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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 won't 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 won't iterate again if given the same expression) >>> replacer.add(Equality(a_*x, b_), b_/a_) >>> replacer._replacer.matcher.clear() >>> replacer.replace(eq) 4/3 Úcommon_constraintscCst ¡|_||_dSrD)r3ZManyToOneReplacerÚ _replacerÚ_common_constraint)rLryr@r@rArPæs  zReplacer.__init__Ú lambda_strrd.cCstdƒt|tƒƒS)Nzfrom sympy import *)ÚexecÚevalÚlocals)rLr|r@r@rAÚ _get_lambdaês zReplacer._get_lambdaÚconstraint_exprÚcondition_templatec CsRttdd„| t¡ƒƒ}d |¡}t|ƒ}| |¡}t |  d|›d|›d¡¡S)NcSrgrDrh©Úxr@r@rAÚïóz1Replacer._get_custom_constraint..ú, úlambda z: (ú)) ÚlistÚmapÚatomsrUÚjoinrwÚformatr3ZCustomConstraintr€)rLrr‚ZwildsZ lambdaargsZfullexprZ conditionr@r@rAÚ_get_custom_constraintîs  ÿzReplacer._get_custom_constraintcCó | |d¡S)Nz ({}) != False©r©rLrr@r@rAÚ_get_custom_constraint_nonfalseöó z(Replacer._get_custom_constraint_nonfalsecCr)Nz ({}) == Truer‘r’r@r@rAÚ_get_custom_constraint_trueùr”z$Replacer._get_custom_constraint_trueruÚresultÚconditions_trueÚconditions_nonfalseNc s°t|ƒ}t|ƒ}dd tdd„| t¡ƒ¡›dt|ƒ›}ˆ |¡}ˆjdd…}‡fdd„|Dƒ}‡fdd„|Dƒ} | |¡| | ¡ˆj   t   t j |g|¢RŽ|¡¡dS) Nrˆr‡cSrgrDrhrƒr@r@rAr…ÿr†zReplacer.add..z: cóg|]}ˆ |¡‘qSr@)r•©Ú.0Zcondr\r@rAÚ ó ÿz Replacer.add..cr™r@)r“ršr\r@rArœr)rrr‹rŒrUrwr€r{ÚextendrzÚaddr3ZReplacementRuleÚPattern) rLrur–r—r˜r|Z lambda_exprZ constraintsZconstraint_conditions_trueZconstraint_conditions_nonfalser@r\rArŸüs *  ÿ ÿ  ÿz Replacer.addcCs |j |¡SrD)rzÚreplace)rLrur@r@rAr¡ r”zReplacer.replace)rQrRrSÚ__doc__rŠrPrVrr.r€rr“r•rrŸr¡r@r@r@rArx¬s8,rx)T)Or¢rsÚtypingrrZsympy.core.sympifyrZsympy.externalrZsympy.functionsrrrr r r r r rrZ%sympy.functions.elementary.hyperbolicrrrrrrrrrrrrZ(sympy.functions.elementary.trigonometricrrrrr r!Z'sympy.functions.special.error_functionsr"r#r$r%r&Zsympyr'r(r)r*r+r,r-r.r/r0r1Zsympy.utilities.decoratorr2r3r4r5r6r7Zmatchpy.expressions.functionsr8r9r:ÚregisterrBrJrKrUrnrqrrrwrxr@r@r@rAÚs°  08 4                                                       '