* Implementation of GiNaC's color (SU(3) Lie algebra) objects. */
/*
- * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
-#include <algorithm>
+#include <iostream>
#include <stdexcept>
#include "color.h"
-#include "ex.h"
#include "idx.h"
#include "ncmul.h"
+#include "symmetry.h"
+#include "operators.h"
#include "numeric.h"
+#include "mul.h"
#include "power.h" // for sqrt()
+#include "symbol.h"
#include "archive.h"
-#include "debugmsg.h"
#include "utils.h"
namespace GiNaC {
GINAC_IMPLEMENT_REGISTERED_CLASS(color, indexed)
-GINAC_IMPLEMENT_REGISTERED_CLASS(su3one, tensor)
-GINAC_IMPLEMENT_REGISTERED_CLASS(su3t, tensor)
-GINAC_IMPLEMENT_REGISTERED_CLASS(su3f, tensor)
-GINAC_IMPLEMENT_REGISTERED_CLASS(su3d, tensor)
+
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3one, tensor,
+ print_func<print_dflt>(&su3one::do_print).
+ print_func<print_latex>(&su3one::do_print_latex))
+
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3t, tensor,
+ print_func<print_dflt>(&su3t::do_print).
+ print_func<print_latex>(&su3t::do_print))
+
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3f, tensor,
+ print_func<print_dflt>(&su3f::do_print).
+ print_func<print_latex>(&su3f::do_print))
+
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3d, tensor,
+ print_func<print_dflt>(&su3d::do_print).
+ print_func<print_latex>(&su3d::do_print))
//////////
-// default constructor, destructor, copy constructor assignment operator and helpers
+// default constructors
//////////
color::color() : representation_label(0)
{
- debugmsg("color default constructor", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_color;
}
-void color::copy(const color & other)
-{
- inherited::copy(other);
- representation_label = other.representation_label;
-}
-
-DEFAULT_DESTROY(color)
-DEFAULT_CTORS(su3one)
-DEFAULT_CTORS(su3t)
-DEFAULT_CTORS(su3f)
-DEFAULT_CTORS(su3d)
+DEFAULT_CTOR(su3one)
+DEFAULT_CTOR(su3t)
+DEFAULT_CTOR(su3f)
+DEFAULT_CTOR(su3d)
//////////
// other constructors
/** Construct object without any color index. This constructor is for
* internal use only. Use the color_ONE() function instead.
* @see color_ONE */
-color::color(const ex & b, unsigned rl = 0) : inherited(b), representation_label(rl)
+color::color(const ex & b, unsigned char rl) : inherited(b), representation_label(rl)
{
- debugmsg("color constructor from ex,unsigned", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_color;
}
/** Construct object with one color index. This constructor is for internal
* use only. Use the color_T() function instead.
* @see color_T */
-color::color(const ex & b, const ex & i1, unsigned rl = 0) : inherited(b, i1), representation_label(rl)
+color::color(const ex & b, const ex & i1, unsigned char rl) : inherited(b, i1), representation_label(rl)
{
- debugmsg("color constructor from ex,ex,unsigned", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_color;
}
-color::color(unsigned rl, const exvector & v, bool discardable) : inherited(indexed::unknown, v, discardable), representation_label(rl)
+color::color(unsigned char rl, const exvector & v, bool discardable) : inherited(sy_none(), v, discardable), representation_label(rl)
