o 8Va @spddlmZddlmZmZddlmZGdddeZddZddl m Z m Z dd l m Z d d Zee d<d S) )Basic)adjoint conjugate) MatrixExprc@sveZdZdZdZddZeddZeddZdd d Z d d Z ddZ ddZ ddZ ddZddZddZdS) Transposea] The transpose of a matrix expression. This is a symbolic object that simply stores its argument without evaluating it. To actually compute the transpose, use the ``transpose()`` function, or the ``.T`` attribute of matrices. Examples ======== >>> from sympy.matrices import MatrixSymbol, Transpose >>> from sympy.functions import transpose >>> A = MatrixSymbol('A', 3, 5) >>> B = MatrixSymbol('B', 5, 3) >>> Transpose(A) A.T >>> A.T == transpose(A) == Transpose(A) True >>> Transpose(A*B) (A*B).T >>> transpose(A*B) B.T*A.T TcKsb|j}|ddrt|tr|jdi|}t|dd}|dur-|}|dur)|St|St|S)NdeepT_eval_transpose)argget isinstancerdoitgetattrr)selfZhintsr rresultr r F/usr/lib/python3/dist-packages/sympy/matrices/expressions/transpose.pyr "s zTranspose.doitcCs |jdS)Nr)argsrr r rr -s z Transpose.argcCs|jjdddS)N)r shaperr r rr1szTranspose.shapeFcKs|jj||fd|i|S)Nexpand)r _entry)rijrkwargsr r rr5szTranspose._entrycC t|jSN)rr rr r r _eval_adjoint8 zTranspose._eval_adjointcCrr)rr rr r r_eval_conjugate;rzTranspose._eval_conjugatecCs|jSr)r rr r rr>szTranspose._eval_transposecCddlm}||jS)N)Trace)Ztracer"r )rr"r r r _eval_traceA  zTranspose._eval_tracecCr )Nr)det)Z&sympy.matrices.expressions.determinantr%r )rr%r r r_eval_determinantEr$zTranspose._eval_determinantcCs |j|Sr)r _eval_derivative)rxr r rr'Is zTranspose._eval_derivativecCs|jd|}dd|DS)NrcSsg|]}|qSr ) transpose).0rr r r Osz;Transpose._eval_derivative_matrix_lines..)r_eval_derivative_matrix_lines)rr(linesr r rr,Msz'Transpose._eval_derivative_matrix_linesN)F)__name__ __module__ __qualname____doc__Z is_Transposer propertyr rrrrrr#r&r'r,r r r rrs     rcCst|jddS)zMatrix transposeF)r)rr )exprr r rr)Rsr))askQ) handlers_dictcCstt||r |jS|S)z >>> from sympy import MatrixSymbol, Q, assuming, refine >>> X = MatrixSymbol('X', 2, 2) >>> X.T X.T >>> with assuming(Q.symmetric(X)): ... print(refine(X.T)) X )r4r5Z symmetricr )r3Z assumptionsr r rrefine_Transpose[s r7N)ZsympyrZsympy.functionsrrZ"sympy.matrices.expressions.matexprrrr)Zsympy.assumptions.askr4r5Zsympy.assumptions.refiner6r7r r r rs  K