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KleinianGroups

KleinianGroups is a Magma package computing fundamental domains for arithmetic Kleinian groups. It is distributed under the GPL v3+ licence.

Current version: 1.0 (2012-09-25) [ tar.gz | zip ]

Changelog

A description of the algorithm can be found in my article Computing arithmetic Kleinian groups.

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Algebras

I wrote a PARI library for computing with associative algebras over **Q** or **Fp** and central simple algebras over number fields. It is now contained in PARI/GP as a module. Apart from basic operations, I implemented the following algorithms:

- Associative algebras: Jacobson radical, simple components of a semisimple algebra, splitting of a simple algebra over a finite field.
- Central simple algebras over number fields: Hasse invariants, creation from the Hasse invariants, maximal order, arithmetic of lattices.

I am planning to extend these functionalities.

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Other contributions to PARI/GP

I contribute to the development of PARI/GP on a regular basis. In addition to the algebras module, here are some examples:

- Character table of finite groups.
- Computation of abelian extensions from explicit class field theory.
- Computation of subfields of a number field: all, maximal ones, the maximal CM subfield.
- Mod N linear algebra and generic linear algebra over rings that are not necessarily commutative or domains but satisfying a certain principality condition.
- Computation of the projective galois representation attached to a tetrahedral or octahedral weight one modular form.

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abelianbnf

abelianbnf is a GP script that computes the class group of certain Galois number fields by exploiting the existence of norm relations, using the algorithm described in this article. It is distributed under the GPL v3+ licence.

Current version : 1.0 (2020-09) [ tar.gz | zip | HAL | Software Heritage ]

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Sorting

With John Cremona and Drew Sutherland, I defined an implemented a sorting and labeling scheme for ideals in number fields. I wrote the GP code. The description and the code are available on Github.