+ i. Rt^RIt^RIHtHtHtHtHt^RIH t ^RI H t ^RI H t HtHtHtHtHtHtHtHtHt^RIHtHtHtHtHtHtHtHtH t H!t!H"t"H#t#^RI$H%t%H&t&H't'H(t(H)t)H*t*^RI+H,t,H-t-H.t.H/t/H0t0^R I1H2t2^R I3H4t4^R I5H6t6^R I7H8t8^R I9H:t:^RI;HH?t?^RI@HAtA^RIBHCtC^RIDHEtE^RIFHGtG] !R4tHR-R./tI]H'Ed^RIHHJtJHKtKHLtLHMtM^RINHOtOHPtPHQtQ]JP!]C4]JP!]:4]MP!]:4]JP!]24]MP!]24]KP!]24]LP!]24]JP!]84]MP!]84]KP!]84]LP!]84]JP!]<4]KP!]<4]JP!]=4]KP!]=4]JP!]A4]JP!] 4]JP!]4]JP!]4]JP!]-4]JP!],4]JP!]4]JP!]04]JP!].4]JP!]/4]JP!]4]JP!]4]JP!]4]JP!]4]JP!]4]JP!]4]JP!]4]JP!]4]JP!] 4]JP!]!4]JP!]#4]JP!]"4]JP!]'4]JP!])4]JP!]%4]JP!](4]JP!]&4]JP!]*4]JP!]4]JP!]4]JP!]4]JP!]4]JP!]4]JP!]4]OP!]C4R4tS]OP!]44R4tS]QP!]C4R4tS]QP!]44R4tS]PP!]44R.Rl4tT]H'd^RIHHUtUM !RR4tU]G!R/R7!R R!]U]?44tV]G!R/R7!R"R#]V44tW]G!R/R7!R$R%]V44tX]G!R/R7!R&R']V44tYR(tZ!R)R*]4t[]G!R/R7!R+R,44t\R#)0zj 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_lencl\VP^,3VP^,,4#)iter_args operations&_/var/www/html/photoedit/myenv/lib/python3.14/site-packages/sympy/utilities/matchpy_connector.py_rF[s'Y__Q')IOOA,>>??c,\VP4#Nr@rCs&rErFrF_sIOO$$rGcH^\VP^,4,#)lenrBrCs&rErFrFcs3yq)***rGc,\VP4#rIrLrCs&rErFrFgs9??##rGc \V4!V!#rI)type) old_operation new_operands variable_names&&&rEsympy_op_factoryrTksM"L11rG)Wildcardc&a]tRt^stoRtRtVtR#)rUc6WnW nW0nW@nR#rI) min_count fixed_sizerSoptional)self min_lengthrYrSrZs&&&&&rE__init__Wildcard.__init__ts'N(O!. $MrG)rYrXrZrSN)__name__ __module__ __qualname____firstlineno__r]__static_attributes____classdictcell__ __classdict__s@rErUrUss % %rGrU)modulescaa]tRt^{toR RltRtR RltRt]R Rl4t V3Rlt V3RlRlt R t R t V3R ltR tVtV;t#) _WildAbstractc VPpVPpVe \V4p\P!WV\ V4V4R#rI)r\rYrrUr]str)r[rSrZ assumptionsr\rYs&&&, rEr]_WildAbstract.__init__s=__ __  )H$JM8JHUrGc ~RVPRVPRVPRVPRVP/#r\rYrXrSrZror[s&rE __getstate___WildAbstract.__getstate__s; $// $//  T//    rGc TVPW04\P!WV3/VB#rI) _sanitizeri__xnew__)clsrSrZrls&&&,rE__new___WildAbstract.__new__s& k'%%c(RkRRrGc2VPVP3#rIrSrZrps&rE__getnewargs___WildAbstract.__getnewargs__s!!4==00rGc 4\P!W3/VBpV#rI)r1ru)rvrSrZrlobjs&&&, rEru_WildAbstract.__xnew__sooc@K@ rGc<VP'dB\SV` 4VPVPVP VP3,#\SV` 4VPVPVP 3,#rI)rZsuper_hashable_contentrXrYrS)r[ __class__s&rEr_WildAbstract._hashable_contentsg ===7,.$..$//SWSeSegkgtgt1uu u7,.$..$//SWSeSe1ff frGc<V^8dQhRR/#)returnri)formatrfs"rE __annotate___WildAbstract.__annotate__sTT/TrGcP\V4!VPVPR7#)rz)rPrSrZrps&rE__copy___WildAbstract.__copy__sDz(:(:T]]SSrGc\V4#rI)rkrps&rE__repr___WildAbstract.__repr__s 4yrGcVP#rInamerps&rE__str___WildAbstract.