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) 1999-2017 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