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d}t|�S | dkrdt ft dff}t|�S | dkr%d}t|�S td��)a Returns a Pauli matrix `\sigma_i` with ``i=1,2,3``.
References
==========
.. [1] https://en.wikipedia.org/wiki/Pauli_matrices
Examples
========
>>> from sympy.physics.matrices import msigma
>>> msigma(1)
Matrix([
[0, 1],
[1, 0]])
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| t |
� S )a� Returns the Parallel Axis Theorem matrix to translate the inertia
matrix a distance of `(dx, dy, dz)` for a body of mass m.
Examples
========
To translate a body having a mass of 2 units a distance of 1 unit along
the `x`-axis we get:
>>> from sympy.physics.matrices import pat_matrix
>>> pat_matrix(2, 1, 0, 0)
Matrix([
[0, 0, 0],
[0, 2, 0],
[0, 0, 2]])
r
)r ) �m�dx�dy�dz�dxdy�dydz�dzdx�dxdx�dydy�dzdzr r r r �
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a� Returns a Dirac gamma matrix `\gamma^\mu` in the standard
(Dirac) representation.
Explanation
===========
If you want `\gamma_\mu`, use ``gamma(mu, True)``.
We use a convention:
`\gamma^5 = i \cdot \gamma^0 \cdot \gamma^1 \cdot \gamma^2 \cdot \gamma^3`
`\gamma_5 = i \cdot \gamma_0 \cdot \gamma_1 \cdot \gamma_2 \cdot \gamma_3 = - \gamma^5`
References
==========
.. [1] https://en.wikipedia.org/wiki/Gamma_matrices
Examples
========
>>> from sympy.physics.matrices import mgamma
>>> mgamma(1)
Matrix([
[ 0, 0, 0, 1],
[ 0, 0, 1, 0],
[ 0, -1, 0, 0],
[-1, 0, 0, 0]])
)r r r
r � zInvalid Dirac indexr )�r r r r �r r r r �r r r r �r r r r r )�r r r r �r r r r �r r r r �r r r r r
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�r) )r r% r! r" iO z1DFT(n).as_mutable(), DFT(n), DFT(n).as_explicit()z1.9)�issue�
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Deprecated. Use DFT from sympy.matrices.expressions.fourier instead.
To get identical behavior to ``mdft(n)``, use ``DFT(n).as_mutable()``.
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