B [@sPdZddlmZmZddlmZddlmZmZddl m Z Gddde Z dS) zc This module contains query handlers responsible for calculus queries: infinitesimal, finite, etc. )print_functiondivision) conjuncts)Qask) CommonHandlerc @seZdZdZeddZeddZeddZedd Zed d Z e Z ee j gd \ Z ZZZZZZZZee jgd \ZZdS)AskFiniteHandlera Handler for key 'finite'. Test that an expression is bounded respect to all its variables. Examples of usage: >>> from sympy import Symbol, Q >>> from sympy.assumptions.handlers.calculus import AskFiniteHandler >>> from sympy.abc import x >>> a = AskFiniteHandler() >>> a.Symbol(x, Q.positive(x)) == None True >>> a.Symbol(x, Q.finite(x)) True cCs*|jdk r|jSt|t|kr&dSdS)ap Handles Symbol. Examples ======== >>> from sympy import Symbol, Q >>> from sympy.assumptions.handlers.calculus import AskFiniteHandler >>> from sympy.abc import x >>> a = AskFiniteHandler() >>> a.Symbol(x, Q.positive(x)) == None True >>> a.Symbol(x, Q.finite(x)) True NT)Z is_finiterfiniter)expr assumptionsr Blib/python3.7/site-packages/sympy/assumptions/handlers/calculus.pySymbols  zAskFiniteHandler.SymbolcCs~d}d}xp|jD]f}tt||}|r*qtt||}|dkrJ||ksb|dkrf||ksb||krfdS|}|dk r|}qW|S)a 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 positive)r r signresultarg_boundedsr r r Add7sB zAskFiniteHandler.AddcCsnd}xd|jD]Z}tt||}|r(q q |dkrb|dkr Unbounded Bounded ** Bounded -> Bounded Abs()<=1 ** Positive -> Bounded Abs()>=1 ** Negative -> Bounded Otherwise unknown NFT) rrr baseexprabsrnegative)r r Z base_boundedZ exp_boundedr r r Pows $$zAskFiniteHandler.PowcCstt|jd|S)Nr)rrr r)r r r r r logszAskFiniteHandler.log N)__name__ __module__ __qualname____doc__ staticmethodrrrrr rrZ AlwaysTrueZcosZsinNumberZPiZExp1Z GoldenRatioZTribonacciConstantZ ImaginaryUnitrZ AlwaysFalseZInfinityZNegativeInfinityr r r r r s  V 8  "rN) r&Z __future__rrZsympy.logic.boolalgrZsympy.assumptionsrrZsympy.assumptions.handlersrrr r r r s