Open Access
2007 Sparse Representation for Cyclotomic Fields
Claus Fieker
Experiment. Math. 16(4): 493-500 (2007).


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 $\Q$


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Claus Fieker. "Sparse Representation for Cyclotomic Fields." Experiment. Math. 16 (4) 493 - 500, 2007.


Published: 2007
First available in Project Euclid: 6 March 2008

zbMATH: 1175.11074
MathSciNet: MR2378488

Primary: 11-04
Secondary: 11R18 , 11Y16

Keywords: Cyclotomic fields , sparse representation

Rights: Copyright © 2007 A K Peters, Ltd.

Vol.16 • No. 4 • 2007
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