ó ¡¼™\c@ sldZddlmZmZddlmZddlmZmZddl m Z de fd„ƒYZ dS( sc This module contains query handlers responsible for calculus queries: infinitesimal, finite, etc. iÿÿÿÿ(tprint_functiontdivision(t conjuncts(tQtask(t CommonHandlertAskFiniteHandlerc B s¬eZdZed„ƒZed„ƒZed„ƒZed„ƒZed„ƒZeZ ee j ƒgd\ Z Z ZZZZZZZee jƒgd\ZZRS(s 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 cC s9|jdk r|jStj|ƒt|ƒkr5tSdS(sp 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 N(t is_finitetNoneRtfiniteRtTrue(texprt assumptions((sBlib/python2.7/site-packages/sympy/assumptions/handlers/calculus.pytSymbols cC s»d}t}x¨|jD]}ttj|ƒ|ƒ}|r@qnttj|ƒ|ƒ}|dkrp||ks”|dkr˜||ks”||kr˜dS|}|tk r|}qqW|S(s 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. iÿÿÿÿN(R targsRRR tpositiveRtFalse(R R tsigntresulttargt_boundedts((sBlib/python2.7/site-packages/sympy/assumptions/handlers/calculus.pytAdd7sB$  cC sžt}x‘|jD]†}ttj|ƒ|ƒ}|r:qq|dkr|dkrVdSttj|ƒ|ƒdkrxdS|tk r–d}q–qt}qW|S(sž 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 N(R RRRR RtnonzeroR(R R RRR((sBlib/python2.7/site-packages/sympy/assumptions/handlers/calculus.pytMuls(     cC s0ttj|jƒ|ƒ}ttj|jƒ|ƒ}|dkrR|dkrRdS|tkr}ttj|jƒ|ƒr}tS|r|rtSt |jƒdktkrÇttj |jƒ|ƒrÇtSt |jƒdktkrttj |jƒ|ƒrtSt |jƒdktkr,|tkr,tSdS(sà Unbounded ** NonZero -> Unbounded Bounded ** Bounded -> Bounded Abs()<=1 ** Positive -> Bounded Abs()>=1 ** Negative -> Bounded Otherwise unknown iN( RRR tbasetexpRRRR tabsRtnegative(R R t base_boundedt exp_bounded((sBlib/python2.7/site-packages/sympy/assumptions/handlers/calculus.pytPowÅs ' 66'cC sttj|jdƒ|ƒS(Ni(RRR R(R R ((sBlib/python2.7/site-packages/sympy/assumptions/handlers/calculus.pytlogÞsi i(t__name__t __module__t__doc__t staticmethodR RRRR RRt AlwaysTruetcostsintNumbertPitExp1t GoldenRatiotTribonacciConstantt ImaginaryUnitRt AlwaysFalsetInfinitytNegativeInfinity(((sBlib/python2.7/site-packages/sympy/assumptions/handlers/calculus.pyR sV81N( R#t __future__RRtsympy.logic.boolalgRtsympy.assumptionsRRtsympy.assumptions.handlersRR(((sBlib/python2.7/site-packages/sympy/assumptions/handlers/calculus.pyts