c31a83c91ae6cce517399b13538869d1496e69b9
[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 "ex.h"
28 #include "idx.h"
29 #include "ncmul.h"
30 #include "numeric.h"
31 #include "power.h" // for sqrt()
32 #include "print.h"
33 #include "archive.h"
34 #include "debugmsg.h"
35 #include "utils.h"
36
37 namespace GiNaC {
38
39 GINAC_IMPLEMENT_REGISTERED_CLASS(color, indexed)
40 GINAC_IMPLEMENT_REGISTERED_CLASS(su3one, tensor)
41 GINAC_IMPLEMENT_REGISTERED_CLASS(su3t, tensor)
42 GINAC_IMPLEMENT_REGISTERED_CLASS(su3f, tensor)
43 GINAC_IMPLEMENT_REGISTERED_CLASS(su3d, tensor)
44
45 //////////
46 // default constructor, destructor, copy constructor assignment operator and helpers
47 //////////
48
49 color::color() : representation_label(0)
50 {
51         debugmsg("color default constructor", LOGLEVEL_CONSTRUCT);
52         tinfo_key = TINFO_color;
53 }
54
55 void color::copy(const color & other)
56 {
57         inherited::copy(other);
58         representation_label = other.representation_label;
59 }
60
61 DEFAULT_DESTROY(color)
62 DEFAULT_CTORS(su3one)
63 DEFAULT_CTORS(su3t)
64 DEFAULT_CTORS(su3f)
65 DEFAULT_CTORS(su3d)
66
67 //////////
68 // other constructors
69 //////////
70
71 /** Construct object without any color index. This constructor is for
72  *  internal use only. Use the color_ONE() function instead.
73  *  @see color_ONE */
74 color::color(const ex & b, unsigned rl = 0) : inherited(b), representation_label(rl)
75 {
76         debugmsg("color constructor from ex,unsigned", LOGLEVEL_CONSTRUCT);
77         tinfo_key = TINFO_color;
78 }
79
80 /** Construct object with one color index. This constructor is for internal
81  *  use only. Use the color_T() function instead.
82  *  @see color_T */
83 color::color(const ex & b, const ex & i1, unsigned rl = 0) : inherited(b, i1), representation_label(rl)
84 {
85         debugmsg("color constructor from ex,ex,unsigned", LOGLEVEL_CONSTRUCT);
86         tinfo_key = TINFO_color;
87 }
88
89 color::color(unsigned rl, const exvector & v, bool discardable) : inherited(indexed::unknown, v, discardable), representation_label(rl)
90 {
91         debugmsg("color constructor from unsigned,exvector", LOGLEVEL_CONSTRUCT);
92         tinfo_key = TINFO_color;
93 }
94
95 color::color(unsigned rl, exvector * vp) : inherited(indexed::unknown, vp), representation_label(rl)
96 {
97         debugmsg("color constructor from unsigned,exvector *", LOGLEVEL_CONSTRUCT);
98         tinfo_key = TINFO_color;
99 }
100
101 //////////
102 // archiving
103 //////////
104
105 color::color(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
106 {
107         debugmsg("color constructor from archive_node", LOGLEVEL_CONSTRUCT);
108         n.find_unsigned("representation", representation_label);
109 }
110
111 void color::archive(archive_node &n) const
112 {
113         inherited::archive(n);
114         n.add_unsigned("representation", representation_label);
115 }
116
117 DEFAULT_UNARCHIVE(color)
118 DEFAULT_ARCHIVING(su3one)
119 DEFAULT_ARCHIVING(su3t)
120 DEFAULT_ARCHIVING(su3f)
121 DEFAULT_ARCHIVING(su3d)
122
123 //////////
124 // functions overriding virtual functions from bases classes
125 //////////
126
127 int color::compare_same_type(const basic & other) const
128 {
129         GINAC_ASSERT(other.tinfo() == TINFO_color);
130         const color &o = static_cast<const color &>(other);
131
132         if (representation_label != o.representation_label) {
133                 // different representation label
134                 return representation_label < o.representation_label ? -1 : 1;
135         }
136
137         return inherited::compare_same_type(other);
138 }
139
