## Experimental Mathematics

### Sparse Representation for Cyclotomic Fields

Claus Fieker

#### Abstract

Currently, all major implementations of cyclotomic fields as well as number fields are based on a dense model in which elements are represented either as dense polynomials in the generator of the field or as coefficient vectors with respect to a fixed basis. While this representation allows for the asymptotically fastest arithmetic for general elements, it is unsuitable for fields of degree greater than $10^4$ that arise in certain applications such as character theory for finite groups. We propose instead a sparse representation for cyclotomic fields that is particularly tailored to representation theory. We implemented our ideas in MAGMA and used it for fields of degree greater than $10^6$ over $\Q$

#### Article information

Source
Experiment. Math., Volume 16, Issue 4 (2007), 493-500.

Dates
First available in Project Euclid: 6 March 2008