This is the end of previous patch. -- Vladimir V. Kisil email: kisilv@maths.leeds.ac.uk -- www: http://maths.leeds.ac.uk/~kisilv/ Index: check/exam_clifford.cpp =================================================================== RCS file: /home/cvs/GiNaC/check/exam_clifford.cpp,v retrieving revision 1.24 diff -r1.24 exam_clifford.cpp 24a25,26
const numeric half(1, 2);
27c29 < ex e = e1 - e2; ---
ex e = normal(e1 - e2); 29,30c31,32 < clog << e1 << "-" << e2 << " erroneously returned " < << e << " instead of 0" << endl;
clog << "(" << e1 << ") - (" << e2 << ") erroneously returned " << e << " instead of 0" << endl;
38c40 < ex e = simplify_indexed(e1) - e2; ---
ex e = normal(simplify_indexed(e1) - e2); 40,41c42,43 < clog << "simplify_indexed(" << e1 << ")-" << e2 << " erroneously returned " < << e << " instead of 0" << endl;
clog << "simplify_indexed(" << e1 << ") - (" << e2 << ") erroneously returned " << e << " instead of 0" << endl;
46a49,88
static unsigned check_equal_lst(const ex &e1, const ex &e2) { for(int i = 0; i++; i < e1.nops()) { ex e = e1.op(i) - e2.op(i); if (!e.is_zero()) { clog << "(" << e1 << ") - (" << e2 << ") erroneously returned " << e << " instead of 0 (in the entry " << i << ")" << endl; return 1; } } return 0; }
static unsigned check_equal_simplify_term(const ex &e1, const ex &e2, varidx &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()))); if (!(canonicalize_clifford(esub).is_zero())) { clog << "simplify_indexed(" << e1 << ") - (" << e2 << ") erroneously returned " << canonicalize_clifford(esub) << " instead of 0 for mu=" << j << endl; return 1; } } return 0; }
static unsigned check_equal_simplify_term2(const ex &e1, const ex &e2) { 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; return 1; } return 0; }
264a307
271c314,316 < ex G = A; ---
matrix A_symm(4,4), A2(4, 4); A_symm = A.add(A.transpose()).mul(half); A2 = A_symm.mul(A_symm); 273,274d317 < matrix A2(4, 4); < A2 = A.mul(A); 276c319 <
bool anticommuting = ex_to<clifford>(clifford_unit(nu, A)).is_anticommuting(); 280,281c323,324 < e = dirac_ONE() * clifford_unit(mu, G) * dirac_ONE(); < result += check_equal(e, clifford_unit(mu, G));
e = dirac_ONE(2) * clifford_unit(mu, A, 2) * dirac_ONE(2); result += check_equal(e, clifford_unit(mu, A, 2)); 283,284c326,327 < e = clifford_unit(varidx(2, 4), G) * clifford_unit(varidx(1, 4), G) < * clifford_unit(varidx(1, 4), G) * clifford_unit(varidx(2, 4), G);
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); 287c330,334 < e = clifford_unit(nu, G) * clifford_unit(nu.toggle_variance(), G);
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); 290,291c337,338 < e = clifford_unit(nu, G) * clifford_unit(nu, G); < result += check_equal_simplify(e, indexed(G, sy_symm(), nu, nu) * 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()); 293,294c340,341 < e = clifford_unit(nu, G) * clifford_unit(nu.toggle_variance(), G) * clifford_unit(mu, G); < result += check_equal_simplify(e, A.trace() * clifford_unit(mu, G));
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)); 296,297c343,347 < e = clifford_unit(nu, G) * clifford_unit(mu, G) * clifford_unit(nu.toggle_variance(), G); < result += check_equal_simplify(e, 2*indexed(G, sy_symm(), mu, mu)*clifford_unit(mu, G) - A.trace()*clifford_unit(mu, G));
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));
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); 299,300c349,350 < e = clifford_unit(nu, G) * clifford_unit(nu.toggle_variance(), G) < * clifford_unit(mu, G) * clifford_unit(mu.toggle_variance(), G);
e = clifford_unit(nu, A) * clifford_unit(nu.toggle_variance(), A) * clifford_unit(mu, A) * clifford_unit(mu.toggle_variance(), A); 303,304c353,354 < e = clifford_unit(mu, G) * clifford_unit(nu, G) < * clifford_unit(nu.toggle_variance(), G) * clifford_unit(mu.toggle_variance(), G);
