New Strategies for Standard Bases over Z
Christian Eder, Gerhard Pfister, Adrian Popescu
TL;DR
This paper discusses new strategies for computing standard bases over principal ideal rings, focusing on pair set creation, coefficient growth avoidance, and normal form algorithms for non-global orderings.
Contribution
It introduces novel methods for constructing pair sets, controlling coefficient growth, and computing normal forms in the context of standard bases over Z.
Findings
Effective pair set creation strategies
Methods to prevent coefficient explosion
A normal form algorithm for non-global orderings
Abstract
Experiences with the implementation of strong Gr\"obner bases respectively standard bases for polynomial rings over principal ideal rings are explained: different strategies for creating the pair set, methods to avoid coefficient growth and a normal form algorithm for non-global orderings.
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Taxonomy
TopicsPolynomial and algebraic computation · Commutative Algebra and Its Applications · Coding theory and cryptography