B [+S@sdZddlmZmZddlmZmZddlmZm Z ddl m Z ddl m Z mZddlmZGdd d eZGd d d eZGd d d eZGdddeZGdddeZGdddeZGdddeZGdddeZGdddeZGdddeZdS)zL Handlers for predicates related to set membership: integer, rational, etc. )print_functiondivision)Qask) CommonHandlertest_closed_group)pi)explog)Ic@seZdZdZeddZeddZeddZedd ZeZ ee j gd \Z Z ee jgd \ZZZZZZZed d ZeddZeddZeZZdS)AskIntegerHandlerzc Handler for Q.integer Test that an expression belongs to the field of integer numbers cCs|jS)N) is_integer)expr assumptionsr>lib/python3.7/site-packages/sympy/assumptions/handlers/sets.pyExprszAskIntegerHandler.ExprcCs<y"t|}||ds tdStk r6dSXdS)NrTF)introundZequals TypeError)rrirrr_numbers zAskIntegerHandler._numbercCs |jrt||St||tjS)z Integer + Integer -> Integer Integer + !Integer -> !Integer !Integer + !Integer -> ? ) is_numberr rrrinteger)rrrrrAdd"s zAskIntegerHandler.AddcCs|jrt||Sd}x||jD]n}tt||s|jrh|jdkrVtt d||S|jd@rdSqtt ||r|rd}qdSqdSqW|SdS)z Integer*Integer -> Integer Integer*Irrational -> !Integer Odd/Even -> !Integer Integer*Rational -> ? TNF) rr rargsrrr is_RationalqevenZ irrational)rrZ_outputargrrrMul-s     zAskIntegerHandler.MulrcCsdS)NFr)rrrrrRationalPszAskIntegerHandler.RationalcCstt|jd|S)Nr)rrrr)rrrrrAbsVszAskIntegerHandler.AbscCstt|jd|S)Nr)rrZinteger_elementsr)rrrrr MatrixElementZszAskIntegerHandler.MatrixElementN)__name__ __module__ __qualname____doc__ staticmethodrrrr"Powr AlwaysTruerZInteger AlwaysFalsePiExp1 GoldenRatioTribonacciConstantInfinityNegativeInfinity ImaginaryUnitr$r%r& DeterminantTracerrrrr s     r c@seZdZdZeddZeddZeZeddZee j Z ee j Z ee jgd\ZZZZZZZed d Zed d Zed dZegd\ZZZZZeeZZdS)AskRationalHandlerze Handler for Q.rational Test that an expression belongs to the field of rational numbers cCs|jS)N)Z is_rational)rrrrrrhszAskRationalHandler.ExprcCs$|jr|drdSt||tjS)z Rational + Rational -> Rational Rational + !Rational -> !Rational !Rational + !Rational -> ? rF)r as_real_imagrrrational)rrrrrrls zAskRationalHandler.AddcCsPtt|j|r$tt|j|Stt|j|rLtt|j|rLdSdS)z Rational ** Integer -> Rational Irrational ** Rational -> Irrational Rational ** Irrational -> ? FN)rrrr r:baseZprime)rrrrrr,zs zAskRationalHandler.Powr#cCs0|jd}tt||r,tt||SdS)Nr)rrrr:nonzero)rrxrrrr s zAskRationalHandler.expcCs"|jd}tt||rdSdS)NrF)rrrr:)rrr=rrrcots zAskRationalHandler.cotcCs4|jd}tt||r0tt|d|SdS)Nrr)rrrr:r<)rrr=rrrr s zAskRationalHandler.logN) r'r(r)r*r+rrr"r,rr-r$Z AlwaysNoneFloatr.r5r3r4r/r0r1r2r r>r sincostanasinatanacosacotrrrrr8as        r8c@s$eZdZeddZeddZdS)AskIrrationalHandlercCs|jS)N)Z is_irrational)rrrrrrszAskIrrationalHandler.ExprcCs>tt||}|r6tt||}|dkr0dS| S|SdS)N)rrrealr:)rrZ_realZ _rationalrrrBasicszAskIrrationalHandler.BasicN)r'r(r)r+rrJrrrrrHs rHc @seZdZdZeddZeddZeddZedd Zed d Z ee j gd \ Z Z ZZZZZZZee jgd \ZZZeddZeZeddZeddZeddZeZZdS)AskRealHandlerz] Handler for Q.real Test that an expression belongs to the field of real numbers cCs|jS)N)Zis_real)rrrrrrszAskRealHandler.ExprcCs&|dd}|jdkr"| SdS)Nrr)r9evalf_prec)rrrrrrrs