o à8Vaã @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 ee e¡ dd „ƒZ#e $e ee¡dd „ƒZ#e "e¡dd „ƒZ#e $e ee¡dd „ƒZ#e  "e¡dd „ƒZ#e  $ee ¡dd „ƒZ#e! "e¡dd „ƒZ#e! $ee ¡dd „ƒZ#dS)zc This module contains query handlers responsible for calculus queries: infinitesimal, finite, etc. é)ÚQÚask)ÚAddÚMulÚPowÚSymbol) ÚComplexInfinityÚExp1Ú GoldenRatioÚ ImaginaryUnitÚInfinityÚNaNÚNegativeInfinityÚNumberÚPiÚTribonacciConstantÚE)ÚcosÚexpÚlogÚsignÚsin)Ú conjunctsé)ÚFinitePredicateÚInfinitePredicateÚPositiveInfinitePredicateÚNegativeInfinitePredicatecCs*|jdur|jSt |¡t|ƒvrdSdS)z Handles Symbol. NT)Z is_finiterÚfiniter©ÚexprÚ assumptions©r"úE/usr/lib/python3/dist-packages/sympy/assumptions/handlers/calculus.pyÚ_s r$cCs|d}d}|jD]4}tt |¡|ƒ}|rqtt |¡|ƒ}|dkr$||ks0|dur3||ks0||kr3dS|}|dur;|}q|S)ab Return True if expr is bounded, False if not and None if unknown. Truth Table: +-------+-----+-----------+-----------+ | | | | | | | B | U | ? | | | | | | +-------+-----+---+---+---+---+---+---+ | | | | | | | | | | | |'+'|'-'|'x'|'+'|'-'|'x'| | | | | | | | | | +-------+-----+---+---+---+---+---+---+ | | | | | | B | B | U | ? | | | | | | +---+---+-----+---+---+---+---+---+---+ | | | | | | | | | | | |'+'| | U | ? | ? | U | ? | ? | | | | | | | | | | | | +---+-----+---+---+---+---+---+---+ | | | | | | | | | | | U |'-'| | ? | U | ? | ? | U | ? | | | | | | | | | | | | +---+-----+---+---+---+---+---+---+ | | | | | | | |'x'| | ? | ? | | | | | | | +---+---+-----+---+---+---+---+---+---+ | | | | | | ? | | | ? | | | | | | +-------+-----+-----------+---+---+---+ * 'B' = Bounded * 'U' = Unbounded * '?' = unknown boundedness * '+' = positive sign * '-' = negative sign * 'x' = sign unknown * All Bounded -> True * 1 Unbounded and the rest Bounded -> False * >1 Unbounded, all with same known sign -> False * Any Unknown and unknown sign -> None * Else -> None When the signs are not the same you can have an undefined result as in oo - oo, hence 'bounded' is also undefined. éÿÿÿÿTNF)ÚargsrrrÚextended_positive)r r!rÚresultÚargÚ_boundedÚsr"r"r#r$s(> ÿÿÿ€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$qs' €cCsð|jtkrtt |j¡|ƒStt |j¡|ƒ}tt |j¡|ƒ}|dur*|dur*dS|dur9tt |j¡|ƒr9dS|r?|r?dSt|jƒdkdkrStt |j¡|ƒrSdSt|jƒdkdkrgtt  |j¡|ƒrgdSt|jƒdkdkrv|durvdSdS)z¹ * Unbounded ** NonZero -> Unbounded * Bounded ** Bounded -> Bounded * Abs()<=1 ** Positive -> Bounded * Abs()>=1 ** Negative -> Bounded * Otherwise unknown NFTé) Úbaserrrrrr,Úabsr'Zextended_negative)r r!Z base_boundedZ exp_boundedr"r"r#r$¨s" $$cCstt |j¡|ƒS©N)rrrrrr"r"r#r$ÈscCs2tt |jd¡|ƒr dStt |jd¡|ƒS)NrF)rrZinfiniter&Zzerorr"r"r#r$ÌscCódS©NTr"rr"r"r#r$ÔscCr1©NFr"rr"r"r#r$ÙócCsdSr0r"rr"r"r#r$Ýr4cCr1r2r"rr"r"r#r$år4cCr1r2r"rr"r"r#r$ír4cCr1r3r"rr"r"r#r$òr4cCr1r2r"rr"r"r#r$úr4cCr1r3r"rr"r"r#r$ÿr4N)%Ú__doc__Zsympy.assumptionsrrZ sympy.corerrrrZsympy.core.numbersrr r r r r rrrrrZsympy.functionsrrrrrZsympy.logic.boolalgrZpredicates.calculusrrrrÚregisterr$Z register_manyr"r"r"r#ÚsJ4   Q 6   ÿ