AUTHOR: William Stein (with input from David Joyner, David Kohel, and Joe Wetherell)
The module rings.fraction_field defines the following methods:
R) |
Create the fraction field of the integral domain R.
INPUT: R -- an integral domain
We create some example fraction fields.
sage: FractionField(IntegerRing()) Rational Field sage: FractionField(PolynomialRing(RationalField())) Fraction field of Univariate Polynomial Ring in x over Rational Field sage: FractionField(PolynomialRing(IntegerRing())) Fraction field of Univariate Polynomial Ring in x over Integer Ring sage: FractionField(MPolynomialRing(RationalField(),2)) Fraction field of Polynomial ring in x_0, x_1 over Rational Field
Dividing elements often implicitly creates elements of the fraction field.
sage: x = PolynomialRing(RationalField()).gen() sage: f = x/(x+1) sage: g = x**3/(x+1) sage: f/g 1/x^2 sage: g/f x^2
The module rings.fraction_field defines the following classes: