Real and Imaginary Quadratic Representations of Hyperelliptic Function Elds
نویسنده
چکیده
A hyperelliptic function eld can be represented as imaginary or as real quadratic extension of the rational function eld. We show that in both cases one can compute in the class group of the function eld using reduced ideals of the orders involved. Furthermore, we show how the two representations are connected and compare the computational complexity.
منابع مشابه
Real and imaginary quadratic representations of hyperelliptic function fields
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’...
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تاریخ انتشار 2007