o ݹi.@sdZddlZddlmZmZmZmZmZddlm Z ddl m Z ddl m Z mZmZmZmZmZmZmZmZmZddlmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#ddl$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*dd l+m,Z,m-Z-m.Z.m/Z/m0Z0dd l1m2Z2dd l3m4Z4dd l5m6Z6dd l7m8Z8ddl9m:Z:ddl;mm?Z?ddl@mAZAddlBmCZCddlDmEZEddlFmGZGe dZHddgiZIeHrddlHmJZJmKZKmLZLmMZMddlNmOZOmPZPmQZQeJReCeJRe:eMRe:eJRe2eMRe2eKRe2eLRe2eJRe8eMRe8eKRe8eLRe8eJRe<eKRe<eJRe=eKRe=eJReAeJRe eJReeJReeJRe-eJRe,eJReeJRe0eJRe.eJRe/eJReeJReeJReeJReeJReeJReeJReeJReeJRe eJRe!eJRe#eJRe"eJRe'eJRe)eJRe%eJRe(eJRe&eJRe*eJReeJReeJReeJReeJReeJReeOReCddZSeORe4ddZSeQReCddZSeQRe4ddZSePRe4d4dd ZTeHrdd!lHmUZUnGd"d#d#ZUeGd$d%Gd&d'd'eUe?ZVeGd$d%Gd(d)d)eVZWeGd$d%Gd*d+d+eVZXeGd$d%Gd,d-d-eVZYd.d/ZZGd0d1d1eZ[eGd$d%Gd2d3d3Z\dS)5zj 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_lencCst|jdf|jdS)Nriter_args operationrE^/home/ubuntu/veenaModal/venv/lib/python3.10/site-packages/sympy/utilities/matchpy_connector.py_[srGcC t|jSNr@rCrErErFrG_ cCsdt|jdS)Nr?lenrBrCrErErFrGcscCrHrIrKrCrErErFrGgrJTcCs t||SrI)type) old_operation new_operands variable_namerErErFsympy_op_factoryks rQ)Wildcardc@seZdZddZdS)rRcCs||_||_||_||_dSrI) min_count fixed_sizerPoptional)self min_lengthrTrPrUrErErF__init__ts zWildcard.__init__N)__name__ __module__ __qualname__rXrErErErFrRss rR)r6)modulescszeZdZUeed<eed<dddZddZddd Zd d Z e dd d Z fddZ dddZ ddZddZZS) _WildAbstractrWrTNcKs6|j}|j}|durt|}t|||t||dSrI)rWrTrrRrXstr)rVrPrU assumptionsrWrTrErErFrXs z_WildAbstract.__init__cCs|j|j|j|j|jdS)NrWrTrSrPrUr`rVrErErF __getstate__s z_WildAbstract.__getstate__cKs"|||tj|||fi|SrI) _sanitizer]__xnew__)clsrPrUr_rErErF__new__s z_WildAbstract.__new__cCs |j|jfSrIrPrUrarErErF__getnewargs__ z_WildAbstract.__getnewargs__cKstj||fi|}|SrI)r1rd)rerPrUr_objrErErFrdsz_WildAbstract.__xnew__cs>|jrt|j|j|j|jfSt|j|j|jfSrI)rUsuper_hashable_contentrSrTrPra __class__rErFrlsz_WildAbstract._hashable_contentreturncCst||j|jdS)Nrg)rMrPrUrarErErF__copy__sz_WildAbstract.__copy__cCst|SrIr^rarErErF__repr__sz_WildAbstract.__repr__cCs|jSrInamerarErErF__str__sz_WildAbstract.__str__)NN)ror])rYrZr[int__annotations__boolrXrbrfrh staticmethodrdrlrprrru __classcell__rErErmrFr]{s      r]c@eZdZdZdZdS)WildDotr?TNrYrZr[rWrTrErErErFr|r|c@r{)WildPlusr?FNr}rErErErFrr~rc@r{)WildStarrFNr}rErErErFrr~rcCs6t|}tdd|}tdd|}tdd|}|S)NzWildDot\('(\w+)'\)z\1zWildPlus\('(\w+)'\)z*\1zWildStar\('(\w+)'\))r4resub)exprsrErErF _get_sreprs rc@seZdZUeed<eed<dS)ReplacementInfo replacementinfoN)rYrZr[rrwrErErErFrs  rc @seZdZdZgddfdededefddZded ed e ffd d Z d e ded ed e ffddZ d e d ed e ffddZ d e d ed e ffddZ ggdfde dee dee ded df ddZddefddZdS) 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_constraintslambdifyrcCs&t|_||_||_||_i|_dSrI)r6ManyToOneMatcher_matcher_common_constraint _lambdify_info _wildcards)rVrrrrErErFrXs  zReplacer.__init__ lambda_strro.cCstdt|tS)Nzfrom sympy import *)execevallocals)rVrrErErF _get_lambda s zReplacer._get_lambdaconstraint_exprcondition_templatec CsNdd|tD}d|}t|}||}t|d|d|dS)NcSsg|]}|jqSrErs.0xrErErF sz3Replacer._get_custom_constraint.., lambda z: ())atomsr]joinrformatr6CustomConstraintr)rVrrwilds lambdaargsfullexpr conditionrErErF_get_custom_constraints  zReplacer._get_custom_constraintcC ||dS)Nz ({}) != FalserrVrrErErF_get_custom_constraint_nonfalseriz(Replacer._get_custom_constraint_nonfalsecCr)Nz ({}) == TruerrrErErF_get_custom_constraint_trueriz$Replacer._get_custom_constraint_trueNrconditions_trueconditions_nonfalsec st|}t|}jdd}fdd|D}fdd|D}||||tj|g|R} jrTdddd|tDdt |} | } | }nj d d |t Djrjt||}j| |dS) Ncg|]}|qSrE)rrcondrarErFr# z Replacer.add..crrE)rrrarErFr%rrrcss|]}|jVqdSrIrsrrErErF +szReplacer.add..z: cSsi|]}t||qSrErq)rirErErF /sz Replacer.add..)rrextendr6Patternrrrr]rrrupdaterRrrradd) rVrrrrr constraintsconstraint_conditions_trueconstraint_conditions_nonfalsepatternr lambda_exprrErarFrs(    *  z Replacer.add max_countc sg}d}d}|rt|dks||krtd}t|D]N\}}zAttj|\}} jr5|j} ||j n|} j rB| di| } n| fdd| D} tj ||| }d}Wn tyeYqw|d7}|rt|dks||ksjr{||fS|S)NTrFcsi|] \}}j||qSrE)r)rkvrarErFrIsz$Replacer.replace..r?rE)r6preorder_iter_with_positionnextrArmatchrrappendrrxreplaceitems functionsreplace StopIteration) rV expressionrinfosreplaced replace_countsubexprposreplacement_datasubstrresultrErarFr4s4 zReplacer.replace)r)rYrZr[__doc__listrxrXr^rr,rrrrrrrrvrrErErErFrs"8 r)T)]rrtypingrrrrrsympy.core.sympifyrsympy.externalrsympy.functionsr r r r r rrrrr%sympy.functions.elementary.hyperbolicrrrrrrrrrrrr(sympy.functions.elementary.trigonometricrr 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.relationalr/r0sympy.core.symbolr1&sympy.functions.elementary.exponentialr2sympy.integrals.integralsr3sympy.printing.reprr4sympy.utilities.decoratorr5r6__doctest_requires__r8r9r:r;matchpy.expressions.functionsr<r=r>registerrGrQrRr]r|rrrrrrErErErFs  08                                                                  0