Paper Info
Title
Gröbner fans of x-homogeneous ideals in R〚t〛[x].
Abstract
We generalise the notion of a Gröbner fan to ideals in R〚t〛[x1,…,xn] for certain classes of coefficient rings R and give a constructive proof that the Gröbner fan is a rational polyhedral fan. For this we introduce the notion of initially reduced standard bases and show how these can be computed in finite time. We deduce algorithms for computing the Gröbner fan, implemented in the computer algebra system Singular. The problem is motivated by the wish to compute tropical varieties over the p-adic numbers.
Year
DOI
Venue
2017
10.1016/j.jsc.2016.11.016
Journal of Symbolic Computation
Keywords
Field
DocType
13P10,13F25,16W60,12J25,16W60
Discrete mathematics,Constructive proof,Homogeneous,Pure mathematics,Symbolic computation,Mathematics,Finite time
Journal
Volume
ISSN
Citations 
83
0747-7171
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Thomas Markwig101.69
Yue Ren213.90