ó ~9­\c@ s^dZddlmZmZddlmZmZddlmZm Z ddl m Z ddl m Z mZddlmZdefd „ƒYZd efd „ƒYZd efd „ƒYZdefd„ƒYZdefd„ƒYZdefd„ƒYZdefd„ƒYZdefd„ƒYZdefd„ƒYZdefd„ƒYZdS(sL Handlers for predicates related to set membership: integer, rational, etc. iÿÿÿÿ(tprint_functiontdivision(tQtask(t CommonHandlerttest_closed_group(tpi(texptlog(tItAskIntegerHandlercB sÎeZdZed„ƒZed„ƒZed„ƒZed„ƒZeZee j ƒgd\Z Z ee j ƒgd\ZZZZZZZed„ƒZed„ƒZed „ƒZeZZRS( sc Handler for Q.integer Test that an expression belongs to the field of integer numbers cC s|jS(N(t is_integer(texprt assumptions((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pytExprscC sOy6t|jƒƒ}||jdƒs1t‚ntSWntk rJtSXdS(Ni(tinttroundtequalst TypeErrortTruetFalse(R R ti((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyt_numbers  cC s,|jrtj||ƒSt||tjƒS(s Integer + Integer -> Integer Integer + !Integer -> !Integer !Integer + !Integer -> ? (t is_numberR RRRtinteger(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pytAdd"s cC sÏ|jrtj||ƒSt}x©|jD]š}ttj|ƒ|ƒs)|jrŽ|j dkryttj d|ƒ|ƒS|j d@rÀdSqÃttj |ƒ|ƒr¼|rµt }qÀdSqÃdSq)q)W|SdS(s¥ Integer*Integer -> Integer Integer*Irrational -> !Integer Odd/Even -> !Integer Integer*Rational -> ? iiN(RR RRtargsRRRt is_RationaltqteventNonet irrationalR(R R t_outputtarg((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pytMul-s     iicC stS(N(R(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pytRationalPscC sttj|jdƒ|ƒS(Ni(RRRR(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pytAbsVscC sttj|jdƒ|ƒS(Ni(RRtinteger_elementsR(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyt MatrixElementZs(t__name__t __module__t__doc__t staticmethodRRRR"tPowRt AlwaysTrueRtIntegert AlwaysFalsetPitExp1t GoldenRatiotTribonacciConstanttInfinitytNegativeInfinityt ImaginaryUnitR#R$R&t DeterminanttTrace(((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR s  +tAskRationalHandlercB sàeZdZed„ƒZed„ƒZeZed„ƒZeej ƒZ eej ƒZ eej ƒgd\ZZZZZZZed„ƒZed„ƒZed„ƒZegd\ZZZZZeeZZRS( se Handler for Q.rational Test that an expression belongs to the field of rational numbers cC s|jS(N(t is_rational(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyRhscC s3|jr |jƒdr tSnt||tjƒS(s‡ Rational + Rational -> Rational Rational + !Rational -> !Rational !Rational + !Rational -> ? i(Rt as_real_imagRRRtrational(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyRls cC suttj|jƒ|ƒr4ttj|jƒ|ƒSttj|jƒ|ƒrqttj|jƒ|ƒrqtSndS(s‹ Rational ** Integer -> Rational Irrational ** Rational -> Irrational Rational ** Irrational -> ? N(RRRRR;tbasetprimeR(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR+zs icC s@|jd}ttj|ƒ|ƒr<ttj|ƒ|ƒSdS(Ni(RRRR;tnonzero(R R tx((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyRs cC s-|jd}ttj|ƒ|ƒr)tSdS(Ni(RRRR;R(R R R?((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pytcot•s cC sD|jd}ttj|ƒ|ƒr@ttj|dƒ|ƒSdS(Nii(RRRR;R>(R R R?