KASH3 Ref - Function Fields

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| ### Keyword Function 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);
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