U L?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||jdkr0tdt||S)Nz&Input to Determinant, %s, not a matrixFzDet of a non-square matrix)r is_Matrix TypeErrorstrZ is_squarerr__new__clsZmatrX/var/www/html/venv/lib/python3.8/site-packages/sympy/matrices/expressions/determinant.pyr s  zDeterminant.__new__cCs |jdSNrargsselfrrrarg$szDeterminant.argcCs |jjjSN)rkindZ element_kindrrrrr(szDeterminant.kindcKs6|j}|ddr|jf|}|}|dk r2|S|S)NdeepT)rgetdoitZ_eval_determinant)rhintsrresultrrrr,s  zDeterminant.doitN) __name__ __module__ __qualname____doc__Zis_commutativer propertyrrrrrrrr s   rcCs t|S)z Matrix Determinant Examples ======== >>> from sympy import MatrixSymbol, det, eye >>> A = MatrixSymbol('A', 3, 3) >>> det(A) Determinant(A) >>> det(eye(3)) 1 )rrZmatexprrrrdet8sr$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$Input to Permanent, %s, not a matrix)rr r r rr r rrrr XszPermanent.__new__cCs |jdSrrrrrrr_sz Permanent.argFcKst|jtr|jS|SdSr) isinstancerrper)rexpandrrrrrcs  zPermanent.doitN)F)rrr r!r r"rrrrrrr%Hs  r%cCs t|S)a Matrix Permanent Examples ======== >>> from sympy import MatrixSymbol, Matrix, per, ones >>> A = MatrixSymbol('A', 3, 3) >>> per(A) Permanent(A) >>> per(ones(5, 5)) 120 >>> M = Matrix([1, 2, 5]) >>> per(M) 8 )r%rr#rrrr'isr')askQ) handlers_dictcCsLtt|j|rtjStt|j|r0tjStt|j|rHtjS|S)z >>> from sympy import MatrixSymbol, Q, assuming, refine, det >>> X = MatrixSymbol('X', 2, 2) >>> det(X) Determinant(X) >>> with assuming(Q.orthogonal(X)): ... print(refine(det(X))) 1 ) r)r*Z orthogonalrrZOneZsingularZZeroZunit_triangular)exprZ assumptionsrrrrefine_Determinants r-N)Zsympy.core.basicrZsympy.core.exprrZsympy.core.singletonrZsympy.core.sympifyrZsympy.matrices.exceptionsrZsympy.matrices.matrixbaserrr$r%r'Zsympy.assumptions.askr)r*Zsympy.assumptions.refiner+r-rrrrs      /!