g.n dZddlZddlmZmZmZmZmZddlm Z ddl m Z ddl m Z mZmZmZmZmZmZmZmZmZddlmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#ddl$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*dd l+m,Z,m-Z-m.Z.m/Z/m0Z0dd l1m2Z2dd l3m4Z4dd l5m6Z6dd l7m8Z8ddl9m:Z:ddl;mm?Z?ddl@mAZAddlBmCZCddlDmEZEddlFmGZGe dZHddgiZIeHrddlHmJZJmKZKmLZLmMZMddlNmOZOmPZPmQZQeJjReCeJjRe:eMjRe:eJjRe2eMjRe2eKjRe2eLjRe2eJjRe8eMjRe8eKjRe8eLjRe8eJjRe<eKjRe<eJjRe=eKjRe=eJjReAeJjRe eJjReeJjReeJjRe-eJjRe,eJjReeJjRe0eJjRe.eJjRe/eJjReeJjReeJjReeJjReeJjReeJjReeJjReeJjReeJjRe eJjRe!eJjRe#eJjRe"eJjRe'eJjRe)eJjRe%eJjRe(eJjRe&eJjRe*eJjReeJjReeJjReeJjReeJjReeJjReeOjReCdZSeOjRe4dZSeQjReCdZSeQjRe4dZSePjRe4d1dZTeHrddlHmUZUn Gd d!ZUeGd"#Gd$d%eUe?ZVeGd"#Gd&d'eVZWeGd"#Gd(d)eVZXeGd"#Gd*d+eVZYd,ZZGd-d.eZ[eGd"#Gd/d0Z\dS)2zj The objects in this module allow the usage of the MatchPy pattern matching library on SymPy expressions. N)ListCallable NamedTupleAnyDict)_sympify) import_module) logsincostancotcscsecerfgamma uppergamma) acoshasinhatanhacothacschasechcoshsinhtanhcothsechcsch)atanacscasinacotacosasec)fresnelcfresnelserfcerfiEi)Add)Basic)Expr)Mul)Pow)Equality Unequality)Symbol)exp)Integral)srepr)doctest_depends_onmatchpy)*) OperationCommutativeOperationAssociativeOperationOneIdentityOperation)op_itercreate_operation_expressionop_lencTt|jdf|jdzS)Nriter_args operations ]/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/utilities/matchpy_connector.py_rH[s&Y_Q')IOA,>>???c*t|jSNrBrEs rGrHrH_sIO$$$rIc<dt|jdzS)NrAlenrDrEs rGrHrHcs3yq)****rIc*t|jSrKrMrEs rGrHrHgs9?###rITc&t||SrK)type) old_operation new_operands variable_names rGsympy_op_factoryrUks"tM""L11rI)WildcardceZdZdZdS)rVc>||_||_||_||_dSrK) min_count fixed_sizerToptional)self min_lengthrZrTr[s rG__init__zWildcard.__init__ts#'DN(DO!.D $DMMMrIN)__name__ __module__ __qualname__r^rIrGrVrVss# % % % % %rIrV)r7)modulesc|eZdZUeed<eed<ddZdZddZdZ e ddZ fd Z dd Z d Zd ZxZS) _WildAbstractr]rZNc |j}|j}|t|}tj|||t ||dSrK)r]rZrrVr^str)r\rTr[ assumptionsr]rZs rGr^z_WildAbstract.__init__sJ_ _  ))H$ JM8J8JHUUUUUrIcD|j|j|j|j|jdS)Nr]rZrYrTr[rjr\s rG __getstate__z_WildAbstract.__getstate__s+//!/    rIc V|||tj|||fi|SrK) _sanitizere__xnew__)clsrTr[rhs rG__new__z_WildAbstract.__new__s3 k3'''%c=(RRkRRRrIc|j|jfSrKrTr[rks rG__getnewargs__z_WildAbstract.__getnewargs__s!4=00rIc ,tj||fi|}|SrK)r2ro)rprTr[rhobjs rGroz_WildAbstract.__xnew__s oc=@@K@@ rIc|jr;t|j|j|j|jfzSt|j|j|jfzSrK)r[super_hashable_contentrYrZrT)r\ __class__s rGryz_WildAbstract._hashable_contentsh = g77,,..$.$/SWSegkgt1uu u77,,..$.$/SWSe1ff frIreturncJt||j|jS)Nrs)rQrTr[rks rG__copy__z_WildAbstract.__copy__s"tDzz(:T]SSSSrIc t|SrKrgrks rG__repr__z_WildAbstract.__repr__s4yyrIc|jSrKnamerks rG__str__z_WildAbstract.__str__s yrI)NN)r{re)r_r`raint__annotations__boolr^rlrqrt staticmethodroryr}rr __classcell__)rzs@rGrere{sOOOVVVV   SSSS111\ggggg TTTTrIreceZdZdZdZdS)WildDotrATNr_r`rar]rZrbrIrGrrsJJJJrIrceZdZdZdZdS)WildPlusrAFNrrbrIrGrrJJJJrIrceZdZdZdZdS)WildStarrFNrrbrIrGrrrrIrct|}tjdd|}tjdd|}tjdd|}|S)NzWildDot\('(\w+)'\)z\1zWildPlus\('(\w+)'\)z*\1zWildStar\('(\w+)'\))r5resub)exprss rG _get_sreprrsN d A $eQ//A %vq11A %vq11A HrIc$eZdZUeed<eed<dS)ReplacementInfo replacementinfoN)r_r`rarrrbrIrGrrs% IIIIIrIrc eZdZdZgddfdededefdZdeded e ffd Z d e d eded e ffd Z d e ded e ffdZ d e ded e ffdZ ggdfde dee dee deddf dZddefdZdS)Replacera 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._matcher.clear() >>> replacer.replace(eq) 4/3 Fcommon_constraintslambdifyrczt|_||_||_||_i|_dSrK)r7ManyToOneMatcher_matcher_common_constraint _lambdify_info _wildcards)r\rrrs rGr^zReplacer.