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Medientyp:
E-Artikel
Titel:
Real and Imaginary Quadratic Representations of Hyperelliptic Function Fields
Beteiligte:
Paulus, Sachar;
Rück, Hans-Georg
Erschienen:
American Mathematical Society, 1999
Erschienen in:Mathematics of Computation
Sprache:
Englisch
ISSN:
0025-5718;
1088-6842
Entstehung:
Anmerkungen:
Beschreibung:
<p>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.</p>