epsilon tensor contractions evaluate to metric tensors instead of deltas,

[ginac.git] / ginac / tensor.cpp

diff --git a/ginac/tensor.cpp b/ginac/tensor.cpp
index 28a7d7bf61b7d8831ce8c3c312b4027668c49b73..7b3d1417cf40362dfe38cbef2c3312061e38cbfd 100644 (file)
--- a/ginac/tensor.cpp
+++ b/ginac/tensor.cpp
@@ -499,7 +499,7 @@ bool tensepsilon::contract_with(exvector::iterator self, exvector::iterator othe
 {
        GINAC_ASSERT(is_ex_of_type(*self, indexed));
        GINAC_ASSERT(is_ex_of_type(*other, indexed));
-       GINAC_ASSERT(is_ex_of_type(self->op(0), spinmetric));
+       GINAC_ASSERT(is_ex_of_type(self->op(0), tensepsilon));
        unsigned num = self->nops() - 1;
 
        if (is_ex_exactly_of_type(other->op(0), tensepsilon) && num+1 == other->nops()) {
@@ -507,13 +507,56 @@ bool tensepsilon::contract_with(exvector::iterator self, exvector::iterator othe
                // Contraction of two epsilon tensors is a determinant
                ex dim = ex_to<idx>(self->op(1)).get_dim();
                matrix M(num, num);
-               for (int i=0; i<num; i++)
-                       for (int j=0; j<num; j++)
-                               M(i, j) = delta_tensor(self->op(i+1), other->op(j+1));
+               for (int i=0; i<num; i++) {
+                       for (int j=0; j<num; j++) {
+                               if (minkowski)
+                                       M(i, j) = lorentz_g(self->op(i+1), other->op(j+1), pos_sig);
+                               else
+                                       M(i, j) = metric_tensor(self->op(i+1), other->op(j+1));
+                       }
+               }
                int sign = minkowski ? -1 : 1;
                *self = sign * M.determinant().simplify_indexed();
                *other = _ex1();
                return true;
+
+       } else if (other->return_type() == return_types::commutative) {
+
+#if 0
+               // This handles eps.i.j.k * p.j * p.k = 0
+               // Maybe something like this should go to simplify_indexed() because
+               // such relations are true for any antisymmetric tensors...
+               exvector c;
+
+               // Handle all indices of the epsilon tensor
+               for (int i=0; i<num; i++) {
+                       ex idx = self->op(i+1);
+
+                       // Look whether there's a contraction with this index
+                       exvector::const_iterator ait, aitend = v.end();
+                       for (ait = v.begin(); ait != aitend; ait++) {
+                               if (ait == self)
+                                       continue;
+                               if (is_a<indexed>(*ait) && ait->return_type() == return_types::commutative && ex_to<indexed>(*ait).has_dummy_index_for(idx) && ait->nops() == 2) {
+
+                                       // Yes, did we already have another contraction with the same base expression?
+                                       ex base = ait->op(0);
+                                       if (std::find_if(c.begin(), c.end(), bind2nd(ex_is_equal(), base)) == c.end()) {
+
+                                               // No, add the base expression to the list
+                                               c.push_back(base);
+
+                                       } else {
+
+                                               // Yes, the contraction is zero
+                                               *self = _ex0();
+                                               *other = _ex0();
+                                               return true;
+                                       }
+                               }
+                       }
+               }
+#endif
        }
 
        return false;