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math.AC2015★ 2 cited
Gröbner Fans of x-homogeneous Ideals in R[[t]][x]
Thomas Markwig, Yue Ren
We generalise the notion of Gröbner fan to ideals in R[[t]][x_1,...,x_n] for certain classes of coefficient rings R and give a constructive proof that the Gröbner fan is a rational…
math.AC2007★ 36 cited
A Field of Generalised Puiseux Series for Tropical Geometry
Thomas Markwig
In this paper we define a field K of characteristic zero with valuation whose value group is the real numbers, and we show that this field of generalised Puiseux series is algebrai…
math.AC2007
Standard Bases in K[[t_1,...,t_m]][x_1,...,x_n]^s
Thomas Markwig
In this paper we study standard bases for submodules of K[[t_1,...,t_m]][x_1,...,x_n]^s respectively of their localisation with respect to a t-local monomial ordering. The main ste…