{
- debugmsg("color constructor from unsigned,exvector", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_color;
}
-color::color(unsigned rl, exvector * vp) : inherited(indexed::unknown, vp), representation_label(rl)
+color::color(unsigned char rl, std::auto_ptr<exvector> vp) : inherited(sy_none(), vp), representation_label(rl)
{
- debugmsg("color constructor from unsigned,exvector *", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_color;
}
// archiving
//////////
-color::color(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
+color::color(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
{
- debugmsg("color constructor from archive_node", LOGLEVEL_CONSTRUCT);
- n.find_unsigned("representation", representation_label);
+ unsigned rl;
+ n.find_unsigned("label", rl);
+ representation_label = rl;
}
void color::archive(archive_node &n) const
{
inherited::archive(n);
- n.add_unsigned("representation", representation_label);
+ n.add_unsigned("label", representation_label);
}
DEFAULT_UNARCHIVE(color)
DEFAULT_ARCHIVING(su3d)
//////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
//////////
int color::compare_same_type(const basic & other) const
{
- GINAC_ASSERT(other.tinfo() == TINFO_color);
+ GINAC_ASSERT(is_a<color>(other));
const color &o = static_cast<const color &>(other);
if (representation_label != o.representation_label) {
return inherited::compare_same_type(other);
}
+bool color::match_same_type(const basic & other) const
+{
+ GINAC_ASSERT(is_a<color>(other));
+ const color &o = static_cast<const color &>(other);
+
+ return representation_label == o.representation_label;
+}
+
DEFAULT_COMPARE(su3one)
DEFAULT_COMPARE(su3t)
DEFAULT_COMPARE(su3f)
DEFAULT_COMPARE(su3d)
-DEFAULT_PRINT(su3one, "ONE")
+DEFAULT_PRINT_LATEX(su3one, "ONE", "\\mathbb{1}")
DEFAULT_PRINT(su3t, "T")
DEFAULT_PRINT(su3f, "f")
DEFAULT_PRINT(su3d, "d")
/** Perform automatic simplification on noncommutative product of color
* objects. This removes superfluous ONEs. */
-ex color::simplify_ncmul(const exvector & v) const
+ex color::eval_ncmul(const exvector & v) const
{
- //!! TODO: sort by representation label
exvector s;
s.reserve(v.size());
+ // Remove superfluous ONEs
exvector::const_iterator it = v.begin(), itend = v.end();
while (it != itend) {
- if (!is_ex_of_type(it->op(0), su3one))
+ if (!is_a<su3one>(it->op(0)))
s.push_back(*it);
it++;
}
- if (s.size() == 0)
- return color(su3one());
- else if (s.size() == v.size())
- return simplified_ncmul(v);
+ if (s.empty())
+ return color(su3one(), representation_label);
else
- return simplified_ncmul(s);
+ return hold_ncmul(s);
}
-ex color::thisexprseq(const exvector & v) const
+ex color::thiscontainer(const exvector & v) const
{
return color(representation_label, v);
}
-ex color::thisexprseq(exvector * vp) const
+ex color::thiscontainer(std::auto_ptr<exvector> vp) const
{
return color(representation_label, vp);
}
/** Automatic symbolic evaluation of indexed symmetric structure constant. */
ex su3d::eval_indexed(const basic & i) const
{
- GINAC_ASSERT(is_of_type(i, indexed));
+ GINAC_ASSERT(is_a<indexed>(i));
GINAC_ASSERT(i.nops() == 4);
