Complexity of deciding whether a tropical linear prevariety is a tropical variety
Complexity of deciding whether a tropical linear prevariety is a tropical variety
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确定热带线性预品种是否为热带品种的复杂性
DOI：
10.1007/s00200-019-00407-w
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Nicolai N. Vorobjov
中科院分区：
文献类型：
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作者：
D. Grigoriev;Nicolai N. Vorobjov
本文给出了一个判定热带线性前变种是否为热带线性变种的单指数复杂度算法。该算法依赖于一个标准是一个热带线性品种之间的对偶热带正交化和双热带正交化的子集A的向量空间。我们还给出了一个例子，一个可数家庭的热带超平面，使他们的交集是不是一个热带prevariety。
We give an algorithm, with a singly exponential complexity, deciding whether a tropical linearprevarietyis a tropical linearvariety. The algorithm relies on a criterion to be a tropical linear variety in terms of a duality between the tropical orthogonalizationand the double tropical orthogonalizationof a subsetAof the vector space. We also give an example of a countable family of tropical hyperplanes such that their intersection is not a tropical prevariety.