {
99         return make_return_type_t<color>(representation_label);
100 }
101
102 //////////
103 // archiving
104 //////////
105
106 void color::read_archive(const archive_node& n, lst& sym_lst)
107 {
108         inherited::read_archive(n, sym_lst);
109         unsigned rl;
110         n.find_unsigned("label", rl);
111         representation_label = rl;
112 }
113
114 void color::archive(archive_node &n) const
115 {
116         inherited::archive(n);
117         n.add_unsigned("label", representation_label);
118 }
119
120 GINAC_BIND_UNARCHIVER(color);
121 GINAC_BIND_UNARCHIVER(su3one);
122 GINAC_BIND_UNARCHIVER(su3t);
123 GINAC_BIND_UNARCHIVER(su3f);
124 GINAC_BIND_UNARCHIVER(su3d);
125
126 //////////
127 // functions overriding virtual functions from base classes
128 //////////
129
130 int color::compare_same_type(const basic & other) const
131 {
132         GINAC_ASSERT(is_a<color>(other));
133         const color &o = static_cast<const color &>(other);
134
135         if (representation_label != o.representation_label) {
136                 // different representation label
137                 return representation_label < o.representation_label ? -1 : 1;
138         }
139
140         return inherited::compare_same_type(other);
141 }
142
143 bool color::match_same_type(const basic & other) const
144 {
145         GINAC_ASSERT(is_a<color>(other));
146         const color &o = static_cast<const color &>(other);
147
148         return representation_label == o.representation_label;
149 }
150
151 DEFAULT_COMPARE(su3one)
152 DEFAULT_COMPARE(su3t)
153 DEFAULT_COMPARE(su3f)
154 DEFAULT_COMPARE(su3d)
155
156 DEFAULT_PRINT_LATEX(su3one, "ONE", "\\mathbb{1}")
157 DEFAULT_PRINT(su3t, "T")
158 DEFAULT_PRINT(su3f, "f")
159 DEFAULT_PRINT(su3d, "d")
160
161 /** Perform automatic simplification on noncommutative product of color
162  *  objects. This removes superfluous ONEs. */
163 ex color::eval_ncmul(const exvector & v) const
164 {
165         exvector s;
166         s.reserve(v.size());
167
168         // Remove superfluous ONEs
169         for (auto & it : v) {
170                 if (!is_a<su3one>(it.op(0)))
171                         s.push_back(it);
172         }
173
174         if (s.empty())
175                 return color(su3one(), representation_label);
176         else
177                 return hold_ncmul(s);
178 }
179
180 ex color::thiscontainer(const exvector & v) const
181 {
182         return color(representation_label, v);
183 }
184
185 ex color::thiscontainer(exvector && v) const
186 {
187         return color(representation_label, std::move(v));
188 }
189
190 /** Given a vector iv3 of three indices and a vector iv2 of two indices that
191  *  is a subset of iv3, return the (free) index that is in iv3 but not in
192  *  iv2 and the sign introduced by permuting that index to the front.
193  *
194  *  @param iv3 Vector of 3 indices
195  *  @param iv2 Vector of 2 indices, must be a subset of iv3
196  *  @param sig Returns sign introduced by index permutation
197  *  @return the free index (the one that is in iv3 but not in iv2) */
198 static ex permute_free_index_to_front(const exvector & iv3, const exvector & iv2, int & sig)
199 {
200         GINAC_ASSERT(iv3.size() == 3);
201         GINAC_ASSERT(iv2.size() == 2);
202
203         sig = 1;
204
205 #define TEST_PERMUTATION(A,B,C,P) \
206         if (iv3[B].is_equal(iv2[0]) && iv3[C].is_equal(iv2[1])) { \
207                 sig = P; \
208                 return iv3[A]; \
209         }
210         
211         TEST_PERMUTATION(0,1,2,  1);
212         TEST_PERMUTATION(0,2,1, -1);
213         TEST_PERMUTATION(1,0,2, -1);
214         TEST_PERMUTATION(1,2,0,  1);
215         TEST_PERMUTATION(2,0,1,  1);
216         TEST_PERMUTATION(2,1,0, -1);
217
218         throw(std::logic_error("permute_free_index_to_front(): no valid permutation found"));
219 }
220
221 /** Automatic symbolic evaluation of indexed symmetric structure constant. */
222 ex su3d::eval_indexed(const basic & i) const
223 {
224         GINAC_ASSERT(is_a<indexed>(i));
225         GINAC_ASSERT(i.nops() == 4);
226         GINAC_ASSERT(is_a<su3d>(i.op(0)));
227
228         // Convolutions are zero
229         if (!(static_cast<const indexed &>(i).get_dummy_indices().empty()))
230                 return _ex0;
231
232         // Numeric evaluation
233         if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
234
235                 // Sort indices
236                 int v[3];
237                 for (unsigned j=0; j<3; j++)
238                         v[j] = ex_to<numeric>(ex_to<idx>(i.op(j + 1)).get_value()).to_int();
239                 if (v[0] > v[1]) std::swap(v[0], v[1]);
240                 if (v[0] > v[2]) std::swap(v[0], v[2]);
241                 if (v[1] > v[2]) std::swap(v[1], v[2]);
242
243 #define CMPINDICES(A,B,C) ((v[0] == (A)) && (v[1] == (B)) && (v[2] == (C)))
244
245                 // Check for non-zero elements
246                 if (CMPINDICES(1,4,6) || CMPINDICES(1,5,7) || CMPINDICES(2,5,6)
247                  || CMPINDICES(3,4,4) || CMPINDICES(3,5,5))
248                         return _ex1_2;
249                 else if (CMPINDICES(2,4,7) || CMPINDICES(3,6,6) || CMPINDICES(3,7,7))
