An explicit treatment of biquadratic function fields

We provide a comprehensive description of biquadratic function fields and their properties, including a characterization of the cyclic and radical cases as well as the constant field. For the cyclic scenario, we provide simple explicit formulas for the ramification index of any rational place, the field discriminant, the genus, and an algorithmically suitable integral basis. In terms of computation, we only require square and fourth power testing of constants, extended gcd computations of polynomials, and the squarefree factorization of polynomials over the base field.