U ˜9%eT'ã@sdZddlZddlmZmZddlmZddlmZddl m Z m Z m Z m Z mZmZmZmZmZmZddlmZmZmZmZmZmZmZmZmZmZmZm Z ddl!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'dd l(m)Z)m*Z*m+Z+m,Z,m-Z-dd l.m/Z/dd l0m1Z1dd l2m3Z3dd l4m5Z5ddl6m7Z7ddl8m9Z9m:Z:ddl;mZ>ddl?m@Z@ddlAmBZBddlCmDZDedƒZEeEràddlEmFZFmGZGmHZHmIZIddlJmKZKmLZLmMZMeF Ne@¡eF Ne7¡eI Ne7¡eF Ne/¡eI Ne/¡eG Ne/¡eH Ne/¡eF Ne5¡eI Ne5¡eG Ne5¡eH Ne5¡eF Ne9¡eG Ne9¡eF Ne:¡eG Ne:¡eF Ne>¡eF Ne ¡eF Ne¡eF Ne¡eF Ne*¡eF Ne)¡eF Ne¡eF Ne-¡eF Ne+¡eF Ne,¡eF Ne ¡eF Ne ¡eF Ne ¡eF Ne¡eF Ne¡eF Ne¡eF Ne¡eF Ne¡eF Ne¡eF Ne¡eF Ne ¡eF Ne¡eF Ne$¡eF Ne&¡eF Ne"¡eF Ne%¡eF Ne#¡eF Ne'¡eF Ne¡eF Ne¡eF Ne¡eF Ne¡eF Ne¡eF Ne¡eK Ne@¡dd„ƒZOeK Ne1¡dd„ƒZOeM Ne@¡dd„ƒZOeM Ne1¡dd„ƒZOeL Ne1¡d1dd„ƒZPeErôdd lEmQZQnGd!d"„d"ƒZQeDd#d$Gd%d&„d&eQe<ƒƒZReDd#d$Gd'd(„d(eRƒƒZSeDd#d$Gd)d*„d*eRƒƒZTeDd#d$Gd+d,„d,eRƒƒZUd-d.„ZVeDd#d$Gd/d0„d0ƒƒZWdS)2zj The objects in this module allow the usage of the MatchPy pattern matching library on SymPy expressions. éN)ÚListÚCallable)Ú_sympify)Ú import_module) ÚlogÚsinÚcosÚtanÚcotÚcscÚsecÚerfÚgammaÚ uppergamma) ÚacoshÚasinhÚatanhÚacothÚacschÚasechÚcoshÚsinhÚtanhÚcothÚsechÚcsch)ÚatanÚacscÚasinÚacotÚacosÚasec)ÚfresnelcÚfresnelsÚerfcÚerfiÚEi)ÚAdd)ÚBasic)ÚExpr)ÚMul)ÚPow)ÚEqualityÚ Unequality)ÚSymbol)Úexp)ÚIntegral)Úsrepr)Údoctest_depends_onÚmatchpy)Ú OperationÚCommutativeOperationÚAssociativeOperationÚOneIdentityOperation)Úop_iterÚcreate_operation_expressionÚop_lencCst|jdf|jdƒS)Nré©ÚiterÚ_args©Z operation©r@ú`/var/www/html/Darija-Ai-API/env/lib/python3.8/site-packages/sympy/utilities/matchpy_connector.pyÚ_VsrBcCs t|jƒS©Nr<r?r@r@rArBZscCsdt|jdƒS)Nr;©Úlenr>r?r@r@rArB^scCs t|jƒSrCrDr?r@r@rArBbsTcCs t|ƒ|ŽSrC)Útype)Z old_operationZ new_operandsÚ variable_namer@r@rAÚsympy_op_factoryfsrH)ÚWildcardc@seZdZdd„ZdS)rIcCs||_||_||_||_dSrC)Ú min_countÚ fixed_sizerGÚoptional)ÚselfÚ min_lengthrKrGrLr@r@rAÚ__init__oszWildcard.__init__N)Ú__name__Ú __module__Ú __qualname__rOr@r@r@rArInsrI)r3)Úmodulescs~eZdZUeed<eed<ddd„Zdd„Zddd „Zd d „Z e dd d „ƒZ ‡fdd„Z ddœdd„Z dd„Zdd„Z‡ZS)Ú _WildAbstractrNrKNcKs6|j}|j}|dk rt|ƒ}t |||t|ƒ|¡dSrC)rNrKrrIrOÚstr)rMrGrLÚ assumptionsrNrKr@r@rArO{s z_WildAbstract.__init__cCs|j|j|j|j|jdœS)N©rNrKrJrGrLrW©rMr@r@rAÚ __getstate__‚s ûz_WildAbstract.__getstate__cKs| ||¡tj|||f|ŽSrC)Ú _sanitizerTÚ__xnew__)ÚclsrGrLrVr@r@rAÚ__new__‹s z_WildAbstract.