Details:
Title  Computing border bases  Author(s)  Achim Kehrein, Martin Kreuzer  Type  Article in Journal  Abstract  This paper presents several algorithms that compute border bases of a
zerodimensional ideal. The first relates to the FGLM algorithm as it
uses a linear basis transformation. In particular, it is able to
compute border bases that do not contain a reduced Gröbner basis.
The second algorithm is based on a generic algorithm by Bernard
Mourrain originally designed for computing an ideal basis that need
not be a border basis. Our fully detailed algorithm
computes a border basis of a zerodimensional
ideal from a given set of generators. To obtain concrete instructions
we appeal to a degreecompatible term ordering $\sigma$ and hence
compute a border basis that contains the reduced $\sigma$Gröbner basis.
We show an example in which this computation actually has advantages over Buchberger's algorithm. Moreover, we formulate and prove two optimizations
of the Border Basis Algorithm which reduce the dimensions of the
linear algebra subproblems.
 Keywords  border basis, Gröbner basis, Buchberger's algorithm, zerodimensional ideal  Length  20 
File 
 Language  English  Journal  Journal of Pure and Applied Algebra  Volume  205  Number  2  Pages  279295  Publisher  Elsevier  Year  2006  Month  May  Edition  0  Translation 
No  Refereed 
Yes 