140 DEFAULT_COMPARE(su3one)
141 DEFAULT_COMPARE(su3t)
142 DEFAULT_COMPARE(su3f)
143 DEFAULT_COMPARE(su3d)
144
145 DEFAULT_PRINT(su3one, "ONE")
146 DEFAULT_PRINT(su3t, "T")
147 DEFAULT_PRINT(su3f, "f")
148 DEFAULT_PRINT(su3d, "d")
149
150 /** Perform automatic simplification on noncommutative product of color
151  *  objects. This removes superfluous ONEs. */
152 ex color::simplify_ncmul(const exvector & v) const
153 {
154         //!! TODO: sort by representation label
155         exvector s;
156         s.reserve(v.size());
157
158         exvector::const_iterator it = v.begin(), itend = v.end();
159         while (it != itend) {
160                 if (!is_ex_of_type(it->op(0), su3one))
161                         s.push_back(*it);
162                 it++;
163         }
164
165         if (s.size() == 0)
166                 return color(su3one());
167         else if (s.size() == v.size())
168                 return simplified_ncmul(v);
169         else
170                 return simplified_ncmul(s);
171 }
172
173 ex color::thisexprseq(const exvector & v) const
174 {
175         return color(representation_label, v);
176 }
177
178 ex color::thisexprseq(exvector * vp) const
179 {
180         return color(representation_label, vp);
181 }
182
183 /** Given a vector iv3 of three indices and a vector iv2 of two indices that
184  *  is a subset of iv3, return the (free) index that is in iv3 but not in
185  *  iv2 and the sign introduced by permuting that index to the front.
186  *
187  *  @param iv3 Vector of 3 indices
188  *  @param iv2 Vector of 2 indices, must be a subset of iv3
189  *  @param sig Returs sign introduced by index permutation
190  *  @return the free index (the one that is in iv3 but not in iv2) */
191 static ex permute_free_index_to_front(const exvector & iv3, const exvector & iv2, int & sig)
192 {
193         GINAC_ASSERT(iv3.size() == 3);
194         GINAC_ASSERT(iv2.size() == 2);
195
196         sig = 1;
197
198 #define TEST_PERMUTATION(A,B,C,P) \
199         if (iv3[B].is_equal(iv2[0]) && iv3[C].is_equal(iv2[1])) { \
200                 sig = P; \
201                 return iv3[A]; \
202         }
203         
204         TEST_PERMUTATION(0,1,2,  1);
205         TEST_PERMUTATION(0,2,1, -1);
206         TEST_PERMUTATION(1,0,2, -1);
207         TEST_PERMUTATION(1,2,0,  1);
208         TEST_PERMUTATION(2,0,1,  1);
209         TEST_PERMUTATION(2,1,0, -1);
210
211         throw(std::logic_error("permute_free_index_to_front(): no valid permutation found"));
212 }
213
214 /** Automatic symbolic evaluation of indexed symmetric structure constant. */
215 ex su3d::eval_indexed(const basic & i) const
216 {
217         GINAC_ASSERT(is_of_type(i, indexed));
218         GINAC_ASSERT(i.nops() == 4);
219         GINAC_ASSERT(is_ex_of_type(i.op(0), su3d));
220
221         // Convolutions are zero
222         if (static_cast<const indexed &>(i).get_dummy_indices().size() != 0)
223                 return _ex0();
224
225         // Numeric evaluation
226         if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
227
228                 // Sort indices
229                 int v[3];
230                 for (unsigned j=0; j<3; j++)
231                         v[j] = ex_to_numeric(ex_to_idx(i.op(j + 1)).get_value()).to_int();
232                 if (v[0] > v[1]) std::swap(v[0], v[1]);
233                 if (v[0] > v[2]) std::swap(v[0], v[2]);
234                 if (v[1] > v[2]) std::swap(v[1], v[2]);
235
236 #define CMPINDICES(A,B,C) ((v[0] == (A)) && (v[1] == (B)) && (v[2] == (C)))
237
238                 // Check for non-zero elements
239                 if (CMPINDICES(1,4,6) || CMPINDICES(1,5,7) || CMPINDICES(2,5,6)