__new__cCs |j|jfSrC©rGrLrXr@r@rAÚ__getnewargs__sz_WildAbstract.__getnewargs__cKstj||f|Ž}|SrC)r.r[)r\rGrLrVÚobjr@r@rAr[’sz_WildAbstract.__xnew__csB|jr$tƒ ¡|j|j|j|jfStƒ ¡|j|j|jfSdSrC)rLÚsuperÚ_hashable_contentrJrKrGrX©Ú __class__r@rArb—sz_WildAbstract._hashable_content)ÚreturncCst|ƒ|j|jdS)Nr^)rFrGrLrXr@r@rAÚ__copy__sz_WildAbstract.__copy__cCst|ƒSrC)rUrXr@r@rAÚ__repr__ sz_WildAbstract.__repr__cCs|jSrC©ÚnamerXr@r@rAÚ__str__£sz_WildAbstract.__str__)NN)NN)NN)rPrQrRÚintÚ__annotations__ÚboolrOrYr]r_Ú staticmethodr[rbrfrgrjÚ __classcell__r@r@rcrArTvs     rTc@seZdZdZdZdS)ÚWildDotr;TN©rPrQrRrNrKr@r@r@rArp§srpc@seZdZdZdZdS)ÚWildPlusr;FNrqr@r@r@rArr­srrc@seZdZdZdZdS)ÚWildStarrFNrqr@r@r@rArs³srscCs6t|ƒ}t dd|¡}t dd|¡}t dd|¡}|S)NzWildDot\('(\w+)'\)z\1zWildPlus\('(\w+)'\)z*\1zWildStar\('(\w+)'\))r1ÚreÚsub)ÚexprÚsr@r@rAÚ _get_srepr¹s rxc@s¸eZdZdZgfedœdd„Zeedefdœdd„Z eeedefd œd d „Z eedefd œd d„Z eedefd œdd„Z ggfeee ee eddœdd„Zeedœdd„ZdS)ÚReplacera  Replacer object to perform multiple pattern matching and subexpression replacements in SymPy expressions. Examples ======== Example to construct a simple first degree equation solver: >>> from sympy.utilities.matchpy_connector import WildDot, Replacer >>> from sympy import Equality, Symbol >>> x = Symbol("x") >>> a_ = WildDot("a_", optional=1) >>> b_ = WildDot("b_", optional=0) The lines above have defined two wildcards, ``a_`` and ``b_``, the coefficients of the equation `a x + b = 0`. The optional values specified indicate which expression to return in case no match is found, they are necessary in equations like `a x = 0` and `x + b = 0`. Create two constraints to make sure that ``a_`` and ``b_`` will not match any expression containing ``x``: >>> from matchpy import CustomConstraint >>> free_x_a = CustomConstraint(lambda a_: not a_.has(x)) >>> free_x_b = CustomConstraint(lambda b_: not b_.has(x)) Now create the rule replacer with the constraints: >>> replacer = Replacer(common_constraints=[free_x_a, free_x_b]) Add the matching rule: >>> replacer.add(Equality(a_*x + b_, 0), -b_/a_) Let's try it: >>> replacer.replace(Equality(3*x + 4, 0)) -4/3 Notice that it will not match equations expressed with other patterns: >>> eq = Equality(3*x, 4) >>> replacer.replace(eq) Eq(3*x, 4) In order to extend the matching patterns, define