X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fclifford.cpp;h=e62def5047707a969d313bafd0759b37e071112c;hp=d520822d6d8d3e38aed5699321434ef021c8e559;hb=2700b3fa9c3a81236e8ceccb6aa9d5ea5848a1a0;hpb=1c9720626245312534c8311b47a8749dd2e18526

diff --git a/ginac/clifford.cpp b/ginac/clifford.cpp
index d520822d..e62def50 100644
--- a/ginac/clifford.cpp
+++ b/ginac/clifford.cpp
@@ -26,6 +26,8 @@
 #include "ncmul.h"
 #include "symbol.h"
 #include "numeric.h" // for I
+#include "lst.h"
+#include "relational.h"
 #include "print.h"
 #include "archive.h"
 #include "debugmsg.h"
@@ -336,6 +338,49 @@ static bool is_clifford_tinfo(unsigned ti, unsigned char rl)
 	return ti == (TINFO_clifford + rl);
 }
 
+/** Check whether a given tinfo key (as returned by return_type_tinfo()
+ *  is that of a clifford object (with an arbitrary representation label). */
+static bool is_clifford_tinfo(unsigned ti)
+{
+	return (ti & ~0xff) == TINFO_clifford;
+}
+
+/** Take trace of a string of an even number of Dirac gammas given a vector
+ *  of indices. */
+static ex trace_string(exvector::const_iterator ix, unsigned num)
+{
+	// Tr gamma.mu gamma.nu = 4 g.mu.nu
+	if (num == 2)
+		return lorentz_g(ix[0], ix[1]);
+
+	// Tr gamma.mu gamma.nu gamma.rho gamma.sig = 4 (g.mu.nu g.rho.sig + g.nu.rho g.mu.sig - g.mu.rho g.nu.sig
+	else if (num == 4)
+		return lorentz_g(ix[0], ix[1]) * lorentz_g(ix[2], ix[3])
+		     + lorentz_g(ix[1], ix[2]) * lorentz_g(ix[0], ix[3])
+		     - lorentz_g(ix[0], ix[2]) * lorentz_g(ix[1], ix[3]);
+
+	// Traces of 6 or more gammas are computed recursively:
+	// Tr gamma.mu1 gamma.mu2 ... gamma.mun =
+	//   + g.mu1.mu2 * Tr gamma.mu3 ... gamma.mun
+	//   - g.mu1.mu3 * Tr gamma.mu2 gamma.mu4 ... gamma.mun
+	//   + g.mu1.mu4 * Tr gamma.mu3 gamma.mu3 gamma.mu5 ... gamma.mun
+	//   - ...
+	//   + g.mu1.mun * Tr gamma.mu2 ... gamma.mu(n-1)
+	exvector v(num - 2);
+	int sign = 1;
+	ex result;
+	for (int i=1; i<num; i++) {
+		for (int n=1, j=0; n<num; n++) {
+			if (n == i)
+				continue;
+			v[j++] = ix[n];
+		}
+		result += sign * lorentz_g(ix[0], ix[i]) * trace_string(v.begin(), num-2);
+		sign = -sign;
+	}
+	return result;
+}
+
 ex dirac_trace(const ex & e, unsigned char rl, const ex & trONE)
 {
 	if (is_ex_of_type(e, clifford)) {
@@ -393,58 +438,41 @@ ex dirac_trace(const ex & e, unsigned char rl, const ex & trONE)
 			if (num == 5)
 				return trONE * I * eps0123(e.op(1).op(1), e.op(2).op(1), e.op(3).op(1), e.op(4).op(1));
 
