From: Christian Bauer <Christian.Bauer@uni-mainz.de>
Date: Fri, 30 Mar 2001 18:14:32 +0000 (+0000)
Subject: - added Clifford contractions:
X-Git-Tag: release_0-8-1~37
X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=commitdiff_plain;h=0376c72554e3892589cb554311ed28bcb77c7dda

- added Clifford contractions:
   gamma~mu*gamma~alpha*gamma~beta*gamma.mu
   gamma~mu*gamma~alpha*gamma~beta*gamma~delta*gamma.mu
- detection of free indices of the complete product in
  simplify_indexed_product() could go wrong if contractions resulted in
  composite expressions
---

diff --git a/ginac/clifford.cpp b/ginac/clifford.cpp
index 94f434a7..c1c069dc 100644
--- a/ginac/clifford.cpp
+++ b/ginac/clifford.cpp
@@ -117,15 +117,40 @@ bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other
 
 	if (is_ex_of_type(other->op(0), diracgamma)) {
 
+		ex dim = ex_to_idx(self->op(1)).get_dim();
+
 		// gamma~mu*gamma.mu = dim*ONE
 		if (other - self == 1) {
-			*self = ex_to_idx(self->op(1)).get_dim();
+			*self = dim;
 			*other = dirac_one();
 			return true;
 
 		// gamma~mu*gamma~alpha*gamma.mu = (2-dim)*gamma~alpha
-		} else if (other - self == 2) {
-			*self = 2 - ex_to_idx(self->op(1)).get_dim();
+		} else if (other - self == 2
+		        && is_ex_of_type(self[1], clifford)) {
+			*self = 2 - dim;
+			*other = _ex1();
+			return true;
+
+		// gamma~mu*gamma~alpha*gamma~beta*gamma.mu = 4*g~alpha~beta+(dim-4)*gamam~alpha*gamma~beta
+		} else if (other - self == 3
+		        && is_ex_of_type(self[1], clifford)
+		        && is_ex_of_type(self[2], clifford)) {
+			*self = 4 * metric_tensor(self[1].op(1), self[2].op(1)) * dirac_one() + (dim - 4) * self[1] * self[2];
+			self[1] = _ex1();
+			self[2] = _ex1();
+			*other = _ex1();
+			return true;
+
+		// gamma~mu*gamma~alpha*gamma~beta*gamma~delta*gamma.mu = -2*gamma~delta*gamma~beta*gamma~alpha+(4-dim)*gamma~alpha*gamma~beta*gamma~delta
+		} else if (other - self == 4
+		        && is_ex_of_type(self[1], clifford)
+		        && is_ex_of_type(self[2], clifford)
+		        && is_ex_of_type(self[3], clifford)) {
+			*self = -2 * self[3] * self[2] * self[1] + (4 - dim) * self[1] * self[2] * self[3];
+			self[1] = _ex1();
+			self[2] = _ex1();
+			self[3] = _ex1();
 			*other = _ex1();
 			return true;
 		}
diff --git a/ginac/indexed.cpp b/ginac/indexed.cpp
index 255fed53..e27a7f62 100644
--- a/ginac/indexed.cpp
+++ b/ginac/indexed.cpp
@@ -653,10 +653,8 @@ try_again:
 	exvector un, dummy_indices;
 	it1 = v.begin(); itend = v.end();
 	while (it1 != itend) {
-		if (is_ex_of_type(*it1, indexed)) {
-			const indexed & o = ex_to_indexed(*it1);
-			un.insert(un.end(), o.seq.begin() + 1, o.seq.end());
-		}
+		exvector free_indices_of_factor = it1->get_free_indices();
+		un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
 		it1++;
 	}
 	find_free_and_dummy(un, free_indices, dummy_indices);