- GINAC_ASSERT(is_ex_of_type(i.op(0), su3d));
+ GINAC_ASSERT(is_a<su3d>(i.op(0)));
// Convolutions are zero
- if (static_cast<const indexed &>(i).get_dummy_indices().size() != 0)
- return _ex0();
+ if (!(static_cast<const indexed &>(i).get_dummy_indices().empty()))
+ return _ex0;
// Numeric evaluation
if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
// Sort indices
int v[3];
for (unsigned j=0; j<3; j++)
- v[j] = ex_to_numeric(ex_to_idx(i.op(j + 1)).get_value()).to_int();
+ v[j] = ex_to<numeric>(ex_to<idx>(i.op(j + 1)).get_value()).to_int();
if (v[0] > v[1]) std::swap(v[0], v[1]);
if (v[0] > v[2]) std::swap(v[0], v[2]);
if (v[1] > v[2]) std::swap(v[1], v[2]);
// Check for non-zero elements
if (CMPINDICES(1,4,6) || CMPINDICES(1,5,7) || CMPINDICES(2,5,6)
|| CMPINDICES(3,4,4) || CMPINDICES(3,5,5))
- return _ex1_2();
+ return _ex1_2;
else if (CMPINDICES(2,4,7) || CMPINDICES(3,6,6) || CMPINDICES(3,7,7))
- return _ex_1_2();
+ return _ex_1_2;
else if (CMPINDICES(1,1,8) || CMPINDICES(2,2,8) || CMPINDICES(3,3,8))
- return sqrt(_ex3())/3;
+ return sqrt(_ex3)*_ex1_3;
else if (CMPINDICES(8,8,8))
- return -sqrt(_ex3())/3;
+ return sqrt(_ex3)*_ex_1_3;
else if (CMPINDICES(4,4,8) || CMPINDICES(5,5,8)
|| CMPINDICES(6,6,8) || CMPINDICES(7,7,8))
- return -sqrt(_ex3())/6;
+ return sqrt(_ex3)/_ex_6;
else
- return _ex0();
+ return _ex0;
}
// No further simplifications
/** Automatic symbolic evaluation of indexed antisymmetric structure constant. */
ex su3f::eval_indexed(const basic & i) const
{
- GINAC_ASSERT(is_of_type(i, indexed));
+ GINAC_ASSERT(is_a<indexed>(i));
GINAC_ASSERT(i.nops() == 4);
- GINAC_ASSERT(is_ex_of_type(i.op(0), su3f));
+ GINAC_ASSERT(is_a<su3f>(i.op(0)));
// Numeric evaluation
if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
// Sort indices, remember permutation sign
int v[3];
for (unsigned j=0; j<3; j++)
- v[j] = ex_to_numeric(ex_to_idx(i.op(j + 1)).get_value()).to_int();
+ v[j] = ex_to<numeric>(ex_to<idx>(i.op(j + 1)).get_value()).to_int();
int sign = 1;
if (v[0] > v[1]) { std::swap(v[0], v[1]); sign = -sign; }
if (v[0] > v[2]) { std::swap(v[0], v[2]); sign = -sign; }
return sign;
else if (CMPINDICES(1,4,7) || CMPINDICES(2,4,6)
|| CMPINDICES(2,5,7) || CMPINDICES(3,4,5))
- return _ex1_2() * sign;
+ return _ex1_2 * sign;
else if (CMPINDICES(1,5,6) || CMPINDICES(3,6,7))
- return _ex_1_2() * sign;
+ return _ex_1_2 * sign;
else if (CMPINDICES(4,5,8) || CMPINDICES(6,7,8))
- return sqrt(_ex3())/2 * sign;
+ return sqrt(_ex3)/2 * sign;
else
- return _ex0();
+ return _ex0;
}
// No further simplifications
}
+/** Contraction of generator with something else. */
+bool su3t::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
+{
+ GINAC_ASSERT(is_a<indexed>(*self));
+ GINAC_ASSERT(is_a<indexed>(*other));
+ GINAC_ASSERT(self->nops() == 2);
+ GINAC_ASSERT(is_a<su3t>(self->op(0)));
+ unsigned char rl = ex_to<color>(*self).get_representation_label();
+
+ if (is_exactly_a<su3t>(other->op(0))) {
+
+ // Contraction only makes sense if the represenation labels are equal
+ GINAC_ASSERT(is_a<color>(*other));
+ if (ex_to<color>(*other).get_representation_label() != rl)
+ return false;
+
+ // T.a T.a = 4/3 ONE