zAskRealHandler._numbercCs |jrt||St||tjS)z\ Real + Real -> Real Real + (Complex & !Real) -> !Real )rrKrrrrI)rrrrrrs zAskRealHandler.AddcCs\|jrt||Sd}x@|jD]2}tt||r4qtt||rN|dA}qPqW|SdS)z Real*Real -> Real Real*Imaginary -> !Real Imaginary*Imaginary -> Real TN)rrKrrrrrI imaginary)rrresultr!rrrr"s   zAskRealHandler.MulcCs|jrt||S|jjtkrtt|jj d|rLtt|j|rLdS|jj dt t }tt d||rtt d||j|SdStt|j|rtt |j|rtt|j|}|dk r| SdStt|j|rttt|j|}|dk r|Stt |j|rtt |j|r|jjrltt|jj|rltt|j|Stt |j|rdStt|j|rdStt|j|rdSdS)a] Real**Integer -> Real Positive**Real -> Real Real**(Integer/Even) -> Real if base is nonnegative Real**(Integer/Odd) -> Real Imaginary**(Integer/Even) -> Real Imaginary**(Integer/Odd) -> not Real Imaginary**Real -> ? since Real could be 0 (giving real) or 1 (giving imaginary) b**Imaginary -> Real if log(b) is imaginary and b != 0 and exponent != integer multiple of I*pi/log(b) Real**Real -> ? e.g. sqrt(-1) is imaginary and sqrt(2) is not rTrNF)rrKrr;funcr rrrNrr rrrIoddr rr rpositivenegative)rrrrRimlogrrrr,s>     zAskRealHandler.Pow cCstt|jd|rdSdS)NrT)rrrIr)rrrrrrA'szAskRealHandler.sincCs.tt|jdttt|jdB|S)Nr)rrrrr rrI)rrrrrr .szAskRealHandler.expcCstt|jd|S)Nr)rrrSr)rrrrrr 2szAskRealHandler.logcCstt|jd|S)Nr)rrZ real_elementsr)rrrrrr&6szAskRealHandler.MatrixElementN) r'r(r)r*r+rrrr"r,rr-r$r@r/r0r1r2r%reimr.r5r3r4rArBr r r&r6r7rrrrrKs   8"    rKc@s>eZdZdZeddZegd\ZZeej gd\Z Z dS)AskExtendedRealHandlerz Handler for Q.extended_real Test that an expression belongs to the field of extended real numbers, that is real numbers union {Infinity, -Infinity} cCst||tjS)N)rrZ extended_real)rrrrrrDszAskExtendedRealHandler.AddrN) r'r(r)r*r+rr"r,rr-r3r4rrrrrZ=s rZc@sNeZdZdZeddZeddZeddZedd Zegd \Z Z d S) AskHermitianHandlerzi Handler for Q.hermitian Test that an expression belongs to the field of Hermitian operators cCs |jrt||St||tjS)zb Hermitian + Hermitian -> Hermitian Hermitian + !Hermitian -> !Hermitian )rrKrrr hermitian)rrrrrrSs zAskHermitianHandler.AddcCs|jrt||Sd}d}xb|jD]T}tt||r@|dA}ntt||sRPtt||r"|d7}|dkr"Pq"W|SdS)z As long as there is at most only one noncommutative term: Hermitian*Hermitian -> Hermitian Hermitian*Antihermitian -> !Hermitian Antihermitian*Antihermitian -> Hermitian rTrN) rrKrrrr antihermitianr\ commutative)rrnccountrOr!rrrr"]s   zAskHermitianHandler.MulcCs>|jrt||Stt|j|r:tt|j|r:dSdS)z1 Hermitian**Integer -> Hermitian TN) rrKrrrr\r;rr )rrrrrr,us  zAskHermitianHandler.PowcCstt|jd|rdSdS)NrT)rrr\r)rrrrrrAszAskHermitianHandler.sinrN) r'r(r)r*r+rr"r,rArBr rrrrr[Ms   r[c @seZdZdZeddZeddZegd\ZZee j gd\ Z Z Z ZZZZZZZee jgd\ZZedd ZeZZd S) AskComplexHandlerzc Handler for Q.complex Test that an expression belongs to the field of complex numbers cCs|jS)N)Z is_complex)rrrrrrszAskComplexHandler.ExprcCst||tjS)N)rrcomplex)rrrrrrszAskComplexHandler.Addr cCstt|jd|S)Nr)rrZcomplex_elementsr)rrrrrr&szAskComplexHandler.MatrixElementN)r'r(r)r*r+rrr"r,rr-NumberrArBr r rXrY NumberSymbolr%r5r.r3r4r&r6r7rrrrr`s  $ r`c@s~eZdZdZeddZeddZeddZedd Zed d Z ed d Z eddZ eddZ e Z eejZdS)AskImaginaryHandlerz 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 cCs|jS)N)Z is_imaginary)rrrrrrszAskImaginaryHandler.ExprcCs&|dd}|jdkr"| SdS)Nrrr)r9rLrM)rrrrrrrs zAskImaginaryHandler._numbercCs~|jrt||Sd}xb|jD]2}tt||r4qtt||rN|d7}qPqW|dkr`dS|dksvt|j|krzdSdS)z Imaginary + Imaginary -> Imaginary Imaginary + Complex -> ? Imaginary + Real -> !Imaginary rrTFN) rrerrrrrNrIlen)rrrealsr!rrrrs   zAskImaginaryHandler.AddcCsp|jrt||Sd}d}xP|jD]0}tt||r@|dA}q"tt||s"Pq"W|t|jkrhdS|SdS)zV Real*Imaginary -> Imaginary Imaginary*Imaginary -> Real FrTN) rrerrrrrNrIrg)rrrOrhr!rrrr"s   zAskImaginaryHandler.MulcCs|jrt||S|jjtkrtt|jj d|rtt|j|rLdS|jj dt t }tt d||rttd||j|Stt|j|rtt |j|rtt |j|}|dk r|SdStt|j|r ttt|j|}|dk r dStt|jt|j@|rtt|j|rDdStt|j|}|s`|Stt |j|rxdStt d|j|}|rtt|j|S|SdS)a 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 rFrrPN)rrerr;rQr rrrNrr rrrRr rIrSr:rT)rrrrRrUZratZhalfrrrr,s>     zAskImaginaryHandler.PowcCstt|jd|r4tt|jd|r0dSdS|jdjtkrb|jdjdtt gkrbdStt|jd|}|dkrdSdS)NrFT) rrrIrrSrQr r rN)rrrYrrrr szAskImaginaryHandler.logcCs2|jdtt}ttd|t|@|S)Nrr)rr rrrr)rrarrrr *szAskImaginaryHandler.expcCs|ddk S)Nrr)r9)rrrrrrc/szAskImaginaryHandler.NumberN)r'r(r)r*r+rrrr"r,r r rcrdrr-r5rrrrres    3   rec@s4eZdZdZeddZeddZeddZdS) AskAntiHermitianHandlerz 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 cCs |jrt||St||tjS)zz Antihermitian + Antihermitian -> Antihermitian Antihermitian + !Antihermitian -> !Antihermitian )rrerrrr])rrrrrr?s zAskAntiHermitianHandler.AddcCs|jrt||Sd}d}xb|jD]T}tt||r@|dA}ntt||sRPtt||r"|d7}|dkr"Pq"W|SdS)z As long as there is at most only one noncommutative term: Hermitian*Hermitian -> !Antihermitian Hermitian*Antihermitian -> Antihermitian Antihermitian*Antihermitian -> !Antihermitian rFTrN) rrerrrrr]r\r^)rrr_rOr!rrrr"Is   zAskAntiHermitianHandler.MulcCs~|jrt||Stt|j|rtt |j|rztt |j|rddStt |j|rzdSdS)z Hermitian**Integer -> !Antihermitian Antihermitian**Even -> !Antihermitian Antihermitian**Odd -> Antihermitian FTN) rrerrrr\r;rr r]r rR)rrrrrr,as zAskAntiHermitianHandler.PowN)r'r(r)r*r+rr"r,rrrrrj8s rjc@seZdZdZeddZeddZeddZedd Zee j gd \Z Z Z ZZee jgd \ZZZZZed d Zed dZeddZegd \ZZZZZeeZZdS)AskAlgebraicHandlerzHandler for Q.algebraic key. cCst||tjS)N)rr algebraic)rrrrrrwszAskAlgebraicHandler.AddcCst||tjS)N)rrrl)rrrrrr"{szAskAlgebraicHandler.MulcCs|jjott|j|S)N)r rrrrlr;)rrrrrr,s zAskAlgebraicHandler.PowcCs |jdkS)Nr)r)rrrrrr$szAskAlgebraicHandler.Rationalr?cCs0|jd}tt||r,tt||SdS)Nr)rrrrlr<)rrr=rrrr s zAskAlgebraicHandler.expcCs"|jd}tt||rdSdS)NrF)rrrrl)rrr=rrrr>s zAskAlgebraicHandler.cotcCs4|jd}tt||r0tt|d|SdS)Nrr)rrrrlr<)rrr=rrrr s zAskAlgebraicHandler.logN) r'r(r)r*r+rr"r,r$rr-r@r1r2r5ZAlgebraicNumberr.r3r4ZComplexInfinityr/r0r r>r rArBrCrDrErFrGrrrrrkts       rkN)r*Z __future__rrZsympy.assumptionsrrZsympy.assumptions.handlersrrZsympy.core.numbersrZ&sympy.functions.elementary.exponentialr r Zsympyr r r8rHrKrZr[r`rerjrkrrrrs$  TD;<