Nicolas Gürel
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Research Interests
Nicolas Gürel has a total of 3 co-authors. Here are the top co-authors by number of shared publications:
- Abdolali Basiri
Department of Mathematics and Computer Sciences, Damghan University, Damghan, Iran
1 shared publication - Andreas Enge
INRIA Saclay–Île-de-France & Laboratoire d’Informatique (CNRS/UMR 7161), École polytechnique, 91128 Palaiseau Cedex, France
1 shared publication - Jean-Charles Faugère
Laboratoire d’Informatique de Paris 6 (CNRS/UMR 7606), 4 place Jussieu, 75252 Paris Cedex 05, France
1 shared publication
Latest Publications
- Open Access
- 20 July 2004
- Published by American Mathematical Society (AMS) in Mathematics of Computation
- Vol. 74 (249) , 389-410
The arithmetic of Jacobian groups of superelliptic cubics
We present two algorithms for the arithmetic of cubic curves with a totally ramified prime at infinity. The first algorithm, inspired by Cantor’s reduction for hyperelliptic curves, is easily implemented with a few lines of code, making use of a polynomial arithmetic package. We prove explicit reducedness criteria for superelliptic curves of genus 3 and 4, which show the correctness of the algorithm. The second approach, quite general in nature and applicable to further classes of curves, uses the FGLM algorithm for switching between Gröbner bases for different orderings. Carrying out the computations symbolically, we obtain explicit reduction formulae in terms of the input data.
- 20 July 2004
- Published by American Mathematical Society (AMS) in Mathematics of Computation
- Vol. 74 (249) , 389-410
Open AccessThe arithmetic of Jacobian groups of superelliptic cubics
We present two algorithms for the arithmetic of cubic curves with a totally ramified prime at infinity. The first algorithm, inspired by Cantor’s reduction for hyperelliptic curves, is easily implemented with a few lines of code, making use of a polynomial arithmetic package. We prove explicit reducedness criteria for superelliptic curves of genus 3 and 4, which show the correctness of the algorithm. The second approach, quite general in nature and applicable to further classes of curves, uses the FGLM algorithm for switching between Gröbner bases for different orderings. Carrying out the computations symbolically, we obtain explicit reduction formulae in terms of the input data.