((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR›s i(R'R(R)R*RRR"R+RR,R#t AlwaysNonetFloatR.R5R3R4R/R0R1R2RR@Rtsintcosttantasintatantacostacot(((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR8as +tAskIrrationalHandlercB s&eZed„ƒZed„ƒZRS(cC s|jS(N(t is_irrational(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR¨scC sSttj|ƒ|ƒ}|rKttj|ƒ|ƒ}|dkrFdS| S|SdS(N(RRtrealR;R(R R t_realt _rational((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pytBasic¬s (R'R(R*RRO(((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyRJ¥stAskRealHandlerc B sõeZdZed„ƒZed„ƒZed„ƒZed„ƒZed„ƒZee j ƒgd\ Z Z Z ZZZZZZee jƒgd\ZZZed„ƒZeZed „ƒZed „ƒZed „ƒZeZZRS( s] Handler for Q.real Test that an expression belongs to the field of real numbers cC s|jS(N(tis_real(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR¾scC s1|jƒdjdƒ}|jdkr-| SdS(Nii(R:tevalft_prec(R R R((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyRÂscC s,|jrtj||ƒSt||tjƒS(s\ Real + Real -> Real Real + (Complex & !Real) -> !Real (RRPRRRRL(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyRÌs cC s||jrtj||ƒSt}xV|jD]G}ttj|ƒ|ƒrJq)ttj|ƒ|ƒro|tA}q)Pq)W|SdS(s‚ Real*Real -> Real Real*Imaginary -> !Real Imaginary*Imaginary -> Real N( RRPRRRRRRLt imaginary(R R tresultR!((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR"Ös  cC s`|jrtj||ƒS|jjtkrÈttj|jj dƒ|ƒrottj|jƒ|ƒrot Sn|jj dt t }ttj d|ƒ|ƒrÄttjd||jƒ|ƒSdSttj|jƒ|ƒr1ttj |jƒ|ƒr1ttj|jƒ|ƒ}|dk r*| SdSnttj|jƒ|ƒr€ttjt|jƒƒ|ƒ}|dk r€|Snttj|jƒ|ƒr\ttj|jƒ|ƒr\|jjrùttj|jjƒ|ƒrùttj|jƒ|ƒSttj |jƒ|ƒrt Sttj|jƒ|ƒr7t Sttj|jƒ|ƒrYtSq\ndS(s] Real**Integer -> Real Positive**Real -> Real Real**(Integer/Even) -> Real if base is nonnegative Real**(Integer/Odd) -> Real Imaginary**(Integer/Even) -> Real Imaginary**(Integer/Odd) -> not Real Imaginary**Real -> ? since Real could be 0 (giving real) or 1 (giving imaginary) b**Imaginary -> Real if log(b) is imaginary and b != 0 and exponent != integer multiple of I*pi/log(b) Real**Real -> ? e.g. sqrt(-1) is imaginary and sqrt(2) is not iiiÿÿÿÿN(RRPRR<tfuncRRRRTRRR RRRLtoddRRRRRtpositivetnegativeR(R R RRWtimlog((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR+ês> "! !  i icC s'ttj|jdƒ|ƒr#tSdS(Ni(RRRLRR(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyRC'scC s9ttj|jdttƒtj|jdƒB|ƒS(Ni(RRRRR RRL(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR.scC sttj|jdƒ|ƒS(Ni(RRRXR(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR2scC sttj|jdƒ|ƒS(Ni(RRt real_elementsR(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR&6s(R'R(R)R*RRRR"R+RR,R#RBR/R0R1R2R$tretimR.R5R3R4RCRDRRR&R6R7(((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyRP¸s  81tAskExtendedRealHandlercB sLeZdZed„ƒZegd\ZZeejƒgd\Z Z RS(s¥ Handler for Q.extended_real Test that an expression belongs to the field of extended real numbers, that is real numbers union {Infinity, -Infinity} cC st||tjƒS(N(RRt extended_real(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyRDsi( R'R(R)R*RR"R+RR,R3R4(((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR^=stAskHermitianHandlercB