Given a zero-dimensional ideal I âŠ‚ K[x1, . . . ,xn] of degreeD, the transformation of the ordering of its GrÃ¶bner basis from DRL to LEX is a key step in polynomial system solving and turns out to beâ€¦ (More)

Let I in K[x1,...,xn] be a 0-dimensional ideal of degree D where K is a field. It is well-known that obtaining efficient algorithms for change of ordering of GrÃ¶bner bases of I is crucial inâ€¦ (More)

Polynomial systems can be used to formulate a large variety of non-linear problems. Polynomial systems over finite fields are of particular interest because of their applications in Cryptography,â€¦ (More)

This paper presents algorithms for decomposing any zero-dimensional polynomial set into simple sets over an arbitrary finite field, with an associated ideal or zero decomposition. As a key ingredientâ€¦ (More)

This paper presents an algorithm for decomposing any positive-dimensional polynomial set into simple sets over an arbitrary finite field. The algorithm is based on some relationship establishedâ€¦ (More)

A characteristic pair is a pair (G, C) of polynomial sets in which G is a reduced lexicographic GrÃ¶bner basis, C is the minimal triangular set contained in G, and C is normal. In this paper, we showâ€¦ (More)

This paper is concerned with stability analysis of biological networks modeled as discrete and finite dynamical systems. We show how to use algebraic methods based on quantifier elimination, realâ€¦ (More)