Otj ddlmZddlmZddlmZddlmZddlm Z ddl m Z GddeZ d Z Gd d eZd Zdd lmZmZddlmZdZeed<dS))Basic)Expr)S)sympify)NonSquareMatrixError) MatrixBasecNeZdZdZdZdZedZedZdZ dS) DeterminantaMatrix Determinant Represents the determinant of a matrix expression. Examples ======== >>> from sympy import MatrixSymbol, Determinant, eye >>> A = MatrixSymbol('A', 3, 3) >>> Determinant(A) Determinant(A) >>> Determinant(eye(3)).doit() 1 Tct|}|jstdt|z|jdurt dt j||S)Nz&Input to Determinant, %s, not a matrixFzDet of a non-square matrix)r is_Matrix TypeErrorstr is_squarerr__new__clsmats d/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/sympy/matrices/expressions/determinant.pyrzDeterminant.__new__s`cll} QDs3xxOPP P =E ! !&'CDD D}S#&&&c|jdSNrargsselfs rargzDeterminant.arg$y|rc$|jjjSN)rkind element_kindrs rr zDeterminant.kind(sx}))rc |j}|ddr |jdi|}|}||S|S)NdeepT)rgetdoit_eval_determinant)rhintsrresults rr&zDeterminant.doit,sWh 99VT " " $#(##U##C&&((  M rN) __name__ __module__ __qualname____doc__is_commutativerpropertyrr r&r$rrr r sy  N'''X**X*     rr cDt|S)z Matrix Determinant Examples ======== >>> from sympy import MatrixSymbol, det, eye >>> A = MatrixSymbol('A', 3, 3) >>> det(A) Determinant(A) >>> det(eye(3)) 1 )r r&matexprs rdetr38s w   $ $ & &&rc6eZdZdZdZedZddZdS) PermanentaMatrix Permanent Represents the permanent of a matrix expression. Examples ======== >>> from sympy import MatrixSymbol, Permanent, ones >>> A = MatrixSymbol('A', 3, 3) >>> Permanent(A) Permanent(A) >>> Permanent(ones(3, 3)).doit() 6 ct|}|jstdt|zt j||S)Nz$Input to Permanent, %s, not a matrix)rr r rrrrs rrzPermanent.__new__XsDcll} OBSXXMNN N}S#&&&rc|jdSrrrs rrz Permanent.arg_rrFc lt|jtr|jS|Sr) isinstancerrper)rexpandr(s rr&zPermanent.doitcs+ dh + + 8<<>> !KrN)F)r*r+r,r-rr/rr&r$rrr5r5Hs\  '''Xrr5cDt|S)a Matrix Permanent Examples ======== >>> from sympy import MatrixSymbol, Matrix, per, ones >>> A = MatrixSymbol('A', 3, 3) >>> per(A) Permanent(A) >>> per(ones(5, 5)) 120 >>> M = Matrix([1, 2, 5]) >>> per(M) 8 )r5r&r1s rr:r:is" W   " " $ $$r)askQ) handlers_dictc8ttj|j|r tjSttj|j|r tjSttj|j|r tjS|S)z >>> from sympy import MatrixSymbol, Q, assuming, refine, det >>> X = MatrixSymbol('X', 2, 2) >>> det(X) Determinant(X) >>> with assuming(Q.orthogonal(X)): ... print(refine(det(X))) 1 ) r=r> orthogonalrrOnesingularZerounit_triangular)expr assumptionss rrefine_DeterminantrHsy 1< ! !;//u QZ ! !; / /v Q tx ( (+ 6 6u KrN)sympy.core.basicrsympy.core.exprrsympy.core.singletonrsympy.core.sympifyrsympy.matrices.exceptionsrsympy.matrices.matrixbaserr r3r5r:sympy.assumptions.askr=r>sympy.assumptions.refiner?rHr$rrrQs2"""""" """"""&&&&&&::::::000000,,,,,$,,,^''' B%%%&)(((((((222222( 2 mr