KeywordFunction Fields
Description
In KASH3, creation of an algebraic function field begins with choosing a bivariate polynomial 'f' over 'k', which is separable and monic in the second variable, such that 'f(T,y) = 0'. For this there have to be defined the field 'k', the polynomial rings 'k[T]' and 'k[T][y]', respectively (see example). It is afterwards possible to define an algebraic function field. We test first whether the bivariate polynomial is irreducible and separable in the second variable. Then as a first application, one can compute the genus of the function field by calling 'Genus' function.
Examples
k := FiniteField(25);
kT := RationalFunctionField(k);
kTy := PolynomialAlgebra(kT);
T := kT.1;; y := kTy.1;;
f := y^3 + T^4 + 1;
K := FunctionField(f);
Genus(K);
