ó ¡¼™\c@ s…dZddlmZmZddlmZddlmZddlm Z m Z ddl m Z e deefd„ƒYƒZ d S( s0Implementation of :class:`FractionField` class. iÿÿÿÿ(tprint_functiontdivision(tCompositeDomain(tField(tCoercionFailedtGeneratorsError(tpublict FractionFieldcB s&eZdZeZZeZeZddd„Z d„Z e d„ƒZ e d„ƒZ e d„ƒZd„Zd„Zd„Zd „Zd „Zd „Zd „Zd „Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Z d„Z!d„Z"d„Z#RS(s@A class for representing multivariate rational function fields. cC s§ddlm}t||ƒr@|dkr@|dkr@|}n||||ƒ}||_|j|_|j|_|j|_|j|_|j |_ |j |_ dS(Niÿÿÿÿ(t FracField( tsympy.polys.fieldsRt isinstancetNonetfieldtdtypetgenstngenstsymbolstdomaintdom(tselftdomain_or_fieldRtorderRR ((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pyt__init__s'       cC s|jj|ƒS(N(R t field_new(Rtelement((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pytnew&scC s |jjS(N(R tzero(R((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pyR)scC s |jjS(N(R tone(R((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pyR-scC s |jjS(N(R R(R((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pyR1scC s.t|jƒddjtt|jƒƒdS(Nt(t,t)(tstrRtjointmapR(R((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pyt__str__5scC s(t|jj|jj|j|jfƒS(N(thasht __class__t__name__R R RR(R((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pyt__hash__8scC sCt|tƒoB|jj|j|jf|jj|j|jfkS(s.Returns `True` if two domains are equivalent. (R RR R RR(Rtother((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pyt__eq__;scC s |jƒS(sConvert `a` to a SymPy object. (tas_expr(Rta((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pytto_sympyAscC s|jj|ƒS(s'Convert SymPy's expression to `dtype`. (R t from_expr(RR*((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pyt from_sympyEscC s||jj||ƒƒS(s*Convert a Python `int` object to `dtype`. (Rtconvert(tK1R*tK0((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pytfrom_ZZ_pythonIscC s||jj||ƒƒS(s/Convert a Python `Fraction` object to `dtype`. (RR.(R/R*R0((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pytfrom_QQ_pythonMscC s||jj||ƒƒS(s(Convert a GMPY `mpz` object to `dtype`. (RR.(R/R*R0((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pyt from_ZZ_gmpyQscC s||jj||ƒƒS(s(Convert a GMPY `mpq` object to `dtype`. (RR.(R/R*R0((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pyt from_QQ_gmpyUscC s||jj||ƒƒS(s*Convert a mpmath `mpf` object to `dtype`. (RR.(R/R*R0((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pytfrom_RealFieldYscC s |j|kr|j|ƒSdS(s*Convert an algebraic number to ``dtype``. N(RR(R/R*R0((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pytfrom_AlgebraicField]scC s0y|j|ƒSWnttfk r+dSXdS(s#Convert a polynomial to ``dtype``. N(RRRR (R/R*R0((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pytfrom_PolynomialRingbscC s3y|j|jƒSWnttfk r.dSXdS(s*Convert a rational function to ``dtype``. N(t set_fieldR RRR (R/R*R0((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pytfrom_FractionFieldiscC s|jjƒjƒS(s(Returns a field associated with `self`. (R tto_ringt to_domain(R((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pytget_ringpscC s|jj|jjƒS(s%Returns True if `LC(a)` is positive. (Rt is_positivetnumertLC(RR*((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pyR=tscC s|jj|jjƒS(s%Returns True if `LC(a)` is negative. (Rt is_negativeR>R?(RR*((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pyR@xscC s|jj|jjƒS(s)Returns True if `LC(a)` is non-positive. (Rtis_nonpositiveR>R?(RR*((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pyRA|scC s|jj|jjƒS(s)Returns True if `LC(a)` is non-negative. (Rtis_nonnegativeR>R?(RR*((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pyRB€scC s|jS(sReturns numerator of ``a``. (R>(RR*((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pyR>„scC s|jS(sReturns denominator of ``a``. (tdenom(RR*((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pyRCˆscC s|j|jj|ƒƒS(sReturns factorial of `a`. (R Rt factorial(RR*((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pyRDŒsN($R%t __module__t__doc__tTruetis_FractionFieldtis_Fracthas_assoc_Ringthas_assoc_FieldR RRtpropertyRRRR"R&R(R+R-R1R2R3R4R5R6R7R9R<R=R@RARBR>RCRD(((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pyR s<                      N(RFt __future__RRt#sympy.polys.domains.compositedomainRtsympy.polys.domains.fieldRtsympy.polys.polyerrorsRRtsympy.utilitiesRR(((s@lib/python2.7/site-packages/sympy/polys/domains/fractionfield.pyts