a RG5d§ 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) TcCs>t|ƒ}t|ƒ}|jstdƒ‚|js0td|ƒ‚t |||¡S)Nzmat should be a matrixzInverse of non-square matrix %s)rÚ is_MatrixÚ TypeErrorÚ is_squarerrÚ__new__)ÚclsÚmatÚexp©rú^/var/www/html/django/DPS/env/lib/python3.9/site-packages/sympy/matrices/expressions/inverse.pyr #s zInverse.__new__cCs |jdS©Nr)Úargs©ÚselfrrrÚarg.sz Inverse.argcCs|jjS©N)rÚshaperrrrr2sz Inverse.shapecCs|jSr)rrrrrÚ _eval_inverse6szInverse._eval_inversecCsddlm}d||jƒS)Nr)Údeté)Ú&sympy.matrices.expressions.determinantrr)rrrrrÚ_eval_determinant9s zInverse._eval_determinantcKsBd|vr|ddkr|S|j}| dd¡r:|jfi|¤Ž}| ¡S)NZ inv_expandFÚdeepT)rÚgetÚdoitÚinverse)rÚhintsrrrrr=s  z Inverse.doitcCsB|jd}| |¡}|D]$}|j|j 9_|j|9_q|Sr)rÚ_eval_derivative_matrix_linesÚ first_pointerÚTÚsecond_pointer)rÚxrÚlinesÚlinerrrr"Gs   z%Inverse._eval_derivative_matrix_linesN)Ú__name__Ú __module__Ú __qualname__Ú__doc__Ú is_InverserÚ NegativeOnerr Úpropertyrrrrrr"rrrrrs    r)ÚaskÚQ)Ú handlers_dictcCsTtt |¡|ƒr|jjStt |¡|ƒr2|j ¡Stt |¡|ƒrPtd|jƒ‚|S)zÌ >>> from sympy import MatrixSymbol, Q, assuming, refine >>> X = MatrixSymbol('X', 2, 2) >>> X.I X**(-1) >>> with assuming(Q.orthogonal(X)): ... print(refine(X.I)) X.T zInverse of singular matrix %s) r0r1Ú orthogonalrr$ÚunitaryÚ conjugateÚsingularÚ ValueError)ÚexprÚ assumptionsrrrÚrefine_InverseTs  r:N)Úsympy.core.sympifyrÚ sympy.corerrÚsympy.matrices.commonrZ!sympy.matrices.expressions.matpowrrÚsympy.assumptions.askr0r1Úsympy.assumptions.refiner2r:rrrrÚs   H