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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 Gröbner 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)

- Chenqi Mou
- 2013

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