ó ¡¼™\c@ s¾dZddlmZmZddlmZddlmZddlm Z ddl m Z ddl m Z ddlmZmZmZdd lmZed ee efd „ƒYƒZd S( s0Implementation of :class:`FractionField` class. iÿÿÿÿ(tprint_functiontdivision(tField(tCompositeDomain(tCharacteristicZero(tDMF(tGeneratorsNeeded(tdict_from_basictbasic_from_dictt _dict_reorder(tpublict FractionFieldcB seZdZeZeZZeZeZ d„Z d„Z d„Z d„Z d„Zd„Zd„Zd„Zd „Zd „Zd „Zd „Zd „Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Z d„Z!RS(s3A class for representing rational function fields. cG s”|stdƒ‚nt|ƒd}t|ƒ|_|jj||d|ƒ|_|jj||d|ƒ|_||_|_||_|_ dS(Nsgenerators not specifieditring( Rtlentngenstdtypetzerotonetdomaintdomtsymbolstgens(tselfRRtlev((sDlib/python2.7/site-packages/sympy/polys/domains/old_fractionfield.pyt__init__scC s)|j||jt|jƒdd|ƒS(NiR (RRR R(Rtelement((sDlib/python2.7/site-packages/sympy/polys/domains/old_fractionfield.pytnew$scC s.t|jƒddjtt|jƒƒdS(Nt(t,t)(tstrRtjointmapR(R((sDlib/python2.7/site-packages/sympy/polys/domains/old_fractionfield.pyt__str__'scC s%t|jj|j|j|jfƒS(N(thasht __class__t__name__RRR(R((sDlib/python2.7/site-packages/sympy/polys/domains/old_fractionfield.pyt__hash__*scC sCt|tƒoB|j|jkoB|j|jkoB|j|jkS(s0Returns ``True`` if two domains are equivalent. (t isinstanceR RRR(Rtother((sDlib/python2.7/site-packages/sympy/polys/domains/old_fractionfield.pyt__eq__-scC s8t|jƒjƒ|jŒt|jƒjƒ|jŒS(s!Convert ``a`` to a SymPy object. (Rtnumert to_sympy_dictRtdenom(Rta((sDlib/python2.7/site-packages/sympy/polys/domains/old_fractionfield.pytto_sympy2sc C sÄ|jƒ\}}t|d|jƒ\}}t|d|jƒ\}}x0|jƒD]"\}}|jj|ƒ||>> from sympy.polys.polyclasses import DMF >>> from sympy.polys.domains import ZZ, QQ >>> from sympy.abc import x >>> f = DMF(([ZZ(1), ZZ(2)], [ZZ(1), ZZ(1)]), ZZ) >>> QQx = QQ.old_frac_field(x) >>> ZZx = ZZ.old_frac_field(x) >>> QQx.from_FractionField(f, ZZx) (x + 2)/(x + 1) N( RRR)R9RAR+tsettissubsetR RBRCRD(R:R,R;tnmonomstncoeffstdmonomstdcoeffsRG((sDlib/python2.7/site-packages/sympy/polys/domains/old_fractionfield.pytfrom_FractionFieldis"''+.cC s#ddlm}||j|jŒS(s)Returns a ring associated with ``self``. iÿÿÿÿ(tPolynomialRing(tsympy.polys.domainsRPRR(RRP((sDlib/python2.7/site-packages/sympy/polys/domains/old_fractionfield.pytget_ringscG stdƒ‚dS(s(Returns a polynomial ring, i.e. `K[X]`. snested domains not allowedN(tNotImplementedError(RR((sDlib/python2.7/site-packages/sympy/polys/domains/old_fractionfield.pyt poly_ring”scG stdƒ‚dS(s'Returns a fraction field, i.e. `K(X)`. snested domains not allowedN(RS(RR((sDlib/python2.7/site-packages/sympy/polys/domains/old_fractionfield.pyt frac_field˜scC s|jj|jƒjƒƒS(s#Returns True if ``a`` is positive. (Rt is_positiveR)tLC(RR,((sDlib/python2.7/site-packages/sympy/polys/domains/old_fractionfield.pyRVœscC s|jj|jƒjƒƒS(s#Returns True if ``a`` is negative. (Rt is_negativeR)RW(RR,((sDlib/python2.7/site-packages/sympy/polys/domains/old_fractionfield.pyRX scC s|jj|jƒjƒƒS(s'Returns True if ``a`` is non-positive. (Rtis_nonpositiveR)RW(RR,((sDlib/python2.7/site-packages/sympy/polys/domains/old_fractionfield.pyRY¤scC s|jj|jƒjƒƒS(s'Returns True if ``a`` is non-negative. (Rtis_nonnegativeR)RW(RR,((sDlib/python2.7/site-packages/sympy/polys/domains/old_fractionfield.pyRZ¨scC s |jƒS(sReturns numerator of ``a``. (R)(RR,((sDlib/python2.7/site-packages/sympy/polys/domains/old_fractionfield.pyR)¬scC s |jƒS(sReturns denominator of ``a``. (R+(RR,((sDlib/python2.7/site-packages/sympy/polys/domains/old_fractionfield.pyR+°scC s|j|jj|ƒƒS(sReturns factorial of ``a``. (RRt factorial(RR,((sDlib/python2.7/site-packages/sympy/polys/domains/old_fractionfield.pyR[´s("R$t __module__t__doc__RRtTruetis_FractionFieldtis_Fracthas_assoc_Ringthas_assoc_FieldRRR!R%R(R-R0R<R=R>R?R@RHRORRRTRURVRXRYRZR)R+R[(((sDlib/python2.7/site-packages/sympy/polys/domains/old_fractionfield.pyR s:              &         N(R]t __future__RRtsympy.polys.domains.fieldRt#sympy.polys.domains.compositedomainRt&sympy.polys.domains.characteristiczeroRtsympy.polys.polyclassesRtsympy.polys.polyerrorsRtsympy.polys.polyutilsRRR tsympy.utilitiesR R (((sDlib/python2.7/site-packages/sympy/polys/domains/old_fractionfield.pyts