another one (we also need to clear the cache, because the previous result has already been memorized and the pattern matcher will not iterate again if given the same expression) >>> replacer.add(Equality(a_*x, b_), b_/a_) >>> replacer._replacer.matcher.clear() >>> replacer.replace(eq) 4/3 )Úcommon_constraintscCst ¡|_||_dSrC)r3ZManyToOneReplacerÚ _replacerÚ_common_constraint)rMrzr@r@rArOûs zReplacer.__init__.)Ú lambda_strrecCstdƒt|tƒƒS)Nzfrom sympy import *)ÚexecÚevalÚlocals)rMr}r@r@rAÚ _get_lambdaÿszReplacer._get_lambda)Úconstraint_exprÚcondition_templaterec CsNdd„| t¡Dƒ}d |¡}t|ƒ}| |¡}t | d|›d|›d¡¡S)NcSsg|] }|j‘qSr@rh©Ú.0Úxr@r@rAÚ sz3Replacer._get_custom_constraint..ú, úlambda z: (ú))ÚatomsrTÚjoinrxÚformatr3ZCustomConstraintr)rMr‚rƒZwildsZ lambdaargsZfullexprÚ conditionr@r@rAÚ_get_custom_constraints  ÿzReplacer._get_custom_constraint)r‚recCs | |d¡S)Nz ({}) != False©r©rMr‚r@r@rAÚ_get_custom_constraint_nonfalse sz(Replacer._get_custom_constraint_nonfalsecCs | |d¡S)Nz ({}) == Truerr‘r@r@rAÚ_get_custom_constraint_truesz$Replacer._get_custom_constraint_trueN)rvÚresultÚconditions_trueÚconditions_nonfalserec s®t|ƒ}t|ƒ}dd dd„| t¡Dƒ¡›dt|ƒ›}ˆ |¡}ˆjdd…}‡fdd„|Dƒ}‡fdd„|Dƒ} | |¡| | ¡ˆj  t   t j |f|žŽ|¡¡dS) Nr‰rˆcss|] }|jVqdSrCrhr„r@r@rAÚ szReplacer.add..z: csg|]}ˆ |¡‘qSr@)r“©r…ZcondrXr@rAr‡sz Replacer.add..csg|]}ˆ |¡‘qSr@)r’r˜rXr@rAr‡s) rrŒr‹rTrxrr|Úextendr{Úaddr3ZReplacementRuleÚPattern) rMrvr”r•r–r}Z lambda_exprÚ constraintsZconstraint_conditions_trueZconstraint_conditions_nonfalser@rXrAršs *  ÿ ÿ  ÿz Replacer.add)rvrecCs |j |¡SrC)r{Úreplace)rMrvr@r@rAr szReplacer.replace)rPrQrRÚ__doc__ÚlistrOrUrr)rrr’r“rršrr@r@r@rAryÁs8$ry)T)XržrtÚtypingrrZsympy.core.sympifyrZsympy.externalrZsympy.functionsrrrr r r r r rrZ%sympy.functions.elementary.hyperbolicrrrrrrrrrrrrZ(sympy.functions.elementary.trigonometricrrrrr r!Z'sympy.functions.special.error_functionsr"r#r$r%r&Zsympy.core.addr'Zsympy.core.basicr(Zsympy.core.exprr)Zsympy.core.mulr*Zsympy.core.powerr+Zsympy.core.relationalr,r-Zsympy.core.symbolr.Z&sympy.functions.elementary.exponentialr/Zsympy.integrals.integralsr0Zsympy.printing.reprr1Zsympy.utilities.decoratorr2r3r4r5r6r7Zmatchpy.expressions.functionsr8r9r:ÚregisterrBrHrIrTrprrrsrxryr@r@r@rAÚsÀ  08                                                                 0