__init__s60022 "4! /1rI lambda_strr{.cXtdt|tS)Nzfrom sympy import *)execevallocals)r\rs rG _get_lambdazReplacer._get_lambda s% "###J)))rIconstraint_exprcondition_templatec $d|tD}d|}t|}||}t |d|d|dS)Ncg|] }|j Srbr.0xs rG z3Replacer._get_custom_constraint..sFFFAFFFrI, lambda z: ())atomsrejoinrformatr7CustomConstraintr)r\rrwilds lambdaargsfullexpr conditions rG_get_custom_constraintzReplacer._get_custom_constraintsFF!6!6}!E!EFFFYYu%% o..&--h77 ''   BzBBiBBB C CEE ErIc.||dS)Nz ({}) != Falserr\rs rG_get_custom_constraint_nonfalsez(Replacer._get_custom_constraint_nonfalses**?OLLLrIc.||dS)Nz ({}) == Truerrs rG_get_custom_constraint_truez$Replacer._get_custom_constraint_trues**?NKKKrINrconditions_trueconditions_nonfalsect|}t|}jdd}fd|D}fd|D}||||tj|g|R} jrbddd|tDdt|} | } | }n<j d|tDjrt||}j| |dS)Nc:g|]}|Srb)rrcondr\s rGrz Replacer.add..#s:&P&P&P7;D , ,T 2 2&P&P&PrIc:g|]}|Srb)rrs rGrz Replacer.add..%s:*X*X*X;?D 0 0 6 6*X*X*XrIrrc3$K|] }|jV dSrKrrs rG zReplacer.add..+s$-X-Xaf-X-X-X-X-X-XrIz: c.i|]}t||Srbr)ris rG z Replacer.add../s #L#L#L!CFFA#L#L#LrI)rrextendr7PatternrrrrerrrupdaterVrrradd) r\rrrrr constraintsconstraint_conditions_trueconstraint_conditions_nonfalsepatternr lambda_exprs ` rGrz Replacer.adds~~{++ -aaa0 &P&P&P&P?N&P&P&P"*X*X*X*XCV*X*X*X&56669:::/$5555 > Nv499-X-Xdjj>W>W-X-X-X#Y#Yvv]ghs]t]tvvJ**:66K%KK O " "#L#Ltzz(7K7K#L#L#L M M M : =)+t<.Is)6g6g6gQUQRTUtq7I16g6g6grIrArb)r7preorder_iter_with_positionnextrCrmatchrrappendrrxreplaceitems functionsreplace StopIteration) r\ expressionrinfosreplaced replace_countsubexprposreplacement_datasubstrresults ` rGrzReplacer.replace4s  IMM]Y-F-FH ' C CJ O O   .24 8K8KG8T8T3U3U.V.V+$ez7&6&B  %5%:;;;;&6 ~i!,!5!5u!5!5!,!5!56g6g6g6gY^YdYdYfYf6g6g6g!h!h!(!2!:!::sF!S!SJ#HE$D Q M+ IMM]Y-F-F, : u$ $ sCD DD)r)r_r`ra__doc__listrr^rgrr-rrrrrrrrrrbrIrGrrs66p35u[`22422TX2222*c*hsDy.A****EdEPSEX`adfjajXkEEEEMtMQTVZQZH[MMMML4LHSRVYDWLLLLJL.0d000DJ0!%d08;0GK0000,  S      rIr)T)]rrtypingrrrrrsympy.core.sympifyrsympy.externalr sympy.functionsr r r r rrrrrr%sympy.functions.elementary.hyperbolicrrrrrrrrrrrr(sympy.functions.elementary.trigonometricr r!r"r#r$r%'sympy.functions.special.error_functionsr&r'r(r)r*sympy.core.addr+sympy.core.basicr,sympy.core.exprr-sympy.core.mulr.sympy.core.powerr/sympy.core.relationalr0r1sympy.core.symbolr2&sympy.functions.elementary.exponentialr3sympy.integrals.integralsr4sympy.printing.reprr5sympy.utilities.decoratorr6r7__doctest_requires__r9r:r;r<matchpy.expressions.functionsr=r>r?registerrHrUrVrerrrrrrrbrIrGr s  88888888888888''''''((((((WWWWWWWWWWWWWWWWWWWWWWWW~~~~~~~~~~~~~~~~~~~~~~~~~~~~WWWWWWWWWWWWWWWWVVVVVVVVVVVVVV""""""  88888888$$$$$$666666......%%%%%%888888 - " " , L2ccccccccccccZZZZZZZZZZIx   Is!!#&&&Is!!#&&&!!#&&&!!#&&&Is!!#&&&!!#&&&!!#&&&Ix   !!(+++Iz"""!!*---IsIsIuIz"""Ix   Ix   IsIrItItIsIsIsIsIsIsItItItItItItItItItItItItIuIuIuIuIuIuWh@@ @We%%%V_X+++V_U$$$* )%00222102 %       %%%%%%%%L)))-----Hf--*)-`L)))m*) L)))}*) L)))}*)    j L)))HHHHHHH*)HHHrI