ó ¡¼™\c@ sÄdZddlmZmZddlmZmZddlmZddl m Z ddl m Z m Z defd„ƒYZd efd „ƒYZd efd „ƒYZd efd„ƒYZdS(sD Handlers for keys related to number theory: prime, even, odd, etc. iÿÿÿÿ(tprint_functiontdivision(tQtask(t CommonHandler(tisprime(tStFloattAskPrimeHandlercB s¨eZdZed„ƒZed„ƒZed„ƒZed„ƒZed„ƒZed„ƒZ ee j ƒgd\Z Z ZZed„ƒZed „ƒZRS( sî Handler for key 'prime' Test that an expression represents a prime number. When the expression is an exact number, the result (when True) is subject to the limitations of isprime() which is used to return the result. cC s|jS(N(tis_prime(texprt assumptions((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pytExprscC sq|jtƒ }y8t|jƒƒ}||jdƒtkrGt‚nWntk r\tSX|rmt|ƒSdS(Ni(tatomsRtinttroundtequalstFalset TypeErrorR(R R texactti((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pyt_numbers  cC s|jrtj||ƒSdS(N(t is_numberRR(R R ((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pytBasic's cC sw|jrtj||ƒSx-|jD]"}ttj|ƒ|ƒs#dSq#Wx'|jD]}|jrS|jrSt SqSWdS(N( RRRtargsRRtintegertNonet is_compositeR(R R targ((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pytMul,s cC sW|jrtj||ƒSttj|jƒ|ƒrSttj|jƒ|ƒrStSdS(s0 Integer**Integer -> !Prime N( RRRRRRtexptbaseR(R R ((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pytPow7s  cC s t|ƒS(N(R(R R ((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pytIntegerBsicC stj||ƒS(N(RR(R R ((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pyRHscC stj||ƒS(N(RR(R R ((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pyt NumberSymbolLs(t__name__t __module__t__doc__t staticmethodR RRRR R!Rt AlwaysFalsetRationaltInfinitytNegativeInfinityt ImaginaryUnitRR"(((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pyR s  "tAskCompositeHandlercB s&eZed„ƒZed„ƒZRS(cC s|jS(N(R(R R ((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pyR SscC s‹ttj|ƒ|ƒ}|rƒttj|ƒ|ƒ}|r|ttj|ƒ|ƒ}|dkrddS|jdƒrwtS| S|Sn|SdS(Ni(RRtpositiveRtprimeRRR(R R t _positivet_integert_prime((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pyRWs (R#R$R&R R(((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pyR,QstAskEvenHandlercB sÏeZed„ƒZed„ƒZed„ƒZed„ƒZed„ƒZed„ƒZed„ƒZ ee j ƒgd\Z Z ZZed„ƒZed „ƒZed „ƒZed „ƒZRS( cC s|jS(N(tis_even(R R ((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pyR mscC sny2t|jƒƒ}||jdƒs1t‚nWntk rFtSXt|ttfƒr`tS|ddkS(Nii(RRRRRt isinstancetfloatR(R R R((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pyRqs  cC s|jrtj||ƒSdS(N(RR2R(R R ((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pyR~s cC sJ|jrtj||ƒStdtdf\}}}}x |jD]Ô}ttj|ƒ|ƒrãttj|ƒ|ƒr€t }qttj |ƒ|ƒr¥|d7}q| r|dkrttj ||ƒ|ƒràt }qàqn,ttj |ƒ|ƒr|rPnt }nP|}qAW|r#tS|r-t S|t |jƒkrFtSdS(s  Even * Integer -> Even Even * Odd -> Even Integer * Odd -> ? Odd * Odd -> Odd Even * Even -> Even Integer * Integer -> Even if Integer + Integer = Odd otherwise -> ? iiN( RR2RRRRRRteventTruetoddt irrationaltlen(R R R6R8R9taccR((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pyRƒs0     cC sy|jrtj||ƒSt}xS|jD]D}ttj|ƒ|ƒrJq)ttj|ƒ|ƒrl| }q)Pq)W|SdS(s] Even + Odd -> Odd Even + Even -> Even Odd + Odd -> Even N( RR2RR7RRRR6R8(R R t_resultR((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pytAdd¬s  cC sµ|jrtj||ƒSttj|jƒ|ƒr±ttj|jƒ|ƒrhttj|j ƒ|ƒSttj |jƒtj |j ƒ@|ƒr˜t S|j t jkr±t SndS(N(RR2RRRRRR-R6RtnegativeR8RRt NegativeOne(R R ((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pyR Ás ,cC st|jd@ƒ S(Ni(tbooltp(R R ((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pyR!ÍsicC stj||ƒS(N(R2R(R R ((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pyR"ÓscC s@ttj|jdƒ|ƒr<ttj|jdƒ|ƒSdS(Ni(RRtrealRR6(R R ((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pytAbs×scC s@ttj|jdƒ|ƒr<ttj|jdƒ|ƒSdS(Ni(RRRBRR6(R R ((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pytreÜscC s'ttj|jdƒ|ƒr#tSdS(Ni(RRRBRR7(R R ((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pytimás(R#R$R&R RRRR=R R!RR'R(R)R*R+R"RCRDRE(((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pyR2ks ) "t AskOddHandlercB s,eZdZed„ƒZed„ƒZRS(sT Handler for key 'odd' Test that an expression represents an odd number cC s|jS(N(tis_odd(R R ((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pyR íscC sOttj|ƒ|ƒ}|rKttj|ƒ|ƒ}|dkrFdS| S|S(N(RRRR6R(R R R0t_even((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pyRñs (R#R$R%R&R R(((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pyRFçsN(R%t __future__RRtsympy.assumptionsRRtsympy.assumptions.handlersRt sympy.ntheoryRt sympy.coreRRRR,R2RF(((sAlib/python2.7/site-packages/sympy/assumptions/handlers/ntheory.pytsE|