\h. SrSSKrSSKJrJrJrJrJr SSKJ r SSK J r SSK J r JrJrJrJrJrJrJrJrJr SSKJrJrJrJrJrJrJrJrJ r J!r!J"r"J#r# SSK$J%r%J&r&J'r'J(r(J)r)J*r* SS K+J,r,J-r-J.r.J/r/J0r0 SS K1J2r2 SS K3J4r4 SS K5J6r6 SS K7J8r8 SSK9J:r: SSK;JJ?r? SSK@JArA SSKBJCrC SSKDJErE SSKFJGrG \ "S5rHSS/0rI\H(GaSSKHJJrJJKrKJLrLJMrM SSKNJOrOJPrPJQrQ \JR"\C5 \JR"\:5 \MR"\:5 \JR"\25 \MR"\25 \KR"\25 \LR"\25 \JR"\85 \MR"\85 \KR"\85 \LR"\85 \JR"\<5 \KR"\<5 \JR"\=5 \KR"\=5 \JR"\A5 \JR"\ 5 \JR"\5 \JR"\5 \JR"\-5 \JR"\,5 \JR"\5 \JR"\05 \JR"\.5 \JR"\/5 \JR"\5 \JR"\5 \JR"\5 \JR"\5 \JR"\5 \JR"\5 \JR"\5 \JR"\5 \JR"\ 5 \JR"\!5 \JR"\#5 \JR"\"5 \JR"\'5 \JR"\)5 \JR"\%5 \JR"\(5 \JR"\&5 \JR"\*5 \JR"\5 \JR"\5 \JR"\5 \JR"\5 \JR"\5 \JR"\5 \OR"\C5S5rS\OR"\45S5rS\QR"\C5S5rS\QR"\45S5rS\PR"\45S0Sj5rT\H(aSSKHJUrU O "SS 5rU\G"S!S"9"S#S$\U\?55rV\G"S!S"9"S%S&\V55rW\G"S!S"9"S'S(\V55rX\G"S!S"9"S)S*\V55rYS+rZ"S,S-\5r[\G"S!S"9"S.S/55r\g)1zj The objects in this module allow the usage of the MatchPy pattern matching library on SymPy expressions. N)ListCallable NamedTupleAnyDict)_sympify) import_module) logsincostancotcscsecerfgamma uppergamma) acoshasinhatanhacothacschasechcoshsinhtanhcothsechcsch)atanacscasinacotacosasec)fresnelcfresnelserfcerfiEi)Add)Basic)Expr)Mul)Pow)Equality Unequality)Symbol)exp)Integral)srepr)doctest_depends_onmatchpy)*) OperationCommutativeOperationAssociativeOperationOneIdentityOperation)op_itercreate_operation_expressionop_lencT[URS4URS-5$)Nriter_args operations Y/var/www/auris/envauris/lib/python3.13/site-packages/sympy/utilities/matchpy_connector.py_rH[s'Y__Q')IOOA,>>??c,[UR5$NrBrEs rGrHrH_sIOO$$rIc8S[URS5-$)NrAlenrDrEs rGrHrHcs3yq)***rIc,[UR5$rKrMrEs rGrHrHgs9??##rIc[U5"U6$rK)type) old_operation new_operands variable_names rGsympy_op_factoryrUksM"L11rI)Wildcardc\rSrSrSrSrg)rVsc4XlX lX0lX@lgrK) min_count fixed_sizerToptional)self min_lengthr[rTr\s rG__init__Wildcard.__init__ts'N(O!. $MrI)r[rZr\rTN)__name__ __module__ __qualname____firstlineno__r___static_attributes__rIrGrVrVss %rIrV)r7)modulesc^\rSrSr%\\S'\\S'SSjrSrSSjr Sr \ SSj5r U4S jr SS jrS rS rS rU=r$) _WildAbstract{r^r[c URnURnUb [U5n[R"XU[ U5U5 grK)r^r[rrVr_str)r]rTr\ assumptionsr^r[s rGr__WildAbstract.__init__s=__ __  )H$JM8JHUrIcvURURURURURS.$)Nr^r[rZrTr\rpr]s rG __getstate___WildAbstract.__getstate__s1////!//   rIc TURX05 [R"XU40UD6$rK) _sanitizeri__xnew__)clsrTr\rms rG__new___WildAbstract.__new__s& k'%%c(RkRRrIc2URUR4$rKrTr\rqs rG__getnewargs___WildAbstract.__getnewargs__s!!4==00rIc 4[R"X40UD6nU$rK)r2rv)rwrTr\rmobjs rGrv_WildAbstract.__xnew__sooc@K@ rIc>UR(a=[TU] 5URURUR UR4-$[TU] 5URURUR 4-$rK)r\super_hashable_contentrZr[rT)r] __class__s rGr_WildAbstract._hashable_contentse ==7,.