HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt età la diffusion… (More)
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.
titot, " Computing representations for radicals of finitely generated differential ideals " , Special issue " Jacobi's Legacy Résumé Abstract Ce papier s'intéresse aux systèmes d'´ equations différentielles polynomiales, ordinaires ou aux dérivées partielles. La théorie sous-jacente est l'algèbre différentielle de Ritt et Kolchin. Nous décrivons un… (More)
We present a new algorithm for solving basic parametric constructible or semi-algebraic If Π U denotes the canonical pro jection onto the parameter's space, solving C or S is reduced to the computation of submanifolds U ⊂ C d (resp. U ⊂ R d) such that (Π U −1 (U) ∩ C, Π U) is an analytic covering of U (we say that U has the (Π U , C)-covering property).… (More)
Optimal solutions are given for the two following problems: the condition for a degree 4 polytmmial to have only positive valves and the condition for an ellipse to be inside the unit circle. The aim of this paper is to give optimal solutions for two classical quantifier elimination problems. These solutions are not obtained by existing general algorithms.… (More)