e = clifford_unit(mu, A) * clifford_unit(nu, A) * clifford_unit(nu.toggle_variance(), A) * clifford_unit(mu.toggle_variance(), A); 307,323c357,370 < e = clifford_unit(mu, G) * clifford_unit(nu, G) < * clifford_unit(mu.toggle_variance(), G) * clifford_unit(nu.toggle_variance(), G); < result += check_equal_simplify(e, 2*A2.trace()*dirac_ONE() - pow(A.trace(), 2)*dirac_ONE()); < < e = clifford_unit(mu.toggle_variance(), G) * clifford_unit(nu, G) < * clifford_unit(mu, G) * clifford_unit(nu.toggle_variance(), G); < result += check_equal_simplify(e, 2*A2.trace()*dirac_ONE() - pow(A.trace(), 2)*dirac_ONE()); < < e = clifford_unit(nu.toggle_variance(), G) * clifford_unit(rho.toggle_variance(), G) < * clifford_unit(mu, G) * clifford_unit(rho, G) * clifford_unit(nu, G); < e = e.simplify_indexed().collect(clifford_unit(mu, G)); < result += check_equal(e, (pow(A.trace(), 2)+4-4*A.trace()*indexed(A, mu, mu)) * clifford_unit(mu, G)); < < e = clifford_unit(nu.toggle_variance(), G) * clifford_unit(rho, G) < * clifford_unit(mu, G) * clifford_unit(rho.toggle_variance(), G) * clifford_unit(nu, G); < e = e.simplify_indexed().collect(clifford_unit(mu, G)); < result += check_equal(e, (pow(A.trace(), 2)+4-4*A.trace()*indexed(A, mu, mu))* clifford_unit(mu, G));
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)); } 325,327c372 < // canonicalize_clifford() checks < 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()*indexed(G, sy_symm(), mu, nu));
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()); 329,338c374,406 < e = (clifford_unit(mu, G) * clifford_unit(nu, G) * clifford_unit(lam, G) < + clifford_unit(nu, G) * clifford_unit(lam, G) * clifford_unit(mu, G) < + clifford_unit(lam, G) * clifford_unit(mu, G) * clifford_unit(nu, G) < - clifford_unit(nu, G) * clifford_unit(mu, G) * clifford_unit(lam, G) < - clifford_unit(lam, G) * clifford_unit(nu, G) * clifford_unit(mu, G) < - clifford_unit(mu, G) * clifford_unit(lam, G) * clifford_unit(nu, G)) / 6 < + indexed(G, sy_symm(), mu, nu) * clifford_unit(lam, G) < - indexed(G, sy_symm(), mu, lam) * clifford_unit(nu, G) < + indexed(G, sy_symm(), nu, lam) * clifford_unit(mu, G) < - clifford_unit(mu, G) * clifford_unit(nu, G) * clifford_unit(lam, G);
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)); 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);
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)); 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);
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); 344,345c412,413 < ex c = clifford_unit(nu, G, 1); < e = lst_to_clifford(lst(t, x, y, z), mu, G, 1) * lst_to_clifford(lst(1, 2, 3, 4), c);
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); 347c415,443 < result += check_equal((e*e1).simplify_indexed().normal(), dirac_ONE(1));
result += check_equal_lst((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); 352c448,449 < static unsigned clifford_check7()
static unsigned clifford_check7(const ex & G, const symbol & dim)
358d454 < symbol dim("D"); 362c458 < ex e; ---
ex e, G_base; 364c460,463 < ex G = minkmetric();
if (is_a<indexed>(G)) G_base = G.op(0); else G_base = G; 389,404c488,519 < // canonicalize_clifford() checks < 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()*indexed(G, sy_symm(), mu, nu)); < < e = (clifford_unit(mu, G) * clifford_unit(nu, G) * clifford_unit(lam, G) < + clifford_unit(nu, G) * clifford_unit(lam, G) * clifford_unit(mu, G) < + clifford_unit(lam, G) * clifford_unit(mu, G) * clifford_unit(nu, G) < - clifford_unit(nu, G) * clifford_unit(mu, G) * clifford_unit(lam, G) < - clifford_unit(lam, G) * clifford_unit(nu, G) * clifford_unit(mu, G) < - clifford_unit(mu, G) * clifford_unit(lam, G) * clifford_unit(nu, G)) / 6 < + indexed(G, sy_symm(), mu, nu) * clifford_unit(lam, G) < - indexed(G, sy_symm(), mu, lam) * clifford_unit(nu, G) < + indexed(G, sy_symm(), nu, lam) * clifford_unit(mu, G) < - clifford_unit(mu, G) * clifford_unit(nu, G) * clifford_unit(lam, G); < result += check_equal(canonicalize_clifford(e), 0); <
