- // canonicalize indices
-
- bool antisymmetric=false;
-
- switch (type) {
- case color_f:
- antisymmetric=true; // no break here!
- case color_d:
- case color_delta8:
- {
- exvector iv=seq;
- int sig=canonicalize_indices(iv,antisymmetric);
- if (sig!=INT_MAX) {
- // something has changed while sorting indices, more evaluations later
- if (sig==0) return _ex0();
- return ex(sig)*color(type,iv,representation_label);
- }
- }
- break;
- default:
- // nothing to canonicalize
- break;
- }
-
- switch (type) {
- case color_delta8:
- {
- GINAC_ASSERT(seq.size()==2);
- const coloridx & idx1=ex_to_coloridx(seq[0]);
- const coloridx & idx2=ex_to_coloridx(seq[1]);
-
- // check for delta8_{a,a} where a is a symbolic index, replace by 8
- if ((idx1.is_symbolic())&&(idx1.is_equal_same_type(idx2))) {
- return ex(COLOR_EIGHT);
- }
-
- // check for delta8_{a,b} where a and b are numeric indices, replace by 0 or 1
- if ((!idx1.is_symbolic())&&(!idx2.is_symbolic())) {
- if ((idx1.get_value()!=idx2.get_value())) {
- return _ex1();
- } else {
- return _ex0();
- }
- }
+ // canonicalize indices
+
+ bool antisymmetric=false;
+
+ switch (type) {
+ case color_f:
+ antisymmetric=true; // no break here!
+ case color_d:
+ case color_delta8:
+ {
+ exvector iv=seq;
+ int sig=canonicalize_indices(iv,antisymmetric);
+ if (sig!=INT_MAX) {
+ // something has changed while sorting indices, more evaluations later
+ if (sig==0) return _ex0();
+ return ex(sig)*color(type,iv,representation_label);
+ }
+ }
+ break;
+ default:
+ // nothing to canonicalize
+ break;
+ }
+
+ switch (type) {
+ case color_delta8:
+ {
+ GINAC_ASSERT(seq.size()==2);
+ const coloridx & idx1=ex_to_coloridx(seq[0]);
+ const coloridx & idx2=ex_to_coloridx(seq[1]);
+
+ // check for delta8_{a,a} where a is a symbolic index, replace by 8
+ if ((idx1.is_symbolic())&&(idx1.is_equal_same_type(idx2))) {
+ return ex(COLOR_EIGHT);
+ }
+
+ // check for delta8_{a,b} where a and b are numeric indices, replace by 0 or 1
+ if ((!idx1.is_symbolic())&&(!idx2.is_symbolic())) {
+ if ((idx1.get_value()!=idx2.get_value())) {
+ return _ex1();
+ } else {
+ return _ex0();
+ }
+ }
+ }
+ break;
+ case color_d:
+ // check for d_{a,a,c} (=0) when a is symbolic
+ {
+ GINAC_ASSERT(seq.size()==3);
+ const coloridx & idx1=ex_to_coloridx(seq[0]);
+ const coloridx & idx2=ex_to_coloridx(seq[1]);
+ const coloridx & idx3=ex_to_coloridx(seq[2]);
+
+ if (idx1.is_equal_same_type(idx2) && idx1.is_symbolic()) {
+ return _ex0();
+ } else if (idx2.is_equal_same_type(idx3) && idx2.is_symbolic()) {
+ return _ex0();
+ }
+
+ // check for three numeric indices
+ if (!(idx1.is_symbolic()||idx2.is_symbolic()||idx3.is_symbolic())) {
+ GINAC_ASSERT(idx1.get_value()<=idx2.get_value());
+ GINAC_ASSERT(idx2.get_value()<=idx3.get_value());
+ if (CMPINDICES(1,4,6)||CMPINDICES(1,5,7)||CMPINDICES(2,5,6)||
+ CMPINDICES(3,4,4)||CMPINDICES(3,5,5)) {
+ return _ex1_2();
+ } else if (CMPINDICES(2,4,7)||CMPINDICES(3,6,6)||CMPINDICES(3,7,7)) {
+ return -_ex1_2();
+ } else if (CMPINDICES(1,1,8)||CMPINDICES(2,2,8)||CMPINDICES(3,3,8)) {
+ return 1/sqrt(numeric(3));
+ } else if (CMPINDICES(8,8,8)) {
+ return -1/sqrt(numeric(3));
