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_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
from sympy.physics.paulialgebra import Pauli, evaluate_pauli_product from sympy.physics.matrices import mdft, mgamma, msigma, pat_matrix mdft(4) # expression of discrete Fourier transform as a matrix multiplication mgamma(2) # Dirac gamma matrix in the Dirac representation msigma(2) # Pauli matrix with (1,2,3) pat_matrix(3, 1, 0, 0) # computer Parallel Axis Theorem matrix to translate the inertia matrix a distance of dx, dy, dz for a body of mass m. evaluate_pauli_product(4*x*Pauli(3)*Pauli(2))
from sympy.physics.paulialgebra import Pauli, evaluate_pauli_product
from sympy.physics.matrices import mdft, mgamma, msigma, pat_matrix
mdft(4) # expression of discrete Fourier transform as a matrix multiplication
mgamma(2) # Dirac gamma matrix in the Dirac representation
msigma(2) # Pauli matrix with (1,2,3)
pat_matrix(
3, 1, 0, 0
) # computer Parallel Axis Theorem matrix to translate the inertia matrix a distance of dx, dy, dz for a body of mass m.
evaluate_pauli_product(4 * x * Pauli(3) * Pauli(2))