240                  || CMPINDICES(3,4,4) || CMPINDICES(3,5,5))
241                         return _ex1_2();
242                 else if (CMPINDICES(2,4,7) || CMPINDICES(3,6,6) || CMPINDICES(3,7,7))
243                         return _ex_1_2();
244                 else if (CMPINDICES(1,1,8) || CMPINDICES(2,2,8) || CMPINDICES(3,3,8))
245                         return sqrt(_ex3())/3;
246                 else if (CMPINDICES(8,8,8))
247                         return -sqrt(_ex3())/3;
248                 else if (CMPINDICES(4,4,8) || CMPINDICES(5,5,8)
249                       || CMPINDICES(6,6,8) || CMPINDICES(7,7,8))
250                         return -sqrt(_ex3())/6;
251                 else
252                         return _ex0();
253         }
254
255         // No further simplifications
256         return i.hold();
257 }
258
259 /** Automatic symbolic evaluation of indexed antisymmetric structure constant. */
260 ex su3f::eval_indexed(const basic & i) const
261 {
262         GINAC_ASSERT(is_of_type(i, indexed));
263         GINAC_ASSERT(i.nops() == 4);
264         GINAC_ASSERT(is_ex_of_type(i.op(0), su3f));
265
266         // Numeric evaluation
267         if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
268
269                 // Sort indices, remember permutation sign
270                 int v[3];
271                 for (unsigned j=0; j<3; j++)
272                         v[j] = ex_to_numeric(ex_to_idx(i.op(j + 1)).get_value()).to_int();
273                 int sign = 1;
274                 if (v[0] > v[1]) { std::swap(v[0], v[1]); sign = -sign; }
275                 if (v[0] > v[2]) { std::swap(v[0], v[2]); sign = -sign; }
276                 if (v[1] > v[2]) { std::swap(v[1], v[2]); sign = -sign; }
277
278                 // Check for non-zero elements
279                 if (CMPINDICES(1,2,3))
280                         return sign;
281                 else if (CMPINDICES(1,4,7) || CMPINDICES(2,4,6)
282                       || CMPINDICES(2,5,7) || CMPINDICES(3,4,5))
283                         return _ex1_2() * sign;
284                 else if (CMPINDICES(1,5,6) || CMPINDICES(3,6,7))
285                         return _ex_1_2() * sign;
286                 else if (CMPINDICES(4,5,8) || CMPINDICES(6,7,8))
287                         return sqrt(_ex3())/2 * sign;
288                 else
289                         return _ex0();
290         }
291
292         // No further simplifications
293         return i.hold();
294 }
295
296
297 /** Contraction of an indexed symmetric structure constant with something else. */
298 bool su3d::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
299 {
300         GINAC_ASSERT(is_ex_of_type(*self, indexed));
301         GINAC_ASSERT(is_ex_of_type(*other, indexed));
302         GINAC_ASSERT(self->nops() == 4);
303         GINAC_ASSERT(is_ex_of_type(self->op(0), su3d));
304
305         if (is_ex_exactly_of_type(other->op(0), su3d)) {
306
307                 // Find the dummy indices of the contraction
308                 exvector dummy_indices;
309                 dummy_indices = ex_to_indexed(*self).get_dummy_indices(ex_to_indexed(*other));
310
311                 // d.abc*d.abc=40/3
312                 if (dummy_indices.size() == 3) {
313                         *self = numeric(40, 3);
314                         *other = _ex1();
315                         return true;
316
317                 // d.akl*d.bkl=5/3*delta.ab
318                 } else if (dummy_indices.size() == 2) {
319                         exvector a = index_set_difference(ex_to_indexed(*self).get_indices(), dummy_indices);