s]eZdZed„ƒZed„ƒZed„ƒZed„ƒZegd\ZZ RS(si Handler for Q.hermitian Test that an expression belongs to the field of Hermitian operators cC s,|jrtj||ƒSt||tjƒS(sb Hermitian + Hermitian -> Hermitian Hermitian + !Hermitian -> !Hermitian (RRPRRRt hermitian(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyRSs cC s¸|jrtj||ƒSd}t}xŒ|jD]}}ttj|ƒ|ƒrZ|tA}nttj|ƒ|ƒsvPnttj |ƒ|ƒr/|d7}|dkr¬Pq¬q/q/W|SdS(sß As long as there is at most only one noncommutative term: Hermitian*Hermitian -> Hermitian Hermitian*Antihermitian -> !Hermitian Antihermitian*Antihermitian -> Hermitian iiN( RRPRRRRRt antihermitianRat commutative(R R tnccountRUR!((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR"]s     cC sZ|jrtj||ƒSttj|jƒ|ƒrVttj|jƒ|ƒrVt SndS(s1 Hermitian**Integer -> Hermitian N( RRPRRRRaR<RRR(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR+us  cC s'ttj|jdƒ|ƒr#tSdS(Ni(RRRaRR(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyRC€si( R'R(R)R*RR"R+RCRDR(((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR`Ms   tAskComplexHandlerc B s¨eZdZed„ƒZed„ƒZegd\ZZeej ƒgd\ Z Z Z Z ZZZZZZeejƒgd\ZZed„ƒZeZZRS(sc Handler for Q.complex Test that an expression belongs to the field of complex numbers cC s|jS(N(t is_complex(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyRŽscC st||tjƒS(N(RRtcomplex(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR’sii cC sttj|jdƒ|ƒS(Ni(RRtcomplex_elementsR(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR&s(R'R(R)R*RRR"R+RR,tNumberRCRDRRR\R]t NumberSymbolR$R5R.R3R4R&R6R7(((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyReˆs4tAskImaginaryHandlercB s›eZdZed„ƒZed„ƒZed„ƒZed„ƒZed„ƒZed„ƒZ ed„ƒZ ed„ƒZ e Z ee jƒZRS( sž Handler for Q.imaginary Test that an expression belongs to the field of imaginary numbers, that is, numbers in the form x*I, where x is real cC s|jS(N(t is_imaginary(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR«scC s1|jƒdjdƒ}|jdkr-| SdS(Niii(R:RRRS(R R tr((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR¯scC s­|jrtj||ƒSd}x‡|jD]G}ttj|ƒ|ƒrJq)ttj|ƒ|ƒro|d7}q)Pq)W|dkr„tS|dks¥t |jƒ|kr©t SdS(sƒ Imaginary + Imaginary -> Imaginary Imaginary + Complex -> ? Imaginary + Real -> !Imaginary iiN( RRkRRRRRTRLRtlenR(R R trealsR!((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR¹s   !cC s›|jrtj||ƒSt}d}xo|jD]G}ttj|ƒ|ƒrZ|tA}q/ttj |ƒ|ƒs/Pq/q/W|t |jƒkr“tS|SdS(sV Real*Imaginary -> Imaginary Imaginary*Imaginary -> Real iN( RRkRRRRRRTRRLRn(R R RURoR!((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR"Òs  cC sU|jrtj||ƒS|jjtkrÇttj|jj dƒ|ƒrÇttj|jƒ|ƒrlt S|jj dt t }ttj d|ƒ|ƒrÄttjd||jƒ|ƒSqÇnttj|jƒ|ƒr/ttj |jƒ|ƒr/ttj|jƒ|ƒ}|dk r(|SdSnttj|jƒ|ƒr~ttjt|jƒƒ|ƒ}|dk r~t Snttj|jƒtj|jƒ@|ƒrQttj|jƒ|ƒrÈt Sttj|jƒ|ƒ}|sí|Sttj |jƒ|ƒr t Sttj d|jƒ|ƒ}|rJttj|jƒ|ƒS|SndS(s Imaginary**Odd -> Imaginary Imaginary**Even -> Real b**Imaginary -> !Imaginary if exponent is an integer multiple of I*pi/log(b) Imaginary**Real -> ? Positive**Real -> Real Negative**Integer -> Real Negative**(Integer/2) -> Imaginary Negative**Real -> not Imaginary if exponent is not Rational iiiÿÿÿÿN(RRkRR<RVRRRRTRRR RRRWRRRLRXR;RY(R R RRWRZtratthalf((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR+æs> "' ! +cC s·ttj|jdƒ|ƒrFttj|jdƒ|ƒrBtSdS|jdjtkr„|jdjdtt gkr„t Snttj |jdƒ|ƒ}|tkr³tSdS(Ni( RRRLRRXRRVRR RRT(R R R]((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyRs! cC s=|jdtt}ttjd|ƒtj|ƒ@|ƒS(Nii(RR RRRR(R R ta((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR*scC s|jƒddk S(Nii(R:(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyRi/s(R'R(R)R*RRRR"R+RRRiRjRR,R5(((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyRk¤s 3tAskAntiHermitianHandlercB s;eZdZed„ƒZed„ƒZed„ƒZRS(s° Handler for Q.antihermitian Test that an expression belongs to the field of anti-Hermitian operators, that is, operators in the form x*I, where x is Hermitian cC s,|jrtj||ƒSt||tjƒS(sz Antihermitian + Antihermitian -> Antihermitian Antihermitian + !Antihermitian -> !Antihermitian (RRkRRRRb(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR?s cC s¸|jrtj||ƒSd}t}xŒ|jD]}}ttj|ƒ|ƒrZ|tA}nttj |ƒ|ƒsvPnttj |ƒ|ƒr/|d7}|dkr¬Pq¬q/q/W|SdS(sì As long as there is at most only one noncommutative term: Hermitian*Hermitian -> !Antihermitian Hermitian*Antihermitian -> Antihermitian Antihermitian*Antihermitian -> !Antihermitian iiN( RRkRRRRRRbRRaRc(R R RdRUR!((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR"Is     cC s¶|jrtj||ƒSttj|jƒ|ƒrVttj|jƒ|ƒr²t Sn\ttj |jƒ|ƒr²ttj |jƒ|ƒrt Sttj |jƒ|ƒr²t SndS(s’ Hermitian**Integer -> !Antihermitian Antihermitian**Even -> !Antihermitian Antihermitian**Odd -> Antihermitian N(RRkRRRRaR<RRRRbRRWR(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR+as (R'R(R)R*RR"R+(((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyRs8s tAskAlgebraicHandlercB sêeZdZed„ƒZed„ƒZed„ƒZed„ƒZeej ƒgd\Z Z Z Z Zeejƒgd\ZZZZZed„ƒZed„ƒZed„ƒZegd\ZZZZZeeZZRS( sHandler for Q.algebraic key. cC st||tjƒS(N(RRt algebraic(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyRwscC st||tjƒS(N(RRRu(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR"{scC s%|jjo$ttj|jƒ|ƒS(N(RRRRRuR<(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR+scC s |jdkS(Ni(R(R R ((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR#„sicC s@|jd}ttj|ƒ|ƒr<ttj|ƒ|ƒSdS(Ni(RRRRuR>(R R R?((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyRŽs cC s-|jd}ttj|ƒ|ƒr)tSdS(Ni(RRRRuR(R R R?((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyR@”s cC sD|jd}ttj|ƒ|ƒr@ttj|dƒ|ƒSdS(Nii(RRRRuR>(R R R?((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyRšs (R'R(R)R*RR"R+R#RR,RBR1R2R5tAlgebraicNumberR.R3R4tComplexInfinityR/R0RR@RRCRDRERFRGRHRI(((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyRtts%%N(R)t __future__RRtsympy.assumptionsRRtsympy.assumptions.handlersRRtsympy.core.numbersRt&sympy.functions.elementary.exponentialRRtsympyR R R8RJRPR^R`ReRkRsRt(((s>lib/python2.7/site-packages/sympy/assumptions/handlers/sets.pyts TD…;”<