o i @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 TypeErrorstrZ is_squarerr__new__clsmatru/var/www/html/eduruby.in/lip-sync/lip-sync-env/lib/python3.10/site-packages/sympy/matrices/expressions/determinant.pyr s   zDeterminant.__new__cC |jdSNrargsselfrrrarg$ zDeterminant.argcCs |jjjSN)rkindZ element_kindrrrrr(rzDeterminant.kindcKs:|j}|ddr|jdi|}|}|dur|S|S)NdeepTr)rgetdoitZ_eval_determinant)rhintsrresultrrrr,s zDeterminant.doitN) __name__ __module__ __qualname____doc__Zis_commutativer propertyrrrrrrrr 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 )rrZmatexprrrrdet8s 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$Input to Permanent, %s, not a matrix)rr r r rr r rrrr Xs zPermanent.__new__cCrrrrrrrr_rz Permanent.argFcKst|jtr |jS|Sr) isinstancerrper)rexpandrrrrrcs  zPermanent.doitN)F)r!r"r#r$r r%rrrrrrr)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)rr'rrrr+is r+)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 ) r-r.Z orthogonalrrZOneZsingularZZeroZunit_triangular)exprZ assumptionsrrrrefine_Determinants r1N)Zsympy.core.basicrZsympy.core.exprrZsympy.core.singletonrZsympy.core.sympifyrZsympy.matrices.exceptionsrZsympy.matrices.matrixbaserrr(r)r+Zsympy.assumptions.askr-r.Zsympy.assumptions.refiner/r1rrrrs     /!