$..$//SWSeSegkgtgt1uu u7,.$..$//SWSeSe1ff frIcJ[U5"URURS9$)Nr{)rQrTr\rqs rG__copy___WildAbstract.__copy__sDz(:(:T]]SSrIc[U5$rK)rlrqs rG__repr___WildAbstract.__repr__s 4yrIcUR$rKnamerqs rG__str___WildAbstract.__str__s yyrIrf)NN)returnri)rarbrcrdint__annotations__boolr_rrrxr| staticmethodrvrrrrre __classcell__)rs@rGriri{sSOV S1g TrIric\rSrSrSrSrSrg)WildDotrATrfNrarbrcrdr^r[rerfrIrGrrs JJrIrc\rSrSrSrSrSrg)WildPlusrAFrfNrrfrIrGrr JJrIrc\rSrSrSrSrSrg)WildStarrFrfNrrfrIrGrrrrIrc[U5n[R"SSU5n[R"SSU5n[R"SSU5nU$)NzWildDot\('(\w+)'\)z\1zWildPlus\('(\w+)'\)z*\1zWildStar\('(\w+)'\))r5resub)exprss rG _get_sreprrsI d A $eQ/A %vq1A %vq1A HrIc*\rSrSr%\\S'\\S'Srg)ReplacementInfo replacementinforfN)rarbrcrdrrrerfrIrGrrs  IrIrc \rSrSrSr/SS4S\S\S\4SjjrS\S \ S \ 44S jr S \ S \S \ S \ 44Sjr S \ S \ S \ 44Sjr S \ S \ S \ 44Sjr//S4S\ S\\ S\\ S\S S4 SjjrSS\4SjjrSrg)Replacerak 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_constraintslambdifyrch[R5UlXlX lX0l0UlgrK)r7ManyToOneMatcher_matcher_common_constraint _lambdify_info _wildcards)r]rrrs rGr_Replacer.__init__s)002 "4! /1rI lambda_strr.c@[S5 [U[55$)Nzfrom sympy import *)execevallocals)r]rs rG _get_lambdaReplacer._get_lambda s "#J))rIconstraint_exprcondition_templatec UR[5Vs/sHo3RPM nnSRU5n[ U5nUR U5n[ RURSUSUS355$s snf)N, lambda z: ()) atomsrirjoinrformatr7CustomConstraintr)r]rrxwilds lambdaargsfullexpr conditions rG_get_custom_constraintReplacer._get_custom_constraints!0!6!6}!EF!EA!EFYYu% o.&--h7 ''   wzl#i[B CE E GsBc&URUS5$)Nz ({}) != Falserr]rs rG_get_custom_constraint_nonfalse(Replacer._get_custom_constraint_nonfalses**?OLLrIc&URUS5$)Nz ({}) == Truerrs rG_get_custom_constraint_true$Replacer._get_custom_constraint_trues**?NKKrINrconditions_trueconditions_nonfalsec[U5n[U5nURSSnUVs/sHopRU5PM nnUVs/sHopRU5PM n nUR U5 UR U 5 [ R "U/UQ76n UR(aNSSRSUR[555S[U53n URU 5n U nOIURRUR[5V s0sHn [!U 5U _M sn 5 UR"(a [%X%5nUR&R)X5 gs snfs snfs sn f)Nrrc38# UHoRv M g7frKr).0rs rG Replacer.add..+s-X>Wff>Wsz: )rrrrextendr7PatternrrrrirrrupdaterVrlrrradd)r]rrrrr constraintscondconstraint_conditions_trueconstraint_conditions_nonfalsepatternr lambda_expris rGr Replacer.addsb~{+ --a0 ?N&P?Nt , ,T 2 #&PDW*XCV4 0 0 6CV '*X569://$55 >>"499-Xdjj>W-X#Y"ZZ\]ghs]t\uvJ**:6K%K OO " "tzz(7K#L7K!CFAI7K#L M ::)+r?registerrHrUrVrirrrrrrrfrIrGrs 88'(WWW~~~~WWVV"  8$6.%8  " , ccZZ x  s!!#& s!!#&!!#&!!#& s!!#&!!#&!!#& x !!(+ z"!!*- s s u z" x  x  s r t t s s s s s s t t t t t t t t t t t t u u u u u u h@ @ e%% __X++ __U$$!))%0212  %%L)-Hf-*-`L)m* L)}* L)}*  j L)HH*HrI