U me|@sdZddlmZmZmZmZddlmZmZddl m Z m Z m Z ddl mZmZmZddlmZmZmZddlmZe gZeeegZegZdd Zd d Zd d ZddZddZdddZddZ ddZ!dddZ"dS)z SymPy interface to Unification engine See sympy.unify for module level docstring See sympy.unify.core for algorithmic docstring )BasicAddMulPow)AssocOp LatticeOp)MatAddMatMul MatrixExpr)Union Intersection FiniteSet)CompoundVariable CondVariable)corecs&ttttttf}tfdd|DS)Nc3s|]}t|VqdSN issubclass).0Zaopop6/tmp/pip-unpacked-wheel-rdz2gdd2/sympy/unify/usympy.py sz$sympy_associative..)rrr r r r any)rZ assoc_opsrrrsympy_associativesrcs$tttttf}tfdd|DS)Nc3s|]}t|VqdSrr)rZcoprrrrsz$sympy_commutative..)rrr r r r)rZcomm_opsrrrsympy_commutativesrcCst|tot|jSr) isinstancerrrxrrris_associativesr!cCs@t|tsdSt|jrdSt|jtr.)rrrrrrallargsrrrrr#s    r#csfdd}|S)Ncs t|pt|tot|jSr)rrrrrtyprr matchtype%s zmk_matchtype..matchtyper)r)r*rr(r mk_matchtype$s r+rcsV|krt|St|ttfr"|St|tr2|jr6|St|jtfdd|jDS)z% Turn a SymPy object into a Compound c3s|]}t|VqdSr deconstructr$ variablesrrr3szdeconstruct..) rrrrZis_Atomr __class__tupler')sr/rr.rr-*sr-cstttfrjStts"StfddtDrPjtt j ddiStfddt Drt j jftt j Sjtt j SdS)z% Turn a Compound into a SymPy object c3s|]}tj|VqdSrrrrclstrrr;szconstruct..evaluateFc3s|]}tj|VqdSrr3r4r6rrr=sN)rrrr%rreval_false_legalrmapr"r'basic_new_legalr__new__r6rr6rr"5s r"cCs tt|S)z[ Rebuild a SymPy expression. This removes harm caused by Expr-Rules interactions. )r"r-)r2rrrrebuildBsr=Nc+spfdd|pi}fdd|D}tj|||fttd|}|D]}dd|DVqRdS)af Structural unification of two expressions/patterns. Examples ======== >>> from sympy.unify.usympy import unify >>> from sympy import Basic, S >>> from sympy.abc import x, y, z, p, q >>> next(unify(Basic(S(1), S(2)), Basic(S(1), x), variables=[x])) {x: 2} >>> expr = 2*x + y + z >>> pattern = 2*p + q >>> next(unify(expr, pattern, {}, variables=(p, q))) {p: x, q: y + z} Unification supports commutative and associative matching >>> expr = x + y + z >>> pattern = p + q >>> len(list(unify(expr, pattern, {}, variables=(p, q)))) 12 Symbols not indicated to be variables are treated as literal, else they are wild-like and match anything in a sub-expression. >>> expr = x*y*z + 3 >>> pattern = x*y + 3 >>> next(unify(expr, pattern, {}, variables=[x, y])) {x: y, y: x*z} The x and y of the pattern above were in a Mul and matched factors in the Mul of expr. Here, a single symbol matches an entire term: >>> expr = x*y + 3 >>> pattern = p + 3 >>> next(unify(expr, pattern, {}, variables=[p])) {p: x*y} cs t|Srr,rr.rrszunify..csi|]\}}||qSrrrkv)deconsrr uszunify..)r!r#cSsi|]\}}t|t|qSr)r"r@rrrrD|sN)itemsrunifyr!r#)r yr2r/kwargsZdsdr)rCr/rrFIs* rF)r)Nr)#__doc__Z sympy.corerrrrZsympy.core.operationsrrZsympy.matricesrr r Zsympy.sets.setsr r r Zsympy.unify.corerrrZ sympy.unifyrr;r9illegalrrr!r#r+r-r"r=rFrrrrs$