+ } else if (CMPINDICES(4,4,8)||CMPINDICES(5,5,8)||CMPINDICES(6,6,8)||CMPINDICES(7,7,8)) {
+ return -1/(2*sqrt(numeric(3)));
+ }
+ return _ex0();
+ }
+ }
+ break;
+ case color_f:
+ {
+ GINAC_ASSERT(seq.size()==3);
+ const coloridx & idx1=ex_to_coloridx(seq[0]);
+ const coloridx & idx2=ex_to_coloridx(seq[1]);
+ const coloridx & idx3=ex_to_coloridx(seq[2]);
+
+ // check for three numeric indices
+ if (!(idx1.is_symbolic()||idx2.is_symbolic()||idx3.is_symbolic())) {
+ GINAC_ASSERT(idx1.get_value()<=idx2.get_value());
+ GINAC_ASSERT(idx2.get_value()<=idx3.get_value());
+ if (CMPINDICES(1,2,3)) {
+ return _ex1();
+ } else if (CMPINDICES(1,4,7)||CMPINDICES(2,4,6)||
+ CMPINDICES(2,5,7)||CMPINDICES(3,4,5)) {
+ return _ex1_2();
+ } else if (CMPINDICES(1,5,6)||CMPINDICES(3,6,7)) {
+ return -_ex1_2();
+ } else if (CMPINDICES(4,5,8)||CMPINDICES(6,7,8)) {
+ return sqrt(numeric(3))/2;
+ } else if (CMPINDICES(8,8,8)) {
+ return -1/sqrt(numeric(3));
+ } else if (CMPINDICES(4,4,8)||CMPINDICES(5,5,8)||CMPINDICES(6,6,8)||CMPINDICES(7,7,8)) {
+ return -1/(2*sqrt(numeric(3)));
+ }
+ return _ex0();
+ }
+ break;
+ }
+ default:
+ // nothing to evaluate
+ break;
- // simplifications: contract delta8_{a,b} where possible
- // sort delta8,f,d,T(rl=0),T(rl=1),...,ONE(rl=0),ONE(rl=1),...
- // remove superfluous ONEs
-
- // contract indices of delta8_{a,b} if they are different and symbolic
-
- exvector v_contracted=v;
- unsigned replacements;
- bool something_changed=false;
-
- exvector::iterator it=v_contracted.begin();
- while (it!=v_contracted.end()) {
- // process only delta8 objects
- if (is_ex_exactly_of_type(*it,color) && (ex_to_color(*it).type==color_delta8)) {
- color & d8=ex_to_nonconst_color(*it);
- GINAC_ASSERT(d8.seq.size()==2);
- const coloridx & first_idx=ex_to_coloridx(d8.seq[0]);
- const coloridx & second_idx=ex_to_coloridx(d8.seq[1]);
- // delta8_{a,a} should have been contracted in color::eval()
- GINAC_ASSERT((!first_idx.is_equal(second_idx))||(!first_idx.is_symbolic()));
- ex saved_delta8=*it; // save to restore it later
-
- // try to contract first index
- replacements=1;
- if (first_idx.is_symbolic()) {
- replacements = subs_index_in_exvector(v_contracted,first_idx,second_idx);
- if (replacements==1) {
- // not contracted except in itself, restore delta8 object
- *it=saved_delta8;
- } else {
- // a contracted index should occur exactly twice
- GINAC_ASSERT(replacements==2);
- *it=_ex1();
- something_changed=true;
- }
- }
-
- // try second index only if first was not contracted
- if ((replacements==1)&&(second_idx.is_symbolic())) {
- // first index not contracted, *it is guaranteed to be the original delta8 object
- replacements = subs_index_in_exvector(v_contracted,second_idx,first_idx);
- if (replacements==1) {
- // not contracted except in itself, restore delta8 object
- *it=saved_delta8;
- } else {
- // a contracted index should occur exactly twice
- GINAC_ASSERT(replacements==2);
- *it=_ex1();
- something_changed=true;
- }
- }
- }
- ++it;
- }
-
- if (something_changed) {
- // do more simplifications later
- return nonsimplified_ncmul(v_contracted);
- }
-
- // there were no indices to contract
- // sort delta8,f,d,T(rl=0),T(rl=1),...,ONE(rl=0),ONE(rl=1),...,unknown
