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<varidx>(mu)
+ ? lst (
+ mu == idx(j, mu.get_dim()),
+ ex_to<varidx>(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;
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 <typename IDX> 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<varidx>(mu) ? ex_to<varidx>(mu).toggle_variance() : mu;
+ ex nu_TOGGLE = is_a<varidx>(nu) ? ex_to<varidx>(nu).toggle_variance() : nu;
+ ex rho_TOGGLE
+ = is_a<varidx>(rho) ? ex_to<varidx>(rho).toggle_variance() : rho;
+
ex e, e1;
- 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));
* 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);
+ 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);
+ * clifford_unit(mu_TOGGLE, A) * clifford_unit(nu_TOGGLE, 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());
+ 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_variance(), A) * clifford_unit(nu, A)
- * clifford_unit(mu, A) * clifford_unit(nu.toggle_variance(), A);
+ 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_variance(), A) * clifford_unit(nu.toggle_variance(), A) - pow(A.trace(), 2)*dirac_ONE());
+ 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_variance(), A) * clifford_unit(rho.toggle_variance(), A)
+ 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_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));
- 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));
- 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
+/* 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));
+ result += check_equal_simplify_term2((e*e1).simplify_indexed(), dirac_ONE(1));
- // 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<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);
+/* 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);
return result;
}
-
static unsigned clifford_check7(const ex & G, const symbol & dim)
{
// checks general identities and contractions
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<varidx>(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, 1))));
+ result += clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, 1))));; cout << '.' << flush;
+ result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix(lst(-1, -1, -1, -1))))+clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst(-1, -1, -1, -1))));; cout << '.' << flush;
+ result += clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, -1))))+clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, -1))));; cout << '.' << flush;
+ result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix(lst(-1, 0, 1, -1))))+clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst(-1, 0, 1, -1))));; cout << '.' << flush;
+ result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix(lst(-3, 0, 2, -1))))+clifford_check6<idx>(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<varidx>(ex_to<matrix>(diag_matrix(lst(-1, 1, s, t))))+clifford_check6<idx>(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<varidx>(A)+clifford_check6<idx>(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<varidx>(A)+clifford_check6<idx>(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<varidx>(A)+clifford_check6<idx>(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<varidx>(A)+clifford_check6<idx>(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<varidx>(A)+clifford_check6<idx>(A);; cout << '.' << flush;
symbol dim("D");
result += clifford_check7(minkmetric(), dim); cout << '.' << flush;
git://www.ginac.de / ginac.git / blobdiff