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| from sympy.physics.matrices import msigma, mgamma, minkowski_tensor, pat_matrix, mdft | |
| from sympy.core.numbers import (I, Rational) | |
| from sympy.core.singleton import S | |
| from sympy.functions.elementary.miscellaneous import sqrt | |
| from sympy.matrices.dense import (Matrix, eye, zeros) | |
| from sympy.testing.pytest import warns_deprecated_sympy | |
| def test_parallel_axis_theorem(): | |
| # This tests the parallel axis theorem matrix by comparing to test | |
| # matrices. | |
| # First case, 1 in all directions. | |
| mat1 = Matrix(((2, -1, -1), (-1, 2, -1), (-1, -1, 2))) | |
| assert pat_matrix(1, 1, 1, 1) == mat1 | |
| assert pat_matrix(2, 1, 1, 1) == 2*mat1 | |
| # Second case, 1 in x, 0 in all others | |
| mat2 = Matrix(((0, 0, 0), (0, 1, 0), (0, 0, 1))) | |
| assert pat_matrix(1, 1, 0, 0) == mat2 | |
| assert pat_matrix(2, 1, 0, 0) == 2*mat2 | |
| # Third case, 1 in y, 0 in all others | |
| mat3 = Matrix(((1, 0, 0), (0, 0, 0), (0, 0, 1))) | |
| assert pat_matrix(1, 0, 1, 0) == mat3 | |
| assert pat_matrix(2, 0, 1, 0) == 2*mat3 | |
| # Fourth case, 1 in z, 0 in all others | |
| mat4 = Matrix(((1, 0, 0), (0, 1, 0), (0, 0, 0))) | |
| assert pat_matrix(1, 0, 0, 1) == mat4 | |
| assert pat_matrix(2, 0, 0, 1) == 2*mat4 | |
| def test_Pauli(): | |
| #this and the following test are testing both Pauli and Dirac matrices | |
| #and also that the general Matrix class works correctly in a real world | |
| #situation | |
| sigma1 = msigma(1) | |
| sigma2 = msigma(2) | |
| sigma3 = msigma(3) | |
| assert sigma1 == sigma1 | |
| assert sigma1 != sigma2 | |
| # sigma*I -> I*sigma (see #354) | |
| assert sigma1*sigma2 == sigma3*I | |
| assert sigma3*sigma1 == sigma2*I | |
| assert sigma2*sigma3 == sigma1*I | |
| assert sigma1*sigma1 == eye(2) | |
| assert sigma2*sigma2 == eye(2) | |
| assert sigma3*sigma3 == eye(2) | |
| assert sigma1*2*sigma1 == 2*eye(2) | |
| assert sigma1*sigma3*sigma1 == -sigma3 | |
| def test_Dirac(): | |
| gamma0 = mgamma(0) | |
| gamma1 = mgamma(1) | |
| gamma2 = mgamma(2) | |
| gamma3 = mgamma(3) | |
| gamma5 = mgamma(5) | |
| # gamma*I -> I*gamma (see #354) | |
| assert gamma5 == gamma0 * gamma1 * gamma2 * gamma3 * I | |
| assert gamma1 * gamma2 + gamma2 * gamma1 == zeros(4) | |
| assert gamma0 * gamma0 == eye(4) * minkowski_tensor[0, 0] | |
| assert gamma2 * gamma2 != eye(4) * minkowski_tensor[0, 0] | |
| assert gamma2 * gamma2 == eye(4) * minkowski_tensor[2, 2] | |
| assert mgamma(5, True) == \ | |
| mgamma(0, True)*mgamma(1, True)*mgamma(2, True)*mgamma(3, True)*I | |
| def test_mdft(): | |
| with warns_deprecated_sympy(): | |
| assert mdft(1) == Matrix([[1]]) | |
| with warns_deprecated_sympy(): | |
| assert mdft(2) == 1/sqrt(2)*Matrix([[1,1],[1,-1]]) | |
| with warns_deprecated_sympy(): | |
| assert mdft(4) == Matrix([[S.Half, S.Half, S.Half, S.Half], | |
| [S.Half, -I/2, Rational(-1,2), I/2], | |
| [S.Half, Rational(-1,2), S.Half, Rational(-1,2)], | |
| [S.Half, I/2, Rational(-1,2), -I/2]]) | |