o 8Vap@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)Nc3|]}t|VqdSN issubclass).0Zaopop4/usr/lib/python3/dist-packages/sympy/unify/usympy.py z$sympy_associative..)rrr r r r any)rZ assoc_opsrrrsympy_associativesrcs$tttttf}tfdd|DS)Nc3rrr)rZcoprrrrrz$sympy_commutative..)rrr r r r)rZcomm_opsrrrsympy_commutativesrcCst|to t|jSr) isinstancerrrxrrris_associativesr#cCs@t|tsdSt|jrdSt|jtrtdd|jDSdS)NFTcss|]}t|jVqdSr) constructis_commutativerargrrrr"rz!is_commutative..)r rrrrrallargsr!rrrr%s   r%csfdd}|S)Ncs t|pt|tot|jSr)r rrrr!typrr matchtype%s zmk_matchtype..matchtyper)r+r,rr*r mk_matchtype$s r-rcsV|vrt|St|ttfr|St|tr|jr|St|jtfdd|jDS)z% Turn a SymPy object into a Compound c3s|]}t|VqdSr deconstructr& variablesrrr3rzdeconstruct..) rr rrZis_Atomr __class__tupler))sr1rr0rr/*sr/cstttfr jSttsStfddtDr(jtt j ddiStfddt DrAt j jgtt j RSjtt j S)z% Turn a Compound into a SymPy object c3|] }tj|VqdSrrrrclstrrr;zconstruct..ZevaluateFc3r5rr6r7r9rrr=r;)r rrr'rreval_false_legalrmapr$r)basic_new_legalr__new__r9rr9rr$5s r$cCs tt|S)z[ Rebuild a SymPy expression. This removes harm caused by Expr-Rules interactions. )r$r/)r4rrrrebuildBs r@Nc+srfdd|p i}fdd|D}tj|||fttd|}|D] }dd|DVq*dS)aZ Structural unification of two expressions/patterns. Examples ======== >>> from sympy.unify.usympy import unify >>> from sympy import Basic >>> from sympy.abc import x, y, z, p, q >>> next(unify(Basic(1, 2), Basic(1, x), variables=[x])) {x: 2} >>> expr = 2*x + y + z >>> pattern = 2*p + q >>> next(unify(expr, pattern, {}, variables=(p, q))) {p: x, q: y + z} Unification supports commutative and associative matching >>> expr = x + y + z >>> pattern = p + q >>> len(list(unify(expr, pattern, {}, variables=(p, q)))) 12 Symbols not indicated to be variables are treated as literal, else they are wild-like and match anything in a sub-expression. >>> expr = x*y*z + 3 >>> pattern = x*y + 3 >>> next(unify(expr, pattern, {}, variables=[x, y])) {x: y, y: x*z} The x and y of the pattern above were in a Mul and matched factors in the Mul of expr. Here, a single symbol matches an entire term: >>> expr = x*y + 3 >>> pattern = p + 3 >>> next(unify(expr, pattern, {}, variables=[p])) {p: x*y} cs t|Srr.r!r0rrss zunify..csi|] \}}||qSrrrkv)deconsrr uzunify..)r#r%cSsi|] \}}t|t|qSr)r$rBrrrrF|rGN)itemsrunifyr#r%)r"yr4r1kwargsZdsdr)rEr1rrIIs *rI)r)Nr)#__doc__Z sympy.corerrrrZsympy.core.operationsrrZsympy.matricesrr r Zsympy.sets.setsr r r Zsympy.unify.corerrrZ sympy.unifyrr>r<Zillegalrrr#r%r-r/r$r@rIrrrrs&