On the Theories of Triangular Sets

Abstract

Different notions of triangular sets are presented. The relationship between these notions are studied. The main result is that four different existing notions of good triangular sets are equivalent.

On the Regularity Property of Differential Polynomials Modulo Regular Differential Chains

“…Triangularity plus condition b is the regular chain condition of [1]. Autoreduced regular differential chains are the same objects as Ritt characteristic sets.…”

Algebraic Approaches to Stability Analysis of Biological Systems

“…The triangular sets T i and systems [T i , U i ] may satisfy some additional requirements for being regular, simple, or irreducible [3,4,43].…”

Efficient Computations of Irredundant Triangular Decompositions with the RegularChains Library

“…We refer to [1,6,5] for the notion of a regular chain, its related concepts, such as initial, saturated ideals, quasi-components and the related operations.…”