Computer Packages
I mostly code in Magma. Here is a list of
Magma tips and tricks I learned and collected.
Instructions on how to use each package are included in the attached README files.
We invite also to look at the code to produce the examples for the corresponding papers.
Don't hesitate to contact me if you have questions and/or comments!
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AlgEt - part of Magma, since v2.29 - GitHub
- It provides functionalities to compute with orders in étale algebras over Q.
- In particular, one can compute isomorphism classes of modules and the monoid of the ideal classes of the fractional ideals of the order.
- The version available through GitHub includes functionalities for isomorphism classes of finitely generated modules over orders, which are not part of a Magma release.
- This packages is based on theory developed in Papers [3], [9], [10] and [13].
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IdlClQuat - Magma - GitHub
- It provides functionalities to compute the isomorphism classes of ideals of an order in a quaternion algebra.
- This is a collaboration with Harry Smit.
- Currently, there is no plan to expand it.
- This packages is based on theory developed in Paper [11].
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AbVarFq - Magma - GitHub
- It provides functionalities to
compute isomorphism classes of abelian varieties (in the ordinary case and over a prime field) and polarizations (in the ordinary case).
- The package requires AlgEt.
- This packages is based on theory developed in Papers [3], [4] and [5].
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PolsAbVarFpCanLift - Magma - GitHub
- It provides functionalities to compute polarizations for squarefree isogeny classes of abelian varieties over a prime field even when they are not ordinary.
- It is an expansion of the package AbVarFq.
- The package requires AbVarFq (and its dependencies).
- This packages is based on theory developed in Paper [7].
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IsomClAbVarFqCommEndAlg - Magma - GitHub
- It provides functionalities to compute (unpolarized) Fq-isomorphism classes of abelian varieties over Fq belonging to an isogeny class with commutative Fq-endomorphism ring, for any finite field Fq.
In particular, the code works for any p-rank.
- It is an expansion of the package AbVarFq.
- This packages is based on theory developed in Paper [15].
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AbVarFq_LMFDBLabels - Magma - GitHub
- Magma code implementing the labelling scheme for abelian varieties over a finite field in an isogeny class with commutative endomorphism algebra
- This packages is based on theory developed in Paper [16].
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R_ell_isogeny_graphs - Magma - GitHub
- Magma code to compute and SageMath code to vizualize (R,ll)-isogeny graphs
- This code was written jointly with Sarah Arpin.
- This packages is based on theory developed in Paper [18].
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EllipticCurves - Macaulay2 - GitHub
- It provides basic functionalities for computations with elliptic curves.
- Written in collaboration with Alessandro Oneto.
- The development is concluded.