Tristan Vaccon, Thibaut Verron, Kazuhiro Yokoyama,
"On Affine Tropical F5 Algorithms"
: ISSAC '18: 2018 ACM International Symposium on Symbolic and Algebraic Computation, 2018, 7-2018
Original Titel:
On Affine Tropical F5 Algorithms
Sprache des Titels:
Englisch
Original Buchtitel:
ISSAC '18: 2018 ACM International Symposium on Symbolic and Algebraic Computation, 2018
Original Kurzfassung:
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.
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