Vladimirs improvements for the case that clifford objects take idxes without

variance.

diff --git a/check/exam_clifford.cpp b/check/exam_clifford.cpp
index e43708f232e409f328b51cf25984734ed72827cf..d6544eda5a3461480600d9b31a908167df09c830 100644 (file)
--- a/check/exam_clifford.cpp
+++ b/check/exam_clifford.cpp
@@ -59,12 +59,14 @@ static unsigned check_equal_lst(const ex & e1, const ex & e2)
        return 0;
 }
 
-static unsigned check_equal_simplify_term(const ex & e1, const ex & e2, varidx & mu)
+static unsigned check_equal_simplify_term(const ex & e1, const ex & e2, idx & mu)
 {
        ex e = expand_dummy_sum(normal(simplify_indexed(e1) - e2), true);
 
        for (int j=0; j<4; j++) {
-               ex esub = e.subs(lst(mu == idx(j, mu.get_dim()), mu.toggle_variance() == idx(j, mu.get_dim())));
+               ex esub = e.subs(lst(is_a<varidx>(mu) ? 
+                                                        mu == idx(j, mu.get_dim()), ex_to<varidx>(mu).toggle_variance() == idx(j, mu.get_dim()) 
+                                                        : mu == idx(j, mu.get_dim())));
                if (!(canonicalize_clifford(esub).is_zero())) {
                        clog << "simplify_indexed(" << e1 << ") - (" << e2 << ") erroneously returned "
                                 << canonicalize_clifford(esub) << " instead of 0 for mu=" << j << endl;
@@ -306,134 +308,158 @@ static unsigned clifford_check5()
        return result;
 }
 
