#20997: Toy implementation of Matrix-F5 algorithm and various adaptation
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Reporter: TristanVaccon | Owner:
Type: enhancement | Status: new
Priority: minor | Milestone: sage-7.3
Component: padics | Resolution:
Keywords: Matrix-F5 algorithm, Gröbner | Merged in:
bases, tropical Gröbner bases, p-adic |
computation |
Authors: Tristan Vaccon | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by TristanVaccon:
Old description:
> This ticket provides a first toy implementation of the Matrix-F5
> algorithm to compute Gröbner bases.
>
> Many variants of this algorithm are available:
> * The classical one (see https://hal.inria.fr/hal-00974810).
> * An adaptation for more stable computation of p-adic Gröbner bases (see
> http://arxiv.org/abs/1403.5464).
> * Various adaptations to the computation of tropical Gröbner bases (see
> http://arxiv.org/abs/1402.6675).
>
> Doctests are provided.
New description:
This ticket provides a first toy implementation of the Matrix-F5 algorithm
to compute Gröbner bases.
Many variants of this algorithm are available:
* The classical one (see https://hal.inria.fr/hal-00974810).
* An adaptation for more stable computation of p-adic Gröbner bases (see
http://arxiv.org/abs/1403.5464).
* Various adaptations to the computation of tropical Gröbner bases (see
http://arxiv.org/abs/1402.6675).
Doctests are provided.
To implement the algorithms, we define a class of Macaulay matrices with
extra information (signatures, labels, etc...).
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Ticket URL: <https://trac.sagemath.org/ticket/20997#comment:1>
Sage <http://www.sagemath.org>
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