o GZŽh“ ã@stddlmZddlmZmZddlmZddlmZGdd„deƒZ ddl m Z m Z ddl mZd d „Zeed<d S) é)Ú_sympify)ÚSÚBasic)ÚNonSquareMatrixError)ÚMatPowc@sxeZdZdZdZejZejfdd„Ze dd„ƒZ e dd„ƒZ d d „Z d d „Z d d„Zdd„Zdd„Zdd„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) TcCsBt|ƒ}t|ƒ}|jstdƒ‚|jdurtd|ƒ‚t |||¡S)Nzmat should be a matrixFzInverse of non-square matrix %s)rZ is_MatrixÚ TypeErrorZ is_squarerrÚ__new__)ÚclsÚmatÚexp©r úQ/var/www/auris/lib/python3.10/site-packages/sympy/matrices/expressions/inverse.pyr #s  zInverse.__new__cCs |jdS©Nr)Úargs©Úselfr r rÚarg.s z Inverse.argcCs|jjS©N)rÚshaperr r rr2sz Inverse.shapecCs|jSr)rrr r rÚ _eval_inverse6szInverse._eval_inversecCót|j ¡ƒSr)rrZ transposerr r rÚ_eval_transpose9ózInverse._eval_transposecCrr)rrZadjointrr r rÚ _eval_adjoint<rzInverse._eval_adjointcCrr)rrÚ conjugaterr r rÚ_eval_conjugate?rzInverse._eval_conjugatecCsddlm}d||jƒS)Nr)Údeté)Z&sympy.matrices.expressions.determinantrr)rrr r rÚ_eval_determinantBs zInverse._eval_determinantcKsBd|vr |ddkr |S|j}| dd¡r|jdi|¤Ž}| ¡S)NZ inv_expandFÚdeepTr )rÚgetÚdoitZinverse)rÚhintsrr r rr"Fs  z Inverse.doitcCsB|jd}| |¡}|D]}|j|j 9_|j|9_q |Sr)rÚ_eval_derivative_matrix_linesZ first_pointerÚTZsecond_pointer)rÚxrÚlinesÚliner r rr$Ps  z%Inverse._eval_derivative_matrix_linesN)Ú__name__Ú __module__Ú __qualname__Ú__doc__Z is_InverserZ NegativeOner r Úpropertyrrrrrrrr"r$r r r rrs    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 orthogonalrr%ZunitaryrZsingularÚ ValueError)ÚexprZ assumptionsr r rÚrefine_Inverse]s  r3N)Zsympy.core.sympifyrZ sympy.corerrZsympy.matrices.exceptionsrZ!sympy.matrices.expressions.matpowrrZsympy.assumptions.askr.r/Zsympy.assumptions.refiner0r3r r r rÚs   Q