-			// Tr gamma5 gamma.mu1 gamma.mu2 gamma.mu3 gamma.mu4 gamma.mu5 gamma.mu6 = ...
-			if (num == 7) {
-				ex i1 = e.op(1).op(1), i2 = e.op(2).op(1),
-				   i3 = e.op(3).op(1), i4 = e.op(4).op(1),
-				   i5 = e.op(5).op(1), i6 = e.op(6).op(1);
-				return trONE * I * (lorentz_g(i1, i2) * eps0123(i3, i4, i5, i6)
-				                  - lorentz_g(i1, i3) * eps0123(i2, i4, i5, i6)
-				                  + lorentz_g(i1, i4) * eps0123(i2, i3, i5, i6)
-				                  - lorentz_g(i1, i5) * eps0123(i2, i3, i4, i6)
-				                  + lorentz_g(i1, i6) * eps0123(i2, i3, i4, i5)
-				                  + lorentz_g(i2, i3) * eps0123(i1, i4, i5, i6)
-				                  - lorentz_g(i2, i4) * eps0123(i1, i3, i5, i6)
-				                  + lorentz_g(i2, i5) * eps0123(i1, i3, i4, i6)
-				                  - lorentz_g(i2, i6) * eps0123(i1, i3, i4, i5)
-				                  + lorentz_g(i3, i4) * eps0123(i1, i2, i5, i6)
-				                  - lorentz_g(i3, i5) * eps0123(i1, i2, i4, i6)
-				                  + lorentz_g(i3, i6) * eps0123(i1, i2, i4, i5)
-				                  + lorentz_g(i4, i5) * eps0123(i1, i2, i3, i6)
-				                  - lorentz_g(i4, i6) * eps0123(i1, i2, i3, i5)
-				                  + lorentz_g(i5, i6) * eps0123(i1, i2, i3, i4));
-			}
-
-			// Tr gamma5 S_2k =
+	   		// Tr gamma5 S_2k =
 			//   I/4! * epsilon0123.mu1.mu2.mu3.mu4 * Tr gamma.mu1 gamma.mu2 gamma.mu3 gamma.mu4 S_2k
+			exvector ix;
+			ix.reserve(num - 1);
+			for (unsigned i=1; i<num; i++)
+				ix.push_back(e.op(i).op(1));
+			num--;
+			int *iv = new int[num];
 			ex result;
-			for (int i=1; i<num-3; i++) {
-				ex idx1 = e.op(i).op(1);
+			for (int i=0; i<num-3; i++) {
+				ex idx1 = ix[i];
 				for (int j=i+1; j<num-2; j++) {
-					ex idx2 = e.op(j).op(1);
+					ex idx2 = ix[j];
 					for (int k=j+1; k<num-1; k++) {
-						ex idx3 = e.op(k).op(1);
+						ex idx3 = ix[k];
 						for (int l=k+1; l<num; l++) {
-							ex idx4 = e.op(l).op(1);
-							vector<int> iv;
-							iv.reserve(num-1);
+							ex idx4 = ix[l];
+							iv[0] = i; iv[1] = j; iv[2] = k; iv[3] = l;
 							exvector v;
-							v.reserve(num-1);
-							iv.push_back(i); iv.push_back(j); iv.push_back(k); iv.push_back(l);
-							for (int n=1; n<num; n++) {
+							v.reserve(num - 4);
+							for (int n=0, t=4; n<num; n++) {
 								if (n == i || n == j || n == k || n == l)
 									continue;
-								iv.push_back(n);
-								v.push_back(e.op(n));
+								iv[t++] = n;
+								v.push_back(ix[n]);
 							}
-							int sign = permutation_sign(iv);
+							int sign = permutation_sign(iv, iv + num);
 							result += sign * eps0123(idx1, idx2, idx3, idx4)
-							        * dirac_trace(ncmul(v), rl, trONE);
+							        * trace_string(v.begin(), num - 4);
 						}
 					}
 				}
 			}
-			return result * I;
+			delete[] iv;
+			return trONE * I * result;
 
 		} else { // no gamma5
 
@@ -456,33 +484,12 @@ ex dirac_trace(const ex & e, unsigned char rl, const ex & trONE)
 			if (num == 2)
 				return trONE * lorentz_g(e.op(0).op(1), e.op(1).op(1));
 
-			// Tr gamma.mu gamma.nu gamma.rho gamma.sig = 4 (g.mu.nu g.rho.sig + g.nu.rho g.mu.sig - g.mu.rho g.nu.sig
-			if (num == 4)
-				return trONE * (lorentz_g(e.op(0).op(1), e.op(1).op(1)) * lorentz_g(e.op(2).op(1), e.op(3).op(1))
-				              + lorentz_g(e.op(1).op(1), e.op(2).op(1)) * lorentz_g(e.op(0).op(1), e.op(3).op(1))
-				              - lorentz_g(e.op(0).op(1), e.op(2).op(1)) * lorentz_g(e.op(1).op(1), e.op(3).op(1)));
-
-			// Traces of 6 or more gammas are computed recursively:
-			// Tr gamma.mu1 gamma.mu2 ... gamma.mun =
-			//   + g.mu1.mu2 * Tr gamma.mu3 ... gamma.mun
-			//   - g.mu1.mu3 * Tr gamma.mu2 gamma.mu4 ... gamma.mun
-			//   + g.mu1.mu4 * Tr gamma.mu3 gamma.mu3 gamma.mu5 ... gamma.mun
-			//   - ...
-			//   + g.mu1.mun * Tr gamma.mu2 ... gamma.mu(n-1)
-			exvector v(num - 2);
-			int sign = 1;
-			const ex &ix1 = e.op(0).op(1);
-			ex result;
-			for (int i=1; i<num; i++) {
-				for (int n=1, j=0; n<num; n++) {
-					if (n == i)
-						continue;
-					v[j++] = e.op(n);
-				}
-				result += sign * lorentz_g(ix1, e.op(i).op(1)) * dirac_trace(ncmul(v), rl, trONE);
-				sign = -sign;
-			}
-			return result;
+			exvector iv;
+			iv.reserve(num);
+			for (unsigned i=0; i<num; i++)
+				iv.push_back(e.op(i).op(1));
+
+			return trONE * trace_string(iv.begin(), num);
 		}
 	}
 
