Edd (ddlmZddlmZddlmZmZddlmZddl m Z ddl m Z ddl mZddlmZdd lmZdd lmZdd lmZdd lZdd lZdd lmZedZer:ddlmZmZddlm Z m!Z!m"Z"ddl#m$Z$m%Z%eddZ&e!eZ'GddZ(eddZ)eddZ*edddZ+edddZ,eddZ-d S) ) import_module)doctest_depends_on)IntegerFloat)Add)Function)Mul)E)Pow)S)Integral)expN)powsimpmatchpy)ManyToOneReplacerManyToOneMatcher)rubi_exprubi_unevaluated_expr process_trig)op_iterop_len)r)modulescddlm}ddlm}ddlm}ddlm}ddlm }ddl m }ddl m }dd lm}dd lm}dd lm} dd lm} dd lm} ddlm} ddlm} ddlm}ddlm}ddl m!}g}||z }||z }||z }||z }||z }||z }||z }||z }||z }||z }|| z }|| z }|| z }|| z }|| z }||z }||z }tE|}||fS)a9 Returns rubi ManyToOneReplacer by adding all rules from different modules. Uncomment the lines to add integration capabilities of that module. Currently, there are parsing issues with special_function, derivative and miscellaneous_integration. Hence they are commented. r)integrand_simplification)linear_products)quadratic_products)binomial_products)trinomial_products)miscellaneous_algebraic) exponential) logarithms)sine)tangent)secant)miscellaneous_trig) inverse_trig) hyperbolic)inverse_hyperbolic)special_functions)miscellaneous_integration)#3sympy.integrals.rubi.rules.integrand_simplificationr*sympy.integrals.rubi.rules.linear_productsr-sympy.integrals.rubi.rules.quadratic_productsr,sympy.integrals.rubi.rules.binomial_productsr-sympy.integrals.rubi.rules.trinomial_productsr2sympy.integrals.rubi.rules.miscellaneous_algebraicr&sympy.integrals.rubi.rules.exponentialr %sympy.integrals.rubi.rules.logarithmsr!sympy.integrals.rubi.rules.siner""sympy.integrals.rubi.rules.tangentr#!sympy.integrals.rubi.rules.secantr$-sympy.integrals.rubi.rules.miscellaneous_trigr%'sympy.integrals.rubi.rules.inverse_trigr&%sympy.integrals.rubi.rules.hyperbolicr'-sympy.integrals.rubi.rules.inverse_hyperbolicr(,sympy.integrals.rubi.rules.special_functionsr)4sympy.integrals.rubi.rules.miscellaneous_integrationr*r)rrrrrrr r!r"r#r$r%r&r'r(r)r*rulesrubis =lib/python3.11/site-packages/sympy/integrals/rubi/rubimain.pyget_rubi_objectr?s a`````NNNNNNTTTTTTRRRRRRTTTTTT^^^^^^FFFFFFDDDDDD888888>>>>>><<<<<<TTTTTTHHHHHHDDDDDDTTTTTTRRRRRR cbbbbb ))+++ """ ##%%% ""$$$ ##%%% ((***   ""$$$    ##%%%   ##%%% **,,, %(U{c:eZdZdZdZdZdZdZdZdZ dZ dS) LoadRubiReplacerz- Class trick to load RUBI only once. NcttddStj tjSt|}d|_d|_|t_|S)NzMatchPy library not found)rprintrB _instanceobject__new___rubi_rules)clsobjs r>rGzLoadRubiReplacer.__new__Xs_   - . . .4  % .#- -nnS!!  %(" r@c`|j|jSt\}}||_||_|SN)rHr?rI)selfr=r<s r>loadzLoadRubiReplacer.loadds6 : : %'' e   r@cddl}|}t|d5}|||ddddS#1swxYwYdSNrwb)picklerOopendump)rNfilenamerSr=fouts r> to_picklezLoadRubiReplacer.to_picklels yy{{ (D ! ! $T KKd # # # $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $A  AAcddl}|}t|d5}|||ddddS#1swxYwYdSrQ)dillrOrTrU)rNrVr[r=rWs r>to_dillzLoadRubiReplacer.to_dillrs yy{{ (D ! ! "T IIdD ! ! ! " " " " " " " " " " " " " " " " " "rYcddl}t|d5}|||_dddn #1swxYwY|jSNrrb)rSrTrOrH)rNrVrSfins r> from_picklezLoadRubiReplacer.from_picklexs (D ! ! *SS))DJ * * * * * * * * * * * * * * *z<AAcddl}t|d5}|||_dddn #1swxYwY|jSr^)r[rTrOrH)rNrVr[r`s r> from_dillzLoadRubiReplacer.from_dill~s (D ! ! (S3DJ ( ( ( ( ( ( ( ( ( ( ( ( ( ( (zrb) __name__ __module__ __qualname____doc__rErGrOrXr\rardr@r>rBrBQsI   $$$ """  r@rBcz|tr |tt}|S)a Rubi's `rubi_exp` need to be replaced back to SymPy's general `exp`. Examples ======== >>> from sympy import Function, E, Integral >>> from sympy.integrals.rubi.rubimain import process_final_integral >>> from sympy.integrals.rubi.utility_function import rubi_unevaluated_expr >>> from sympy.abc import a, x >>> _E = rubi_unevaluated_expr(E) >>> process_final_integral(Integral(a, x)) Integral(a, x) >>> process_final_integral(_E**5) exp(5) )has_Ereplacer )exprs r>process_final_integralros.$ xx||#||B"" Kr@c&g}g}t|trw|jD]O}t|ttt fr||:||Ptt|t|zS|S)a@ This function is needed to preprocess an expression as done in matchpy `x^a*x^b` in matchpy auotmatically transforms to `x^(a+b)` Examples ======== >>> from sympy.integrals.rubi.rubimain import rubi_powsimp >>> from sympy.abc import a, b, x >>> rubi_powsimp(x**a*x**b) x**(a + b) ) isinstancer argsr rsym_expappendr)rnlst_pow lst_non_powis r> rubi_powsimprxsGK$8 & &A!c8W566 &q!!!!""1%%%%sG}%%c;&777 Kr@Fc6t}|tt}t |}t |}t|ttttfrt||zSt|trAd}|jD](}||t||z })t!|St#t||}t!|S)aW Rule based algorithm for integration. Integrates the expression by applying transformation rules to the expression. Returns `Integrate` if an expression cannot be integrated. Parameters ========== expr : integrand expression var : variable of integration Returns Integral object if unable to integrate. r)rBrOrmrsrrrxrqintrfloatrr rrrr routil_rubi_integrate)rnvar showstepsr=resultsexs r>rubi_integraters    " " $ $D << * *D   D   D$gue455wws{$/) 7 7B t||HR$5$566 6GG%g...!(4"5"566G !' * **r@ ctt|}|tt }t |D]&}|dfd}||kr|cS'|S)Nc,t|tSrM)rqr )xs r>z%util_rubi_integrate..sjH--r@c2|dS)Nr) max_count)rm)rr=s r>rz%util_rubi_integrate..sdll1l33r@)rBrOrrmrsrrange)rnr~max_looprwrr=s @r>r|r|s    " " $ $D   D << * *D 8__,, - - 3 3 3 3   7? NNN  Nr@ct}|j}|t||}|D]\}}t dt t j|t j|\}}t d|t d|t dttjd|d d} t |j | dz t |t dS) z Prints the list or rules which match to `expr`. Parameters ========== expr : integrand expression var : variable of integration zRule matching: z On line:  zPattern matching: z ^\s*rule(\d+)rN) rBmatchermatchr rDinspect getsourcefilegetsourcelinesjoinrzregrouppatterns) rnr}r=rmiterfunecodelinenopattnos r>get_matching_rule_definitionrs   DlG MM(4-- . .E  Q     g#C(()))-c22 f k6""" diioo "###RX.Q88>>qAABB gvax())) a   r@)F)Fr).sympy.externalrsympy.utilities.decoratorr sympy.corerrsympy.core.addrsympy.core.functionrsympy.core.mulr sympy.core.numbersr sympy.core.powerr sympy.core.singletonr sympy.integrals.integralsr sympy.functionsrrsrrsympy.simplify.powsimprrrr%sympy.integrals.rubi.utility_functionrrr!sympy.utilities.matchpy_connectorrrr?rlrBrorxrr|rrir@r>rs((((((888888%%%%%%%%(((((( """"""......****** ****** - " " =";;;;;;;;BAAAAAAA ---33.-3h  q ! !B11111111hL)))*),L)))*)4L)))+++*)+<L)))   *) L)))*)r@