ó Ħĵ™\c@ srdZddlmZmZddlmZddlmZmZddl m Z e defd„ƒYƒZ dS( s(Implementation of :class:`Field` class. i˙˙˙˙(tprint_functiontdivision(tRing(t NotReversiblet DomainError(tpublictFieldcB skeZdZeZeZd„Zd„Zd„Zd„Z d„Z d„Z d„Z d„Z d „ZRS( sRepresents a field domain. cC std|ƒ‚dS(s)Returns a ring associated with ``self``. s#there is no ring associated with %sN(R(tself((s8lib/python2.7/site-packages/sympy/polys/domains/field.pytget_ringscC s|S(s*Returns a field associated with ``self``. ((R((s8lib/python2.7/site-packages/sympy/polys/domains/field.pyt get_fieldscC s||S(s9Exact quotient of ``a`` and ``b``, implies ``__div__``. ((Rtatb((s8lib/python2.7/site-packages/sympy/polys/domains/field.pytexquoscC s||S(s2Quotient of ``a`` and ``b``, implies ``__div__``. ((RR R ((s8lib/python2.7/site-packages/sympy/polys/domains/field.pytquoscC s|jS(s0Remainder of ``a`` and ``b``, implies nothing. (tzero(RR R ((s8lib/python2.7/site-packages/sympy/polys/domains/field.pytrem scC s|||jfS(s2Division of ``a`` and ``b``, implies ``__div__``. (R(RR R ((s8lib/python2.7/site-packages/sympy/polys/domains/field.pytdiv$scC s„y|jƒ}Wntk r'|jSX|j|j|ƒ|j|ƒƒ}|j|j|ƒ|j|ƒƒ}|j||ƒ|S(sÙ Returns GCD of ``a`` and ``b``. This definition of GCD over fields allows to clear denominators in `primitive()`. Examples ======== >>> from sympy.polys.domains import QQ >>> from sympy import S, gcd, primitive >>> from sympy.abc import x >>> QQ.gcd(QQ(2, 3), QQ(4, 9)) 2/9 >>> gcd(S(2)/3, S(4)/9) 2/9 >>> primitive(2*x/3 + S(4)/9) (2/9, 3*x + 2) (RRtonetgcdtnumertlcmtdenomtconvert(RR R tringtptq((s8lib/python2.7/site-packages/sympy/polys/domains/field.pyR(s $$cC s…y|jƒ}Wntk r(||SX|j|j|ƒ|j|ƒƒ}|j|j|ƒ|j|ƒƒ}|j||ƒ|S(sç Returns LCM of ``a`` and ``b``. >>> from sympy.polys.domains import QQ >>> from sympy import S, lcm >>> QQ.lcm(QQ(2, 3), QQ(4, 9)) 4/3 >>> lcm(S(2)/3, S(4)/9) 4/3 (RRRRRRR(RR R RRR((s8lib/python2.7/site-packages/sympy/polys/domains/field.pyRHs  $$cC s|rd|Stdƒ‚dS(s!Returns ``a**(-1)`` if possible. iszero is not reversibleN(R(RR ((s8lib/python2.7/site-packages/sympy/polys/domains/field.pytrevert`s(t__name__t __module__t__doc__tTruetis_Fieldtis_PIDRR R R RRRRR(((s8lib/python2.7/site-packages/sympy/polys/domains/field.pyR s       N( Rt __future__RRtsympy.polys.domains.ringRtsympy.polys.polyerrorsRRtsympy.utilitiesRR(((s8lib/python2.7/site-packages/sympy/polys/domains/field.pyts