- // (if there is at least one unknown object, all Ts will be unknown to not change the order)
-
- exvector delta8vec;
- exvector fvec;
- exvector dvec;
- exvectorvector Tvecs;
- Tvecs.resize(MAX_REPRESENTATION_LABELS);
- exvectorvector ONEvecs;
- ONEvecs.resize(MAX_REPRESENTATION_LABELS);
- exvector unknownvec;
-
- split_color_string_in_parts(v,delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec);
-
- // d_{a,k,l} f_{b,k,l}=0 (includes case a=b)
- if ((dvec.size()>=1)&&(fvec.size()>=1)) {
- for (exvector::iterator it1=dvec.begin(); it1!=dvec.end(); ++it1) {
- for (exvector::iterator it2=fvec.begin(); it2!=fvec.end(); ++it2) {
- GINAC_ASSERT(is_ex_exactly_of_type(*it1,color));
- GINAC_ASSERT(is_ex_exactly_of_type(*it2,color));
- const color & col1=ex_to_color(*it1);
- const color & col2=ex_to_color(*it2);
- exvector iv_intersect=idx_intersect(col1.seq,col2.seq);
- if (iv_intersect.size()>=2) return _ex0();
- }
- }
- }
-
- // d_{a,k,l} d_{b,k,l}=5/3 delta8_{a,b} (includes case a=b)
- if (dvec.size()>=2) {
- for (exvector::iterator it1=dvec.begin(); it1!=dvec.end()-1; ++it1) {
- for (exvector::iterator it2=it1+1; it2!=dvec.end(); ++it2) {
- GINAC_ASSERT(is_ex_exactly_of_type(*it1,color));
- GINAC_ASSERT(is_ex_exactly_of_type(*it2,color));
- const color & col1=ex_to_color(*it1);
- const color & col2=ex_to_color(*it2);
- exvector iv_intersect=idx_intersect(col1.seq,col2.seq);
- if (iv_intersect.size()>=2) {
- if (iv_intersect.size()==3) {
- *it1=numeric(40)/numeric(3);
- *it2=_ex1();
- } else {
- int sig1, sig2; // unimportant, since symmetric
- ex idx1=permute_free_index_to_front(col1.seq,iv_intersect,false,&sig1);
- ex idx2=permute_free_index_to_front(col2.seq,iv_intersect,false,&sig2);
- *it1=numeric(5)/numeric(3)*color(color_delta8,idx1,idx2);
- *it2=_ex1();
- }
- return nonsimplified_ncmul(recombine_color_string(
- delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec));
- }
- }
- }
- }
-
- // f_{a,k,l} f_{b,k,l}=3 delta8_{a,b} (includes case a=b)
- if (fvec.size()>=2) {
- for (exvector::iterator it1=fvec.begin(); it1!=fvec.end()-1; ++it1) {
- for (exvector::iterator it2=it1+1; it2!=fvec.end(); ++it2) {
- GINAC_ASSERT(is_ex_exactly_of_type(*it1,color));
- GINAC_ASSERT(is_ex_exactly_of_type(*it2,color));
- const color & col1=ex_to_color(*it1);
- const color & col2=ex_to_color(*it2);
- exvector iv_intersect=idx_intersect(col1.seq,col2.seq);
- if (iv_intersect.size()>=2) {
- if (iv_intersect.size()==3) {
- *it1=numeric(24);
- *it2=_ex1();
- } else {
- int sig1, sig2;
- ex idx1=permute_free_index_to_front(col1.seq,iv_intersect,true,&sig1);
- ex idx2=permute_free_index_to_front(col2.seq,iv_intersect,true,&sig2);
- *it1=numeric(sig1*sig2*5)/numeric(3)*color(color_delta8,idx1,idx2);
- *it2=_ex1();
- }
- return nonsimplified_ncmul(recombine_color_string(
- delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec));
- }
- }
- }
- }
-
- // d_{a,b,c} T_b T_c = 5/6 T_a
- // f_{a,b,c} T_b T_c = 3/2 I T_a
- for (unsigned rl=0; rl<MAX_REPRESENTATION_LABELS; ++rl) {
- if ((Tvecs[rl].size()>=2)&&((dvec.size()>=1)||(fvec.size()>=1))) {
- for (exvector::iterator it1=Tvecs[rl].begin(); it1!=Tvecs[rl].end()-1; ++it1) {
- exvector iv;