320                         exvector b = index_set_difference(ex_to_indexed(*other).get_indices(), dummy_indices);
321                         GINAC_ASSERT(a.size() > 0);
322                         GINAC_ASSERT(b.size() > 0);
323                         *self = numeric(5, 3) * delta_tensor(a[0], b[0]);
324                         *other = _ex1();
325                         return true;
326                 }
327         }
328
329         return false;
330 }
331
332 /** Contraction of an indexed antisymmetric structure constant with something else. */
333 bool su3f::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
334 {
335         GINAC_ASSERT(is_ex_of_type(*self, indexed));
336         GINAC_ASSERT(is_ex_of_type(*other, indexed));
337         GINAC_ASSERT(self->nops() == 4);
338         GINAC_ASSERT(is_ex_of_type(self->op(0), su3f));
339
340         if (is_ex_exactly_of_type(other->op(0), su3f)) { // f*d is handled by su3d class
341
342                 // Find the dummy indices of the contraction
343                 exvector dummy_indices;
344                 dummy_indices = ex_to_indexed(*self).get_dummy_indices(ex_to_indexed(*other));
345
346                 // f.abc*f.abc=24
347                 if (dummy_indices.size() == 3) {
348                         *self = 24;
349                         *other = _ex1();
350                         return true;
351
352                 // f.akl*f.bkl=3*delta.ab
353                 } else if (dummy_indices.size() == 2) {
354                         int sign1, sign2;
355                         ex a = permute_free_index_to_front(ex_to_indexed(*self).get_indices(), dummy_indices, sign1);
356                         ex b = permute_free_index_to_front(ex_to_indexed(*other).get_indices(), dummy_indices, sign2);
357                         *self = sign1 * sign2 * 3 * delta_tensor(a, b);
358                         *other = _ex1();
359                         return true;
360                 }
361         }
362
363         return false;
364 }
365
366 //////////
367 // global functions
368 //////////
369
370 ex color_ONE(unsigned rl)
371 {
372         return color(su3one(), rl);
373 }
374
375 ex color_T(const ex & a, unsigned rl)
376 {
377         if (!is_ex_of_type(a, idx))
378                 throw(std::invalid_argument("indices of color_T must be of type idx"));
379         if (!ex_to_idx(a).get_dim().is_equal(8))
380                 throw(std::invalid_argument("index dimension for color_T must be 8"));
381
382         return color(su3t(), a, rl);
383 }
384
385 ex color_f(const ex & a, const ex & b, const ex & c)
386 {
387         if (!is_ex_of_type(a, idx) || !is_ex_of_type(b, idx) || !is_ex_of_type(c, idx))
388                 throw(std::invalid_argument("indices of color_f must be of type idx"));
389         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))
390                 throw(std::invalid_argument("index dimension for color_f must be 8"));
391
392         return indexed(su3f(), indexed::antisymmetric, a, b, c);
393 }
394
395 ex color_d(const ex & a, const ex & b, const ex & c)
396 {
397         if (!is_ex_of_type(a, idx) || !is_ex_of_type(b, idx) || !is_ex_of_type(c, idx))
398                 throw(std::invalid_argument("indices of color_d must be of type idx"));
399         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))
400                 throw(std::invalid_argument("index dimension for color_d must be 8"));
401
402         return indexed(su3d(), indexed::symmetric, a, b, c);
403 }
404
405 ex color_h(const ex & a, const ex & b, const ex & c)
406 {
407         return color_d(a, b, c) + I * color_f(a, b, c);
408 }
409
410 } // namespace GiNaC