ó ¡¼™\c@ s˜dZddlmZmZddlmZddlmZddlm Z m Z ddl m Z e de fd„ƒYƒZd efd „ƒYZd S( s.Implementation of :class:`QuotientRing` class.iÿÿÿÿ(tprint_functiontdivision(tFreeModuleQuotientRing(tRing(t NotReversibletCoercionFailed(tpublictQuotientRingElementcB s’eZdZd„Zd„Zd„ZeZd„Zd„Zd„Z d„Z e Z d„Z e Z d „ZeZd „Zd „Zd „ZRS( sº Class representing elements of (commutative) quotient rings. Attributes: - ring - containing ring - data - element of ring.ring (i.e. base ring) representing self cC s||_||_dS(N(tringtdata(tselfRR ((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyt__init__s cC s1ddlm}||jƒdt|jjƒS(Niÿÿÿÿ(tsstrs + (tsympyR R tstrRt base_ideal(R R ((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyt__str__scC spt||jƒ s%|j|jkrYy|jj|ƒ}WqYttfk rUtSXn|j|j|jƒS(N(t isinstancet __class__RtconverttNotImplementedErrorRtNotImplementedR (R tom((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyt__add__"s %cC s#|j|j|jjjdƒƒS(Niÿÿÿÿ(RR R(R ((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyt__neg__,scC s|j| ƒS(N(R(R R((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyt__sub__/scC s| j|ƒS(N(R(R R((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyt__rsub__2scC s]t||jƒsFy|jj|ƒ}WqFttfk rBtSXn|j|j|jƒS(N(RRRRRRRR (R to((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyt__mul__5s cC s|jj|ƒ|S(N(Rtrevert(R R((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyt__rdiv__?scC sZt||jƒsFy|jj|ƒ}WqFttfk rBtSXn|jj|ƒ|S(N(RRRRRRRR(R R((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyt__div__Ds cC s|j|j|ƒS(N(RR (R toth((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyt__pow__NscC s=t||jƒ s%|j|jkr)tS|jj||ƒS(N(RRRtFalsetis_zero(R R((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyt__eq__Qs%cC s ||k S(N((R R((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyt__ne__Vs(t__name__t __module__t__doc__R RRt__radd__RRRRt__rmul__Rt __rtruediv__Rt __truediv__R!R$R%(((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyRs"            t QuotientRingcB sÂeZdZeZeZeZd„Z d„Z d„Z d„Z d„Z d„ZeZeZeZeZeZeZd„Zd„Zd „Zd „Zd „Zd „Zd „Zd„ZRS(sa Class representing (commutative) quotient rings. You should not usually instantiate this by hand, instead use the constructor from the base ring in the construction. >>> from sympy.abc import x >>> from sympy import QQ >>> I = QQ.old_poly_ring(x).ideal(x**3 + 1) >>> QQ.old_poly_ring(x).quotient_ring(I) QQ[x]/ Shorter versions are possible: >>> QQ.old_poly_ring(x)/I QQ[x]/ >>> QQ.old_poly_ring(x)/[x**3 + 1] QQ[x]/ Attributes: - ring - the base ring - base_ideal - the ideal used to form the quotient cC sh|j|ks(td||fƒ‚n||_||_||jjƒ|_||jjƒ|_dS(NsIdeal must belong to %s, got %s(Rt ValueErrorRtzerotone(R Rtideal((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyR ys   cC st|jƒdt|jƒS(Nt/(RRR(R ((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyRscC s%t|jj|j|j|jfƒS(N(thashRR&tdtypeRR(R ((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyt__hash__„scC sCt||jjƒs'|j|ƒ}n|j||jj|ƒƒS(s0Construct an element of `self` domain from `a`. (RRR4Rtreduce_element(R ta((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pytnew‡scC s1t|tƒo0|j|jko0|j|jkS(s.Returns `True` if two domains are equivalent. (RR-RR(R tother((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyR$ŽscC s||jj||ƒƒS(s*Convert a Python `int` object to `dtype`. (RR(tK1R7tK0((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pytfrom_ZZ_python“scC s||jj|ƒƒS(N(Rt from_sympy(R R7((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyR=žscC s|jj|jƒS(N(Rtto_sympyR (R R7((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyR>¡scC s||kr|SdS(N((R R7R;((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pytfrom_QuotientRing¤s cG stdƒ‚dS(s(Returns a polynomial ring, i.e. `K[X]`. snested domains not allowedN(R(R tgens((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyt poly_ring¨scG stdƒ‚dS(s'Returns a fraction field, i.e. `K(X)`. snested domains not allowedN(R(R R@((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyt frac_field¬scC se|jj|jƒ|j}y||jdƒdƒSWn'tk r`td||fƒ‚nXdS(s/ Compute a**(-1), if possible. iis%s not a unit in %rN(RR1R Rtin_terms_of_generatorsR.R(R R7tI((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyR°s  cC s|jj|jƒS(N(RtcontainsR (R R7((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyR#ºscC s t||ƒS(sè Generate a free module of rank ``rank`` over ``self``. >>> from sympy.abc import x >>> from sympy import QQ >>> (QQ.old_poly_ring(x)/[x**2 + 1]).free_module(2) (QQ[x]/)**2 (R(R trank((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyt free_module½s (R&R'R(tTruethas_assoc_RingR"thas_assoc_FieldRR4R RR5R8R$R<tfrom_QQ_pythont from_ZZ_gmpyt from_QQ_gmpytfrom_RealFieldtfrom_GlobalPolynomialRingtfrom_FractionFieldR=R>R?RARBRR#RG(((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pyR-Zs0            N(R(t __future__RRtsympy.polys.agca.modulesRtsympy.polys.domains.ringRtsympy.polys.polyerrorsRRtsympy.utilitiesRtobjectRR-(((s?lib/python2.7/site-packages/sympy/polys/domains/quotientring.pytsJ