o ݹiw @sdZddlmZmZddlmZmZmZmZm Z ddl m Z m Z m Z mZmZmZmZmZmZmZmZddlmZmZmZmZmZddlmZddlmZm Z m!Z!m"Z"e#e d d Z$e#ed d Z$e#ed d Z$e#ed d Z$e#edd Z$e#edd Z$e%eeeeee eee dd Z$e%ee e dd Z$e#edd Z$e #edd Z$e!#e dd Z$e!%e edd Z$e"#e dd Z$e"%e edd Z$dS)zc This module contains query handlers responsible for calculus queries: infinitesimal, finite, etc. )Qask)ExprAddMulPowSymbol) NegativeInfinity GoldenRatioInfinityExp1ComplexInfinity ImaginaryUnitNaNNumberPiETribonacciConstant)cosexplogsignsin) conjuncts)FinitePredicateInfinitePredicatePositiveInfinitePredicateNegativeInfinitePredicatecCs*|jdur|jSt|t|vrdSdS)z Handles Symbol. NT) is_finiterfiniterexpr assumptionsr$`/home/ubuntu/veenaModal/venv/lib/python3.10/site-packages/sympy/assumptions/handlers/calculus.py_s r&cCsxd}d}|jD]2}tt||}|rqtt||}|dkr$||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. TNF)argsrrr extended_positive)r"r#rresultarg_boundedsr$r$r%r& s> cCsd}d}|jD]F}tt||}|r'tt||dur&|dur$dSd}q|durF|dur2dStt||dur?dS|durEd}q|rKdSd}q|S)a) Return True if expr is bounded, False if not and None if unknown. Truth Table: +---+---+---+--------+ | | | | | | | B | U | ? | | | | | | +---+---+---+---+----+ | | | | | | | | | | s | /s | | | | | | | +---+---+---+---+----+ | | | | | | B | B | U | ? | | | | | | +---+---+---+---+----+ | | | | | | | U | | U | U | ? | | | | | | | +---+---+---+---+----+ | | | | | | ? | | | ? | | | | | | +---+---+---+---+----+ * B = Bounded * U = Unbounded * ? = unknown boundedness * s = signed (hence nonzero) * /s = not signed TFN)r(rrr zeroextended_nonzero)r"r#r* possible_zeror+r,r$r$r%r&rs,' cCs<|jtkrtt|j|Stt|j|}tt|j|}|dur*|dur*dS|dur9tt|j|r9dS|re|rett|j|}tt|j|}|durY|durYdS|durc|durcdSdSt |jdkdkrytt |j|rydSt |jdkdkrtt |j|rdSt |jdkdkr|durdSdS)z * Unbounded ** NonZero -> Unbounded * Bounded ** Bounded -> Bounded * Abs()<=1 ** Positive -> Bounded * Abs()>=1 ** Negative -> Bounded * Otherwise unknown NFT) baserrrr rr/r.negativeabsr)extended_negative)r"r# base_bounded exp_bounded is_base_zerois_exp_negativer$r$r%r&s. $$cCstt|j|SN)rrr rr!r$r$r%r&scCs2tt|jd|r dStt|jd|S)NrF)rrinfiniter(r.r!r$r$r%r&scCdSNTr$r!r$r$r%r&scCr<NFr$r!r$r$r%r&cCsdSr:r$r!r$r$r%r&r?cCs"t||}|durdS| Sr:)rr _eval_ask)r"r#rr$r$r%r&scCr<r=r$r!r$r$r%r&r?cCr<r>r$r!r$r$r%r&r?cCr<r=r$r!r$r$r%r& r?cCr<r>r$r!r$r$r%r&r?N)&__doc__sympy.assumptionsrr sympy.corerrrrrsympy.core.numbersr r r r r rrrrrrsympy.functionsrrrrrsympy.logic.boolalgrpredicates.calculusrrrrregisterr& register_manyr$r$r$r%sJ4   Q < %