Title  Idealization of modules in computer algebra 
Author(s)  Martin Kreuzer, Lorenzo Robbiano 
Type  Article in Conference Proceedings 
Abstract  Based on an explicit description of the idealization of a graded
submodule of a graded free module, we examine the behaviour of
Gröbner bases and minimal homogeneous systems of generators under
this process. Then we show how one can idealize a homogeneous
presentation. Using this theory, we present a unified description
of several strategies for computing minimal homogeneous presentations
and minimal graded free resolutions, in particular of the vertical
and horizontal strategies. We obtain a simple and compact algorithm
for computing minimal graded free resolutions degreebydegree
which lands itself well to further optimizations. 
Keywords  idealization, Gröbner basis, homogeneous presentation, minimal graded free resolution 
Length  17 
File 

Language  English 
Series  NATO Science Series III 
Pages  226243 
Publisher  IOS Press 
Address  Amsterdam 
Year  2005 
Editor  S. Cojocaru, G. Pfister and V. Ufnarovski 
Edition  0 
Translation 
No 
Refereed 
No 
Book  Computational NonCommutative and Commutative Algebraic Geometry 
Conferencename  NATO Workshop 2004 (Chisinau/Moldavia) 