Module Expr Str ImportFrom alias alias ImportFrom alias alias alias alias ImportFrom alias ImportFrom alias FunctionDef arguments args NameParam defaults body Expr Str If CompareEq NameLoad Num body Assign NameStore TupleLoad TupleLoad Num Num TupleLoad Num Num orelse If CompareEq NameLoad Num body Assign NameStore TupleLoad TupleLoad Num UnaryOpUSub NameLoad TupleLoad NameLoad Num orelse If CompareEq NameLoad Num body Assign NameStore TupleLoad TupleLoad Num Num TupleLoad Num Num orelse Raise Call NameLoad Str Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults body Expr Str Assign NameStore BinOpMult UnaryOpUSub NameLoad NameLoad Assign NameStore BinOpMult UnaryOpUSub NameLoad NameLoad Assign NameStore BinOpMult UnaryOpUSub NameLoad NameLoad Assign NameStore BinOpPow NameLoad Num Assign NameStore BinOpPow NameLoad Num Assign NameStore BinOpPow NameLoad Num Assign NameStore TupleLoad TupleLoad BinOpAdd NameLoad NameLoad NameLoad NameLoad TupleLoad NameLoad BinOpAdd NameLoad NameLoad NameLoad TupleLoad NameLoad NameLoad BinOpAdd NameLoad NameLoad Return BinOpMult NameLoad Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults NameLoad body Expr Str If UnaryOpNot CompareIn NameLoad ListLoad Num Num Num Num Num body Raise Call NameLoad Str If CompareEq NameLoad Num body Assign NameStore TupleLoad TupleLoad Num Num Num Num TupleLoad Num Num Num Num TupleLoad Num Num Num Num TupleLoad Num Num Num Num orelse If CompareEq NameLoad Num body Assign NameStore TupleLoad TupleLoad Num Num Num Num TupleLoad Num Num Num Num TupleLoad Num Num Num Num TupleLoad Num Num Num Num orelse If CompareEq NameLoad Num body Assign NameStore TupleLoad TupleLoad Num Num Num UnaryOpUSub NameLoad TupleLoad Num Num NameLoad Num TupleLoad Num NameLoad Num Num TupleLoad UnaryOpUSub NameLoad Num Num Num orelse If CompareEq NameLoad Num body Assign NameStore TupleLoad TupleLoad Num Num Num Num TupleLoad Num Num Num Num TupleLoad Num Num Num Num TupleLoad Num Num Num Num orelse If CompareEq NameLoad Num body Assign NameStore TupleLoad TupleLoad Num Num Num Num TupleLoad Num Num Num Num TupleLoad Num Num Num Num TupleLoad Num Num Num Num Assign NameStore Call NameLoad NameLoad If NameLoad body If CompareIn NameLoad ListLoad Num Num Num Num body Assign NameStore UnaryOpUSub NameLoad Return NameLoad decorator_list Assign NameStore Call NameLoad TupleLoad TupleLoad Num Num Num Num TupleLoad Num Num Num Num TupleLoad Num Num Num Num TupleLoad Num Num Num Num FunctionDef arguments args NameParam defaults body Expr Str Assign NameStore ListComp ListComp NameLoad comprehension NameStore Call NameLoad NameLoad comprehension NameStore Call NameLoad NameLoad Assign NameStore Call NameLoad BinOpDiv BinOpMult BinOpMult Num NameLoad NameLoad NameLoad Assign SubscriptStore NameLoad Index Num BinOpMult ListLoad Num NameLoad For NameStore Call NameLoad NameLoad body Assign SubscriptStore SubscriptLoad NameLoad Index NameLoad Index Num Num For NameStore Call NameLoad Num NameLoad body For NameStore Call NameLoad NameLoad NameLoad body Assign SubscriptStore SubscriptLoad NameLoad Index NameLoad Index NameLoad SubscriptStore SubscriptLoad NameLoad Index NameLoad Index NameLoad BinOpPow NameLoad BinOpMult NameLoad NameLoad Return BinOpMult BinOpDiv Num Call NameLoad NameLoad Call NameLoad NameLoad decorator_list
N/A N/A Known matrices related to physics __future__ print_function division sympy Matrix I pi sqrt sympy.functions exp sympy.core.compatibility range msigma N/A N/A i N/A N/A N/A Returns a Pauli matrix `\sigma_i` with `i=1,2,3`

