ó Ħĵ™\c@ sxdZddlmZmZddlmZddlmZmZm Z ddl m Z e defd„ƒYƒZ dS( s'Implementation of :class:`Ring` class. i˙˙˙˙(tprint_functiontdivision(tDomain(tExactQuotientFailedt NotInvertiblet NotReversible(tpublictRingcB s˜eZdZeZd„Zd„Zd„Zd„Zd„Z d„Z d„Z d„Z d „Z d „Zd „Zd „Zd „Zd„ZeZRS(sRepresents a ring domain. cC s|S(s)Returns a ring associated with ``self``. ((tself((s7lib/python2.7/site-packages/sympy/polys/domains/ring.pytget_ringscC s+||rt|||ƒ‚n||SdS(s>Exact quotient of ``a`` and ``b``, implies ``__floordiv__``. N(R(Rtatb((s7lib/python2.7/site-packages/sympy/polys/domains/ring.pytexquos cC s||S(s7Quotient of ``a`` and ``b``, implies ``__floordiv__``. ((RR R ((s7lib/python2.7/site-packages/sympy/polys/domains/ring.pytquoscC s||S(s4Remainder of ``a`` and ``b``, implies ``__mod__``. ((RR R ((s7lib/python2.7/site-packages/sympy/polys/domains/ring.pytremscC s t||ƒS(s5Division of ``a`` and ``b``, implies ``__divmod__``. (tdivmod(RR R ((s7lib/python2.7/site-packages/sympy/polys/domains/ring.pytdiv#scC sB|j||ƒ\}}}|j|ƒr2||Stdƒ‚dS(s"Returns inversion of ``a mod b``. s zero divisorN(tgcdextis_oneR(RR R tsttth((s7lib/python2.7/site-packages/sympy/polys/domains/ring.pytinvert'scC s#|j|ƒr|Stdƒ‚dS(s!Returns ``a**(-1)`` if possible. s"only unity is reversible in a ringN(RR(RR ((s7lib/python2.7/site-packages/sympy/polys/domains/ring.pytrevert0scC s.y|j|ƒtSWntk r)tSXdS(N(RtTrueRtFalse(RR ((s7lib/python2.7/site-packages/sympy/polys/domains/ring.pytis_unit7s   cC s|S(sReturns numerator of ``a``. ((RR ((s7lib/python2.7/site-packages/sympy/polys/domains/ring.pytnumer>scC s|jS(sReturns denominator of `a`. (tone(RR ((s7lib/python2.7/site-packages/sympy/polys/domains/ring.pytdenomBscC s t‚dS(sÊ Generate a free module of rank ``rank`` over self. >>> from sympy.abc import x >>> from sympy import QQ >>> QQ.old_poly_ring(x).free_module(2) QQ[x]**2 N(tNotImplementedError(Rtrank((s7lib/python2.7/site-packages/sympy/polys/domains/ring.pyt free_moduleFs cG sEddlm}|||jdƒjg|D]}|g^q,ŒƒS(sħ Generate an ideal of ``self``. >>> from sympy.abc import x >>> from sympy import QQ >>> QQ.old_poly_ring(x).ideal(x**2) i˙˙˙˙(tModuleImplementedIdeali(tsympy.polys.agca.idealsR!R t submodule(RtgensR!tx((s7lib/python2.7/site-packages/sympy/polys/domains/ring.pytidealQs cC sNddlm}ddlm}t||ƒsA|j|Œ}n|||ƒS(sÖ Form a quotient ring of ``self``. Here ``e`` can be an ideal or an iterable. >>> from sympy.abc import x >>> from sympy import QQ >>> QQ.old_poly_ring(x).quotient_ring(QQ.old_poly_ring(x).ideal(x**2)) QQ[x]/ >>> QQ.old_poly_ring(x).quotient_ring([x**2]) QQ[x]/ The division operator has been overloaded for this: >>> QQ.old_poly_ring(x)/[x**2] QQ[x]/ i˙˙˙˙(tIdeal(t QuotientRing(R"R't sympy.polys.domains.quotientringR(t isinstanceR&(RteR'R(((s7lib/python2.7/site-packages/sympy/polys/domains/ring.pyt quotient_ring^s cC s |j|ƒS(N(R,(RR+((s7lib/python2.7/site-packages/sympy/polys/domains/ring.pyt__div__vs(t__name__t __module__t__doc__Rtis_RingR R R RRRRRRRR R&R,R-t __truediv__(((s7lib/python2.7/site-packages/sympy/polys/domains/ring.pyR s"           N( R0t __future__RRtsympy.polys.domains.domainRtsympy.polys.polyerrorsRRRtsympy.utilitiesRR(((s7lib/python2.7/site-packages/sympy/polys/domains/ring.pyts