Details:
Title  Standard bases in K[[t 1, … ,t m]][x 1, … ,x n]^s  Author(s)  Thomas Markwig  Type  Article in Journal  Abstract  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 step is to prove the existence of a division with remainder generalising and combining the division theorems of Grauert–Hironaka and Mora. Everything else then translates naturally. Setting either m = 0 or n = 0 we get standard bases for polynomial rings respectively for power series rings as a special case. We then apply this technique to show that the t initial ideal of an ideal over the Puiseux series field can be read of from a standard basis of its generators. This is an important step in the constructive proof that each point in the tropical variety of such an ideal admits a lifting.  Keywords  Standard basis, Monomial ordering, Division with remainder, Power series  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717108000461 
Language  English  Journal  Journal of Symbolic Computation  Volume  43  Number  11  Pages  765  786  Year  2008  Edition  0  Translation 
No  Refereed 
No 
