o *ήcd'@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@ddlAmBZBddlCmDZDedZEeErddlEmFZFmGZGmHZHmIZIddlJmKZKmLZLmMZMeFNe@eFNe7eINe7eFNe/eINe/eGNe/eHNe/eFNe5eINe5eGNe5eHNe5eFNe9eGNe9eFNe:eGNe:eFNe>eFNe eFNeeFNeeFNe*eFNe)eFNeeFNe-eFNe+eFNe,eFNe eFNe eFNe eFNeeFNeeFNeeFNeeFNeeFNeeFNeeFNe eFNeeFNe$eFNe&eFNe"eFNe%eFNe#eFNe'eFNeeFNeeFNeeFNeeFNeeFNeeKNe@ddZOeKNe1ddZOeMNe@ddZOeMNe1ddZOeLNe1d1ddZPeErdd lEmQZQnGd!d"d"ZQeDd#d$Gd%d&d&eQe<ZReDd#d$Gd'd(d(eRZSeDd#d$Gd)d*d*eRZTeDd#d$Gd+d,d,eRZUd-d.ZVeDd#d$Gd/d0d0ZWdS)2zj The objects in this module allow the usage of the MatchPy pattern matching library on SymPy expressions. N)ListCallable)_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 operationrAH/tmp/pip-target-vg8gfxp4/lib/python/sympy/utilities/matchpy_connector.py_VsrCcC t|jSNr<r?rArArBrCZ cCsdt|jdS)Nr;lenr>r?rArArBrC^scCrDrErGr?rArArBrCbrFTcCs t||SrE)type) old_operation new_operands variable_namerArArBsympy_op_factoryfs rM)Wildcardc@seZdZddZdS)rNcCs||_||_||_||_dSrE) min_count fixed_sizerLoptional)self min_lengthrPrLrQrArArB__init__os zWildcard.__init__N)__name__ __module__ __qualname__rTrArArArBrNns rN)r3)modulescszeZdZUeed<eed<dddZddZddd Zd d Z e dd d Z fddZ dddZ ddZddZZS) _WildAbstractrSrPNcKs6|j}|j}|durt|}t|||t||dSrE)rSrPrrNrTstr)rRrLrQ assumptionsrSrPrArArBrT{s z_WildAbstract.__init__cCs|j|j|j|j|jdS)NrSrPrOrLrQr\rRrArArB __getstate__s z_WildAbstract.__getstate__cKs"|||tj|||fi|SrE) _sanitizerY__xnew__)clsrLrQr[rArArB__new__s z_WildAbstract.__new__cCs |j|jfSrErLrQr]rArArB__getnewargs__ z_WildAbstract.__getnewargs__cKstj||fi|}|SrE)r.r`)rarLrQr[objrArArBr`sz_WildAbstract.__xnew__cs>|jrt|j|j|j|jfSt|j|j|jfSrE)rQsuper_hashable_contentrOrPrLr] __class__rArBrhsz_WildAbstract._hashable_contentreturncCst||j|jdS)Nrc)rIrLrQr]rArArB__copy__sz_WildAbstract.__copy__cCst|SrE)rZr]rArArB__repr__sz_WildAbstract.__repr__cC|jSrEnamer]rArArB__str__sz_WildAbstract.__str__)NN)rkrY)rUrVrWint__annotations__boolrTr^rbrd staticmethodr`rhrlrmrq __classcell__rArArirBrYvs      rYc@eZdZdZdZdS)WildDotr;TNrUrVrWrSrPrArArArBrxrxc@rw)WildPlusr;FNryrArArArBr{rzr{c@rw)WildStarrFNryrArArArBr|rzr|cCs6t|}tdd|}tdd|}tdd|}|S)NzWildDot\('(\w+)'\)z\1zWildPlus\('(\w+)'\)z*\1zWildStar\('(\w+)'\))r1resub)exprsrArArB _get_sreprs rc @seZdZdZgfdefddZdededeffdd Z d ed ededeffd d Z d ededeffddZ d ededeffddZ ggfdedede ede eddf ddZdedefddZdS)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._replacer.matcher.clear() >>> replacer.replace(eq) 4/3 common_constraintscCst|_||_dSrE)r3ManyToOneReplacer _replacer_common_constraint)rRrrArArBrTs  zReplacer.__init__ lambda_strrk.cCstdt|tS)Nzfrom sympy import *)execevallocals)rRrrArArB _get_lambdas zReplacer._get_lambdaconstraint_exprcondition_templatec CsRttdd|t}d|}t|}||}t| d|d|dS)NcSrnrEroxrArArBz1Replacer._get_custom_constraint.., lambda z: ()) listmapatomsrYjoinrformatr3CustomConstraintr)rRrrwilds lambdaargsfullexpr conditionrArArB_get_custom_constraints  zReplacer._get_custom_constraintcC ||dS)Nz ({}) != FalserrRrrArArB_get_custom_constraint_nonfalse rez(Replacer._get_custom_constraint_nonfalsecCr)Nz ({}) == TruerrrArArB_get_custom_constraint_truerez$Replacer._get_custom_constraint_truerresultconditions_trueconditions_nonfalseNc st|}t|}ddtdd|tdt|}|}jdd}fdd|D}fdd|D} |||| j t t j |g|R|dS) NrrcSrnrErorrArArBrrzReplacer.add..z: cg|]}|qSrA)r.0condr]rArB  z Replacer.add..crrA)rrr]rArBrr)rrrrrYrrrextendraddr3ReplacementRulePattern) rRrrrrr lambda_expr constraintsconstraint_conditions_trueconstraint_conditions_nonfalserAr]rBrs *     z Replacer.addcCs |j|SrE)rreplace)rRrrArArBr rezReplacer.replace)rUrVrW__doc__rrTrZrr)rrrrrrrrArArArBrs8,r)T)Xrr}typingrrsympy.core.sympifyrsympy.externalrsympy.functionsrrrr r r r r rr%sympy.functions.elementary.hyperbolicrrrrrrrrrrrr(sympy.functions.elementary.trigonometricrrrrr r!'sympy.functions.special.error_functionsr"r#r$r%r&sympy.core.addr'sympy.core.basicr(sympy.core.exprr)sympy.core.mulr*sympy.core.powerr+sympy.core.relationalr,r-sympy.core.symbolr.&sympy.functions.elementary.exponentialr/sympy.integrals.integralsr0sympy.printing.reprr1sympy.utilities.decoratorr2r3r4r5r6r7matchpy.expressions.functionsr8r9r:registerrCrMrNrYrxr{r|rrrArArArBs  08                                                                 0