250                         return _ex_1_2;
251                 else if (CMPINDICES(1,1,8) || CMPINDICES(2,2,8) || CMPINDICES(3,3,8))
252                         return sqrt(_ex3)*_ex1_3;
253                 else if (CMPINDICES(8,8,8))
254                         return sqrt(_ex3)*_ex_1_3;
255                 else if (CMPINDICES(4,4,8) || CMPINDICES(5,5,8)
256                       || CMPINDICES(6,6,8) || CMPINDICES(7,7,8))
257                         return sqrt(_ex3)/_ex_6;
258                 else
259                         return _ex0;
260         }
261
262         // No further simplifications
263         return i.hold();
264 }
265
266 /** Automatic symbolic evaluation of indexed antisymmetric structure constant. */
267 ex su3f::eval_indexed(const basic & i) const
268 {
269         GINAC_ASSERT(is_a<indexed>(i));
270         GINAC_ASSERT(i.nops() == 4);
271         GINAC_ASSERT(is_a<su3f>(i.op(0)));
272
273         // Numeric evaluation
274         if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
275
276                 // Sort indices, remember permutation sign
277                 int v[3];
278                 for (unsigned j=0; j<3; j++)
279                         v[j] = ex_to<numeric>(ex_to<idx>(i.op(j + 1)).get_value()).to_int();
280                 int sign = 1;
281                 if (v[0] > v[1]) { std::swap(v[0], v[1]); sign = -sign; }
282                 if (v[0] > v[2]) { std::swap(v[0], v[2]); sign = -sign; }
283                 if (v[1] > v[2]) { std::swap(v[1], v[2]); sign = -sign; }
284
285                 // Check for non-zero elements
286                 if (CMPINDICES(1,2,3))
287                         return sign;
288                 else if (CMPINDICES(1,4,7) || CMPINDICES(2,4,6)
289                       || CMPINDICES(2,5,7) || CMPINDICES(3,4,5))
290                         return _ex1_2 * sign;
291                 else if (CMPINDICES(1,5,6) || CMPINDICES(3,6,7))
292                         return _ex_1_2 * sign;
293                 else if (CMPINDICES(4,5,8) || CMPINDICES(6,7,8))
294                         return sqrt(_ex3)/2 * sign;
295                 else
296                         return _ex0;
297         }
298
299         // No further simplifications
300         return i.hold();
301 }
302
303
304 /** Contraction of generator with something else. */
305 bool su3t::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
306 {
307         GINAC_ASSERT(is_a<indexed>(*self));
308         GINAC_ASSERT(is_a<indexed>(*other));
309         GINAC_ASSERT(self->nops() == 2);
310         GINAC_ASSERT(is_a<su3t>(self->op(0)));
311         unsigned char rl = ex_to<color>(*self).get_representation_label();
312
313         if (is_exactly_a<su3t>(other->op(0))) {
314
315                 // Contraction only makes sense if the representation labels are equal
316                 GINAC_ASSERT(is_a<color>(*other));
317                 if (ex_to<color>(*other).get_representation_label() != rl)
318                         return false;
319
320                 // T.a T.a = 4/3 ONE
321                 if (other - self == 1) {
322                         *self = numeric(4, 3);
323                         *other = color_ONE(rl);
324                         return true;
325
326                 // T.a T.b T.a = -1/6 T.b
327                 } else if (other - self == 2
328                         && is_a<color>(self[1])) {
329                         *self = numeric(-1, 6);
330                         *other = _ex1;
331                         return true;
332
333                 // T.a S T.a = 1/2 Tr(S) - 1/6 S
334                 } else {
335                         auto it = self + 1;
336                         while (it != other) {
337                                 if (!is_a<color>(*it)) {
338                                         return false;
339                                 }
340                                 it++;
341                         }
342
343                         it = self + 1;
344                         ex S = _ex1;
345                         while (it != other) {
346                                 S *= *it;
347                                 *it++ = _ex1;
348                         }
349
350                         *self = color_trace(S, rl) * color_ONE(rl) / 2 - S / 6;
351                         *other = _ex1;
352                         return true;
353                 }
354         }
355
356         return false;
357 }
358
359 /** Contraction of an indexed symmetric structure constant with something else. */
360 bool su3d::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
361 {
362         GINAC_ASSERT(is_a<indexed>(*self));
363         GINAC_ASSERT(is_a<indexed>(*other));
364         GINAC_ASSERT(self->nops() == 4);
365         GINAC_ASSERT(is_a<su3d>(self->op(0)));
366
367         if (is_exactly_a<su3d>(other->op(0))) {
368
369                 // Find the dummy indices of the contraction
370                 exvector self_indices = ex_to<indexed>(*self).get_indices();
371                 exvector other_indices = ex_to<indexed>(*other).get_indices();
372                 exvector all_indices = self_indices;
