Real and imaginary quadratic representations of hyperelliptic function fields
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- by Sachar Paulus and Hans-Georg Rück PDF
- Math. Comp. 68 (1999), 1233-1241 Request permission
Abstract:
A hyperelliptic function field can be always be represented as a real quadratic extension of the rational function field. If at least one of the rational prime divisors is rational over the field of constants, then it also can be represented as an imaginary quadratic extension of the rational function field. The arithmetic in the divisor class group can be realized in the second case by Cantor’s algorithm. We show that in the first case one can compute in the divisor class group of the function field using reduced ideals and distances of ideals in the orders involved. Furthermore, we show how the two representations are connected and compare the computational complexity.References
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Additional Information
- Sachar Paulus
- Affiliation: Institut für Theoretische Informatik, TU Darmstadt, Alexanderstraße 10, 64283 Darmstadt (Germany)
- Email: sachar@cdc.informatik.th-darmstadt.de
- Hans-Georg Rück
- Affiliation: Institut für Experimentelle Mathematik, Universität GH Essen, Ellernstr.29, 45326 Essen (Germany)
- Email: rueck@exp-math.uni-essen.de
- Received by editor(s): July 24, 1997
- Received by editor(s) in revised form: November 3, 1997, and January 20, 1998
- Published electronically: February 15, 1999
- © Copyright 1999 American Mathematical Society
- Journal: Math. Comp. 68 (1999), 1233-1241
- MSC (1991): Primary 11R58, 14Q05; Secondary 11R65, 14H05, 14H40
- DOI: https://doi.org/10.1090/S0025-5718-99-01066-2
- MathSciNet review: 1627817