Abstract
Let K be a field equipped with a valuation. Tropical varieties over K can be defined with a theory of Gr{ö}bner bases taking into account the valuation of K.Because of the use of the valuation, the theory of tropical Gr{ö}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{ö}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{ö}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.
| Original language | English |
|---|---|
| Title of host publication | ISSAC '18: 2018 ACM International Symposium on Symbolic and Algebraic Computation, 2018 |
| Number of pages | 8 |
| Publication status | Published - Jul 2018 |
Fields of science
- 101 Mathematics
- 101001 Algebra
- 101005 Computer algebra
- 101013 Mathematical logic
- 102031 Theoretical computer science
JKU Focus areas
- Computation in Informatics and Mathematics
- Engineering and Natural Sciences (in general)