+/* We make two identical checks with metrics defined through a matrix in
+ * the cases when used indexes have or have not variance.
+ * To this end we recycle the code through the following macros */
+
+#define CHECK6(IDX,TOGGLE) {IDX v(symbol("v"), 4), nu(symbol("nu"), 4), mu(symbol("mu"), 4), \
+              psi(symbol("psi"),4), lam(symbol("lambda"), 4),\
+              xi(symbol("xi"), 4),  rho(symbol("rho"),4);\
+\
+/* checks general identities and contractions for clifford_unit*/\
+       e = dirac_ONE(2) * clifford_unit(mu, A, 2) * dirac_ONE(2);\
+       result += check_equal(e, clifford_unit(mu, A, 2));\
+\
+       e = clifford_unit(idx(2, 4), A) * clifford_unit(idx(1, 4), A)\
+         * clifford_unit(idx(1, 4), A) * clifford_unit(idx(2, 4), A);\
+       result += check_equal(e, A(1, 1) * A(2, 2) * dirac_ONE());\
+\
+       e = clifford_unit(IDX(2, 4), A) * clifford_unit(IDX(1, 4), A)\
+         * clifford_unit(IDX(1, 4), A) * clifford_unit(IDX(2, 4), A);\
+       result += check_equal(e, A(1, 1) * A(2, 2) * dirac_ONE());\
+\
+       e = clifford_unit(nu, A) * clifford_unit(nu TOGGLE, A);\
+       result += check_equal_simplify(e, A.trace() * dirac_ONE());\
+\
+       e = clifford_unit(nu, A) * clifford_unit(nu, A);\
+       result += check_equal_simplify(e, indexed(A_symm, sy_symm(), nu, nu) * dirac_ONE());\
+\
+       e = clifford_unit(nu, A) * clifford_unit(nu TOGGLE, A) * clifford_unit(mu, A);\
+       result += check_equal_simplify(e, A.trace() * clifford_unit(mu, A));\
+\
+       e = clifford_unit(nu, A) * clifford_unit(mu, A) * clifford_unit(nu TOGGLE, A);\
+       \
+       result += check_equal_simplify_term(e,  2 * indexed(A_symm, sy_symm(), nu TOGGLE, mu) *clifford_unit(nu, A)-A.trace()*clifford_unit(mu, A), mu);\
+\
+       e = clifford_unit(nu, A) * clifford_unit(nu TOGGLE, A)\
+         * clifford_unit(mu, A) * clifford_unit(mu TOGGLE, A);\
+       result += check_equal_simplify(e, pow(A.trace(), 2) * dirac_ONE());\
+\
+       e = clifford_unit(mu, A) * clifford_unit(nu, A)\
+         * clifford_unit(nu TOGGLE, A) * clifford_unit(mu TOGGLE, A);\
+       result += check_equal_simplify(e, pow(A.trace(), 2)  * dirac_ONE());\
+\
+       e = clifford_unit(mu, A) * clifford_unit(nu, A)\
+         * clifford_unit(mu TOGGLE, A) * clifford_unit(nu TOGGLE, A);\
+\
+       result += check_equal_simplify_term2(e, 2*indexed(A_symm, sy_symm(), nu TOGGLE, mu TOGGLE) * clifford_unit(mu, A) * clifford_unit(nu, A) - pow(A.trace(), 2)*dirac_ONE());\
+\
+       e = clifford_unit(mu TOGGLE, A) * clifford_unit(nu, A)\
+         * clifford_unit(mu, A) * clifford_unit(nu TOGGLE, A);\
+\
+       result += check_equal_simplify_term2(e, 2*indexed(A_symm, nu, mu) * clifford_unit(mu TOGGLE, A) * clifford_unit(nu TOGGLE, A) - pow(A.trace(), 2)*dirac_ONE());\
+\
+       e = clifford_unit(nu TOGGLE, A) * clifford_unit(rho TOGGLE, A)\
+         * clifford_unit(mu, A) * clifford_unit(rho, A) * clifford_unit(nu, A);\
+       e = e.simplify_indexed().collect(clifford_unit(mu, A));\
+       \
+       result += check_equal_simplify_term(e, 4* indexed(A_symm, sy_symm(), nu TOGGLE,  rho)*indexed(A_symm, sy_symm(), rho TOGGLE, mu) *clifford_unit(nu, A) \
+                                           - 2*A.trace() * (clifford_unit(rho, A) * indexed(A_symm, sy_symm(), rho TOGGLE, mu) \
+                                                            + clifford_unit(nu, A) * indexed(A_symm, sy_symm(), nu TOGGLE, mu)) + pow(A.trace(),2)* clifford_unit(mu, A), mu);\
+\
+       e = clifford_unit(nu TOGGLE, A) * clifford_unit(rho, A)\
