X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=check%2Fexam_clifford.cpp;h=b067438bb1edbd310c0b942ed0cf84da4d6debd5;hp=68393673f78d4672432ee82d499e5cb6b05204ee;hb=8cffcdf13d817a47f217f1a1043317d95969e070;hpb=37d324b137fcb61384203b711e91d8919535f237 diff --git a/check/exam_clifford.cpp b/check/exam_clifford.cpp index 68393673..b067438b 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) 1999-2008 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2019 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 @@ -20,11 +20,12 @@ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA */ -#include #include "ginac.h" -using namespace std; using namespace GiNaC; +#include +using namespace std; + const numeric half(1, 2); static unsigned check_equal(const ex &e1, const ex &e2) @@ -66,14 +67,14 @@ 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++) { + for (int j=0; j<4; j++) { ex esub = e.subs( is_a(mu) - ? lst ( + ? lst { mu == idx(j, mu.get_dim()), ex_to(mu).toggle_variance() == idx(j, mu.get_dim()) - ) - : lst(mu == 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 " @@ -86,7 +87,7 @@ static unsigned check_equal_simplify_term(const ex & e1, const ex & e2, idx & mu static unsigned check_equal_simplify_term2(const ex & e1, const ex & e2) { - ex e = expand_dummy_sum(normal(simplify_indexed(e1) - e2), true); + ex e = expand_dummy_sum(normal(simplify_indexed(e1) - e2), true); if (!(canonicalize_clifford(e).is_zero())) { clog << "simplify_indexed(" << e1 << ") - (" << e2 << ") erroneously returned " << canonicalize_clifford(e) << " instead of 0" << endl; @@ -241,15 +242,15 @@ static unsigned clifford_check3() result += check_equal(dirac_trace(e, 0), dirac_ONE(1) / 4); result += check_equal(dirac_trace(e, 1), dirac_ONE(0) / 4); result += check_equal(dirac_trace(e, 2), e); - result += check_equal(dirac_trace(e, lst(0, 1)), 1); + result += check_equal(dirac_trace(e, lst{0, 1}), 1); e = dirac_gamma(mu, 0) * dirac_gamma(mu.toggle_variance(), 1) * dirac_gamma(nu, 0) * dirac_gamma(nu.toggle_variance(), 1); result += check_equal_simplify(dirac_trace(e, 0), 4 * dim * dirac_ONE(1)); result += check_equal_simplify(dirac_trace(e, 1), 4 * dim * dirac_ONE(0)); - // Fails with new tinfo mechanism because the order of gamme matrices with different rl depends on luck. + // Fails with new tinfo mechanism because the order of gamma matrices with different rl depends on luck. // TODO: better check. //result += check_equal_simplify(dirac_trace(e, 2), canonicalize_clifford(e)); // e will be canonicalized by the calculation of the trace - result += check_equal_simplify(dirac_trace(e, lst(0, 1)), 16 * dim); + result += check_equal_simplify(dirac_trace(e, lst{0, 1}), 16 * dim); return result; } @@ -416,51 +417,50 @@ template unsigned clifford_check6(const matrix &A) 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); + 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)); /* lst_to_clifford() and clifford_to_lst() check for vectors*/ - e = lst(t, x, y, z); + 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); + 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 */ - 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); + 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); + matrix 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); + 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); + 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); + matrix 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)); + 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); + 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; @@ -503,7 +503,8 @@ static unsigned clifford_check7(const ex & G, const symbol & dim) result += check_equal(e, pow(scalar*(dim-2), 2).expand() * clifford_unit(mu, G)); // canonicalize_clifford() checks, only for symmetric metrics - if (ex_to(ex_to(ex_to(clifford_unit(mu, G)).get_metric()).get_symmetry()).has_symmetry()) { + if (is_a(ex_to(clifford_unit(mu, G)).get_metric()) && + ex_to(ex_to(ex_to(clifford_unit(mu, G)).get_metric()).get_symmetry()).has_symmetry()) { e = clifford_unit(mu, G) * clifford_unit(nu, G) + clifford_unit(nu, G) * clifford_unit(mu, G); result += check_equal(canonicalize_clifford(e), 2*dirac_ONE()*unit.get_metric(nu, mu)); @@ -541,12 +542,49 @@ static unsigned clifford_check8() { unsigned result = 0; - realsymbol a("a"); + realsymbol a("a"), b("b"), x("x"); varidx mu(symbol("mu", "\\mu"), 1); - ex e = clifford_unit(mu, diag_matrix(lst(-1))), e0 = e.subs(mu==0); + ex e = clifford_unit(mu, diag_matrix({-1})), e0 = e.subs(mu==0); result += ( exp(a*e0)*e0*e0 == -exp(e0*a) ) ? 0 : 1; + ex P = color_T(idx(a,8))*color_T(idx(b,8))*(x*dirac_ONE()+sqrt(x-1)*e0); + ex P_prime = color_T(idx(a,8))*color_T(idx(b,8))*(x*dirac_ONE()-sqrt(x-1)*e0); + + result += check_equal(clifford_prime(P), P_prime); + result += check_equal(clifford_star(P), P); + result += check_equal(clifford_bar(P), P_prime); + + return result; +} + +static unsigned clifford_check9() +{ + unsigned result = 0; + + realsymbol a("a"), b("b"), x("x");; + varidx mu(symbol("mu", "\\mu"), 4), nu(symbol("nu", "\\nu"), 4); + + ex e = clifford_unit(mu, lorentz_g(mu, nu)); + ex e0 = e.subs(mu==0); + ex e1 = e.subs(mu==1); + ex e2 = e.subs(mu==2); + ex e3 = e.subs(mu==3); + ex one = dirac_ONE(); + + ex P = color_T(idx(a,8))*color_T(idx(b,8)) + *(x*one+sqrt(x-1)*e0+sqrt(x-2)*e0*e1 +sqrt(x-3)*e0*e1*e2 +sqrt(x-4)*e0*e1*e2*e3); + ex P_prime = color_T(idx(a,8))*color_T(idx(b,8)) + *(x*one-sqrt(x-1)*e0+sqrt(x-2)*e0*e1 -sqrt(x-3)*e0*e1*e2 +sqrt(x-4)*e0*e1*e2*e3); + ex P_star = color_T(idx(a,8))*color_T(idx(b,8)) + *(x*one+sqrt(x-1)*e0+sqrt(x-2)*e1*e0 +sqrt(x-3)*e2*e1*e0 +sqrt(x-4)*e3*e2*e1*e0); + ex P_bar = color_T(idx(a,8))*color_T(idx(b,8)) + *(x*one-sqrt(x-1)*e0+sqrt(x-2)*e1*e0 -sqrt(x-3)*e2*e1*e0 +sqrt(x-4)*e3*e2*e1*e0); + + result += check_equal(clifford_prime(P), P_prime); + result += check_equal(clifford_star(P), P_star); + result += check_equal(clifford_bar(P), P_bar); + return result; } @@ -563,45 +601,45 @@ unsigned exam_clifford() result += clifford_check5(); cout << '.' << flush; // anticommuting, symmetric examples - 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; + result += clifford_check6(ex_to(diag_matrix({-1, 1, 1, 1}))); + result += clifford_check6(ex_to(diag_matrix({-1, 1, 1, 1})));; cout << '.' << flush; + result += clifford_check6(ex_to(diag_matrix({-1, -1, -1, -1})))+clifford_check6(ex_to(diag_matrix({-1, -1, -1, -1})));; cout << '.' << flush; + result += clifford_check6(ex_to(diag_matrix({-1, 1, 1, -1})))+clifford_check6(ex_to(diag_matrix({-1, 1, 1, -1})));; cout << '.' << flush; + result += clifford_check6(ex_to(diag_matrix({-1, 0, 1, -1})))+clifford_check6(ex_to(diag_matrix({-1, 0, 1, -1})));; cout << '.' << flush; + result += clifford_check6(ex_to(diag_matrix({-3, 0, 2, -1})))+clifford_check6(ex_to(diag_matrix({-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))))+clifford_check6(ex_to(diag_matrix(lst(-1, 1, s, t))));; cout << '.' << flush; + realsymbol s("s"), t("t"); // symbolic entries in matrix + result += clifford_check6(ex_to(diag_matrix({-1, 1, s, t})))+clifford_check6(ex_to(diag_matrix({-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; + 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)+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; + 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)+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; + 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)+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; + 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)+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; + 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)+clifford_check6(A);; cout << '.' << flush; symbol dim("D"); @@ -617,6 +655,8 @@ unsigned exam_clifford() result += clifford_check8(); cout << '.' << flush; + result += clifford_check9(); cout << '.' << flush; + return result; }