373                 all_indices.insert(all_indices.end(), other_indices.begin(), other_indices.end());
374                 exvector free_indices, dummy_indices;
375                 find_free_and_dummy(all_indices, free_indices, dummy_indices);
376
377                 // d.abc d.abc = 40/3
378                 if (dummy_indices.size() == 3) {
379                         *self = numeric(40, 3);
380                         *other = _ex1;
381                         return true;
382
383                 // d.akl d.bkl = 5/3 delta.ab
384                 } else if (dummy_indices.size() == 2) {
385                         exvector a;
386                         std::back_insert_iterator<exvector> ita(a);
387                         ita = set_difference(self_indices.begin(), self_indices.end(), dummy_indices.begin(), dummy_indices.end(), ita, ex_is_less());
388                         ita = set_difference(other_indices.begin(), other_indices.end(), dummy_indices.begin(), dummy_indices.end(), ita, ex_is_less());
389                         GINAC_ASSERT(a.size() == 2);
390                         *self = numeric(5, 3) * delta_tensor(a[0], a[1]);
391                         *other = _ex1;
392                         return true;
393                 }
394
395         } else if (is_exactly_a<su3t>(other->op(0))) {
396
397                 // d.abc T.b T.c = 5/6 T.a
398                 if (other+1 != v.end()
399                  && is_exactly_a<su3t>(other[1].op(0))
400                  && ex_to<indexed>(*self).has_dummy_index_for(other[1].op(1))) {
401
402                         exvector self_indices = ex_to<indexed>(*self).get_indices();
403                         exvector dummy_indices = {other[0].op(1), 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_exactly_a<su3f>(other->op(0))) { // 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_exactly_a<su3t>(other->op(0))) {
447
448                 // f.abc T.b T.c = 3/2 I T.a
449                 if (other+1 != v.end()
450                  && is_exactly_a<su3t>(other[1].op(0))
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 = {other[0].op(1), other[1].op(1)};
455                         int sig;
456                         ex a = permute_free_index_to_front(self_indices, dummy_indices, sig);
457                         *self = numeric(3, 2) * sig * I;
458                         other[0] = color_T(a, ex_to<color>(other[0]).get_representation_label());
459                         other[1] = _ex1;
460                         return true;
461                 }
462         }
463
464         return false;
465 }
466
467 //////////
468 // global functions
469 //////////
470
471 ex color_ONE(unsigned char rl)
472 {
473         static ex ONE = dynallocate<su3one>();
474         return color(ONE, rl);
475 }
476
477 ex color_T(const ex & a, unsigned char rl)
478 {
479         static ex t = dynallocate<su3t>();
480
481         if (!is_a<idx>(a))
482                 throw(std::invalid_argument("indices of color_T must be of type idx"));
483         if (!ex_to<idx>(a).get_dim().is_equal(8))
484                 throw(std::invalid_argument("index dimension for color_T must be 8"));
485
486         return color(t, a, rl);
487 }
488
489 ex color_f(const ex & a, const ex & b, const ex & c)
490 {
491         static ex f = dynallocate<su3f>();
492
493         if (!is_a<idx>(a) || !is_a<idx>(b) || !is_a<idx>(c))
494                 throw(std::invalid_argument("indices of color_f must be of type idx"));
495         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))
496                 throw(std::invalid_argument("index dimension for color_f must be 8"));
497
498         return indexed(f, antisymmetric3(), a, b, c);
499 }
500
501 ex color_d(const ex & a, const ex & b, const ex & c)
502 {
503         static ex d = dynallocate<su3d>();
504
505         if (!is_a<idx>(a) || !is_a<idx>(b) || !is_a<idx>(c))
506                 throw(std::invalid_argument("indices of color_d must be of type idx"));
507         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))
508                 throw(std::invalid_argument("index dimension for color_d must be 8"));
509
510         return indexed(d, symmetric3(), a, b, c);
511 }
512
513 ex color_h(const ex & a, const ex & b, const ex & c)
514 {
515         return color_d(a, b, c) + I * color_f(a, b, c);
516 }
517
518 /** Check whether a given tinfo key (as returned by return_type_tinfo()
519  *  is that of a color object (with an arbitrary representation label). */
520 static bool is_color_tinfo(const return_type_t& ti)
521 {
522         return *(ti.tinfo) == typeid(color);
523 }
524
525 /** Extract representation label from tinfo key (as returned by
526  *  return_type_tinfo()). */
527 static unsigned char get_representation_label(const return_type_t& ti)
528 {
529         return (unsigned char)ti.rl;
530 }
531
532 ex color_trace(const ex & e, const std::set<unsigned char> & rls)
533 {
534         if (is_a<color>(e)) {
535
536                 unsigned char rl = ex_to<color>(e).get_representation_label();
537
538                 // Are we taking the trace over this object's representation label?