+         * clifford_unit(mu, A) * clifford_unit(rho TOGGLE, A) * clifford_unit(nu, A);\
+       e = e.simplify_indexed().collect(clifford_unit(mu, A));\
+       \
+       result += check_equal_simplify_term(e, 4* indexed(A_symm, sy_symm(), nu TOGGLE,  rho)*indexed(A_symm, sy_symm(), rho TOGGLE, mu) *clifford_unit(nu, A) \
+                                           - 2*A.trace() * (clifford_unit(rho, A) * indexed(A_symm, sy_symm(), rho TOGGLE, mu) \
+                                                            + clifford_unit(nu, A) * indexed(A_symm, sy_symm(), nu TOGGLE, mu)) + pow(A.trace(),2)* clifford_unit(mu, A), mu);\
+\
+       e = clifford_unit(mu, A) * clifford_unit(nu, A) + clifford_unit(nu, A) * clifford_unit(mu, A);\
+       result += check_equal(canonicalize_clifford(e), 2*dirac_ONE()*indexed(A_symm, sy_symm(), mu, nu));\
+\
+       e = (clifford_unit(mu, A) * clifford_unit(nu, A) * clifford_unit(lam, A)\
+                + clifford_unit(nu, A) * clifford_unit(lam, A) * clifford_unit(mu, A)\
+                + clifford_unit(lam, A) * clifford_unit(mu, A) * clifford_unit(nu, A)\
+                - clifford_unit(nu, A) * clifford_unit(mu, A) * clifford_unit(lam, A)\
+                - clifford_unit(lam, A) * clifford_unit(nu, A) * clifford_unit(mu, A)\
+                - clifford_unit(mu, A) * clifford_unit(lam, A) * clifford_unit(nu, A)) / 6\
+               + indexed(A_symm, sy_symm(), mu, nu) * clifford_unit(lam, A)\
+               - indexed(A_symm, sy_symm(), mu, lam) * clifford_unit(nu, A)\
+               + indexed(A_symm, sy_symm(), nu, lam) * clifford_unit(mu, A)\
+               - clifford_unit(mu, A) * clifford_unit(nu, A) * clifford_unit(lam, A);\
+       result += check_equal(canonicalize_clifford(e), 0);\
+\
+/* lst_to_clifford() and clifford_inverse()  check*/\
+       realsymbol x("x"), y("y"), t("t"), z("z");\
+       \
+       ex c = clifford_unit(nu, A, 1);\
+       e = lst_to_clifford(lst(t, x, y, z), mu, A, 1) * lst_to_clifford(lst(1, 2, 3, 4), c);\
+       e1 = clifford_inverse(e);\
+       result += check_equal_simplify_term2((e*e1).simplify_indexed(), dirac_ONE(1));\
+\
+/* Moebius map (both forms) checks for symmetric metrics only */\
+       matrix M1(2, 2),  M2(2, 2);\
+       c = clifford_unit(nu, A);\
+       \
+       e = clifford_moebius_map(0, dirac_ONE(), \
+                                                        dirac_ONE(), 0, lst(t, x, y, z), A); \
+/* this is just the inversion*/\
+       M1 = 0, dirac_ONE(),\
+               dirac_ONE(), 0;\
+       e1 = clifford_moebius_map(M1, lst(t, x, y, z), A); \
+/* the inversion again*/\
+       result += check_equal_lst(e, e1);\
+       \
+       e1 = clifford_to_lst(clifford_inverse(lst_to_clifford(lst(t, x, y, z), mu, A)), c);\
+       result += check_equal_lst(e, e1);\
+       \
+       e = clifford_moebius_map(dirac_ONE(), lst_to_clifford(lst(1, 2, 3, 4), nu, A), \
+                                                        0, dirac_ONE(), lst(t, x, y, z), A); \
+/*this is just a shift*/\
+       M2 = dirac_ONE(), lst_to_clifford(lst(1, 2, 3, 4), c),\
+               0, dirac_ONE();\
+       e1 = clifford_moebius_map(M2, lst(t, x, y, z), c); \
+/* the same shift*/\
+       result += check_equal_lst(e, e1);\
+               \
+       result += check_equal(e, lst(t+1, x+2, y+3, z+4));\
+       \
+/* Check the group law for Moebius maps */\
+       e = clifford_moebius_map(M1, ex_to<lst>(e1), c); \
+/*composition of M1 and M2*/\
+       e1 = clifford_moebius_map(M1.mul(M2), lst(t, x, y, z), c); \
+/* the product M1*M2*/\
+       result += check_equal_lst(e, e1);}
 
