o jg8(@sdZddlZddlmZddlmZddlmZddlm Z ddl m Z m Z ddl mZdd lmZd d gZd d Z  dddZ  dddZ  ddd ZdddZdddZddd ZdS)z.Functions for reordering operator expressions.N)Add)Mul)Integer)Pow) CommutatorAntiCommutator)BosonOp) FermionOp normal_ordernormal_ordered_formcCslg}|jD].}t|tr.t|jdtr.|jddkr.t|jdD] }||jdq"q||q|S)z Helper function for normal_ordered_form and normal_order: Expand a power expression to a multiplication expression so that that the expression can be handled by the normal ordering functions. r)args isinstancerrrangeappend)factors new_factorsfactornr^/var/www/html/zoom/venv/lib/python3.10/site-packages/sympy/physics/quantum/operatorordering.py_expand_powerss   rF c Cst|}g}d}|t|dkr||||d}}tdd||fDr0|||d7}q|jt|jf} |jt|jf} | | krN|||d7}q|d7}|jr|jst|trt|tr|j d|j dkr|rqd} nt ||} |||| n^|||dnTt|t rt|t r|j d|j dkr|rd} nt ||} || || n+|| |dn |j|jkrt|t rt|t r|| |n||||t|dks|t|dkr||d||kr|St |} t| ||d|dS)an Helper function for normal_ordered_form_factor: Write multiplication expression with bosonic or fermionic operators on normally ordered form, using the bosonic and fermionic commutation relations. The resulting operator expression is equivalent to the argument, but will in general be a sum of operator products instead of a simple product. rr css |] }t|ttf VqdS)N)rr r).0frrr 6sz._normal_ordered_form_factor..recursive_limit_recursive_depth independent)rlenanyris_annihilationstrnamerrr rr rrexpandr ) productr!rr rrrcurrentnextkey_1key_2cexprrrr_normal_ordered_form_factor&sd       ) r/cCsHg}|jD]}t|trt||||d}||q||qt|S)z Helper function for normal_ordered_form: loop through each term in an addition expression and call _normal_ordered_form_factor to perform the factor to an normally ordered expression. r)r rrr/rr)r.r!rr new_termstermnew_termrrr_normal_ordered_form_termsjs    r3cCsN||kr td|St|trt||||dSt|tr%t||||dS|S)aWrite an expression with bosonic or fermionic operators on normal ordered form, where each term is normally ordered. Note that this normal ordered form is equivalent to the original expression. Parameters ========== expr : expression The expression write on normal ordered form. independent : bool (default False) Whether to consider operator with different names as operating in different Hilbert spaces. If False, the (anti-)commutation is left explicit. recursive_limit : int (default 10) The number of allowed recursive applications of the function. Examples ======== >>> from sympy.physics.quantum import Dagger >>> from sympy.physics.quantum.boson import BosonOp >>> from sympy.physics.quantum.operatorordering import normal_ordered_form >>> a = BosonOp("a") >>> normal_ordered_form(a * Dagger(a)) 1 + Dagger(a)*a Too many recursions, abortingr)warningswarnrrr3rr/)r.r!rr rrrr s    cCst|}d}g}|t|dkrt||trl||jrlt||dts-|||n||djr<|||n||jd||djdkrZ|||d||n |||d|||d7}net||tr||jrt||dts|||nH||djr|||n9||jd||djdkr|||d ||n|||d |||d7}n||||d7}|t|dks|t|dkr||d||kr|St| }t |||ddS)z Helper function for normal_order: Normal order a multiplication expression with bosonic or fermionic operators. In general the resulting operator expression will not be equivalent to original product. rr rrr ) rr"rrr$rr r rr'r )r(rr rrrr.rrr_normal_order_factorsL    % r8cCsFg}|jD]}t|trt|||d}||q||qt|S)z Helper function for normal_order: look through each term in an addition expression and call _normal_order_factor to perform the normal ordering on the factors. r7)r rrr8rr)r.rr r0r1r2rrr_normal_order_termss    r9cCsJ||kr td|St|trt|||dSt|tr#t|||dS|S)aNormal order an expression with bosonic or fermionic operators. Note that this normal order is not equivalent to the original expression, but the creation and annihilation operators in each term in expr is reordered so that the expression becomes normal ordered. Parameters ========== expr : expression The expression to normal order. recursive_limit : int (default 10) The number of allowed recursive applications of the function. Examples ======== >>> from sympy.physics.quantum import Dagger >>> from sympy.physics.quantum.boson import BosonOp >>> from sympy.physics.quantum.operatorordering import normal_order >>> a = BosonOp("a") >>> normal_order(a * Dagger(a)) Dagger(a)*a r4r7)r5r6rrr9rr8)r.rr rrrr s   )Frr)rr)__doc__r5sympy.core.addrsympy.core.mulrsympy.core.numbersrsympy.core.powerrsympy.physics.quantumrrsympy.physics.quantum.bosonrsympy.physics.quantum.fermionr __all__rr/r3r r8r9r rrrrs2       D  / <