def FractionField(R, names=None): """ Create the fraction field of the integral domain R. INPUT: - ``R`` - an integral domain - ``names`` - ignored EXAMPLES: We create some example fraction fields. :: sage: FractionField(IntegerRing()) Rational Field sage: FractionField(PolynomialRing(RationalField(),'x')) Fraction Field of Univariate Polynomial Ring in x over Rational Field sage: FractionField(PolynomialRing(IntegerRing(),'x')) Fraction Field of Univariate Polynomial Ring in x over Integer Ring sage: FractionField(PolynomialRing(RationalField(),2,'x')) Fraction Field of Multivariate Polynomial Ring in x0, x1 over Rational Field Dividing elements often implicitly creates elements of the fraction field. :: sage: x = PolynomialRing(RationalField(), 'x').gen() sage: f = x/(x+1) sage: g = x**3/(x+1) sage: f/g 1/x^2 sage: g/f x^2 The input must be an integral domain. :: sage: Frac(Integers(4)) Traceback (most recent call last): ... TypeError: R must be an integral domain. """ if not ring.is_Ring(R): raise TypeError, "R must be a ring" if not R.is_integral_domain(): raise TypeError, "R must be an integral domain." return R.fraction_field()