+ if (other - self == 1) {
+ *self = numeric(4, 3);
+ *other = color_ONE(rl);
+ return true;
+
+ // T.a T.b T.a = -1/6 T.b
+ } else if (other - self == 2
+ && is_a<color>(self[1])) {
+ *self = numeric(-1, 6);
+ *other = _ex1;
+ return true;
+
+ // T.a S T.a = 1/2 Tr(S) - 1/6 S
+ } else {
+ exvector::iterator it = self + 1;
+ while (it != other) {
+ if (!is_a<color>(*it)) {
+ return false;
+ }
+ it++;
+ }
+
+ it = self + 1;
+ ex S = _ex1;
+ while (it != other) {
+ S *= *it;
+ *it++ = _ex1;
+ }
+
+ *self = color_trace(S, rl) * color_ONE(rl) / 2 - S / 6;
+ *other = _ex1;
+ return true;
+ }
+ }
+
+ return false;
+}
+
/** Contraction of an indexed symmetric structure constant with something else. */
bool su3d::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
{
- GINAC_ASSERT(is_ex_of_type(*self, indexed));
- GINAC_ASSERT(is_ex_of_type(*other, indexed));
+ GINAC_ASSERT(is_a<indexed>(*self));
+ GINAC_ASSERT(is_a<indexed>(*other));
GINAC_ASSERT(self->nops() == 4);
- GINAC_ASSERT(is_ex_of_type(self->op(0), su3d));
+ GINAC_ASSERT(is_a<su3d>(self->op(0)));
- if (is_ex_exactly_of_type(other->op(0), su3d)) {
+ if (is_exactly_a<su3d>(other->op(0))) {
// Find the dummy indices of the contraction
- exvector dummy_indices;
- dummy_indices = ex_to_indexed(*self).get_dummy_indices(ex_to_indexed(*other));
-
- // d.abc*d.abc=40/3
+ exvector self_indices = ex_to<indexed>(*self).get_indices();
+ exvector other_indices = ex_to<indexed>(*other).get_indices();
+ exvector all_indices = self_indices;
+ all_indices.insert(all_indices.end(), other_indices.begin(), other_indices.end());
+ exvector free_indices, dummy_indices;
+ find_free_and_dummy(all_indices, free_indices, dummy_indices);
+
+ // d.abc d.abc = 40/3
if (dummy_indices.size() == 3) {
*self = numeric(40, 3);
- *other = _ex1();
+ *other = _ex1;
return true;
- // d.akl*d.bkl=5/3*delta.ab
+ // d.akl d.bkl = 5/3 delta.ab
} else if (dummy_indices.size() == 2) {
- exvector a = index_set_difference(ex_to_indexed(*self).get_indices(), dummy_indices);
- exvector b = index_set_difference(ex_to_indexed(*other).get_indices(), dummy_indices);
- GINAC_ASSERT(a.size() > 0);
- GINAC_ASSERT(b.size() > 0);
- *self = numeric(5, 3) * delta_tensor(a[0], b[0]);
- *other = _ex1();
+ exvector a;
+ std::back_insert_iterator<exvector> ita(a);
+ ita = set_difference(self_indices.begin(), self_indices.end(), dummy_indices.begin(), dummy_indices.end(), ita, ex_is_less());
+ ita = set_difference(other_indices.begin(), other_indices.end(), dummy_indices.begin(), dummy_indices.end(), ita, ex_is_less());
+ GINAC_ASSERT(a.size() == 2);
+ *self = numeric(5, 3) * delta_tensor(a[0], a[1]);
+ *other = _ex1;
+ return true;
+ }
+
+ } else if (is_exactly_a<su3t>(other->op(0))) {
+
+ // d.abc T.b T.c = 5/6 T.a
+ if (other+1 != v.end()
+ && is_exactly_a<su3t>(other[1].op(0))
+ && ex_to<indexed>(*self).has_dummy_index_for(other[1].op(1))) {
+
+ exvector self_indices = ex_to<indexed>(*self).get_indices();
+ exvector dummy_indices;
+ dummy_indices.push_back(other[0].op(1));
+ dummy_indices.push_back(other[1].op(1));
+ int sig;
+ ex a = permute_free_index_to_front(self_indices, dummy_indices, sig);
+ *self = numeric(5, 6);
