Otj ddlmZddlmZmZddlmZddlmZGddeZ ddl m Z m Z ddl mZd Zeed<d S) )_sympify)SBasic)NonSquareMatrixError)MatPowceZdZdZdZejZejfdZe dZ e dZ dZ dZ dZd Zd Zd Zd Zd S)Inversea 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) Tct|}t|}|jstd|jdurt d|zt j|||S)Nzmat should be a matrixFzInverse of non-square matrix %s)r is_Matrix TypeError is_squarerr__new__)clsmatexps `/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/sympy/matrices/expressions/inverse.pyrzInverse.__new__#shsmmsmm} 6455 5 =E ! !&'H3'NOO O}S#s+++c|jdSNr)argsselfs rargz Inverse.arg.sy|rc|jjSN)rshapers rrz Inverse.shape2s x~rc|jSr)rrs r _eval_inversezInverse._eval_inverse6s xrcNt|jSr)r r transposers r_eval_transposezInverse._eval_transpose9tx))++,,,rcNt|jSr)r radjointrs r _eval_adjointzInverse._eval_adjoint<stx''))***rcNt|jSr)r r conjugaters r_eval_conjugatezInverse._eval_conjugate?r"rc4ddlm}d||jz S)Nr)det)&sympy.matrices.expressions.determinantr*r)rr*s r_eval_determinantzInverse._eval_determinantBs(>>>>>>TXrc d|vr|ddkr|S|j}|ddr |jdi|}|S)N inv_expandFdeepT)rgetdoitinverse)rhintsrs rr3z Inverse.doitFsc 5 U<%8E%A%AKh 99VT " " $#(##U##C{{}}rc|jd}||}|D](}|xj|j zc_|xj|zc_)|Sr)r_eval_derivative_matrix_lines first_pointerTsecond_pointer)rxrlineslines rr7z%Inverse._eval_derivative_matrix_linesPscil11!44 ( (D   46' )     4 '    rN)__name__ __module__ __qualname____doc__ is_Inverser NegativeOnerrpropertyrrrr!r%r(r-r3r7r1rrr r s.J -Cm , , , ,XX---+++---rr )askQ) handlers_dictcJttj||r |jjSttj||r|jSttj||rtd|jz|S)z >>> 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) rErF orthogonalrr9unitaryr'singular ValueError)expr assumptionss rrefine_InverserO]s 1<  {++Exz QYt__k * *Ex!!### QZ  { + +E848CDDD KrN)sympy.core.sympifyr sympy.corerrsympy.matrices.exceptionsr!sympy.matrices.expressions.matpowrr sympy.assumptions.askrErFsympy.assumptions.refinerGrOr1rrrVs''''''::::::444444NNNNNfNNNb)(((((((222222&* ir