Sparse Representation for Cyclotomic Fields
Fieker, Claus
Experiment. Math., Tome 16 (2007) no. 1, p. 493-500 / Harvested from Project Euclid
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 $\Q$
Publié le : 2007-05-15
Classification:  Cyclotomic fields,  sparse representation,  11-04,  11R18,  11Y16
@article{1204836517,
     author = {Fieker, Claus},
     title = {Sparse Representation for Cyclotomic Fields},
     journal = {Experiment. Math.},
     volume = {16},
     number = {1},
     year = {2007},
     pages = { 493-500},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1204836517}
}
Fieker, Claus. Sparse Representation for Cyclotomic Fields. Experiment. Math., Tome 16 (2007) no. 1, pp.  493-500. http://gdmltest.u-ga.fr/item/1204836517/