+ other[0] = color_T(a, ex_to<color>(other[0]).get_representation_label());
+ other[1] = _ex1;
return true;
}
}
/** Contraction of an indexed antisymmetric structure constant with something else. */
bool su3f::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
{
- GINAC_ASSERT(is_ex_of_type(*self, indexed));
- GINAC_ASSERT(is_ex_of_type(*other, indexed));
+ GINAC_ASSERT(is_a<indexed>(*self));
+ GINAC_ASSERT(is_a<indexed>(*other));
GINAC_ASSERT(self->nops() == 4);
- GINAC_ASSERT(is_ex_of_type(self->op(0), su3f));
+ GINAC_ASSERT(is_a<su3f>(self->op(0)));
- if (is_ex_exactly_of_type(other->op(0), su3f)) { // f*d is handled by su3d class
+ if (is_exactly_a<su3f>(other->op(0))) { // f*d is handled by su3d class
// Find the dummy indices of the contraction
exvector dummy_indices;
- dummy_indices = ex_to_indexed(*self).get_dummy_indices(ex_to_indexed(*other));
+ dummy_indices = ex_to<indexed>(*self).get_dummy_indices(ex_to<indexed>(*other));
- // f.abc*f.abc=24
+ // f.abc f.abc = 24
if (dummy_indices.size() == 3) {
*self = 24;
- *other = _ex1();
+ *other = _ex1;
return true;
- // f.akl*f.bkl=3*delta.ab
+ // f.akl f.bkl = 3 delta.ab
} else if (dummy_indices.size() == 2) {
int sign1, sign2;
- ex a = permute_free_index_to_front(ex_to_indexed(*self).get_indices(), dummy_indices, sign1);
- ex b = permute_free_index_to_front(ex_to_indexed(*other).get_indices(), dummy_indices, sign2);
+ ex a = permute_free_index_to_front(ex_to<indexed>(*self).get_indices(), dummy_indices, sign1);
+ ex b = permute_free_index_to_front(ex_to<indexed>(*other).get_indices(), dummy_indices, sign2);
*self = sign1 * sign2 * 3 * delta_tensor(a, b);
- *other = _ex1();
+ *other = _ex1;
+ return true;
+ }
+
+ } else if (is_exactly_a<su3t>(other->op(0))) {
+
+ // f.abc T.b T.c = 3/2 I T.a
+ if (other+1 != v.end()
+ && is_exactly_a<su3t>(other[1].op(0))
+ && ex_to<indexed>(*self).has_dummy_index_for(other[1].op(1))) {
+
+ exvector self_indices = ex_to<indexed>(*self).get_indices();
+ exvector dummy_indices;
+ dummy_indices.push_back(other[0].op(1));
+ dummy_indices.push_back(other[1].op(1));
+ int sig;
+ ex a = permute_free_index_to_front(self_indices, dummy_indices, sig);
+ *self = numeric(3, 2) * sig * I;
+ other[0] = color_T(a, ex_to<color>(other[0]).get_representation_label());
+ other[1] = _ex1;
return true;
}
}
// global functions
//////////
-ex color_ONE(unsigned rl)
+ex color_ONE(unsigned char rl)
{
return color(su3one(), rl);
}
-ex color_T(const ex & a, unsigned rl)
+ex color_T(const ex & a, unsigned char rl)
{
- if (!is_ex_of_type(a, idx))
+ if (!is_a<idx>(a))
throw(std::invalid_argument("indices of color_T must be of type idx"));
- if (!ex_to_idx(a).get_dim().is_equal(8))
+ if (!ex_to<idx>(a).get_dim().is_equal(8))
throw(std::invalid_argument("index dimension for color_T must be 8"));
return color(su3t(), a, rl);
ex color_f(const ex & a, const ex & b, const ex & c)
{
- if (!is_ex_of_type(a, idx) || !is_ex_of_type(b, idx) || !is_ex_of_type(c, idx))
+ if (!is_a<idx>(a) || !is_a<idx>(b) || !is_a<idx>(c))
throw(std::invalid_argument("indices of color_f must be of type idx"));
- 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))
