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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]])
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