MZdT' dZddlZddlmZmZddlmZddlmZddl 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@ddlAmBZBddlCmDZDedZEeErddlEmFZFmGZGmHZHmIZIddlJmKZKmLZLmMZMeFje@eFje7eIje7eFje/eIje/eGje/eHje/eFje5eIje5eGje5eHje5eFje9eGje9eFje:eGje:eFje>eFje eFjeeFjeeFje*eFje)eFjeeFje-eFje+eFje,eFje eFje eFje eFjeeFjeeFjeeFjeeFjeeFjeeFjeeFje eFjeeFje$eFje&eFje"eFje%eFje#eFje'eFjeeFjeeFjeeFjeeFjeeFjeeKje@dZOeKje1dZOeMje@dZOeMje1dZOeLje1d-dZPeErddlEmQZQn GddZQeDd !Gd"d#eQe<ZReDd !Gd$d%eRZSeDd !Gd&d'eRZTeDd !Gd(d)eRZUd*ZVeDd !Gd+d,ZWy).zj 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_lencTt|jdf|jdzS)Nriter_args operations C/usr/lib/python3/dist-packages/sympy/utilities/matchpy_connector.py_rDVs'Y__Q')IOOA,>>??c,t|jSNr>rAs rCrDrDZsIOO$$rEc8dt|jdzS)Nr=lenr@rAs rCrDrD^s3yq)***rEc,t|jSrGrIrAs rCrDrDbs9??##rEct||SrG)type) old_operation new_operands variable_names rCsympy_op_factoryrQfs#]#\2 2rE)WildcardceZdZdZy)rRc<||_||_||_||_yrG) min_count fixed_sizerPoptional)self min_lengthrVrPrWs rC__init__zWildcard.__init__os'DN(DO!.D $DMrEN)__name__ __module__ __qualname__rZrErCrRrRns %rErR)r4)modulescveZdZUeed<eed<d dZdZd dZdZ e d dZ fdZ d d Z d Zd ZxZS) _WildAbstractrYrVc |j}|j}| t|}tj|||t ||yrG)rYrVrrRrZstr)rXrPrW assumptionsrYrVs rCrZz_WildAbstract.__init__{s?__ __  )H$ JM8JHUrEcv|j|j|j|j|jdS)NrYrVrUrPrWrfrXs rC __getstate__z_WildAbstract.__getstate__s1////!//   rEc V|j||tj|||fi|SrG) _sanitizera__xnew__)clsrPrWrds rC__new__z_WildAbstract.__new__s* k3'%%c=(RkRRrEc2|j|jfSrGrPrWrgs rC__getnewargs__z_WildAbstract.__getnewargs__s!!4==00rEc 4tj||fi|}|SrG)r/rk)rlrPrWrdobjs rCrkz_WildAbstract.__xnew__sooc=@K@ rEc|jr=t| |j|j|j |jfzSt| |j|j|j fzSrG)rWsuper_hashable_contentrUrVrP)rX __class__s rCruz_WildAbstract._hashable_contentse ==7,.$..$//SWSeSegkgtgt1uu u7,.$..$//SWSeSe1ff frEcPt||j|jS)Nro)rMrPrWrgs rC__copy__z_WildAbstract.__copy__stDz(:(:T]]SSrEct|SrG)rcrgs rC__repr__z_WildAbstract.__repr__s 4yrEc|jSrGnamergs rC__str__z_WildAbstract.__str__s yyrE)NN)returnra)r[r\r]int__annotations__boolrZrhrmrp staticmethodrkrurxrzr~ __classcell__)rvs@rCraravsNOV S1g TrEraceZdZdZdZy)WildDotr=TNr[r\r]rYrVr^rErCrrs JJrErceZdZdZdZy)WildPlusr=FNrr^rErCrr JJrErceZdZdZdZy)WildStarrFNrr^rErCrrrrErct|}tjdd|}tjdd|}tjdd|}|S)NzWildDot\('(\w+)'\)z\1zWildPlus\('(\w+)'\)z*\1zWildStar\('(\w+)'\))r2resub)exprss rC _get_sreprrsI d A $eQ/A %vq1A %vq1A HrEc eZdZdZgfdefdZdededeffdZ ded ededeffd Z dededeffd Z dededeffd Z ggfd edede ede eddf dZd edefdZy)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_constraintscDtj|_||_yrG)r4ManyToOneReplacer _replacer_common_constraint)rXrs rCrZzReplacer.__init__s 224"4rE lambda_strr.c@tdt|tS)Nzfrom sympy import *)execevallocals)rXrs rC _get_lambdazReplacer._get_lambdas "#J))rEconstraint_exprcondition_templatec |jtDcgc]}|j}}dj|}t |}|j |}t j|jd|d|dScc}w)N, lambda z: ()) atomsrar}joinrformatr4CustomConstraintr)rXrrxwilds lambdaargsfullexpr conditions rC_get_custom_constraintzReplacer._get_custom_constraints!0!6!6}!EFAFFYYu% o.&--h7 ''   wzl#i[B CE E GsBc&|j|dS)Nz ({}) != FalserrXrs rC_get_custom_constraint_nonfalsez(Replacer._get_custom_constraint_nonfalse s**?OLLrEc&|j|dS)Nz ({}) == Truerrs rC_get_custom_constraint_truez$Replacer._get_custom_constraint_trues**?NKKrErresultconditions_trueconditions_nonfalseNc:t|}t|}ddjd|jtDdt |}|j |}|j dd}|Dcgc]}|j|} }|Dcgc]}|j|} }|j| |j| |jjtjtj|g||ycc}wcc}w)Nrrc34K|]}|jywrGr|).0rs rC zReplacer.add..s)TQ!&&)Tsz: )rrrrarrrrrextendraddr4ReplacementRulePattern) rXrrrrr lambda_expr constraintscondconstraint_conditions_trueconstraint_conditions_nonfalses rCrz Replacer.adds~&!tyy)T$**]:S)TUVVXYcdjYkXlm &&z2 --a0 ?N&P7;D , ,T 2&P"&PDW*X;?D 0 0 6*X&*X569:   # #GOOD$G;$G U W &P*Xs 5DDc8|jj|SrG)rreplace)rXrs rCrzReplacer.replace s~~%%d++rE)r[r\r]__doc__listrZrcrr*rrrrrrrr^rErCrrs6p35545*c*hsDy.A*EdEPSEX`adfjajXkEMtMQTVZQZH[ML4LHSRVYDWLKMpr W Wd WT$Z Wcghlcm Ww{ W,D,T,rEr)T)Xrrtypingrrsympy.core.sympifyrsympy.externalrsympy.functionsrrr r r r r rrr%sympy.functions.elementary.hyperbolicrrrrrrrrrrrr(sympy.functions.elementary.trigonometricrrrr 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-r.sympy.core.symbolr/&sympy.functions.elementary.exponentialr0sympy.integrals.integralsr1sympy.printing.reprr2sympy.utilities.decoratorr3r4r5r6r7r8matchpy.expressions.functionsr9r:r;registerrDrQrRrarrrrrr^rErCrs !'(WWW~~~~WWVV"  8$6.%8  " ccZZIx Is!!!#&Is!!!#&!!!#&!!!#&Is!!!#&!!!#&!!!#&Ix !!!(+Iz"!!!*-IsIsIuIz"Ix Ix IsIrItItIsIsIsIsIsIsItItItItItItItItItItItItIuIuIuIuIuIuWh@ @We%%V__X++V__U$$* ))%0313  %%L)-Hf-*-`L)m* L)}* L)}*  L)_,_,*_,rE