// canonicalize_clifford() checks, only for symmetric metrics if (ex_to<symmetry>(ex_to<indexed>(ex_to<clifford>(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()*indexed(G_base, sy_symm(), nu, mu));
e = (clifford_unit(mu, G) * clifford_unit(nu, G) * clifford_unit(lam, G) + clifford_unit(nu, G) * clifford_unit(lam, G) * clifford_unit(mu, G) + clifford_unit(lam, G) * clifford_unit(mu, G) * clifford_unit(nu, G) - clifford_unit(nu, G) * clifford_unit(mu, G) * clifford_unit(lam, G) - clifford_unit(lam, G) * clifford_unit(nu, G) * clifford_unit(mu, G) - clifford_unit(mu, G) * clifford_unit(lam, G) * clifford_unit(nu, G)) / 6 + indexed(G_base, sy_symm(), mu, nu) * clifford_unit(lam, G) - indexed(G_base, sy_symm(), mu, lam) * clifford_unit(nu, G) + indexed(G_base, sy_symm(), nu, lam) * clifford_unit(mu, G) - clifford_unit(mu, G) * clifford_unit(nu, G) * clifford_unit(lam, G); result += check_equal(canonicalize_clifford(e), 0); } else { e = clifford_unit(mu, G) * clifford_unit(nu, G) + clifford_unit(nu, G) * clifford_unit(mu, G); result += check_equal(canonicalize_clifford(e), dirac_ONE()*(indexed(G_base, mu, nu) + indexed(G_base, nu, mu)));
e = (clifford_unit(mu, G) * clifford_unit(nu, G) * clifford_unit(lam, G) + clifford_unit(nu, G) * clifford_unit(lam, G) * clifford_unit(mu, G) + clifford_unit(lam, G) * clifford_unit(mu, G) * clifford_unit(nu, G) - clifford_unit(nu, G) * clifford_unit(mu, G) * clifford_unit(lam, G) - clifford_unit(lam, G) * clifford_unit(nu, G) * clifford_unit(mu, G) - clifford_unit(mu, G) * clifford_unit(lam, G) * clifford_unit(nu, G)) / 6 + half * (indexed(G_base, mu, nu) + indexed(G_base, nu, mu)) * clifford_unit(lam, G) - half * (indexed(G_base, mu, lam) + indexed(G_base, lam, mu)) * clifford_unit(nu, G) + half * (indexed(G_base, nu, lam) + indexed(G_base, lam, nu)) * clifford_unit(mu, G) - clifford_unit(mu, G) * clifford_unit(nu, G) * clifford_unit(lam, G); result += check_equal(canonicalize_clifford(e), 0); } 420a536,545 // 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;
realsymbol s("s"), t("t"); // symbolic entries in matric result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-1, 1, s, t)))); cout << '.' << flush;
422,425c547,550 < A = -1, 0, 0, 0, < 0, 1, 0, 0, < 0, 0, 1, 0, < 0, 0, 0, 1; ---
A = 1, 0, 0, 0, // anticommuting, not symmetric, Tr=0 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0; 428,431c553,556 < A = -1, 0, 0, 0, < 0,-1, 0, 0, < 0, 0,-1, 0, < 0, 0, 0,-1;
A = 1, 0, 0, 0, // anticommuting, not symmetric, Tr=2 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0; 433,437c558,562 < < A = -1, 0, 0, 0, < 0, 1, 0, 0, < 0, 0, 1, 0, < 0, 0, 0,-1;
A = 1, 0, 0, 0, // not anticommuting, symmetric, Tr=0 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0;
440,443c565,568 < A = -1, 0, 0, 0, < 0, 0, 0, 0, < 0, 0, 1, 0, < 0, 0, 0,-1; ---
A = 1, 0, 0, 0, // not anticommuting, symmetric, Tr=2 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0; 446c571,581 < result += clifford_check7(); 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;
symbol dim("D"); result += clifford_check7(minkmetric(), dim); cout << '.' << flush;
varidx chi(symbol("chi"), dim), xi(symbol("xi"), dim); result += clifford_check7(lorentz_g(xi, chi), dim); cout << '.' << flush;