From: Christian Bauer Date: Thu, 10 May 2001 20:40:16 +0000 (+0000) Subject: more checks (more, MORE, BWAHAHHAAA!... uhm, ...) for noncommutative classes X-Git-Tag: release_0-8-3~13 X-Git-Url: https://ginac.de/ginac.git/tutorial/ginac.git?a=commitdiff_plain;h=4dc267ddbec7fcc1ba15bf0d60d72a346c9efb26;p=ginac.git more checks (more, MORE, BWAHAHHAAA!... uhm, ...) for noncommutative classes --- diff --git a/check/exam_archive.cpp b/check/exam_archive.cpp index 4911a76a..7385727c 100644 --- a/check/exam_archive.cpp +++ b/check/exam_archive.cpp @@ -40,7 +40,7 @@ unsigned exam_archive(void) * epsilon_tensor(idx(fail(), 3), idx(0, 3), idx(y/2, 3)) + lorentz_g( varidx(lst(x, -11*y, acos(2*x).series(x==3-5*I, 3)) * color_ONE() - * metric_tensor(varidx(0, 5), varidx(2, 4)), zeta(3)), + * metric_tensor(spinidx(0, 5, false, true), varidx(2, 4)), zeta(3)), varidx(diag_matrix(lst(-1, Euler, atan(x/y==-15*I/17))) * delta_tensor(idx(x, 2), idx(y, 3)), log(cos(128.0/(x*y))), true), true diff --git a/check/exam_color.cpp b/check/exam_color.cpp index 3097188b..2190db8e 100644 --- a/check/exam_color.cpp +++ b/check/exam_color.cpp @@ -46,13 +46,12 @@ static unsigned check_equal_simplify(const ex &e1, const ex &e2) static unsigned color_check1(void) { - // checks general identities and contractions + // checks general identities and contractions of the structure constants unsigned result = 0; idx a(symbol("a"), 8), b(symbol("b"), 8), c(symbol("c"), 8), d(symbol("d"), 8); - // structure constants result += check_equal(color_d(a, c, a), 0); result += check_equal_simplify(color_d(a, b, c) * color_d(b, d, c), numeric(5,3) * delta_tensor(a, d)); result += check_equal_simplify(color_d(idx(5, 8), b, c) * color_d(b, idx(5, 8), c), numeric(5,3)); @@ -79,6 +78,54 @@ static unsigned color_check1(void) return result; } +static unsigned color_check2(void) +{ + // checks general identities and contractions of the generators + + unsigned result = 0; + + idx a(symbol("a"), 8), b(symbol("b"), 8), c(symbol("c"), 8), k(symbol("k"), 8); + ex e; + + e = color_T(k) * color_T(k); + result += check_equal_simplify(e, 4 * color_ONE() / 3); + e = color_T(k) * color_T(a) * color_T(k); + result += check_equal_simplify(e, -color_T(a) / 6); + e = color_T(k) * color_T(a) * color_T(b) * color_T(k); + result += check_equal_simplify(e, delta_tensor(a, b) * color_ONE() / 4 - color_T(a) * color_T(b) / 6); + e = color_T(k) * color_T(a) * color_T(b) * color_T(c) * color_T(k); + result += check_equal_simplify(e, (color_h(a, b, c) * color_ONE() / 8).expand() - color_T(a) * color_T(b) * color_T(c) / 6); + e = color_T(a) * color_T(b) * color_T(a) * color_T(b); + result += check_equal_simplify(e, -2 * color_ONE() / 9); + e = color_T(a) * color_T(b) * color_T(b) * color_T(a); + result += check_equal_simplify(e, 16 * color_ONE() / 9); + e = color_T(a) * color_T(b) * color_T(c) * color_T(c) * color_T(b) * color_T(a); + result += check_equal_simplify(e, 64 * color_ONE() / 27); + + return result; +} + +static unsigned color_check3(void) +{ + // checks traces + + unsigned result = 0; + + idx a(symbol("a"), 8), b(symbol("b"), 8), c(symbol("c"), 8), k(symbol("k"), 8); + ex e; + + e = color_ONE(); + result += check_equal(color_trace(e), 3); + e = color_T(a); + result += check_equal(color_trace(e), 0); + e = color_T(a) * color_T(b); + result += check_equal(color_trace(e), delta_tensor(a, b) / 2); + e = color_T(a) * color_T(b) * color_T(c); + result += check_equal(color_trace(e), color_h(a, b, c) / 4); + + return result; +} + unsigned exam_color(void) { unsigned result = 0; @@ -87,6 +134,8 @@ unsigned exam_color(void) clog << "----------color objects:" << endl; result += color_check1(); cout << '.' << flush; + result += color_check2(); cout << '.' << flush; + result += color_check3(); cout << '.' << flush; if (!result) { cout << " passed " << endl; diff --git a/check/exam_indexed.cpp b/check/exam_indexed.cpp index 442e36d0..bbbbf427 100644 --- a/check/exam_indexed.cpp +++ b/check/exam_indexed.cpp @@ -274,6 +274,39 @@ static unsigned edyn_check(void) return result; } +static unsigned spinor_check(void) +{ + // check identities of the spinor metric + + unsigned result = 0; + + symbol psi("psi"); + spinidx A(symbol("A"), 2), B(symbol("B"), 2), C(symbol("C"), 2); + ex A_co = A.toggle_variance(), B_co = B.toggle_variance(); + ex e; + + e = spinor_metric(A_co, B_co) * spinor_metric(A, B); + result += check_equal_simplify(e, 2); + e = spinor_metric(A_co, B_co) * spinor_metric(B, A); + result += check_equal_simplify(e, -2); + e = spinor_metric(A_co, B_co) * spinor_metric(A, C); + result += check_equal_simplify(e, delta_tensor(B_co, C)); + e = spinor_metric(A_co, B_co) * spinor_metric(B, C); + result += check_equal_simplify(e, -delta_tensor(A_co, C)); + e = spinor_metric(A_co, B_co) * spinor_metric(C, A); + result += check_equal_simplify(e, -delta_tensor(B_co, C)); + e = spinor_metric(A, B) * indexed(psi, B_co); + result += check_equal_simplify(e, indexed(psi, A)); + e = spinor_metric(A, B) * indexed(psi, A_co); + result += check_equal_simplify(e, -indexed(psi, B)); + e = spinor_metric(A_co, B_co) * indexed(psi, B); + result += check_equal_simplify(e, -indexed(psi, A_co)); + e = spinor_metric(A_co, B_co) * indexed(psi, A); + result += check_equal_simplify(e, indexed(psi, B_co)); + + return result; +} + unsigned exam_indexed(void) { unsigned result = 0; @@ -287,6 +320,7 @@ unsigned exam_indexed(void) result += symmetry_check(); cout << '.' << flush; result += scalar_product_check(); cout << '.' << flush; result += edyn_check(); cout << '.' << flush; + result += spinor_check(); cout << '.' << flush; if (!result) { cout << " passed " << endl;