o à8Va‹ ã@stddlmZddlmZmZddlmZddlmZGdd„deƒZ ddl m Z m Z ddl mZd d „Zeed<d S) é)Ú_sympify)ÚSÚBasic)ÚNonSquareMatrixError)ÚMatPowc@s`eZdZdZdZejZejfdd„Ze dd„ƒZ e dd„ƒZ d d „Z d d „Z d d„Zdd„ZdS)ÚInversea The multiplicative inverse of a matrix expression This is a symbolic object that simply stores its argument without evaluating it. To actually compute the inverse, use the ``.inverse()`` method of matrices. Examples ======== >>> from sympy import MatrixSymbol, Inverse >>> A = MatrixSymbol('A', 3, 3) >>> B = MatrixSymbol('B', 3, 3) >>> Inverse(A) A**(-1) >>> A.inverse() == Inverse(A) True >>> (A*B).inverse() B**(-1)*A**(-1) >>> Inverse(A*B) (A*B)**(-1) TcCs6t|ƒ}|js tdƒ‚|jstd|ƒ‚t |||¡S)Nzmat should be a matrixzInverse of non-square matrix %s)rZ is_MatrixÚ TypeErrorZ is_squarerrÚ__new__)ÚclsZmatÚexp©r úD/usr/lib/python3/dist-packages/sympy/matrices/expressions/inverse.pyr #s  zInverse.__new__cCs |jdS©Nr)Úargs©Úselfr r r Úarg-s z Inverse.argcCs|jjS©N)rÚshaperr r r r1sz Inverse.shapecCs|jSr)rrr r r Ú _eval_inverse5szInverse._eval_inversecCsddlm}d||jƒS)Nr)Údeté)Z&sympy.matrices.expressions.determinantrr)rrr r r Ú_eval_determinant8s zInverse._eval_determinantcKsBd|vr |ddkr |S|j}| dd¡r|jdi|¤Ž}| ¡S)NZ inv_expandFZdeepTr )rÚgetÚdoitZinverse)rZhintsrr r r r<s  z Inverse.doitcCsB|jd}| |¡}|D]}|j|j 9_|j|9_q |Sr)rÚ_eval_derivative_matrix_linesZ first_pointerÚTZsecond_pointer)rÚxrÚlinesÚliner r r rFs  z%Inverse._eval_derivative_matrix_linesN)Ú__name__Ú __module__Ú __qualname__Ú__doc__Z is_InverserZ NegativeOner r Úpropertyrrrrrrr r r r rs   r)ÚaskÚQ)Ú handlers_dictcCsTtt |¡|ƒr |jjStt |¡|ƒr|j ¡Stt |¡|ƒr(td|jƒ‚|S)zÌ >>> from sympy import MatrixSymbol, Q, assuming, refine >>> X = MatrixSymbol('X', 2, 2) >>> X.I X**(-1) >>> with assuming(Q.orthogonal(X)): ... print(refine(X.I)) X.T zInverse of singular matrix %s) r%r&Z orthogonalrrZunitaryÚ conjugateZsingularÚ ValueError)ÚexprZ assumptionsr r r Úrefine_InverseSs  r+N)Zsympy.core.sympifyrZ sympy.corerrZsympy.matrices.commonrZ!sympy.matrices.expressions.matpowrrZsympy.assumptions.askr%r&Zsympy.assumptions.refiner'r+r r r r Ús   G