 static unsigned clifford_check6(const matrix & A)
 {
-       varidx v(symbol("v"), 4), nu(symbol("nu"), 4), mu(symbol("mu"), 4),
-              psi(symbol("psi"),4), lam(symbol("lambda"), 4),
-              xi(symbol("xi"), 4),  rho(symbol("rho"),4);
-
        matrix A_symm(4,4), A2(4, 4);
        A_symm = A.add(A.transpose()).mul(half);
        A2 = A_symm.mul(A_symm);
        
        ex e, e1;
        int result = 0;
-
-       // checks general identities and contractions for clifford_unit
-       e = dirac_ONE(2) * clifford_unit(mu, A, 2) * dirac_ONE(2);
-       result += check_equal(e, clifford_unit(mu, A, 2));
-
-       e = clifford_unit(idx(2, 4), A) * clifford_unit(idx(1, 4), A)
-         * clifford_unit(idx(1, 4), A) * clifford_unit(idx(2, 4), A);
-       result += check_equal(e, A(1, 1) * A(2, 2) * dirac_ONE());
-
-       e = clifford_unit(varidx(2, 4), A) * clifford_unit(varidx(1, 4), A)
-         * clifford_unit(varidx(1, 4), A) * clifford_unit(varidx(2, 4), A);
-       result += check_equal(e, A(1, 1) * A(2, 2) * dirac_ONE());
-
-       e = clifford_unit(nu, A) * clifford_unit(nu.toggle_variance(), A);
-       result += check_equal_simplify(e, A.trace() * dirac_ONE());
-
-       e = clifford_unit(nu, A) * clifford_unit(nu, A);
-       result += check_equal_simplify(e, indexed(A_symm, sy_symm(), nu, nu) * dirac_ONE());
-
-       e = clifford_unit(nu, A) * clifford_unit(nu.toggle_variance(), A) * clifford_unit(mu, A);
-       result += check_equal_simplify(e, A.trace() * clifford_unit(mu, A));
-
-       e = clifford_unit(nu, A) * clifford_unit(mu, A) * clifford_unit(nu.toggle_variance(), A);
        
-       result += check_equal_simplify_term(e,  2 * indexed(A_symm, sy_symm(), nu.toggle_variance(), mu) *clifford_unit(nu, A)-A.trace()*clifford_unit(mu, A), mu);
+       CHECK6(varidx,.toggle_variance())
 
-       e = clifford_unit(nu, A) * clifford_unit(nu.toggle_variance(), A)
-         * clifford_unit(mu, A) * clifford_unit(mu.toggle_variance(), A);
-       result += check_equal_simplify(e, pow(A.trace(), 2) * dirac_ONE());
-
-       e = clifford_unit(mu, A) * clifford_unit(nu, A)
-         * clifford_unit(nu.toggle_variance(), A) * clifford_unit(mu.toggle_variance(), A);
-       result += check_equal_simplify(e, pow(A.trace(), 2)  * dirac_ONE());
-
-       e = clifford_unit(mu, A) * clifford_unit(nu, A)
-         * clifford_unit(mu.toggle_variance(), A) * clifford_unit(nu.toggle_variance(), A);
-
-       result += check_equal_simplify_term2(e, 2*indexed(A_symm, sy_symm(), nu.toggle_variance(), mu.toggle_variance()) * clifford_unit(mu, A) * clifford_unit(nu, A) - pow(A.trace(), 2)*dirac_ONE());
-
-       e = clifford_unit(mu.toggle_variance(), A) * clifford_unit(nu, A)
-         * clifford_unit(mu, A) * clifford_unit(nu.toggle_variance(), A);
-
-       result += check_equal_simplify_term2(e, 2*indexed(A_symm, nu, mu) * clifford_unit(mu.toggle_variance(), A) * clifford_unit(nu.toggle_variance(), A) - pow(A.trace(), 2)*dirac_ONE());
-
-       e = clifford_unit(nu.toggle_variance(), A) * clifford_unit(rho.toggle_variance(), A)
-         * clifford_unit(mu, A) * clifford_unit(rho, A) * clifford_unit(nu, A);
-       e = e.simplify_indexed().collect(clifford_unit(mu, A));
-       
-       result += check_equal_simplify_term(e, 4* indexed(A_symm, sy_symm(), nu.toggle_variance(),  rho)*indexed(A_symm, sy_symm(), rho.toggle_variance(), mu) *clifford_unit(nu, A) 
-                                           - 2*A.trace() * (clifford_unit(rho, A) * indexed(A_symm, sy_symm(), rho.toggle_variance(), mu) 
-                                                            + clifford_unit(nu, A) * indexed(A_symm, sy_symm(), nu.toggle_variance(), mu)) + pow(A.trace(),2)* clifford_unit(mu, A), mu);
+       return result;
+}
 
