Implement matrices with elements in the cyclotomic field - Githubissues

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Collection of sketches / project ideas for RepLAB

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Implement matrices with elements in the cyclotomic field #13

Closed jdbancal closed 2 years ago

jdbancal commented 2 years ago

This would enable RepLAB to perform exact computations involving representations/characters.

One of our collaborators has an implementation lifted from GAP System, see https://github.com/denisrosset/cyclo, see https://www.gap-system.org/Manuals/doc/ref/chap18.html.

SAGE had an implementation, see https://trac.sagemath.org/ticket/8327 and the top-level note on https://doc.sagemath.org/html/en/reference/number_fields/sage/rings/universal_cyclotomic_field.html.

T. Breuer, "Integral Bases for Subfields of Cyclotomic Fields", AAECC, vol. 8, no. 4, pp. 279–289, Apr. 1997, doi: 10.1007/s002000050065, https://link.springer.com/article/10.1007/s002000050065.

jdbancal commented 2 years ago

@denisrosset: Do you agree this is done, or is there something more to be done here?