+ 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))
throw(std::invalid_argument("index dimension for color_f must be 8"));
- return indexed(su3f(), indexed::antisymmetric, a, b, c);
+ return indexed(su3f(), sy_anti(), a, b, c);
}
ex color_d(const ex & a, const ex & b, const ex & c)
{
- if (!is_ex_of_type(a, idx) || !is_ex_of_type(b, idx) || !is_ex_of_type(c, idx))
+ if (!is_a<idx>(a) || !is_a<idx>(b) || !is_a<idx>(c))
throw(std::invalid_argument("indices of color_d must be of type idx"));
- 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))
+ 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))
throw(std::invalid_argument("index dimension for color_d must be 8"));
- return indexed(su3d(), indexed::symmetric, a, b, c);
+ return indexed(su3d(), sy_symm(), a, b, c);
}
ex color_h(const ex & a, const ex & b, const ex & c)
return color_d(a, b, c) + I * color_f(a, b, c);
}
+/** Check whether a given tinfo key (as returned by return_type_tinfo()
+ * is that of a color object with the specified representation label. */
+static bool is_color_tinfo(unsigned ti, unsigned char rl)
+{
+ return ti == (TINFO_color + rl);
+}
+
+ex color_trace(const ex & e, unsigned char rl)
+{
+ if (is_a<color>(e)) {
+
+ if (ex_to<color>(e).get_representation_label() == rl
+ && is_a<su3one>(e.op(0)))
+ return _ex3;
+ else
+ return _ex0;
+
+ } else if (is_exactly_a<mul>(e)) {
+
+ // Trace of product: pull out non-color factors
+ ex prod = _ex1;
+ for (size_t i=0; i<e.nops(); i++) {
+ const ex &o = e.op(i);
+ if (is_color_tinfo(o.return_type_tinfo(), rl))
+ prod *= color_trace(o, rl);
+ else
+ prod *= o;
+ }
+ return prod;
+
+ } else if (is_exactly_a<ncmul>(e)) {
+
+ if (!is_color_tinfo(e.return_type_tinfo(), rl))
+ return _ex0;
+
+ // Expand product, if necessary
+ ex e_expanded = e.expand();
+ if (!is_a<ncmul>(e_expanded))
+ return color_trace(e_expanded, rl);
+
+ size_t num = e.nops();
+
+ if (num == 2) {
+
+ // Tr T_a T_b = 1/2 delta_a_b
+ return delta_tensor(e.op(0).op(1), e.op(1).op(1)) / 2;
+
+ } else if (num == 3) {
+
+ // Tr T_a T_b T_c = 1/4 h_a_b_c
+ return color_h(e.op(0).op(1), e.op(1).op(1), e.op(2).op(1)) / 4;
+
+ } else {
+
+ // Traces of 4 or more generators are computed recursively:
+ // Tr T_a1 .. T_an =
+ // 1/6 delta_a(n-1)_an Tr T_a1 .. T_a(n-2)
+ // + 1/2 h_a(n-1)_an_k Tr T_a1 .. T_a(n-2) T_k
+ const ex &last_index = e.op(num - 1).op(1);
+ const ex &next_to_last_index = e.op(num - 2).op(1);
+ idx summation_index((new symbol)->setflag(status_flags::dynallocated), 8);
+
+ exvector v1;
+ v1.reserve(num - 2);
+ for (size_t i=0; i<num-2; i++)
+ v1.push_back(e.op(i));
+
+ exvector v2 = v1;
+ v2.push_back(color_T(summation_index, rl));
+
+ return delta_tensor(next_to_last_index, last_index) * color_trace(ncmul(v1), rl) / 6
+ + color_h(next_to_last_index, last_index, summation_index) * color_trace(ncmul(v2), rl) / 2;
+ }
+
+ } else if (e.nops() > 0) {
+
+ // Trace maps to all other container classes (this includes sums)
+ pointer_to_map_function_1arg<unsigned char> fcn(color_trace, rl);
+ return e.map(fcn);
+
+ } else
+ return _ex0;
+}
+
} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff