
    Rie3
                     ~   d Z ddlmZmZmZ ddlmZmZmZm	Z	m
Z
mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZ ddlmZ ddlmZmZ eZeZ ddl!m"Z" ddl#m$Z$ ddl%m&Z&m'Z' e&Z(e"Z)dd	l*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z<m=Z=m>Z>m?Z?m@Z@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZHmIZImJZJmKZKmLZLmMZMmNZNmOZO dd
lPmQZQ g dZRdS )zwA module that handles matrices.

Includes functions for fast creating matrices like zero, one/eye, random
matrix, etc.
   )
ShapeErrorNonSquareMatrixError
MatrixKind)GramSchmidt
casoratiandiageyehessianjordan_cell
list2numpymatrix2numpymatrix_multiply_elementwiseones
randMatrix	rot_axis1	rot_axis2	rot_axis3rot_ccw_axis1rot_ccw_axis2rot_ccw_axis3
rot_givenssymarray	wronskianzeros)MutableDenseMatrix)DeferredVector
MatrixBase)MutableSparseMatrix)banded)ImmutableDenseMatrixImmutableSparseMatrix)%MatrixSliceBlockDiagMatrixBlockMatrixFunctionMatrixIdentityInverseMatAddMatMulMatPow
MatrixExprMatrixSymbolTrace	Transpose
ZeroMatrix	OneMatrixblockcutblock_collapsematrix_symbolsAdjointhadamard_productHadamardProductHadamardPowerDeterminantdetdiagonalize_vector
DiagMatrixDiagonalMatrix
DiagonalOftrace
DotProductkronecker_productKroneckerProductPermutationMatrixMatrixPermute	MatrixSet	Permanentper)dotprodsimp)Ir   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   MatrixMutableMatrixr   r   r    r!   ImmutableMatrixSparseMatrixr"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   N)S__doc__commonr   r   r   denser   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   matricesr   r   rI   rH   sparser   sparsetoolsr   	immutabler    r!   rJ   rK   expressionsr"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   	utilitiesrG   __all__     7lib/python3.11/site-packages/sympy/matrices/__init__.py<module>rY      s   
 A @ @ @ @ @ @ @ @ @                                                                                            & % % % % % 0 0 0 0 0 0 0 0"	 ' ' ' ' ' '       B B B B B B B B&"A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A # " " " " "" " "rW   