539                 if (rls.find(rl) == rls.end())
540                         return e;
541
542                 // Yes, all generators are traceless, except for color_ONE
543                 if (is_a<su3one>(e.op(0)))
544                         return _ex3;
545                 else
546                         return _ex0;
547
548         } else if (is_exactly_a<mul>(e)) {
549
550                 // Trace of product: pull out non-color factors
551                 ex prod = _ex1;
552                 for (size_t i=0; i<e.nops(); i++) {
553                         const ex &o = e.op(i);
554                         if (is_color_tinfo(o.return_type_tinfo()))
555                                 prod *= color_trace(o, rls);
556                         else
557                                 prod *= o;
558                 }
559                 return prod;
560
561         } else if (is_exactly_a<ncmul>(e)) {
562
563                 unsigned char rl = get_representation_label(e.return_type_tinfo());
564
565                 // Are we taking the trace over this string's representation label?
566                 if (rls.find(rl) == rls.end())
567                         return e;
568
569                 // Yes, expand product if necessary
570                 ex e_expanded = e.expand();
571                 if (!is_a<ncmul>(e_expanded))
572                         return color_trace(e_expanded, rls);
573
574                 size_t num = e.nops();
575
576                 if (num == 2) {
577
578                         // Tr T_a T_b = 1/2 delta_a_b
579                         return delta_tensor(e.op(0).op(1), e.op(1).op(1)) / 2;
580
581                 } else if (num == 3) {
582
583                         // Tr T_a T_b T_c = 1/4 h_a_b_c
584                         return color_h(e.op(0).op(1), e.op(1).op(1), e.op(2).op(1)) / 4;
585
586                 } else {
587
588                         // Traces of 4 or more generators are computed recursively:
589                         // Tr T_a1 .. T_an =
590                         //     1/6 delta_a(n-1)_an Tr T_a1 .. T_a(n-2)
591                         //   + 1/2 h_a(n-1)_an_k Tr T_a1 .. T_a(n-2) T_k
592                         const ex &last_index = e.op(num - 1).op(1);
593                         const ex &next_to_last_index = e.op(num - 2).op(1);
594                         idx summation_index(dynallocate<symbol>(), 8);
595
596                         exvector v1;
597                         v1.reserve(num - 2);
598                         for (size_t i=0; i<num-2; i++)
599                                 v1.push_back(e.op(i));
600
601                         exvector v2 = v1;
602                         v2.push_back(color_T(summation_index, rl));
603
604                         return delta_tensor(next_to_last_index, last_index) * color_trace(ncmul(v1), rl) / 6
605                                + color_h(next_to_last_index, last_index, summation_index) * color_trace(ncmul(v2), rl) / 2;
606                 }
607
608         } else if (e.nops() > 0) {
609
610                 // Trace maps to all other container classes (this includes sums)
611                 pointer_to_map_function_1arg<const std::set<unsigned char> &> fcn(color_trace, rls);
612                 return e.map(fcn);
613
614         } else
615                 return _ex0;
616 }
617
618 ex color_trace(const ex & e, const lst & rll)
619 {
620         // Convert list to set
621         std::set<unsigned char> rls;
622         for (auto & it : rll) {
623                 if (it.info(info_flags::nonnegint))
624                         rls.insert(ex_to<numeric>(it).to_int());
625         }
626
627         return color_trace(e, rls);
628 }
629
630 ex color_trace(const ex & e, unsigned char rl)
631 {
632         // Convert label to set
633         std::set<unsigned char> rls;
634         rls.insert(rl);
635
636         return color_trace(e, rls);
637 }
638
639 } // namespace GiNaC