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Let <i>I</i> in K[x1,...,x<sub><i>n</i></sub>] be a 0-dimensional ideal of degree <i>D</i> where K is a field. It is well-known that obtaining efficient algorithms for change of ordering of Gr&#246;bner bases of I is crucial in polynomial system solving. Through the algorithm FGLM, this task is classically tackled by linear algebra operations in(More)
Given a zero-dimensional ideal I ⊂ K[x 1 ,. .. , x n ] of degree D, the transformation of the ordering of its Gröbner basis from DRL to LEX is a key step in polynomial system solving and turns out to be the bottleneck of the whole solving process. Thus it is of crucial importance to design efficient algorithms to perform the change of ordering. The main(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, real solution classification and discriminant varieties to detect steady states and to analyze their stability and bifurcations for discrete dynamical systems. For(More)
A characteristic pair is a pair (G, C) of polynomial sets in which G is a reduced lexicographic Gröbner basis, C is the minimal triangular set contained in G, and C is normal. In this paper, we show that any finite polynomial set P can be decomposed algorithmically into finitely many characteristic pairs with associated zero relations, which provide(More)
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