11.6 Fraction Field of Integral Domains

Module: sage.rings.fraction_field

Author Log:

Module-level Functions

FractionField( 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

is_FractionField( x)

Class: FractionField_generic

class FractionField_generic
The fraction field of an integral domain.
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_

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