-       e = clifford_unit(nu.toggle_variance(), A) * clifford_unit(rho, A)
-         * clifford_unit(mu, A) * clifford_unit(rho.toggle_variance(), A) * clifford_unit(nu, A);
-       e = e.simplify_indexed().collect(clifford_unit(mu, A));
+static unsigned clifford_check6a(const matrix & A)
+{
+       matrix A_symm(4,4), A2(4, 4);
+       A_symm = A.add(A.transpose()).mul(half);
+       A2 = A_symm.mul(A_symm);
        
-       result += check_equal_simplify_term(e, 4* indexed(A_symm, sy_symm(), nu.toggle_variance(),  rho)*indexed(A_symm, sy_symm(), rho.toggle_variance(), mu) *clifford_unit(nu, A) 
-                                           - 2*A.trace() * (clifford_unit(rho, A) * indexed(A_symm, sy_symm(), rho.toggle_variance(), mu) 
-                                                            + clifford_unit(nu, A) * indexed(A_symm, sy_symm(), nu.toggle_variance(), mu)) + pow(A.trace(),2)* clifford_unit(mu, A), mu);
-
-       e = clifford_unit(mu, A) * clifford_unit(nu, A) + clifford_unit(nu, A) * clifford_unit(mu, A);
-       result += check_equal(canonicalize_clifford(e), 2*dirac_ONE()*indexed(A_symm, sy_symm(), mu, nu));
-
-       e = (clifford_unit(mu, A) * clifford_unit(nu, A) * clifford_unit(lam, A)
-                + clifford_unit(nu, A) * clifford_unit(lam, A) * clifford_unit(mu, A)
-                + clifford_unit(lam, A) * clifford_unit(mu, A) * clifford_unit(nu, A)
-                - clifford_unit(nu, A) * clifford_unit(mu, A) * clifford_unit(lam, A)
-                - clifford_unit(lam, A) * clifford_unit(nu, A) * clifford_unit(mu, A)
-                - clifford_unit(mu, A) * clifford_unit(lam, A) * clifford_unit(nu, A)) / 6
-               + indexed(A_symm, sy_symm(), mu, nu) * clifford_unit(lam, A)
-               - indexed(A_symm, sy_symm(), mu, lam) * clifford_unit(nu, A)
-               + indexed(A_symm, sy_symm(), nu, lam) * clifford_unit(mu, A)
-               - clifford_unit(mu, A) * clifford_unit(nu, A) * clifford_unit(lam, A);
-       result += check_equal(canonicalize_clifford(e), 0);
+       ex e, e1;
+       int result = 0;
 
-       // lst_to_clifford() and clifford_inverse()  check
-       realsymbol x("x"), y("y"), t("t"), z("z");
-       
-       ex c = clifford_unit(nu, A, 1);
-       e = lst_to_clifford(lst(t, x, y, z), mu, A, 1) * lst_to_clifford(lst(1, 2, 3, 4), c);
-       e1 = clifford_inverse(e);
-       result += check_equal((e*e1).simplify_indexed(), dirac_ONE(1));
-
-       // Moebius map (both forms) checks for symmetric metrics only 
-       matrix M1(2, 2),  M2(2, 2);
-       c = clifford_unit(nu, A);
-       
-       e = clifford_moebius_map(0, dirac_ONE(), 
-                                                        dirac_ONE(), 0, lst(t, x, y, z), A); // this is just the inversion
-       M1 = 0, dirac_ONE(),
-               dirac_ONE(), 0;
-       e1 = clifford_moebius_map(M1, lst(t, x, y, z), A); // the inversion again
-       result += check_equal_lst(e, e1);
-       
-       e1 = clifford_to_lst(clifford_inverse(lst_to_clifford(lst(t, x, y, z), mu, A)), c);
-       result += check_equal_lst(e, e1);
-       
-       e = clifford_moebius_map(dirac_ONE(), lst_to_clifford(lst(1, 2, 3, 4), nu, A), 
-                                                        0, dirac_ONE(), lst(t, x, y, z), A); //this is just a shift
-       M2 = dirac_ONE(), lst_to_clifford(lst(1, 2, 3, 4), c),
-               0, dirac_ONE();
-       e1 = clifford_moebius_map(M2, lst(t, x, y, z), c); // the same shift
-       result += check_equal_lst(e, e1);
-               
-       result += check_equal(e, lst(t+1, x+2, y+3, z+4));
-       
-       // Check the group law for Moebius maps 
-       e = clifford_moebius_map(M1, ex_to<lst>(e1), c); //composition of M1 and M2
-       e1 = clifford_moebius_map(M1.mul(M2), lst(t, x, y, z), c); // the product M1*M2
-       result += check_equal_lst(e, e1);
+       CHECK6(idx,)
 
