o jg@sddlmZddlmZddlmZddlmZddlm Z ddl m Z ddl m Z ddlmZd d Zd d Zd dZGdddeZdS))Add)Tuple)Expr)Mul)Pow)default_sort_key)sympify)MatrixcCs>t|}t|tr|js|js|js|js|jr|jrdSdS)z Helper method used in TrTF) r isinstancer is_Integeris_Float is_Rational is_Number is_Symbolis_commutative)erS/var/www/html/zoom/venv/lib/python3.10/site-packages/sympy/physics/quantum/trace.py _is_scalar s  rcst|dkr|St|tdfddt|Dt||t|dfddttdD}|t|}||t|}|S)a5 Cyclic permutations based on canonical ordering Explanation =========== 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 )keycsg|] \}}|kr|qSrr).0ix)min_itemrr ,sz"_cycle_permute..rcs&g|]}||dgqS)rr)rr)indiceslerrr7s&) lenminr enumeratelistextendappendrangeindex)lsublistidx ordered_lr)rrrr_cycle_permutes    r*cCs<t|dkr|St|dd}||ddt|jS)zk this just moves the last arg to first position to enable expansion of args A,B,A ==> A**2,B rNr)rr!r"rargs)r&rrrr_rearrange_argsBs  r-c@sHeZdZdZddZeddZddZedd Zd d Z d d Z dS)Tra 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.physics.quantum.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 csbt|dkr"t|dtttfst|dnt|d|d}nt|dkr0t|d}ntdt|tr=|St|drKt |jrK|St|t r\t fdd|j DSt|t r| \}}t|dkrqt |St|t |}t|dkrt ||S|St|trt|j drt|j dr|St||St|r|St||S)z Construct a Trace object. Parameters ========== args = SymPy expression indices = tuple/list if indices, optional rrz5Arguments to Tr should be of form (expr[, [indices]])tracecsg|]}t|qSr)r.)rargrrrrszTr.__new__..)rr r!rtuple ValueErrorr r0hasattrcallablerr,rargs_cncr__new__rr)clsr,exprc_partnc_partobjrr2rr8ns<            z Tr.__new__cCs|jd}|j}|jS)Nr)r,kind element_kind)selfr: expr_kindrrrr>s zTr.kindcKs,t|jddr|jdj|jddS|S)a Perform the trace operation. #TODO: Current version ignores the indices set for partial trace. >>> from sympy.physics.quantum.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 r _eval_tracerr2)r5r,rB)r@hintsrrrdoits zTr.doitcCsdS)NTr)r@rrr is_numbersz Tr.is_numbercCst|dkr|t|jdj}n t|t|jdj }t|jdj| d|jdjd| }tt|S)a Permute the arguments cyclically. Parameters ========== pos : integer, if positive, shift-right, else shift-left Examples ======== >>> from sympy.physics.quantum.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) rN)rr,absr!r.r)r@posr,rrrpermutes 0 z Tr.permutecCsFt|jdtrtt|jdj}n|jdg}t||jdfS)Nrr)r r,rr*r-r3)r@r,rrr_hashable_contents zTr._hashable_contentN) __name__ __module__ __qualname____doc__r8propertyr>rDrErHrIrrrrr.Os5   r.N)sympy.core.addrsympy.core.containersrsympy.core.exprrsympy.core.mulrsympy.core.powerrsympy.core.sortingrsympy.core.sympifyrsympy.matricesr rr*r-r.rrrrs       (