Minimal Primary Decomposition and Factorized Groebner Bases

Authors: 
Gräbe, Hans-Gert
Year: 
1997
Language: 
English
Abstract: 
This paper continues our study of applications of factorized Gröbner basis computations in [8] and [9]. We describe a way to interweave factorized Gröbner bases and the ideas in [5] that leads to a significant speed up in the computation of isolated primes for well splitting examples. Based on that observation we generalize the algorithm presented in [22] to the computation of primary decompositions for modules. It rests on an ideal separation argument. We also discuss the practically important question how to extract a minimal primary decomposition, neither addressed in [5] nor in [17]. For that purpose we outline a method to detect necessary embedded primes in the output collection of our algorithm, similar to [22, cor. 2.22]. The algorithms are partly implemented in version 2.2.1 of our REDUCE package CALI [7].
Appeared / Erschienen in: 
J. AAECC 8 (1997), S. 265 - 278
Pubdate / Erscheinungsdatum: 
1997
Pages / Seitenanzahl: 
15
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