ó ¡¼™\c@ sŸddlmZmZddlmZmZmZmZmZm Z m Z ddl m Z ddl mZd„Zd„Zd„Zdefd „ƒYZd S( iÿÿÿÿ(tprint_functiontdivision(tExprtAddtMultPowtsympifytMatrixtTuple(trange(tdefault_sort_keycC s\t|ƒ}t|tƒrX|jsQ|jsQ|jsQ|jsQ|jrX|jrXt Snt S(s Helper method used in Tr( Rt isinstanceRt is_Integertis_Floatt is_Rationalt is_Numbert is_Symboltis_commutativetTruetFalse(te((s/lib/python2.7/site-packages/sympy/core/trace.pyt _is_scalars c C st|ƒdkr|St|dtƒ}gt|ƒD]\}}||kr5|^q5}t|ƒ}|j|ƒ|jt|ƒ|dƒgtt|ƒdƒD]"}|||||d!g^q¤}|jt|ƒƒ}|||||t|ƒ!}|S(s Cyclic permutations based on canonical ordering This method does the sort based ascii values while a better approach would be to used lexicographic sort. TODO: Handle condition such as symbols have subscripts/superscripts in case of lexicographic sort itkeyi( tlentminR t enumeratetlisttextendtappendR tindex( tltmin_itemtitxtindicestletsublisttidxt ordered_l((s/lib/python2.7/site-packages/sympy/core/trace.pyt_cycle_permutes 1  <cC sGt|ƒdkr|St|dƒ}|j|dd!ƒt|ŒjS(sk this just moves the last arg to first position to enable expansion of args A,B,A ==> A**2,B iiÿÿÿÿi(RRRRtargs(RR!((s/lib/python2.7/site-packages/sympy/core/trace.pyt_rearrange_args;s tTrcB sAeZdZd„Zd„Zed„ƒZd„Zd„ZRS(sw Generic Trace operation than can trace over: a) sympy matrix b) operators c) outer products Parameters ========== o : operator, matrix, expr i : tuple/list indices (optional) Examples ======== # TODO: Need to handle printing a) Trace(A+B) = Tr(A) + Tr(B) b) Trace(scalar*Operator) = scalar*Trace(Operator) >>> from sympy.core.trace import Tr >>> from sympy import symbols, Matrix >>> a, b = symbols('a b', commutative=True) >>> A, B = symbols('A B', commutative=False) >>> Tr(a*A,[2]) a*Tr(A) >>> m = Matrix([[1,2],[1,1]]) >>> Tr(m) 2 cG st|ƒdkr^t|dtttfƒsAt|dƒ}nt|dŒ}|d}n4t|ƒdkr†tƒ}|d}n tdƒ‚t|tƒr«|jƒSt|dƒrÓt |jƒrÓ|jƒSt|t ƒr t g|j D]}t ||ƒ^qïŒSt|t ƒrŠ|jƒ\}}t|ƒdkrHt |ŒStj|t |Œ|ƒ}t|ƒdkrƒt |Œ|S|Snrt|tƒrÙt|j dƒrÃt|j dƒrÃ|Stj|||ƒSn#t|ƒré|Stj|||ƒSdS(s Construct a Trace object. Parameters ========== args = sympy expression indices = tuple/list if indices, optional iiis5Arguments to Tr should be of form (expr[, [indices]])ttraceN(RR RRttuplet ValueErrorRR+thasattrtcallableRR(R*Rtargs_cncRt__new__RR(tclsR(R"texprtargtc_parttnc_parttobj((s/lib/python2.7/site-packages/sympy/core/trace.pyR1gs:       ) ' cK s8t|jddƒr4|jdjd|jdƒS|S(s{ Perform the trace operation. #TODO: Current version ignores the indices set for partial trace. >>> from sympy.core.trace import Tr >>> from sympy.physics.quantum.operator import OuterProduct >>> from sympy.physics.quantum.spin import JzKet, JzBra >>> t = Tr(OuterProduct(JzKet(1,1), JzBra(1,1))) >>> t.doit() 1 it _eval_traceR"i(R.R(R8(tselftkwargs((s/lib/python2.7/site-packages/sympy/core/trace.pytdoitœs cC stS(N(R(R9((s/lib/python2.7/site-packages/sympy/core/trace.pyt is_number®scC s‹|dkr)|t|jdjƒ}n!t|ƒt|jdjƒ }t|jdj| |jdjd| !ƒ}tt|ŒƒS(sÀ Permute the arguments cyclically. Parameters ========== pos : integer, if positive, shift-right, else shift-left Examples ======== >>> from sympy.core.trace import Tr >>> from sympy import symbols >>> A, B, C, D = symbols('A B C D', commutative=False) >>> t = Tr(A*B*C*D) >>> t.permute(2) Tr(C*D*A*B) >>> t.permute(-2) Tr(C*D*A*B) i(RR(tabsRR*R(R9tposR(((s/lib/python2.7/site-packages/sympy/core/trace.pytpermuteµs  !1cC s]t|jdtƒr5tt|jdjƒƒ}n|jdg}t|ƒ|jdfS(Nii(R R(RR'R)R,(R9R(((s/lib/python2.7/site-packages/sympy/core/trace.pyt_hashable_contentÒs( t__name__t __module__t__doc__R1R;tpropertyR<R?R@(((s/lib/python2.7/site-packages/sympy/core/trace.pyR*Hs  5  N(t __future__RRtsympyRRRRRRRtsympy.core.compatibilityR tsympy.utilitiesR RR'R)R*(((s/lib/python2.7/site-packages/sympy/core/trace.pyts4  $