        return result;
 }
 
-
 static unsigned clifford_check7(const ex & G, const symbol & dim)
 {
        // checks general identities and contractions
@@ -519,45 +545,45 @@ unsigned exam_clifford()
        result += clifford_check5(); cout << '.' << flush;
 
        // anticommuting, symmetric examples
-       result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, 1)))); cout << '.' << flush;
-       result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-1, -1, -1, -1)))); cout << '.' << flush;
-       result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, -1)))); cout << '.' << flush;
-       result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-1, 0, 1, -1)))); cout << '.' << flush;
-       result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-3, 0, 2, -1)))); cout << '.' << flush;
+       result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, 1))))+clifford_check6a(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, 1))));; cout << '.' << flush;
+       result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-1, -1, -1, -1))))+clifford_check6a(ex_to<matrix>(diag_matrix(lst(-1, -1, -1, -1))));; cout << '.' << flush;
+       result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, -1))))+clifford_check6a(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, -1))));; cout << '.' << flush;
+       result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-1, 0, 1, -1))))+clifford_check6a(ex_to<matrix>(diag_matrix(lst(-1, 0, 1, -1))));; cout << '.' << flush;
+       result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-3, 0, 2, -1))))+clifford_check6a(ex_to<matrix>(diag_matrix(lst(-3, 0, 2, -1))));; cout << '.' << flush;
 
        realsymbol s("s"), t("t"); // symbolic entries in matric
-       result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-1, 1, s, t)))); cout << '.' << flush;
+       result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-1, 1, s, t))))+clifford_check6a(ex_to<matrix>(diag_matrix(lst(-1, 1, s, t))));; cout << '.' << flush;
 
        matrix A(4, 4);
        A = 1, 0, 0, 0, // anticommuting, not symmetric, Tr=0
                0, -1, 0, 0,
                0, 0, 0, -1,
                0, 0, 1, 0; 
-       result += clifford_check6(A); cout << '.' << flush;
+       result += clifford_check6(A)+clifford_check6a(A);; cout << '.' << flush;
 
        A = 1, 0, 0, 0, // anticommuting, not symmetric, Tr=2
                0, 1, 0, 0,
                0, 0, 0, -1,
                0, 0, 1, 0; 
-       result += clifford_check6(A); cout << '.' << flush;
+       result += clifford_check6(A)+clifford_check6a(A);; cout << '.' << flush;
 
        A = 1, 0, 0, 0, // not anticommuting, symmetric, Tr=0
                0, -1, 0, 0,
                0, 0, 0, -1,
                0, 0, -1, 0; 
-       result += clifford_check6(A); cout << '.' << flush;
+       result += clifford_check6(A)+clifford_check6a(A);; cout << '.' << flush;
 
        A = 1, 0, 0, 0, // not anticommuting, symmetric, Tr=2
                0, 1, 0, 0,
                0, 0, 0, -1,
                0, 0, -1, 0; 
-       result += clifford_check6(A); cout << '.' << flush;
+       result += clifford_check6(A)+clifford_check6a(A);; cout << '.' << flush;
 
