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