ó ¡¼™\c@ sàdZddlmZmZddlmZmZddlmZm Z m Z ddl m Z ddl mZddlmZddlmZmZmZdd lmZdd lmZmZed efd „ƒYƒZd S(s)Implementation of :class:`Domain` class. iÿÿÿÿ(tprint_functiontdivision(tBasictsympify(tHAS_GMPYt integer_typest is_sequence(t deprecated(t DomainElement(tlex(tUnificationFailedtCoercionFailedt DomainError(t _unify_gens(tdefault_sort_keytpublictDomaincB sÚeZdZdVZdVZdVZeZeZ eZ eZ eZ Z eZZeZZeZZeZZeZZeZZeZZeZZeZeZ eZ!eZ"eZ#eZ$dVZ%dVZ&e'e(ddddddƒd„ƒƒZ)e'e(ddddddƒd „ƒƒZ*d „Z+d „Z,d „Z-d „Z.d„Z/e'd„ƒZ0d„Z1d„Z2d„Z3dVd„Z4d„Z5d„Z6d„Z7d„Z8d„Z9d„Z:d„Z;d„Z<d„Z=d„Z>d„Z?d„Z@d „ZAd!„ZBd"„ZCd#„ZDd$„ZEd%„ZFd&„ZGdVd'„ZHd(„ZId)„ZJd*„ZKd+„ZLd,„ZMd-„ZNd.„ZOd/„ZPd0„ZQd1„ZRd2„ZSd3„ZTd4„ZUd5„ZVd6„ZWd7„ZXd8„ZYd9„ZZd:„Z[d;„Z\d<„Z]d=„Z^d>„Z_d?„Z`d@„ZadA„ZbdB„ZcdC„ZddD„ZedE„ZfdF„ZgdG„ZhdH„ZidI„ZjdJ„ZkdK„ZldL„ZmdM„ZndN„ZodO„ZpdP„ZqdVdQ„ZrerZsdR„ZtdS„ZudVdT„ZvdU„ZwRS(WsRepresents an abstract domain. t useinsteadtis_Fieldtissuei³1tdeprecated_since_versions1.1cC s|jS(N(R(tself((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyt has_Field3stis_RingcC s|jS(N(R(R((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pythas_Ring8scC s t‚dS(N(tNotImplementedError(R((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyt__init__=scC s|jS(N(trep(R((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyt__str__@scC s t|ƒS(N(tstr(R((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyt__repr__CscC st|jj|jfƒS(N(thasht __class__t__name__tdtype(R((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyt__hash__FscG s |j|ŒS(N(R"(Rtargs((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytnewIscC s|jS(N(R"(R((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyttpLscG s |j|ŒS(s7Construct an element of ``self`` domain from ``args``. (R%(RR$((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyt__call__PscG s |j|ŒS(N(R"(RR$((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytnormalTscC s’|jdk rd|j}nd|jj}t||ƒ}|dk rl|||ƒ}|dk rl|Sntd|t|ƒ||fƒ‚dS(s=Convert ``element`` to ``self.dtype`` given the base domain. tfrom_s)can't convert %s of type %s from %s to %sN(taliastNoneR R!tgetattrR ttype(Rtelementtbasetmethodt_converttresult((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyt convert_fromWs  c C sH|dk r|j||ƒS|j|ƒr/|Sddlm}m}m}m}m}t |t ƒry|j||ƒƒSt rØ|ƒ}t ||j ƒrª|j||ƒS|ƒ} t || j ƒrØ|j|| ƒSnt |t ƒr |dtƒ} |j| |ƒ| ƒSt |tƒr@|dtƒ} |j| |ƒ| ƒSt |tƒre|j||jƒƒS|jr“t|dtƒr“|j|jƒƒSt |tƒrÐy|j|ƒSWq%ttfk rÌq%XnUt|ƒs%y,t|ƒ}t |tƒr|j|ƒSWq%ttfk r!q%Xntd|t|ƒ|fƒ‚dS(s'Convert ``element`` to ``self.dtype``. iÿÿÿÿ(tPythonIntegerRingtGMPYIntegerRingtGMPYRationalFieldt RealFieldt ComplexFieldttolt is_grounds!can't convert %s of type %s to %sN(R+R3tof_typetsympy.polys.domainsR4R5R6R7R8t isinstanceRRR&tfloattFalsetcomplexRtparentt is_NumericalR,tconverttLCRt from_sympyt TypeErrort ValueErrorRRR R-( RR.R/R4R5R6R7R8tintegerst rationalsRA((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyRChsJ (    cC st||jƒS(s%Check if ``a`` is of type ``dtype``. (R=R&(RR.