From a6b2ee0043599892559ef72bacaaae3bcf8a96d0 Mon Sep 17 00:00:00 2001 From: Chris Dams Date: Fri, 8 Sep 2006 19:50:03 +0000 Subject: [PATCH] Vladimirs improvements for the case that clifford objects take idxes without variance. --- check/exam_clifford.cpp | 272 ++++++++++++++++++++++------------------ ginac/clifford.cpp | 22 ++-- 2 files changed, 161 insertions(+), 133 deletions(-) diff --git a/check/exam_clifford.cpp b/check/exam_clifford.cpp index e43708f2..d6544eda 100644 --- 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(mu) ? + mu == idx(j, mu.get_dim()), ex_to(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(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(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(diag_matrix(lst(-1, 1, 1, 1)))); cout << '.' << flush; - result += clifford_check6(ex_to(diag_matrix(lst(-1, -1, -1, -1)))); cout << '.' << flush; - result += clifford_check6(ex_to(diag_matrix(lst(-1, 1, 1, -1)))); cout << '.' << flush; - result += clifford_check6(ex_to(diag_matrix(lst(-1, 0, 1, -1)))); cout << '.' << flush; - result += clifford_check6(ex_to(diag_matrix(lst(-3, 0, 2, -1)))); cout << '.' << flush; + result += clifford_check6(ex_to(diag_matrix(lst(-1, 1, 1, 1))))+clifford_check6a(ex_to(diag_matrix(lst(-1, 1, 1, 1))));; cout << '.' << flush; + result += clifford_check6(ex_to(diag_matrix(lst(-1, -1, -1, -1))))+clifford_check6a(ex_to(diag_matrix(lst(-1, -1, -1, -1))));; cout << '.' << flush; + result += clifford_check6(ex_to(diag_matrix(lst(-1, 1, 1, -1))))+clifford_check6a(ex_to(diag_matrix(lst(-1, 1, 1, -1))));; cout << '.' << flush; + result += clifford_check6(ex_to(diag_matrix(lst(-1, 0, 1, -1))))+clifford_check6a(ex_to(diag_matrix(lst(-1, 0, 1, -1))));; cout << '.' << flush; + result += clifford_check6(ex_to(diag_matrix(lst(-3, 0, 2, -1))))+clifford_check6a(ex_to(diag_matrix(lst(-3, 0, 2, -1))));; cout << '.' << flush; realsymbol s("s"), t("t"); // symbolic entries in matric - result += clifford_check6(ex_to(diag_matrix(lst(-1, 1, s, t)))); cout << '.' << flush; + result += clifford_check6(ex_to(diag_matrix(lst(-1, 1, s, t))))+clifford_check6a(ex_to(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 af54d77b..a0393011 100644 --- 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(indices[0]) && is_a(indices[1])) { + if (indices.size() == 2) { return clifford(unit, mu, metr, rl); } else if (is_a(metr)) { matrix M = ex_to(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(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(mu).get_dim()), - chi((new symbol)->setflag(status_flags::dynallocated), ex_to(mu).get_dim()); + static varidx xi((new symbol)->setflag(status_flags::dynallocated), ex_to(mu).get_dim()), + chi((new symbol)->setflag(status_flags::dynallocated), ex_to(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(G)) { cu = G; } else { - if (is_a(G)) - D = ex_to(G.op(1)).get_dim(); - else if (is_a(G)) + if (is_a(G)) { + D = ex_to(G.op(1)).get_dim(); + varidx mu((new symbol)->setflag(status_flags::dynallocated), D); + cu = clifford_unit(mu, G, rl); + } else if (is_a(G)) { D = ex_to(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); -- 2.44.0