o h @sddlmZddlmZddlmZddlmZddlm Z ddl m Z GdddeZ d d Z Gd d d eZd dZddlmZmZddlmZddZeed<dS))Basic)Expr)S)sympify)NonSquareMatrixError) MatrixBasec@s<eZdZdZdZddZeddZeddZd d Z d S) 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 TcCs<t|}|jstdt||jdurtdt||S)Nz&Input to Determinant, %s, not a matrixFzDet of a non-square matrix)r is_Matrix TypeErrorstr is_squarerr__new__clsmatr\/var/www/html/ai/venv/lib/python3.10/site-packages/sympy/matrices/expressions/determinant.pyr s   zDeterminant.__new__cC |jdSNrargsselfrrrarg$ zDeterminant.argcCs |jjjSN)rkind element_kindrrrrr(rzDeterminant.kindcKs:|j}|ddr|jdi|}|}|dur|S|S)NdeepTr)rgetdoit_eval_determinant)rhintsrresultrrrr ,s zDeterminant.doitN) __name__ __module__ __qualname____doc__is_commutativer propertyrrr rrrrr s   rcC t|S)z Matrix Determinant Examples ======== >>> from sympy import MatrixSymbol, det, eye >>> A = MatrixSymbol('A', 3, 3) >>> det(A) Determinant(A) >>> det(eye(3)) 1 )rr matexprrrrdet8s r-c@s.eZdZdZddZeddZd ddZd S) 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 cCs*t|}|jstdt|t||S)Nz$Input to Permanent, %s, not a matrix)rr r r rr rrrrr Xs zPermanent.__new__cCrrrrrrrr_rz Permanent.argFcKst|jtr |jS|Sr) isinstancerrper)rexpandr"rrrr cs  zPermanent.doitN)F)r$r%r&r'r r)rr rrrrr.Hs  r.cCr*)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 )r.r r+rrrr0is r0)askQ) handlers_dictcCsLtt|j|r tjStt|j|rtjStt|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 ) r2r3 orthogonalrrOnesingularZerounit_triangular)expr assumptionsrrrrefine_Determinants r<N)sympy.core.basicrsympy.core.exprrsympy.core.singletonrsympy.core.sympifyrsympy.matrices.exceptionsrsympy.matrices.matrixbaserrr-r.r0sympy.assumptions.askr2r3sympy.assumptions.refiner4r<rrrrs     /!