@@ -491,56 +498,54 @@ ex dirac_trace(const ex & e, unsigned char rl, const ex & trONE)
 
 ex canonicalize_clifford(const ex & e)
 {
-	if (is_ex_exactly_of_type(e, add)) {
-
-		ex sum = _ex0();
-		for (unsigned i=0; i<e.nops(); i++)
-			sum += canonicalize_clifford(e.op(i));
-		return sum;
-
-	} else if (is_ex_exactly_of_type(e, mul)) {
-
-		ex prod = _ex1();
-		for (unsigned i=0; i<e.nops(); i++)
-			prod *= canonicalize_clifford(e.op(i));
-		return prod;
-
-	} else if (is_ex_exactly_of_type(e, ncmul)) {
-
-		// Expand product, if necessary
-		ex e_expanded = e.expand();
-		if (!is_ex_of_type(e_expanded, ncmul))
-			return canonicalize_clifford(e_expanded);
-
-		if (!is_ex_of_type(e.op(0), clifford))
-			return e;
-
-		exvector v;
-		v.reserve(e.nops());
-		for (int i=0; i<e.nops(); i++)
-			v.push_back(e.op(i));
-
-		// Stupid bubble sort because we only want to swap adjacent gammas
-		exvector::iterator it = v.begin(), next_to_last = v.end() - 1;
-		if (is_ex_of_type(it->op(0), diracgamma5))
-			it++;
-		while (it != next_to_last) {
-			if (it[0].op(1).compare(it[1].op(1)) > 0) {
-				ex save0 = it[0], save1 = it[1];
-				it[0] = lorentz_g(it[0].op(1), it[1].op(1));
-				it[1] = _ex2();
-				ex sum = ncmul(v);
-				it[0] = save1;
-				it[1] = save0;
-				sum -= ncmul(v);
-				return canonicalize_clifford(sum);
+	// Scan for any ncmul objects
+	lst srl;
+	ex aux = e.to_rational(srl);
+	for (unsigned i=0; i<srl.nops(); i++) {
+
+		ex lhs = srl.op(i).lhs();
+		ex rhs = srl.op(i).rhs();
+
+		if (is_ex_exactly_of_type(rhs, ncmul)
+		 && rhs.return_type() == return_types::noncommutative
+		 && is_clifford_tinfo(rhs.return_type_tinfo())) {
+
+			// Expand product, if necessary
+			ex rhs_expanded = rhs.expand();
+			if (!is_ex_of_type(rhs_expanded, ncmul)) {
+				srl.let_op(i) = (lhs == canonicalize_clifford(rhs_expanded));
+				continue;
+
+			} else if (!is_ex_of_type(rhs.op(0), clifford))
+				continue;
+
+			exvector v;
+			v.reserve(rhs.nops());
+			for (unsigned j=0; j<rhs.nops(); j++)
+				v.push_back(rhs.op(j));
+
+			// Stupid recursive bubble sort because we only want to swap adjacent gammas
+			exvector::iterator it = v.begin(), next_to_last = v.end() - 1;
+			if (is_ex_of_type(it->op(0), diracgamma5))
+				it++;
+			while (it != next_to_last) {
+				if (it[0].op(1).compare(it[1].op(1)) > 0) {
+					ex save0 = it[0], save1 = it[1];
+					it[0] = lorentz_g(it[0].op(1), it[1].op(1));
+					it[1] = _ex2();
+					ex sum = ncmul(v);
+					it[0] = save1;
+					it[1] = save0;
+					sum -= ncmul(v, true);
+					srl.let_op(i) = (lhs == canonicalize_clifford(sum));
+					goto next_sym;
+				}
+				it++;
 			}
-			it++;
+next_sym:	;
 		}
-		return ncmul(v);
 	}
-
-	return e;
+	return aux.subs(srl);
 }
 
 } // namespace GiNaC