U Zʹj@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:|js6|js6|js6|js6|jr:|jr:dSdS)z Helper method used in TrTF) r isinstancerZ is_IntegerZis_FloatZ is_RationalZ is_NumberZ is_SymbolZis_commutative)er Z/var/www/html/bwave/python/venv/lib/python3.8/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|qSr r ).0ix)min_itemr r ,sz"_cycle_permute..rcs&g|]}||dgqS)rr )rr)indicesler r r7s) lenminr enumeratelistextendappendrangeindex)lZsublistidxZ 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)rrrrargs)r rr r r _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 csvt|dkrDt|dtttfs.t|dn t|d|d}n$t|dkr`t|d}ntdt|trz|St|drt |jr|St|t rt fdd|j DSt|t r| \}}t|dkrt |St|t |}t|dkrt ||S|Sn\t|trVt|j drFt|j drF|St||Snt|rd|St||SdS) z Construct a Trace object. Parameters ========== args = SymPy expression indices = tuple/list if indices, optional rrz5Arguments to Tr should be of form (expr[, [indices]])tracecsg|]}t|qSr )r&)rargrr r rszTr.__new__..N)rr rrtuple ValueErrorr r(hasattrcallablerr$rZargs_cncr__new__rr)clsr$exprZc_partZnc_partobjr r*r r/ns<              z Tr.__new__cCs|jd}|j}|jS)Nr)r$kindZ element_kind)selfr1Z expr_kindr r r r3s 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_tracerr*)r-r$r5)r4hintsr r r doits zTr.doitcCsdS)NTr )r4r r r is_numbersz Tr.is_numbercCst|dkr|t|jdj}nt|t|jdj }t|jdj| d|jdjd| }tt|S)a Permute the arguments cyclically. Parameters ========== pos : integer, if positive, shift-right, else shift-left Examples ======== >>> from sympy.physics.quantum.trace import Tr >>> from sympy import symbols >>> A, B, C, D = symbols('A B C D', commutative=False) >>> t = Tr(A*B*C*D) >>> t.permute(2) Tr(C*D*A*B) >>> t.permute(-2) Tr(C*D*A*B) rN)rr$absrr&r)r4posr$r r r permutes 0z Tr.permutecCsFt|jdtr&tt|jdj}n |jdg}t||jdfS)Nrr)r r$rr"r%r+)r4r$r r r _hashable_contents zTr._hashable_contentN) __name__ __module__ __qualname____doc__r/propertyr3r7r8r;r<r r r r r&Os5  r&N)Zsympy.core.addrZsympy.core.containersrZsympy.core.exprrZsympy.core.mulrZsympy.core.powerrZsympy.core.sortingrZsympy.core.sympifyrZsympy.matricesr rr"r%r&r r r r s        (