## 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

Permanent link to this document
http://projecteuclid.org/euclid.em/1204836517

Mathematical Reviews number (MathSciNet)
MR2378488

Zentralblatt MATH identifier
1175.11074

#### Citation

Fieker, Claus. Sparse Representation for Cyclotomic Fields. Experiment. Math. 16 (2007), no. 4, 493--500. http://projecteuclid.org/euclid.em/1204836517.