B ™‘[ฏใ@s๊dZddlmZmZddlmZmZmZmZddl m Z m Z m Z ddl mZmZmZddlmZmZddlmZmZmZddlmZe gZeeegZegZd d „Zd d „Zd d„Zdd„Z dd„Z!ddd„Z"dd„Z#dd„Z$ddd„Z%dS)z‚ SymPy interface to Unification engine See sympy.unify for module level docstring See sympy.unify.core for algorithmic docstring ้)ฺprint_functionฺdivision)ฺBasicฺAddฺMulฺPow)ฺMatAddฺMatMulฺ MatrixExpr)ฺUnionฺ Intersectionฺ FiniteSet)ฺAssocOpฺ LatticeOp)ฺCompoundฺVariableฺ CondVariable)ฺcorecs&ttttttf}t‡fdd„|DƒƒS)Nc3s|]}tˆ|ƒVqdS)N)ฺ issubclass)ฺ.0Zaop)ฺopฉ๚1lib/python3.7/site-packages/sympy/unify/usympy.py๚ sz$sympy_associative..)rrr r r r ฺany)rZ assoc_opsr)rrฺsympy_associativesrcs$tttttf}t‡fdd„|DƒƒS)Nc3s|]}tˆ|ƒVqdS)N)r)rZcop)rrrrsz$sympy_commutative..)rrr r r r)rZcomm_opsr)rrฺsympy_commutativesrcCst|tƒot|jƒS)N)ฺ isinstancerrr)ฺxrrrฺis_associativesrcCs@t|tƒsdSt|jƒrdSt|jtƒr.)rrrrrrฺallฺargs)rrrrr!s    r!cs‡fdd„}|S)Ncs t|ˆƒpt|tƒot|jˆƒS)N)rrrr)r)ฺtyprrฺ matchtype's zmk_matchtype..matchtyper)r%r&r)r%rฺ mk_matchtype&s r'rcsV|ˆkrt|ƒSt|ttfƒr"|St|tƒr2|jr6|St|jt‡fdd„|jDƒƒƒS)z% Turn a SymPy object into a Compound c3s|]}t|ˆƒVqdS)N)ฺ deconstruct)rr")ฺ variablesrrr5szdeconstruct..) rrrrZis_Atomrฺ __class__ฺtupler$)ฺsr)r)r)rr(,sr(cs–tˆttfƒrˆjStˆtƒs"ˆSt‡fdd„tDƒƒrPˆjtt ˆj ƒddiŽSt‡fdd„t Dƒƒr€t j ˆjftt ˆj ƒžŽSˆjtt ˆj ƒŽSdS)z% Turn a Compound into a SymPy object c3s|]}tˆj|ƒVqdS)N)rr)rฺcls)ฺtrrr=szconstruct..ZevaluateFc3s|]}tˆj|ƒVqdS)N)rr)rr-)r.rrr?sN)rrrr"rrฺeval_false_legalrฺmapr r$ฺbasic_new_legalrฺ__new__)r.r)r.rr 7s r cCs tt|ƒƒS)zY Rebuild a SymPy expression This removes harm caused by Expr-Rules interactions )r r()r,rrrฺrebuildDsr3Nc+s|‡fdd„‰|pi}t‡fdd„| กDƒƒ}tjˆ|ƒˆ|ƒ|fttdœ|—Ž}x$|D]}tdd„| กDƒƒVqXWdS)a^ Structural unification of two expressions/patterns Examples ======== >>> from sympy.unify.usympy import unify >>> from sympy import Basic, cos >>> from sympy.abc import x, y, z, p, q >>> next(unify(Basic(1, 2), Basic(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|ˆƒS)N)r()r)r)rrฺuszunify..c3s"|]\}}ˆ|ƒˆ|ƒfVqdS)Nr)rฺkฺv)ฺdeconsrrrwszunify..)rr!css"|]\}}t|ƒt|ƒfVqdS)N)r )rr5r6rrrr~sN)ฺdictฺitemsrฺunifyrr!)rฺyr,r)ฺkwargsZdsฺdr)r7r)rr:Ks*  r:)r)Nr)&ฺ__doc__Z __future__rrZ sympy.corerrrrZsympy.matricesrr r Zsympy.sets.setsr r r Zsympy.core.operationsrrZsympy.unify.corerrrZ sympy.unifyrr1r/Zillegalrrrr!r'r(r r3r:rrrrฺs&