- GINAC_ASSERT(is_ex_exactly_of_type(*it1,color)&&ex_to_color(*it1).type==color_T);
- GINAC_ASSERT(is_ex_exactly_of_type(*(it1+1),color)&&ex_to_color(*(it1+1)).type==color_T);
- iv.push_back(ex_to_color(*it1).seq[0]);
- iv.push_back(ex_to_color(*(it1+1)).seq[0]);
-
- // d_{a,b,c} T_b T_c = 5/6 T_a
- for (exvector::iterator it2=dvec.begin(); it2!=dvec.end(); ++it2) {
- GINAC_ASSERT(is_ex_exactly_of_type(*it2,color)&&ex_to_color(*it2).type==color_d);
- const color & dref=ex_to_color(*it2);
- exvector iv_intersect=idx_intersect(dref.seq,iv);
- if (iv_intersect.size()==2) {
- int sig; // unimportant, since symmetric
- ex free_idx=permute_free_index_to_front(dref.seq,iv,false,&sig);
- *it1=color(color_T,free_idx,rl);
- *(it1+1)=color(color_ONE,rl);
- *it2=numeric(5)/numeric(6);
- return nonsimplified_ncmul(recombine_color_string(
- delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec));
- }
- }
-
- // f_{a,b,c} T_b T_c = 3/2 I T_a
- for (exvector::iterator it2=fvec.begin(); it2!=fvec.end(); ++it2) {
- GINAC_ASSERT(is_ex_exactly_of_type(*it2,color)&&ex_to_color(*it2).type==color_f);
- const color & fref=ex_to_color(*it2);
- exvector iv_intersect=idx_intersect(fref.seq,iv);
- if (iv_intersect.size()==2) {
- int sig;
- ex free_idx=permute_free_index_to_front(fref.seq,iv,true,&sig);
- *it1=color(color_T,free_idx,rl);
- *(it1+1)=color(color_ONE,rl);
- *it2=numeric(sig*3)/numeric(2)*I;
- return nonsimplified_ncmul(recombine_color_string(
- delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec));
- }
- }
- }
- }
- }
-
- // clear all ONEs when there is at least one corresponding color_T
- // in this representation, retain one ONE otherwise
- for (unsigned rl=0; rl<MAX_REPRESENTATION_LABELS; ++rl) {
- if (Tvecs[rl].size()!=0) {
- ONEvecs[rl].clear();
- } else if (ONEvecs[rl].size()!=0) {
- ONEvecs[rl].clear();
- ONEvecs[rl].push_back(color(color_ONE,rl));
- }
- }
-
- // return a sorted vector
- return simplified_ncmul(recombine_color_string(delta8vec,fvec,dvec,Tvecs,
- ONEvecs,unknownvec));
+ // simplifications: contract delta8_{a,b} where possible
+ // sort delta8,f,d,T(rl=0),T(rl=1),...,ONE(rl=0),ONE(rl=1),...
+ // remove superfluous ONEs
+
+ // contract indices of delta8_{a,b} if they are different and symbolic
+
+ exvector v_contracted=v;
+ unsigned replacements;
+ bool something_changed=false;
+
+ exvector::iterator it=v_contracted.begin();
+ while (it!=v_contracted.end()) {
+ // process only delta8 objects
+ if (is_ex_exactly_of_type(*it,color) && (ex_to_color(*it).type==color_delta8)) {
+ color & d8=ex_to_nonconst_color(*it);
+ GINAC_ASSERT(d8.seq.size()==2);
+ const coloridx & first_idx=ex_to_coloridx(d8.seq[0]);
+ const coloridx & second_idx=ex_to_coloridx(d8.seq[1]);
+ // delta8_{a,a} should have been contracted in color::eval()
+ GINAC_ASSERT((!first_idx.is_equal(second_idx))||(!first_idx.is_symbolic()));
+ ex saved_delta8=*it; // save to restore it later
+
+ // try to contract first index
+ replacements=1;
+ if (first_idx.is_symbolic()) {
+ replacements = subs_index_in_exvector(v_contracted,first_idx,second_idx);
+ if (replacements==1) {
+ // not contracted except in itself, restore delta8 object
+ *it=saved_delta8;
