Module: sage.rings.fraction_field
Author Log:
Module-level Functions
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 x0, x1 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
x) |
Class: FractionField_generic
self, R) |
Create the fraction field of the integral domain R.
INPUT: R -- an integral domain
sage: K, x = FractionField(PolynomialRing(Q)).objgen() sage: K Fraction Field of Univariate Polynomial Ring in x over Rational Field
Functions: base_ring,
characteristic,
gen,
is_field,
ngens,
ring
Special Functions: __call__,
__cmp__,
__repr__,
_coerce_,
_latex_