* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
+#include <algorithm>
+#include <stdexcept>
+
#include "color.h"
#include "ex.h"
+#include "idx.h"
#include "ncmul.h"
#include "numeric.h"
+#include "power.h" // for sqrt()
#include "archive.h"
#include "debugmsg.h"
#include "utils.h"
* objects. This removes superfluous ONEs. */
ex color::simplify_ncmul(const exvector & v) const
{
- //!! to be implemented
- return nonsimplified_ncmul(v);
+ //!! TODO: sort by representation label
+ exvector s;
+ s.reserve(v.size());
+
+ exvector::const_iterator it = v.begin(), itend = v.end();
+ while (it != itend) {
+ if (!is_ex_of_type(it->op(0), su3one))
+ s.push_back(*it);
+ it++;
+ }
+
+ if (s.size() == 0)
+ return color(su3one());
+ else if (s.size() == v.size())
+ return simplified_ncmul(v);
+ else
+ return simplified_ncmul(s);
}
ex color::thisexprseq(const exvector & v) const
return color(representation_label, vp);
}
+/** Given a vector iv3 of three indices and a vector iv2 of two indices that
+ * is a subset of iv3, return the (free) index that is in iv3 but not in
+ * iv2 and the sign introduced by permuting that index to the front.
+ *
+ * @param iv3 Vector of 3 indices
+ * @param iv2 Vector of 2 indices, must be a subset of iv3
+ * @param sig Returs sign introduced by index permutation
+ * @return the free index (the one that is in iv3 but not in iv2) */
+static ex permute_free_index_to_front(const exvector & iv3, const exvector & iv2, int & sig)
+{
+ GINAC_ASSERT(iv3.size() == 3);
+ GINAC_ASSERT(iv2.size() == 2);
+
+ sig = 1;
+
+#define TEST_PERMUTATION(A,B,C,P) \
+ if (iv3[B].is_equal(iv2[0]) && iv3[C].is_equal(iv2[1])) { \
+ sig = P; \
+ return iv3[A]; \
+ }
+
+ TEST_PERMUTATION(0,1,2, 1);
+ TEST_PERMUTATION(0,2,1, -1);
+ TEST_PERMUTATION(1,0,2, -1);
+ TEST_PERMUTATION(1,2,0, 1);
+ TEST_PERMUTATION(2,0,1, 1);
+ TEST_PERMUTATION(2,1,0, -1);
+
+ throw(std::logic_error("permute_free_index_to_front(): no valid permutation found"));
+}
+
+/** 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(i.nops() == 4);
+ GINAC_ASSERT(is_ex_of_type(i.op(0), su3d));
+
+ // Convolutions are zero
+ if (static_cast<const indexed &>(i).get_dummy_indices().size() != 0)
+ 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();
+ 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]);
+
+#define CMPINDICES(A,B,C) ((v[0] == (A)) && (v[1] == (B)) && (v[2] == (C)))
+
+ // 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();
+ else if (CMPINDICES(2,4,7) || CMPINDICES(3,6,6) || CMPINDICES(3,7,7))
+ return _ex_1_2();
+ else if (CMPINDICES(1,1,8) || CMPINDICES(2,2,8) || CMPINDICES(3,3,8))
+ return sqrt(_ex3())/3;
+ else if (CMPINDICES(8,8,8))
+ return -sqrt(_ex3())/3;
+ else if (CMPINDICES(4,4,8) || CMPINDICES(5,5,8)
+ || CMPINDICES(6,6,8) || CMPINDICES(7,7,8))
+ return -sqrt(_ex3())/6;
+ else
+ return _ex0();
+ }
+
+ // No further simplifications
+ return i.hold();
+}
+
+/** 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(i.nops() == 4);
+ GINAC_ASSERT(is_ex_of_type(i.op(0), su3f));
+
+ // 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();
+ 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; }
+ if (v[1] > v[2]) { std::swap(v[1], v[2]); sign = -sign; }
+
+ // Check for non-zero elements
+ if (CMPINDICES(1,2,3))
+ return sign;
+ else if (CMPINDICES(1,4,7) || CMPINDICES(2,4,6)
+ || CMPINDICES(2,5,7) || CMPINDICES(3,4,5))
+ return _ex1_2() * sign;
+ else if (CMPINDICES(1,5,6) || CMPINDICES(3,6,7))
+ return _ex_1_2() * sign;
+ else if (CMPINDICES(4,5,8) || CMPINDICES(6,7,8))
+ return sqrt(_ex3())/2 * sign;
+ else
+ return _ex0();
+ }
+
+ // No further simplifications
+ return i.hold();
+}
+
+
+/** 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(self->nops() == 4);
+ GINAC_ASSERT(is_ex_of_type(self->op(0), su3d));
+
+ if (is_ex_exactly_of_type(other->op(0), su3d) || is_ex_exactly_of_type(other->op(0), su3f)) {
+
+ // Find the dummy indices of the contraction
+ exvector dummy_indices;
+ dummy_indices = ex_to_indexed(*self).get_dummy_indices(ex_to_indexed(*other));
+
+ if (is_ex_exactly_of_type(other->op(0), su3d)) {
+
+ // d.abc*d.abc=40/3
+ if (dummy_indices.size() == 3) {
+ *self = numeric(40, 3);
+ *other = _ex1();
+ return true;
+
+ // 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();
+ return true;
+ }
+
+ } else {
+
+ // d.akl*f.bkl=0 (includes the case a=b)
+ if (dummy_indices.size() >= 2) {
+ *self = _ex0();
+ *other = _ex0();
+ return true;
+ }
+ }
+ }
+
+ return false;
+}
+
+/** 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(self->nops() == 4);
+ GINAC_ASSERT(is_ex_of_type(self->op(0), su3f));
+
+ 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));
+
+ // f.abc*f.abc=24
+ if (dummy_indices.size() == 3) {
+ *self = 24;
+ *other = _ex1();
+ return true;
+
+ // 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);
+ *self = sign1 * sign2 * 3 * delta_tensor(a, b);
+ *other = _ex1();
+ return true;
+ }
+ }
+
+ return false;
+}
+
//////////
// global functions
//////////
ex color_T(const ex & a, unsigned rl)
{
+ 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))
+ 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))
+ 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))
+ throw(std::invalid_argument("index dimension for color_f must be 8"));
+
return indexed(su3f(), indexed::antisymmetric, 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))
+ throw(std::invalid_argument("index dimension for color_d must be 8"));
+
return indexed(su3d(), indexed::symmetric, a, b, c);
}
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