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 == zero(4)
assert gamma0 * gamma0 == one(4) * minkowski_tensor[0,0]
assert gamma2 * gamma2 != one(4) * minkowski_tensor[0,0]
assert gamma2 * gamma2 == one(4) * minkowski_tensor[2,2]
assert mgamma(5,True) == \
mgamma(0,True)*mgamma(1,True)*mgamma(2,True)*mgamma(3,True)*I
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 == one(2)
assert sigma2*sigma2 == one(2)
assert sigma3*sigma3 == one(2)
assert sigma1*2*sigma1 == 2*one(2)
assert sigma1*sigma3*sigma1 == -sigma3
def DDD_of_matrix(A):
"""Create DDD of a Sympy matrix
@param A: Input matrix
@type A: sympy.Matrix
>>> a,b,c,d,e,f,g,h,i,j=sympy.symbols('abcdefghij')
>>> A = sympy.Matrix((a,b,0,0),(c,d,e,0),(0,f,g,h),(0,0,i,j))
>>> DDD_matrix(A)
"""
print A
if A == sympy.zero(1):
return VertexZero
if A == sympy.one(1):
return VertexOne
# Select row, column
i = 0; j = 0
D0 = copy(A)
D0[i,j] = 0
return DDD(A[i,j],
D1 = DDD_of_matrix(A.minorMatrix(i,j)),
D0 = D0)
def DDD_of_matrix(A):
"""Create DDD of a Sympy matrix
@param A: Input matrix
@type A: sympy.Matrix
>>> a,b,c,d,e,f,g,h,i,j=sympy.symbols('abcdefghij')
>>> A = sympy.Matrix((a,b,0,0),(c,d,e,0),(0,f,g,h),(0,0,i,j))
>>> DDD_matrix(A)
"""
print A
if A == sympy.zero(1):
return VertexZero
if A == sympy.one(1):
return VertexOne
# Select row, column
i = 0; j = 0
D0 = copy(A)
D0[i,j] = 0
return DDD(A[i,j],
D1 = DDD_of_matrix(A.minorMatrix(i,j)),
D0 = D0)