((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyR;žscC s*y|j|ƒWntk r%tSXtS(s'Check if ``a`` belongs to this domain. (RCR R?tTrue(Rta((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyt __contains__¢s  cC s t‚dS(s!Convert ``a`` to a SymPy object. N(R(RRK((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytto_sympy«scC s t‚dS(s%Convert a SymPy object to ``dtype``. N(R(RRK((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyRE¯scC sdS(s.Convert ``ModularInteger(int)`` to ``dtype``. N(R+(tK1RKtK0((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytfrom_FF_python³scC sdS(s.Convert a Python ``int`` object to ``dtype``. N(R+(RNRKRO((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytfrom_ZZ_python·scC sdS(s3Convert a Python ``Fraction`` object to ``dtype``. N(R+(RNRKRO((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytfrom_QQ_python»scC sdS(s.Convert ``ModularInteger(mpz)`` to ``dtype``. N(R+(RNRKRO((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyt from_FF_gmpy¿scC sdS(s,Convert a GMPY ``mpz`` object to ``dtype``. N(R+(RNRKRO((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyt from_ZZ_gmpyÃscC sdS(s,Convert a GMPY ``mpq`` object to ``dtype``. N(R+(RNRKRO((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyt from_QQ_gmpyÇscC sdS(s,Convert a real element object to ``dtype``. N(R+(RNRKRO((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytfrom_RealFieldËscC sdS(s(Convert a complex element to ``dtype``. N(R+(RNRKRO((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytfrom_ComplexFieldÏscC sdS(s*Convert an algebraic number to ``dtype``. N(R+(RNRKRO((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytfrom_AlgebraicFieldÓscC s#|jr|j|j|jƒSdS(s#Convert a polynomial to ``dtype``. N(R:RCRDtdom(RNRKRO((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytfrom_PolynomialRing×s cC sdS(s*Convert a rational function to ``dtype``. N(R+(RNRKRO((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytfrom_FractionFieldÜscC s|j|jƒS(s&Convert a ``EX`` object to ``dtype``. (REtex(RNRKRO((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytfrom_ExpressionDomainàscC s/|jƒdkr+|j|jƒ|jƒSdS(s#Convert a polynomial to ``dtype``. iN(tdegreeRCRDRY(RNRKRO((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytfrom_GlobalPolynomialRingäscC s|j||ƒS(N(R[(RNRKRO((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytfrom_GeneralizedPolynomialRingéscC ss|jr"t|jƒt|ƒ@sD|jrft|jƒt|ƒ@rftd||t|ƒfƒ‚n|j|ƒS(Ns+can't unify %s with %s, given %s generators(t is_CompositetsettsymbolsR ttupletunify(RORNRc((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytunify_with_symbolsìsD"c C sS|dk r|j||ƒS||kr,|S|jr9|S|jrF|S|jsX|jr´|jrj|jn|}|jr‚|jn|}|jrš|jnd}|jr²|jnd}|j|ƒ}t||ƒ}|jrè|jn|j}|j r|j s|j rA|j rA|j s)|j rA|j rA|j ƒ}n|jrr|j sf|j sf|j rr|j } n |j } ddlm} | | kr¤| ||ƒS| |||ƒSd„} |jrâ|jrâ| |j ||ƒS|jr|jr| |j ||ƒS|jr,|jr,| |j ||ƒS|jrQ|jrQ| |j ||ƒS|jsc|jrg|S|jsy|jr}|S|jr½|jr½|j |jj|jƒt|j|jƒŒS|jrÊ|S|jr×|S|jrä|S|jrñ|S|jrþ|S|jr |S|jr?|jr?|j t|j|jdtƒƒSddlm} | S( sZ Construct a minimal domain that contains elements of ``K0`` and ``K1``. Known domains (from smallest to largest): - ``GF(p)`` - ``ZZ`` - ``QQ`` - ``RR(prec, tol)`` - ``CC(prec, tol)`` - ``ALG(a, b, c)`` - ``K[x, y, z]`` - ``K(x, y, z)`` - ``EX`` iÿÿÿÿ(tGlobalPolynomialRingcS s=t|j|jƒ}t|j|jƒ}|d|d|ƒS(NtprecR9(tmaxt precisiont tolerance(tclsRORNRhR9((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyt mkinexact)stkey(tEXN(((R+Rftis_EXRaRYRcReR tordertis_FractionFieldtis_PolynomialRingRtget_ringR t&sympy.polys.domains.old_polynomialringRgtis_ComplexFieldt is_RealFieldtis_AlgebraicFieldtorig_exttis_RationalFieldtis_IntegerRingtis_FiniteFieldRitmodRR<Ro( RORNRct K0_groundt K1_groundt K0_symbolst K1_symbolstdomainRqRlRgRmRo((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyReòst    %     .      "cC st|tƒo|j|jkS(s0Returns ``True`` if two domains are equivalent. (R=RR"(Rtother((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyt__eq__RscC s ||k S(s1Returns ``False`` if two domains are equivalent. ((RRƒ((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyt__ne__VscC sVg}xI|D]A}t|tƒr;|j|j|ƒƒq |j||ƒƒq W|S(s5Rersively apply ``self`` to all elements of ``seq``. (R=tlisttappendtmap(RtseqR2telt((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyRˆZs  cC std|ƒ‚dS(s)Returns a ring associated with ``self``. s#there is no ring associated with %sN(R (R((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyRtfscC std|ƒ‚dS(s*Returns a field associated with ``self``. s$there is no field associated with %sN(R (R((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyt get_fieldjscC s|S(s2Returns an exact domain associated with ``self``. ((R((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyt get_exactnscC s-t|dƒr|j|ŒS|j|ƒSdS(s0The mathematical way to make a polynomial ring. t__iter__N(thasattrt poly_ring(RRc((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyt __getitem__rs cO s,ddlm}||||jdtƒƒS(s(Returns a polynomial ring, i.e. `K[X]`. iÿÿÿÿ(tPolynomialRingRq(t"sympy.polys.domains.polynomialringR‘tgetR (RRctkwargsR‘((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyRyscO s,ddlm}||||jdtƒƒS(s'Returns a fraction field, i.e. `K(X)`. iÿÿÿÿ(t FractionFieldRq(t!sympy.polys.domains.fractionfieldR•R“R (RRcR”R•((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyt frac_field~scO s ddlm}||||ŽS(s(Returns a polynomial ring, i.e. `K[X]`. iÿÿÿÿ(R‘(RuR‘(RRcR”R‘((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyt old_poly_ringƒscO s ddlm}||||ŽS(s'Returns a fraction field, i.e. `K(X)`. iÿÿÿÿ(R•(t%sympy.polys.domains.old_fractionfieldR•(RRcR”R•((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytold_frac_fieldˆscG std|ƒ‚dS(s6Returns an algebraic field, i.e. `K(\alpha, \ldots)`. s$can't create algebraic field over %sN(R (Rt extension((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytalgebraic_fieldscG s t‚dS(s$Inject generators into this domain. N(R(RRc((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytinject‘scC s| S(sReturns True if ``a`` is zero. ((RRK((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytis_zero•scC s ||jkS(sReturns True if ``a`` is one. (tone(RRK((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytis_one™scC s |dkS(s#Returns True if ``a`` is positive. i((RRK((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyt is_positivescC s |dkS(s#Returns True if ``a`` is negative. i((RRK((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyt is_negative¡scC s |dkS(s'Returns True if ``a`` is non-positive. i((RRK((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytis_nonpositive¥scC s |dkS(s'Returns True if ``a`` is non-negative. i((RRK((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytis_nonnegative©scC s t|ƒS(s.Absolute value of ``a``, implies ``__abs__``. (tabs(RRK((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyR¥­scC s| S(s,Returns ``a`` negated, implies ``__neg__``. ((RRK((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytneg±scC s| S(s-Returns ``a`` positive, implies ``__pos__``. ((RRK((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytposµscC s||S(s.Sum of ``a`` and ``b``, implies ``__add__``. ((RRKtb((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytadd¹scC s||S(s5Difference of ``a`` and ``b``, implies ``__sub__``. ((RRKR¨((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytsub½scC s||S(s2Product of ``a`` and ``b``, implies ``__mul__``. ((RRKR¨((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytmulÁscC s||S(s2Raise ``a`` to power ``b``, implies ``__pow__``. ((RRKR¨((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytpowÅscC s t‚dS(s6Exact quotient of ``a`` and ``b``, implies something. N(R(RRKR¨((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytexquoÉscC s t‚dS(s1Quotient of ``a`` and ``b``, implies something. N(R(RRKR¨((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytquoÍscC s t‚dS(s4Remainder of ``a`` and ``b``, implies ``__mod__``. N(R(RRKR¨((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytremÑscC s t‚dS(s0Division of ``a`` and ``b``, implies something. N(R(RRKR¨((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytdivÕscC s t‚dS(s5Returns inversion of ``a mod b``, implies something. N(R(RRKR¨((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytinvertÙscC s t‚dS(s!Returns ``a**(-1)`` if possible. N(R(RRK((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytrevertÝscC s t‚dS(sReturns numerator of ``a``. N(R(RRK((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytnumeráscC s t‚dS(sReturns denominator of ``a``. N(R(RRK((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytdenomåscC s%|j||ƒ\}}}||fS(s&Half extended GCD of ``a`` and ``b``. (tgcdex(RRKR¨tsttth((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyt half_gcdexéscC s t‚dS(s!Extended GCD of ``a`` and ``b``. N(R(RRKR¨((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyRµîscC sC|j||ƒ}|j||ƒ}|j||ƒ}|||fS(s.Returns GCD and cofactors of ``a`` and ``b``. (tgcdR®(RRKR¨Rºtcfatcfb((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyt cofactorsòscC s t‚dS(s Returns GCD of ``a`` and ``b``. N(R(RRKR¨((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyRºùscC s t‚dS(s Returns LCM of ``a`` and ``b``. N(R(RRKR¨((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytlcmýscC s t‚dS(s#Returns b-base logarithm of ``a``. N(R(RRKR¨((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytlogscC s t‚dS(sReturns square root of ``a``. N(R(RRK((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytsqrtscK s|j|ƒj||S(s*Returns numerical approximation of ``a``. (RMtevalf(RRKRhtoptions((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyRÁ scC s|S(N((RRK((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytrealscC s|jS(N(tzero(RRK((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytimagscC s ||kS(s+Check if ``a`` and ``b`` are almost equal. ((RRKR¨Rk((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytalmosteqscC stdƒ‚dS(s*Return the characteristic of this domain. scharacteristic()N(R(R((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pytcharacteristicsN(xR!t __module__t__doc__R+R"RÄRŸR?RRthas_assoc_Ringthas_assoc_FieldR|tis_FFR{tis_ZZRztis_QQRwtis_RRRvtis_CCRxt is_AlgebraicRstis_PolyRrtis_Fractis_SymbolicDomainRpRJtis_ExactRBt is_SimpleRatis_PIDthas_CharacteristicZeroRR*tpropertyRRRRRRR#R%R&R'R(R3RCR;RLRMRERPRQRRRSRTRURVRWRXRZR[R]R_R`RfReR„R…RˆRtR‹RŒRRR—R˜RšRœRRžR R¡R¢R£R¤R¥R¦R§R©RªR«R¬R­R®R¯R°R±R²R³R´R¹RµR½RºR¾R¿RÀRÁtnRÃRÅRÆRÇ(((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyRsÔ         ''         6                   `                                            N(RÉt __future__RRt sympy.coreRRtsympy.core.compatibilityRRRtsympy.core.decoratorsRt!sympy.polys.domains.domainelementRtsympy.polys.orderingsR tsympy.polys.polyerrorsR R R tsympy.polys.polyutilsR tsympy.utilitiesRRtobjectR(((s9lib/python2.7/site-packages/sympy/polys/domains/domain.pyts