用经典标准基技术计算热带品种的田间价值

Yue Ren
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引用次数: 1

摘要

在本报告中,我们讨论了经典Gröbner基(或标准基)技术在热带几何中非平凡值域上多项式环代数问题中的应用。我们将研究的关键问题是给定一个热带品种在多项式环上的理想情况下的计算。本演示中的所有算法都已在计算机代数系统Singular中实现,并且可以作为官方分发的一部分获得。
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Computing tropical varieties over fields with valuation using classical standard basis techniques
In this presentation, we discuss the application of classical Gröbner basis (or standard basis) techniques to algebraic problems in polynomial rings over fields with non-trivial valuation arising in tropical geometry. The key problem we will study is the computation of a tropical variety, given its ideal in the polynomial ring. All algorithms in this presentation have been implemented in the computer algebra system Singular and are available as part of the official distribution.
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