o jgã @s¼dZddlmZmZddlmZmZmZmZddl m Z m Z m Z m Z mZmZmZmZmZmZmZddlmZmZmZmZmZddlmZddlmZmZm Z m!Z!e "e¡d d „ƒZ#e "e¡d d „ƒZ#e "e¡d d „ƒZ#e "e¡d d „ƒZ#e "e¡dd „ƒZ#e "e¡dd „ƒZ#e $eeeee e eee¡ dd „ƒZ#e $ee e ¡dd „ƒZ#e "e¡dd „ƒZ#e $ee e ¡dd „ƒZ#e  "e ¡dd „ƒZ#e  $e e¡dd „ƒZ#e! "e ¡dd „ƒZ#e! $e e¡dd „ƒZ#dS)zc This module contains query handlers responsible for calculus queries: infinitesimal, finite, etc. é)ÚQÚask)ÚAddÚMulÚPowÚSymbol) ÚNegativeInfinityÚ GoldenRatioÚInfinityÚExp1ÚComplexInfinityÚ ImaginaryUnitÚNaNÚNumberÚPiÚEÚTribonacciConstant)ÚcosÚexpÚlogÚsignÚsin)Ú conjunctsé)ÚFinitePredicateÚInfinitePredicateÚPositiveInfinitePredicateÚNegativeInfinitePredicatecCs*|jdur|jSt |¡t|ƒvrdSdS)z Handles Symbol. NT)Ú is_finiterÚfiniter©ÚexprÚ assumptions©r#ú[/var/www/html/zoom/venv/lib/python3.10/site-packages/sympy/assumptions/handlers/calculus.pyÚ_s r%cCsxd}d}|jD]2}tt |¡|ƒ}|rqtt |¡|ƒ}|dkr$||ks.|dur1d||fvr1dS|}|dur9|}q|S)ab Return True if expr is bounded, False if not and None if unknown. Truth Table: +-------+-----+-----------+-----------+ | | | | | | | B | U | ? | | | | | | +-------+-----+---+---+---+---+---+---+ | | | | | | | | | | | |'+'|'-'|'x'|'+'|'-'|'x'| | | | | | | | | | +-------+-----+---+---+---+---+---+---+ | | | | | | B | B | U | ? | | | | | | +---+---+-----+---+---+---+---+---+---+ | | | | | | | | | | | |'+'| | U | ? | ? | U | ? | ? | | | | | | | | | | | | +---+-----+---+---+---+---+---+---+ | | | | | | | | | | | U |'-'| | ? | U | ? | ? | U | ? | | | | | | | | | | | | +---+-----+---+---+---+---+---+---+ | | | | | | | |'x'| | ? | ? | | | | | | | +---+---+-----+---+---+---+---+---+---+ | | | | | | ? | | | ? | | | | | | +-------+-----+-----------+---+---+---+ * 'B' = Bounded * 'U' = Unbounded * '?' = unknown boundedness * '+' = positive sign * '-' = negative sign * 'x' = sign unknown * All Bounded -> True * 1 Unbounded and the rest Bounded -> False * >1 Unbounded, all with same known sign -> False * Any Unknown and unknown sign -> None * Else -> None When the signs are not the same you can have an undefined result as in oo - oo, hence 'bounded' is also undefined. éÿÿÿÿTNF)ÚargsrrrÚextended_positive)r!r"rÚresultÚargÚ_boundedÚsr#r#r$r% s> €cCsld}|jD].}tt |¡|ƒ}|rq|dur1|durdStt |¡|ƒdur*dS|dur0d}qd}q|S)a) Return True if expr is bounded, False if not and None if unknown. Truth Table: +---+---+---+--------+ | | | | | | | B | U | ? | | | | | | +---+---+---+---+----+ | | | | | | | | | | s | /s | | | | | | | +---+---+---+---+----+ | | | | | | B | B | U | ? | | | | | | +---+---+---+---+----+ | | | | | | | U | | U | U | ? | | | | | | | +---+---+---+---+----+ | | | | | | ? | | | ? | | | | | | +---+---+---+---+----+ * B = Bounded * U = Unbounded * ? = unknown boundedness * s = signed (hence nonzero) * /s = not signed TNF)r'rrrÚextended_nonzero)r!r"r)r*r+r#r#r$r%rs' €cCsð|jtkrtt |j¡|ƒStt |j¡|ƒ}tt |j¡|ƒ}|dur*|dur*dS|dur9tt |j¡|ƒr9dS|r?|r?dSt|jƒdkdkrStt |j¡|ƒrSdSt|jƒdkdkrgtt  |j¡|ƒrgdSt|jƒdkdkrv|durvdSdS)z¹ * Unbounded ** NonZero -> Unbounded * Bounded ** Bounded -> Bounded * Abs()<=1 ** Positive -> Bounded * Abs()>=1 ** Negative -> Bounded * Otherwise unknown NFTé) Úbaserrrrrr-Úabsr(Úextended_negative)r!r"Ú base_boundedÚ exp_boundedr#r#r$r%©s" $$cCstt |j¡|ƒS©N)rrrrr r#r#r$r%ÉscCs2tt |jd¡|ƒr dStt |jd¡|ƒS)NrF)rrÚinfiniter'Úzeror r#r#r$r%ÍscCódS©NTr#r r#r#r$r%ÕscCr7©NFr#r r#r#r$r%ÚócCsdSr4r#r r#r#r$r%Þr:cCr7r8r#r r#r#r$r%ær:cCr7r8r#r r#r#r$r%îr:cCr7r9r#r r#r#r$r%ór:cCr7r8r#r r#r#r$r%ûr:cCr7r9r#r r#r#r$r%r:N)%Ú__doc__Úsympy.assumptionsrrÚ sympy.corerrrrÚsympy.core.numbersrr r r r r rrrrrÚsympy.functionsrrrrrÚsympy.logic.boolalgrÚpredicates.calculusrrrrÚregisterr%Ú register_manyr#r#r#r$ÚsJ4   Q 6   ÿ