        A = 1, 1, 0, 0, // not anticommuting, not symmetric, Tr=4
                0, 1, 1, 0,
                0, 0, 1, 1,
                0, 0, 0, 1; 
-       result += clifford_check6(A); cout << '.' << flush;
+       result += clifford_check6(A)+clifford_check6a(A);; cout << '.' << flush;
 
        symbol dim("D");
        result += clifford_check7(minkmetric(), dim); cout << '.' << flush;

diff --git a/ginac/clifford.cpp b/ginac/clifford.cpp
index af54d77bbcb665ef7478c6dfd300c2d4aa4dd109..a0393011af5247cca9e94cd9aacd1059962ebc3f 100644 (file)
--- a/ginac/clifford.cpp
+++ b/ginac/clifford.cpp
@@ -712,14 +712,14 @@ ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl)
 
        exvector indices = metr.get_free_indices();
 
-       if ((indices.size() == 2) && is_a<varidx>(indices[0]) && is_a<varidx>(indices[1])) {
+       if (indices.size() == 2) {
                return clifford(unit, mu, metr, rl);
        } else if (is_a<matrix>(metr)) {
                matrix M = ex_to<matrix>(metr);
                unsigned n = M.rows();
                bool symmetric = true;
 
-               static varidx xi((new symbol)->setflag(status_flags::dynallocated), n),
+               static idx xi((new symbol)->setflag(status_flags::dynallocated), n),
                        chi((new symbol)->setflag(status_flags::dynallocated), n);
                if ((n ==  M.cols()) && (n == ex_to<idx>(mu).get_dim())) {
                        for (unsigned i = 0; i < n; i++) {
@@ -734,8 +734,8 @@ ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl)
                        throw(std::invalid_argument("clifford_unit(): metric for Clifford unit must be a square matrix with the same dimensions as index"));
                }
        } else if (indices.size() == 0) { // a tensor or other expression without indices
-               static varidx xi((new symbol)->setflag(status_flags::dynallocated), ex_to<varidx>(mu).get_dim()),
-                       chi((new symbol)->setflag(status_flags::dynallocated), ex_to<varidx>(mu).get_dim());
+               static varidx xi((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(mu).get_dim()),
+                       chi((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(mu).get_dim());
                return clifford(unit, mu, indexed(metr, xi, chi), rl);
        }  else 
                throw(std::invalid_argument("clifford_unit(): metric for Clifford unit must be of type tensor, matrix or an expression with two free indices"));
@@ -1292,14 +1292,16 @@ ex clifford_moebius_map(const ex & a, const ex & b, const ex & c, const ex & d,
        if (is_a<clifford>(G)) {
                cu = G;
        } else {
-               if (is_a<indexed>(G)) 
-                       D = ex_to<varidx>(G.op(1)).get_dim();
-               else if (is_a<matrix>(G)) 
+               if (is_a<indexed>(G)) {
+                       D = ex_to<idx>(G.op(1)).get_dim();
+                       varidx mu((new symbol)->setflag(status_flags::dynallocated), D);
+                       cu = clifford_unit(mu, G, rl);
+               } else if (is_a<matrix>(G)) {
                        D = ex_to<matrix>(G).rows(); 
-               else throw(std::invalid_argument("clifford_moebius_map(): metric should be an indexed object, matrix, or a Clifford unit"));
+                       idx mu((new symbol)->setflag(status_flags::dynallocated), D);
+                       cu = clifford_unit(mu, G, rl);
+               } else throw(std::invalid_argument("clifford_moebius_map(): metric should be an indexed object, matrix, or a Clifford unit"));
                
-               varidx mu((new symbol)->setflag(status_flags::dynallocated), D);
-               cu = clifford_unit(mu, G, rl);
        }
        
        x = lst_to_clifford(v, cu);