*htSrSSKJr SSKJrJr SSKJr SSKJ r \"S5r \"S5r SSjr SS jr SS jrSS jrSS jrSSjrSSjrSSjrSSjrSSjrSr\S.SSjjrg )z%Generic SymPy-Independent Strategies ) annotations)CallableMapping)TypeVarstdout_S_TcU$Nxs R/home/mande/repo/quber/.venv/lib/python3.13/site-packages/sympy/strategies/core.pyidentityr  Hc^SU4SjjnU$)z/Apply a rule repeatedly until it has no effect cD>T"U5Up!X:waT"U5Up!X:waMU$r r )exprnewoldrules r exhaustive_rlexhaust..exhaustive_rls*:tSjCy#j rrr returnr r )rrs` rexhaustrs rc ^^0mSUU4SjjnU$)zMemoized version of a rule Notes ===== This cache can grow infinitely, so it is not recommended to use this than ``functools.lru_cache`` unless you need very heavy computation. c8>UT;aTU$T"U5nUTU'U$r r )rresultcachers r memoized_rlmemoize..memoized_rl%s+ 5=; $ZF E$KMrrr rr r )rr#r"s` @rmemoizer&sE rc^^SUU4SjjnU$)z%Only apply rule if condition is true c2>T"U5(aT"U5$U$r r )rcondrs rconditioned_rl!condition..conditioned_rl3s :::  rrr )r)rr*s`` r conditionr,/s rc^SU4SjjnU$)zI Compose a sequence of rules so that they apply to the expr sequentially c*>TH nU"U5nM U$r r )rrruless rchain_rlchain..chain_rl>sD:D rrr )r/r0s` rchainr2:s OrNc*^^Tc[mUU4SjnU$)z>Print out before and after expressions each time rule is used c>USnT"U0UD6nX2:wa8TRSTR-5 TRSU<SU<S35 U$)Nrz Rule: %s zIn: z Out: z )write__name__)argskwargsrr!filers rdebug_rldebug..debug_rlJsKAwt&v& > JJ|dmm3 4 JJ4@ A rr)rr9r:s`` rdebugr<Es | Orc^SU4SjjnU$)z*Return original expr if rule returns None c">T"U5nUcU$U$r r )rr!rs r null_safe_rlnull_safe..null_safe_rlVsd >K rrr )rr?s` r null_saferATs rc^^SUU4SjjnU$)z.Return original expr if rule raises exception c2>T"U5$!Ta Us$f=fr r )r exceptionrs rtry_rltryit..try_rl`s& :  K s  rr )rrDrEs`` rtryitrG^s Mrc^SU4SjjnU$)z2Try each of the rules until one works. Then stop. c<>THnU"U5nX :wdMUs $ U$r r )rrlr!r/s r do_one_rldo_one..do_one_rljs'BXF~  rrr )r/rKs` rdo_onerMhs rc^^SUU4SjjnU$)z@Select a rule based on the result of key called on the function cL>TRT"U5[5nU"U5$r )getr)rrJkeyruledicts r switch_rlswitch..switch_rlxs \\#d)X .$xr)rr rr r )rQrRrSs`` rswitchrUss  rcU$r r rs r _identityrWrr) objectivec^^SUU4SjjnU$)aSelect result of rules that minimizes objective >>> from sympy.strategies import minimize >>> inc = lambda x: x + 1 >>> dec = lambda x: x - 1 >>> rl = minimize(inc, dec) >>> rl(4) 3 >>> rl = minimize(inc, dec, objective=lambda x: -x) # maximize >>> rl(4) 5 cN>[TVs/sH o"U5PM snTS9$s snf)N)rQ)min)rrrXr/s rminruleminimize..minrules&5154DJ51yAA1s"r%r )rXr/r\s`` rminimizer^s"BB Nr)rr rr )rCallable[[_T], _T]rr_)rCallable[[_S], _T]rr`)r)zCallable[[_T], bool]rr_rr_)r/r_rr_r )rzCallable[[_T], _T | None]rr_)rQr`rRzMapping[_T, Callable[[_S], _S]]rzCallable[[_S], _S])r/r`rr`)__doc__ __future__rcollections.abcrrtypingrsysrr r rrr&r,r2r<rArGrMrUrWr^r rrrfs,"- T] T] * &8  -  r