6.10.1 rings.fraction_field - Fraction field of any integral domain.

AUTHOR: William Stein (with input from David Joyner, David Kohel, and Joe Wetherell)

The module rings.fraction_field defines the following methods:

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 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:

class FractionField_generic
The fraction field of an integral domain.



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