__str__s yyrGc2<V^8dQh/S[;R&S[;R&#)rr\rY)intbool)rrfs"rErr{sOrGr)NN)r_r`rarbr]rqrwr{ staticmethodrurrrr__annotate_func__rcrd __classcell__)rrfs@@rEriri{sS V S1g TT[rGric]tRt^t^tRtRtR#)WildDotTrNr_r`rarbr\rYrcrrGrErrs JJrGrc]tRt^t^tRtRtR#)WildPlusFrNrrrGrErr JJrGrc]tRt^t^tRtRtR#)WildStarFrNrrrGrErrrrGrc\V4p\P!RRV4p\P!RRV4p\P!RRV4pV#)zWildDot\('(\w+)'\)z\1zWildPlus\('(\w+)'\)z*\1zWildStar\('(\w+)'\))r4resub)exprss& rE _get_sreprrsI d A $eQ/A %vq1A %vq1A HrGc,a]tRt^toV3RltRtVtR#)ReplacementInfoc2<V^8dQh/S[;R&S[;R&#)r replacementinfo)r)rrfs"rErReplacementInfo.__annotate__s IrGrN)r_r`rarbrrcrdres@rErrsrGrca]tRt^toRt.RR3V3RlRlltV3RlRltV3RlRltV3R lR ltV3R lR lt ..R 3V3RlRllt RV3RlRllt Rt Vt R #)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 Fc,<V^8dQhRS[RS[RS[/#)rcommon_constraintslambdifyr)listr)rrfs"rErReplacer.__annotate__s#22422TX2rGcj\P4VnWnW nW0n/VnR#rI)r6ManyToOneMatcher_matcher_common_constraint _lambdify_info _wildcards)r[rrrs&&&&rEr]Replacer.__init__s)002 "4! /1rGc:<V^8dQhRS[RS[RS[3,/#)r lambda_strr.)rkrr,)rrfs"rErr s$**c*hsDy.A*rGc@\R4\V\44#)zfrom sympy import *)execevallocals)r[rs&&rE _get_lambdaReplacer._get_lambda s "#J))rGc@<V^8dQhRS[RS[RS[RS[3,/#)rconstraint_exprcondition_templater.)r,rkr)rrfs"rErrs5EEdEPSEX`adfjajXkErGc VP\4Uu.uFq3PNK ppRPV4p\ V4pVP V4p\ PVPRV RV R244#uupi), lambda z: ()) atomsrirjoinrrr6CustomConstraintr)r[rrxwilds lambdaargsfullexpr conditions&&& rE_get_custom_constraintReplacer._get_custom_constraints!0!6!6}!EF!EA!EFYYu% o.&--h7 ''   wzl#i[B CE E GsBc:<V^8dQhRS[RS[RS[3,/#rrr.r,r)rrfs"rErrs+MMtMQTVZQZH[MrGc&VPVR4#)z ({}) != Falserr[rs&&rE_get_custom_constraint_nonfalse(Replacer._get_custom_constraint_nonfalses**?OLLrGc:<V^8dQhRS[RS[RS[3,/#rr)rrfs"rErrs)LL4LHSRVYDWLrGc&VPVR4#)z ({}) == Truerrs&&rE_get_custom_constraint_true$Replacer._get_custom_constraint_trues**?NKKrGNc V<V^8dQhRS[RS[S[,RS[S[,RS[RR/#)rrconditions_trueconditions_nonfalserrN)r,rr)rrfs"rErrs;000DJ0!%d08;0GK0rGc&\V4p\V4pVPR,pVUu.uFqpPV4NK ppVUu.uFqpPV4NK p pVP V4VP V 4\ P !V.VO5!p VP'dORRPRVP\444 R\V4 2p VPV 4p T pMHVPPVP\4U u/uFp \!V 4V bK up 4VP"'d \%W%4pVP&P)W4R#uupiuupiuup i):NNNrrc38"TFqPxK R#5irIr).0rs& rE Replacer.add..+s-X>Wff>Wsz: N)rrrrextendr6PatternrrrrirrrupdaterUrkrrradd)r[rrrrr constraintscondconstraint_conditions_trueconstraint_conditions_nonfalsepatternr lambda_expris&&&&&& rEr Replacer.addsf~{+ --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 :::)+*EE E%$E%)rrrrr))r_r`rarb__doc__r]rrrrrrrcrdres@rErrsr6p35u[`22**EEMMLLJL.0d00,   rGr)*)T)r6)]rrtypingrrrrrsympy.core.sympifyrsympy.externalrsympy.functionsr r r r r rrrrr%sympy.functions.elementary.hyperbolicrrrrrrrrrrrr(sympy.functions.elementary.trigonometricrr r!r"r#r$'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__r7r8r9r:matchpy.expressions.functionsr;r<r=registerrFrTrUrirrrrrrrrGrEr)s 88'(WWW~~~~WWVV"  8$6.%8  " , 7ccZZ 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*HrG