#include <stdexcept>
#include "color.h"
-#include "ex.h"
#include "idx.h"
#include "ncmul.h"
+#include "symmetry.h"
#include "numeric.h"
+#include "mul.h"
#include "power.h" // for sqrt()
#include "symbol.h"
#include "print.h"
tinfo_key = TINFO_color;
}
-color::color(unsigned char 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 char,exvector", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_color;
}
-color::color(unsigned char rl, exvector * vp) : inherited(indexed::unknown, vp), representation_label(rl)
+color::color(unsigned char rl, exvector * vp) : inherited(sy_none(), vp), representation_label(rl)
{
debugmsg("color constructor from unsigned char,exvector *", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_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")
* objects. This removes superfluous ONEs. */
ex color::simplify_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))
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);
}
/** 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_ex_exactly_of_type(other->op(0), su3t)) {
+
+ // 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_ex_of_type(self[1], color)) {
+ *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_ex_of_type(*it, color)) {
+ 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)) {
// 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_ex_exactly_of_type(other->op(0), su3t)) {
+
+ // d.abc T.b T.c = 5/6 T.a
+ if (other+1 != v.end()
+ && is_ex_exactly_of_type(other[1].op(0), su3t)
+ && 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
// 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_ex_exactly_of_type(other->op(0), su3t)) {
+
+ // f.abc T.b T.c = 3/2 I T.a
+ if (other+1 != v.end()
+ && is_ex_exactly_of_type(other[1].op(0), su3t)
+ && 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;
}
}
{
if (!is_ex_of_type(a, idx))
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);
{
if (!is_ex_of_type(a, idx) || !is_ex_of_type(b, idx) || !is_ex_of_type(c, idx))
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))
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)
{
if (is_ex_of_type(e, color)) {
- if (ex_to_color(e).get_representation_label() == rl
+ if (ex_to<color>(e).get_representation_label() == rl
&& is_ex_of_type(e.op(0), su3one))
- return _ex3();
+ return _ex3;
else
- return _ex0();
-
- } else if (is_ex_exactly_of_type(e, add)) {
-
- // Trace of sum = sum of traces
- ex sum = _ex0();
- for (unsigned i=0; i<e.nops(); i++)
- sum += color_trace(e.op(i), rl);
- return sum;
+ return _ex0;
} else if (is_ex_exactly_of_type(e, mul)) {
// Trace of product: pull out non-color factors
- ex prod = _ex1();
+ ex prod = _ex1;
for (unsigned i=0; i<e.nops(); i++) {
const ex &o = e.op(i);
if (is_color_tinfo(o.return_type_tinfo(), rl))
} else if (is_ex_exactly_of_type(e, ncmul)) {
if (!is_color_tinfo(e.return_type_tinfo(), rl))
- return _ex0();
+ return _ex0;
// Expand product, if necessary
ex e_expanded = e.expand();
exvector v1;
v1.reserve(num - 2);
- for (int i=0; i<num-2; i++)
+ for (unsigned i=0; i<num-2; i++)
v1.push_back(e.op(i));
exvector v2 = v1;
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;
}
- }
- return _ex0();
+ } 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