+ } else {
+ // a contracted index should occur exactly twice
+ GINAC_ASSERT(replacements==2);
+ *it=_ex1();
+ something_changed=true;
+ }
+ }
+
+ // try second index only if first was not contracted
+ if ((replacements==1)&&(second_idx.is_symbolic())) {
+ // first index not contracted, *it is guaranteed to be the original delta8 object
+ replacements = subs_index_in_exvector(v_contracted,second_idx,first_idx);
+ if (replacements==1) {
+ // not contracted except in itself, restore delta8 object
+ *it=saved_delta8;
+ } else {
+ // a contracted index should occur exactly twice
+ GINAC_ASSERT(replacements==2);
+ *it=_ex1();
+ something_changed=true;
+ }
+ }
+ }
+ ++it;
+ }
+
+ if (something_changed) {
+ // do more simplifications later
+ return nonsimplified_ncmul(v_contracted);
+ }
+
+ // there were no indices to contract
+ // sort delta8,f,d,T(rl=0),T(rl=1),...,ONE(rl=0),ONE(rl=1),...,unknown
+ // (if there is at least one unknown object, all Ts will be unknown to not change the order)
+
+ exvector delta8vec;
+ exvector fvec;
+ exvector dvec;
+ exvectorvector Tvecs;
+ Tvecs.resize(MAX_REPRESENTATION_LABELS);
+ exvectorvector ONEvecs;
+ ONEvecs.resize(MAX_REPRESENTATION_LABELS);
+ exvector unknownvec;
+
+ split_color_string_in_parts(v,delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec);
+
+ // d_{a,k,l} f_{b,k,l}=0 (includes case a=b)
+ if ((dvec.size()>=1)&&(fvec.size()>=1)) {
+ for (exvector::iterator it1=dvec.begin(); it1!=dvec.end(); ++it1) {
+ for (exvector::iterator it2=fvec.begin(); it2!=fvec.end(); ++it2) {
+ GINAC_ASSERT(is_ex_exactly_of_type(*it1,color));
+ GINAC_ASSERT(is_ex_exactly_of_type(*it2,color));
+ const color & col1=ex_to_color(*it1);
+ const color & col2=ex_to_color(*it2);
+ exvector iv_intersect=idx_intersect(col1.seq,col2.seq);
+ if (iv_intersect.size()>=2) return _ex0();
+ }
+ }
+ }
+
+ // d_{a,k,l} d_{b,k,l}=5/3 delta8_{a,b} (includes case a=b)
+ if (dvec.size()>=2) {
+ for (exvector::iterator it1=dvec.begin(); it1!=dvec.end()-1; ++it1) {
+ for (exvector::iterator it2=it1+1; it2!=dvec.end(); ++it2) {
+ GINAC_ASSERT(is_ex_exactly_of_type(*it1,color));
+ GINAC_ASSERT(is_ex_exactly_of_type(*it2,color));
+ const color & col1=ex_to_color(*it1);
+ const color & col2=ex_to_color(*it2);
+ exvector iv_intersect=idx_intersect(col1.seq,col2.seq);
+ if (iv_intersect.size()>=2) {
+ if (iv_intersect.size()==3) {
+ *it1=numeric(40)/numeric(3);
+ *it2=_ex1();
+ } else {
+ int sig1, sig2; // unimportant, since symmetric
+ ex idx1=permute_free_index_to_front(col1.seq,iv_intersect,false,&sig1);
+ ex idx2=permute_free_index_to_front(col2.seq,iv_intersect,false,&sig2);
+ *it1=numeric(5)/numeric(3)*color(color_delta8,idx1,idx2);
+ *it2=_ex1();
+ }
+ return nonsimplified_ncmul(recombine_color_string(
+ delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec));
+ }
+ }
+ }
+ }
+
+ // f_{a,k,l} f_{b,k,l}=3 delta8_{a,b} (includes case a=b)
+ if (fvec.size()>=2) {
+ for (exvector::iterator it1=fvec.begin(); it1!=fvec.end()-1; ++it1) {
+ for (exvector::iterator it2=it1+1; it2!=fvec.end(); ++it2) {
+ GINAC_ASSERT(is_ex_exactly_of_type(*it1,color));
+ GINAC_ASSERT(is_ex_exactly_of_type(*it2,color));
+ const color & col1=ex_to_color(*it1);
+ const color & col2=ex_to_color(*it2);
+ exvector iv_intersect=idx_intersect(col1.seq,col2.seq);
+ if (iv_intersect.size()>=2) {
+ if (iv_intersect.size()==3) {
+ *it1=numeric(24);
+ *it2=_ex1();
+ } else {
+ int sig1, sig2;
+ ex idx1=permute_free_index_to_front(col1.seq,iv_intersect,true,&sig1);
+ ex idx2=permute_free_index_to_front(col2.seq,iv_intersect,true,&sig2);
+ *it1=numeric(sig1*sig2*5)/numeric(3)*color(color_delta8,idx1,idx2);
+ *it2=_ex1();
+ }
+ return nonsimplified_ncmul(recombine_color_string(
+ delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec));
+ }
+ }
+ }
+ }
+
+ // d_{a,b,c} T_b T_c = 5/6 T_a
+ // f_{a,b,c} T_b T_c = 3/2 I T_a
+ for (unsigned rl=0; rl<MAX_REPRESENTATION_LABELS; ++rl) {
+ if ((Tvecs[rl].size()>=2)&&((dvec.size()>=1)||(fvec.size()>=1))) {
+ for (exvector::iterator it1=Tvecs[rl].begin(); it1!=Tvecs[rl].end()-1; ++it1) {
+ exvector iv;
+ GINAC_ASSERT(is_ex_exactly_of_type(*it1,color)&&ex_to_color(*it1).type==color_T);
+ GINAC_ASSERT(is_ex_exactly_of_type(*(it1+1),color)&&ex_to_color(*(it1+1)).type==color_T);
+ iv.push_back(ex_to_color(*it1).seq[0]);
+ iv.push_back(ex_to_color(*(it1+1)).seq[0]);
+
+ // d_{a,b,c} T_b T_c = 5/6 T_a
+ for (exvector::iterator it2=dvec.begin(); it2!=dvec.end(); ++it2) {
+ GINAC_ASSERT(is_ex_exactly_of_type(*it2,color)&&ex_to_color(*it2).type==color_d);
+ const color & dref=ex_to_color(*it2);
+ exvector iv_intersect=idx_intersect(dref.seq,iv);
+ if (iv_intersect.size()==2) {
+ int sig; // unimportant, since symmetric
+ ex free_idx=permute_free_index_to_front(dref.seq,iv,false,&sig);
+ *it1=color(color_T,free_idx,rl);
+ *(it1+1)=color(color_ONE,rl);
+ *it2=numeric(5)/numeric(6);
+ return nonsimplified_ncmul(recombine_color_string(
+ delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec));
+ }
+ }
+
+ // f_{a,b,c} T_b T_c = 3/2 I T_a
+ for (exvector::iterator it2=fvec.begin(); it2!=fvec.end(); ++it2) {
+ GINAC_ASSERT(is_ex_exactly_of_type(*it2,color)&&ex_to_color(*it2).type==color_f);
+ const color & fref=ex_to_color(*it2);
+ exvector iv_intersect=idx_intersect(fref.seq,iv);
+ if (iv_intersect.size()==2) {
+ int sig;
+ ex free_idx=permute_free_index_to_front(fref.seq,iv,true,&sig);
+ *it1=color(color_T,free_idx,rl);
+ *(it1+1)=color(color_ONE,rl);
+ *it2=numeric(sig*3)/numeric(2)*I;
+ return nonsimplified_ncmul(recombine_color_string(
+ delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec));
+ }
+ }
+ }
+ }
+ }
+
+ // clear all ONEs when there is at least one corresponding color_T
+ // in this representation, retain one ONE otherwise
+ for (unsigned rl=0; rl<MAX_REPRESENTATION_LABELS; ++rl) {
+ if (Tvecs[rl].size()!=0) {
+ ONEvecs[rl].clear();
+ } else if (ONEvecs[rl].size()!=0) {
+ ONEvecs[rl].clear();
+ ONEvecs[rl].push_back(color(color_ONE,rl));
+ }
+ }
+
+ // return a sorted vector
+ return simplified_ncmul(recombine_color_string(delta8vec,fvec,dvec,Tvecs,
+ ONEvecs,unknownvec));
- GINAC_ASSERT(is_ex_exactly_of_type(e,ncmul));
-
- exvector delta8vec;
- exvector fvec;
- exvector dvec;
- exvectorvector Tvecs;
- Tvecs.resize(MAX_REPRESENTATION_LABELS);
- exvectorvector ONEvecs;
- ONEvecs.resize(MAX_REPRESENTATION_LABELS);
- exvector unknownvec;
-
- split_color_string_in_parts(ex_to_ncmul(e).get_factors(),delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec);
-
- // search for T_k S T_k (=1/2 Tr(S) - 1/6 S)
- for (unsigned rl=0; rl<MAX_REPRESENTATION_LABELS; ++rl) {
- if (Tvecs[rl].size()>=2) {
- for (unsigned i=0; i<Tvecs[rl].size()-1; ++i) {
- for (unsigned j=i+1; j<Tvecs[rl].size(); ++j) {
- ex & t1=Tvecs[rl][i];
- ex & t2=Tvecs[rl][j];
- GINAC_ASSERT(is_ex_exactly_of_type(t1,color)&&
- (ex_to_color(t1).type==color::color_T)&&
- (ex_to_color(t1).seq.size()==1));
- GINAC_ASSERT(is_ex_exactly_of_type(t2,color)&&
- (ex_to_color(t2).type==color::color_T)&&
- (ex_to_color(t2).seq.size()==1));
- const coloridx & idx1=ex_to_coloridx(ex_to_color(t1).seq[0]);
- const coloridx & idx2=ex_to_coloridx(ex_to_color(t2).seq[0]);
-
- if (idx1.is_equal(idx2) && idx1.is_symbolic()) {
- exvector S;
- for (unsigned k=i+1; k<j; ++k) {
- S.push_back(Tvecs[rl][k]);
- }
- t1=_ex1();
- t2=_ex1();
- ex term1=numeric(-1)/numeric(6)*nonsimplified_ncmul(recombine_color_string(
- delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec));
- for (unsigned k=i+1; k<j; ++k) {
- S.push_back(_ex1());
- }
- t1=color_trace_of_one_representation_label(S);
- ex term2=numeric(1)/numeric(2)*nonsimplified_ncmul(recombine_color_string(
- delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec));
- return simplify_color(term1+term2);
- }
- }
- }
- }
- }
-
- // FIXME: higher contractions
-
- return e;
-}
-
+ GINAC_ASSERT(is_ex_exactly_of_type(e,ncmul));
+
+ exvector delta8vec;
+ exvector fvec;
+ exvector dvec;
+ exvectorvector Tvecs;
+ Tvecs.resize(MAX_REPRESENTATION_LABELS);
+ exvectorvector ONEvecs;
+ ONEvecs.resize(MAX_REPRESENTATION_LABELS);
+ exvector unknownvec;
+
+ split_color_string_in_parts(ex_to_ncmul(e).get_factors(),delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec);
+
+ // search for T_k S T_k (=1/2 Tr(S) - 1/6 S)
+ for (unsigned rl=0; rl<MAX_REPRESENTATION_LABELS; ++rl) {
+ if (Tvecs[rl].size()>=2) {
+ for (unsigned i=0; i<Tvecs[rl].size()-1; ++i) {
+ for (unsigned j=i+1; j<Tvecs[rl].size(); ++j) {
+ ex & t1=Tvecs[rl][i];
+ ex & t2=Tvecs[rl][j];
+ GINAC_ASSERT(is_ex_exactly_of_type(t1,color)&&
+ (ex_to_color(t1).type==color::color_T)&&
+ (ex_to_color(t1).seq.size()==1));
+ GINAC_ASSERT(is_ex_exactly_of_type(t2,color)&&
+ (ex_to_color(t2).type==color::color_T)&&
+ (ex_to_color(t2).seq.size()==1));
+ const coloridx & idx1=ex_to_coloridx(ex_to_color(t1).seq[0]);
+ const coloridx & idx2=ex_to_coloridx(ex_to_color(t2).seq[0]);
+
+ if (idx1.is_equal(idx2) && idx1.is_symbolic()) {
+ exvector S;
+ for (unsigned k=i+1; k<j; ++k) {
+ S.push_back(Tvecs[rl][k]);
+ }
+ t1=_ex1();
+ t2=_ex1();
+ ex term1=numeric(-1)/numeric(6)*nonsimplified_ncmul(recombine_color_string(
+ delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec));
+ for (unsigned k=i+1; k<j; ++k) {
+ S.push_back(_ex1());
+ }
+ t1=color_trace_of_one_representation_label(S);
+ ex term2=numeric(1)/numeric(2)*nonsimplified_ncmul(recombine_color_string(
+ delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec));
+ return simplify_color(term1+term2);
+ }
+ }
+ }
+ }
+ }
+
+ // FIXME: higher contractions
+
+ return e;
+}
+