| Autor: |
Vaccon, Tristan, Verron, Thibaut, Yokoyama, Kazuhiro |
| Rok vydání: |
2018 |
| Předmět: |
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| Zdroj: |
ISSAC '18: 2018 ACM International Symposium on Symbolic and Algebraic Computation, 2018 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1145/3208976.3209012 |
| Popis: |
Let $K$ be a field equipped with a valuation. Tropical varieties over $K$ can be defined with a theory of Gr{\"o}bner bases taking into account the valuation of $K$.Because of the use of the valuation, the theory of tropical Gr{\"o}bner bases has proved to provide settings for computations over polynomial rings over a $p$-adic field that are more stable than that of classical Gr{\"o}bner bases.Beforehand, these strategies were only available for homogeneous polynomials. In this article, we extend the F5 strategy to a new definition of tropical Gr{\"o}bner bases in an affine setting.We provide numerical examples to illustrate time-complexity and $p$-adic stability of this tropical F5 algorithm.We also illustrate its merits as a first step before an FGLM algorithm to compute (classical) lex bases over $p$-adics. |
| Databáze: |
arXiv |
| Externí odkaz: |
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