    References
    ==========

    .. [1] http://en.wikipedia.org/wiki/Pauli_matrices

    Examples
    ========

    >>> from sympy.physics.matrices import msigma
    >>> msigma(1)
    Matrix([
    [0, 1],
    [1, 0]])
     N/A N/A i 1 N/A N/A mat N/A N/A 0 1 N/A 1 0 N/A N/A N/A i 2 N/A N/A mat N/A N/A 0 N/A I N/A I 0 N/A N/A N/A i 3 N/A N/A mat N/A N/A 1 0 N/A 0 -1 N/A N/A N/A IndexError Invalid Pauli index N/A N/A Matrix mat N/A pat_matrix N/A N/A m dx dy dz N/A N/A N/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]])

     N/A dxdy N/A N/A dx dy N/A dydz N/A N/A dy dz N/A dzdx N/A N/A dz dx N/A dxdx N/A dx 2 N/A dydy N/A dy 2 N/A dzdz N/A dz 2 N/A mat N/A N/A N/A dydy dzdz dxdy dzdx N/A dxdy N/A dxdx dzdz dydz N/A dzdx dydz N/A dydy dxdx N/A N/A m N/A Matrix mat N/A mgamma N/A N/A mu lower N/A False N/A N/A Returns a Dirac gamma matrix `\gamma^\mu` in the standard
    (Dirac) representation.

    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] http://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]])
     N/A N/A N/A mu N/A 0 1 2 3 5 N/A N/A N/A IndexError Invalid Dirac index N/A N/A mu 0 N/A N/A mat N/A N/A 1 0 0 0 N/A 0 1 0 0 N/A 0 0 -1 0 N/A 0 0 0 -1 N/A N/A N/A mu 1 N/A N/A mat N/A N/A 0 0 0 1 N/A 0 0 1 0 N/A 0 -1 0 0 N/A -1 0 0 0 N/A N/A N/A mu 2 N/A N/A mat N/A N/A 0 0 0 N/A I N/A 0 0 I 0 N/A 0 I 0 0 N/A N/A I 0 0 0 N/A N/A N/A mu 3 N/A N/A mat N/A N/A 0 0 1 0 N/A 0 0 0 -1 N/A -1 0 0 0 N/A 0 1 0 0 N/A N/A N/A mu 5 N/A N/A mat N/A N/A 0 0 1 0 N/A 0 0 0 1 N/A 1 0 0 0 N/A 0 1 0 0 N/A m N/A Matrix mat N/A lower N/A N/A N/A mu N/A 1 2 3 5 N/A N/A m N/A m N/A m N/A N/A minkowski_tensor N/A Matrix N/A N/A 1 0 0 0 N/A 0 -1 0 0 N/A 0 0 -1 0 N/A 0 0 0 -1 mdft N/A N/A n N/A N/A N/A 
    Returns an expression of a discrete Fourier transform as a matrix multiplication.
    It is an n X n matrix.

    References
    ==========

    .. [1] https://en.wikipedia.org/wiki/DFT_matrix

    Examples
    ========

    >>> from sympy.physics.matrices import mdft
    >>> mdft(3)
    Matrix([
    [sqrt(3)/3,                sqrt(3)/3,                sqrt(3)/3],
    [sqrt(3)/3, sqrt(3)*exp(-2*I*pi/3)/3, sqrt(3)*exp(-4*I*pi/3)/3],
    [sqrt(3)/3, sqrt(3)*exp(-4*I*pi/3)/3, sqrt(3)*exp(-8*I*pi/3)/3]])
     N/A mat N/A N/A None N/A x N/A range n N/A y N/A range n N/A base N/A exp N/A N/A N/A -2 pi I n N/A N/A mat N/A 0 N/A N/A 1 n N/A i N/A range n N/A N/A N/A N/A mat N/A i N/A 0 1 N/A i N/A range 1 n N/A N/A j N/A range i n N/A N/A N/A N/A mat N/A i N/A j N/A N/A mat N/A j N/A i N/A base N/A i j N/A N/A N/A 1 N/A sqrt n N/A Matrix mat N/A