An explicit treatment of biquadratic function fields

Qingquan Wu, Renate Scheidler

Abstract


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 on polynomials, and the

squarefree factorization of polynomials over the ground field.

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Contributions to Discrete Mathematics. ISSN: 1715-0868