Experimental Mathematics

Sparse Representation for Cyclotomic Fields

Claus Fieker

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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

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

First available in Project Euclid: 6 March 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11-04: Explicit machine computation and programs (not the theory of computation or programming)
Secondary: 11R18: Cyclotomic extensions 11Y16: Algorithms; complexity [See also 68Q25]

Cyclotomic fields sparse representation


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

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