X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=check%2Fexam_clifford.cpp;h=5b646bf51df4fdd3009cb6774a2dc57781e80a06;hp=b9c1c175c7c4927ce459635e2528dcf078a9fe4f;hb=b2ea74ecbae56d737aacf2cbb418d7c9998718a4;hpb=4cf53676d7823ec3c55a90df7723f7f1492a95b2 diff --git a/check/exam_clifford.cpp b/check/exam_clifford.cpp index b9c1c175..5b646bf5 100644 --- a/check/exam_clifford.cpp +++ b/check/exam_clifford.cpp @@ -3,7 +3,7 @@ * Here we test GiNaC's Clifford algebra objects. */ /* - * GiNaC Copyright (C) 1999-2005 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2010 Johannes Gutenberg University Mainz, Germany * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by @@ -20,7 +20,11 @@ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA */ -#include "exams.h" +#include "ginac.h" +using namespace GiNaC; + +#include +using namespace std; const numeric half(1, 2); @@ -59,12 +63,19 @@ 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( + is_a(mu) + ? lst ( + mu == idx(j, mu.get_dim()), + ex_to(mu).toggle_variance() == idx(j, mu.get_dim()) + ) + : lst(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; @@ -306,92 +317,86 @@ 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 */ -static unsigned clifford_check6(const matrix & A) +template 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); + unsigned result = 0; matrix A_symm(4,4), A2(4, 4); A_symm = A.add(A.transpose()).mul(half); A2 = A_symm.mul(A_symm); - + + 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); + ex mu_TOGGLE = is_a(mu) ? ex_to(mu).toggle_variance() : mu; + ex nu_TOGGLE = is_a(nu) ? ex_to(nu).toggle_variance() : nu; + ex rho_TOGGLE + = is_a(rho) ? ex_to(rho).toggle_variance() : rho; + ex e, e1; - bool anticommuting = ex_to(clifford_unit(nu, A)).is_anticommuting(); - int result = 0; - // checks general identities and contractions for clifford_unit +/* 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); + 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); + 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_variance(), A); + 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_variance(), A) * clifford_unit(mu, A); + 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_variance(), A); - if (anticommuting) - result += check_equal_simplify(e, 2*indexed(A_symm, sy_symm(), mu, mu)*clifford_unit(mu, A) - 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_variance(), mu) *clifford_unit(nu, A)-A.trace()*clifford_unit(mu, A), mu); + 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_variance(), A) - * clifford_unit(mu, A) * clifford_unit(mu.toggle_variance(), A); + 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_variance(), A) * clifford_unit(mu.toggle_variance(), 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_variance(), A) * clifford_unit(nu.toggle_variance(), A); - if (anticommuting) - result += check_equal_simplify(e, 2*A2.trace()*dirac_ONE() - pow(A.trace(), 2)*dirac_ONE()); - - 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); - if (anticommuting) { - result += check_equal_simplify(e, 2*A2.trace()*dirac_ONE() - pow(A.trace(), 2)*dirac_ONE()); - e1 = remove_dirac_ONE(simplify_indexed(e)); - result += check_equal(e1, 2*A2.trace() - pow(A.trace(), 2)); - } + * 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()); - 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(mu_TOGGLE, A) * clifford_unit(nu, A) + * clifford_unit(mu, A) * clifford_unit(nu_TOGGLE, A); - e = clifford_unit(nu.toggle_variance(), A) * clifford_unit(rho.toggle_variance(), 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)); - if (anticommuting) - result += check_equal(e, (4*indexed(A2, sy_symm(), mu, mu) - 4 * indexed(A_symm, sy_symm(), mu, mu)*A.trace() +pow(A.trace(), 2)) * 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); + 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_variance(), A) * clifford_unit(rho, A) - * clifford_unit(mu, A) * clifford_unit(rho.toggle_variance(), A) * clifford_unit(nu, A); + 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)); - if (anticommuting) - result += check_equal(e, (4*indexed(A2, sy_symm(), mu, mu) - 4*indexed(A_symm, sy_symm(), mu, mu)*A.trace() +pow(A.trace(), 2))* 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); + 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)); @@ -408,46 +413,60 @@ static unsigned clifford_check6(const matrix & 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"); - +/* lst_to_clifford() and clifford_inverse() check*/ + realsymbol s("s"), t("t"), x("x"), y("y"), 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)); + result += check_equal_simplify_term2((e*e1).simplify_indexed(), dirac_ONE(1)); + +/* lst_to_clifford() and clifford_to_lst() check for vectors*/ + e = lst(t, x, y, z); + result += check_equal_lst(clifford_to_lst(lst_to_clifford(e, c), c, false), e); + result += check_equal_lst(clifford_to_lst(lst_to_clifford(e, c), c, true), e); + +/* lst_to_clifford() and clifford_to_lst() check for pseudovectors*/ + e = lst(s, t, x, y, z); + result += check_equal_lst(clifford_to_lst(lst_to_clifford(e, c), c, false), e); + result += check_equal_lst(clifford_to_lst(lst_to_clifford(e, c), c, true), e); - // Moebius map (both forms) checks for symmetric metrics only +/* 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 + 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 + 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 + 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 + 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); +/* 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); return result; } - static unsigned clifford_check7(const ex & G, const symbol & dim) { // checks general identities and contractions @@ -519,12 +538,24 @@ static unsigned clifford_check7(const ex & G, const symbol & dim) return result; } +static unsigned clifford_check8() +{ + unsigned result = 0; + + realsymbol a("a"); + varidx mu(symbol("mu", "\\mu"), 1); + + ex e = clifford_unit(mu, diag_matrix(lst(-1))), e0 = e.subs(mu==0); + result += ( exp(a*e0)*e0*e0 == -exp(e0*a) ) ? 0 : 1; + + return result; +} + unsigned exam_clifford() { unsigned result = 0; cout << "examining clifford objects" << flush; - clog << "----------clifford objects:" << endl; result += clifford_check1(); cout << '.' << flush; result += clifford_check2(); cout << '.' << flush; @@ -532,48 +563,47 @@ unsigned exam_clifford() result += clifford_check4(); cout << '.' << flush; 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)))); + 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))))+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))))+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))))+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))))+clifford_check6(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_check6(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_check6(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_check6(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_check6(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_check6(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_check6(A);; cout << '.' << flush; symbol dim("D"); result += clifford_check7(minkmetric(), dim); cout << '.' << flush; @@ -586,12 +616,12 @@ unsigned exam_clifford() result += clifford_check7(indexed(-2*minkmetric(), sy_symm(), xi, chi), dim); cout << '.' << flush; result += clifford_check7(-2*delta_tensor(xi, chi), dim); cout << '.' << flush; - if (!result) { - cout << " passed " << endl; - clog << "(no output)" << endl; - } else { - cout << " failed " << endl; - } + result += clifford_check8(); cout << '.' << flush; return result; } + +int main(int argc, char** argv) +{ + return exam_clifford(); +}