ó ~9­\c@ s{ddlmZmZddlmZmZmZmZddlm Z ddl m Z defd„ƒYZ d„Z d S( iÿÿÿÿ(tprint_functiontdivision(tBasictExprtsympifytS(t MatrixBasei(t ShapeErrortTracecB s_eZdZeZeZd„Zd„Zd„Zd„Z e d„ƒZ d„Z d„Z RS(sÔMatrix Trace Represents the trace of a matrix expression. Examples ======== >>> from sympy import MatrixSymbol, Trace, eye >>> A = MatrixSymbol('A', 3, 3) >>> Trace(A) Trace(A) cC sVt|ƒ}|js.tdt|ƒƒ‚n|jsFtdƒ‚ntj||ƒS(Ns#input to Trace, %s, is not a matrixsTrace of a non-square matrix(Rt is_Matrixt TypeErrortstrt is_squareRRt__new__(tclstmat((s?lib/python2.7/site-packages/sympy/matrices/expressions/trace.pyR s    cC s|S(N((tself((s?lib/python2.7/site-packages/sympy/matrices/expressions/trace.pyt_eval_transpose#scC sddlm}|||ƒS(Niÿÿÿÿ(t_matrix_derivative(t"sympy.matrices.expressions.matexprR(RtvR((s?lib/python2.7/site-packages/sympy/matrices/expressions/trace.pyt_eval_derivative&scC s“|jdj|ƒ}xv|D]n}|jdkrQ|j|j|jj9_n"|jt|j|jjƒ9_tj|_tj|_qW|S(Nii( targst_eval_derivative_matrix_linesthighertfirsttsecondtTRRtOne(Rtxtrtlr((s?lib/python2.7/site-packages/sympy/matrices/expressions/trace.pyR*s " cC s |jdS(Ni(R(R((s?lib/python2.7/site-packages/sympy/matrices/expressions/trace.pytarg6scK s†|jdtƒrV|jj|}y|jƒSWq‚ttfk rRt|ƒSXn,t|jt ƒrut |jƒSt|jƒSdS(Ntdeep( tgettTrueR tdoitt _eval_tracetAttributeErrortNotImplementedErrorRt isinstanceRttrace(RtkwargsR ((s?lib/python2.7/site-packages/sympy/matrices/expressions/trace.pyR$:s cK sUddlm}m}|dƒ}||j||f|d|jjdfƒjƒS(Niÿÿÿÿ(tSumtDummytiii(tsympyR+R,R trowsR$(RtexprR*R+R,R-((s?lib/python2.7/site-packages/sympy/matrices/expressions/trace.pyt_eval_rewrite_as_SumHs (t__name__t __module__t__doc__R#tis_Tracetis_commutativeR RRRtpropertyR R$R1(((s?lib/python2.7/site-packages/sympy/matrices/expressions/trace.pyRs     cC st|ƒjƒS(s"Trace of a Matrix. Sum of the diagonal elements. Examples ======== >>> from sympy import trace, Symbol, MatrixSymbol, pprint, eye >>> n = Symbol('n') >>> X = MatrixSymbol('X', n, n) # A square matrix >>> trace(2*X) 2*Trace(X) >>> trace(eye(3)) 3 (RR$(R0((s?lib/python2.7/site-packages/sympy/matrices/expressions/trace.pyR)NsN(t __future__RRR.RRRRtsympy.matrices.matricesRtmatexprRRR)(((s?lib/python2.7/site-packages/sympy/matrices/expressions/trace.pyts "F