Subsections

• Creation of Structures
• Creation of Elements

Given a ring R, return its field of fractions F, consisting of quotients P/Q, with P, Q in R. If R is itself a polynomial ring, the field of fractions of R will be a rational function field. In such a case, the angle bracket notation may be used to assign names to the indeterminates, just as in the case of polynomial rings: S<t> := FieldOfFractions(R).

Create the field F of rational functions in 1 indeterminate (consisting of quotients of univariate polynomials) over the integral domain R.

FunctionField(R, r) : Rng, RngIntElt -> FldFun

Create the field F of rational functions in r indeterminates over the integral domain R.

One(F) : FldFun -> FldFunElt

Identity(F) : FldFun -> FldFunElt

Zero(F) : FldFun -> FldFunElt

Representative(F) : FldFun -> FldFunElt

elt< F | a, b > : FldFun, RngPolElt, RngPolElt -> FldFunElt

Given the rational function field F (which is the field of fractions of the polynomial ring R), and polynomials a, b in R (with b != 0), construct the rational function a / b.

F ! a : FldFun, FldElt -> FldFunElt

Given the rational function field F as a field of fractions of R, and a polynomial a in R, create the rational function a=a/1 in F.

The i-th generator for the field of fractions K of R over the coefficient ring of R.

> R<x> := PolynomialRing(Integers());
> F<w> := FieldOfFractions(R);
> print F ! x+3;
w + 3
> print F ! [ x, x-1 ];
w/(w - 1)