Contribution a l'algorithmique en algebre differentielle by Lemaire F.

By Lemaire F.

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Algebraic Curves. Princeton University Press (1950) 59. : Lectures on Polytopes. Graduate Texts in Mathematics, vol. 152. ca Abstract. For a regular chain R in dimension one, we propose an algorithm which computes the (non-trivial) limit points of the quasi-component of R, that is, the set W (R)\W (R). Our procedure relies on Puiseux series expansions and does not require to compute a system of generators of the saturated ideal of R. We provide experimental results illustrating the benefits of our algorithms.

2 Using Tropical intersection of Gfan The solution set of the cyclic 8-roots polynomial system consists of space curves. Therefore, all tropisms cones were generated by a single tropism. The computation of the tropical prevariety however, did not lead only to single pretropisms but also to cones of pretropisms. The cyclic 8-roots cones of pretropisms and their dimension are listed in Table 1. Since the one dimensional rays of pretropisms yielded initial form systems with isolated solutions and since all higher dimensional cones are spanned by those one dimensional rays, we can conclude that there are no higher dimensional algebraic sets, as any two dimensional surface degenerates to a curve if we consider only one tropism.

All cyclic p-roots of index 3, found by symmetrypreserving calculations. dk/~ haagerup 11. : Computing tropical varieties. Journal of Symbolic Computation 42(1), 54–73 (2007) 12. : Power Geometry in Algebraic and Differential Equations. NorthHolland Mathematical Library, vol. 57. Elsevier (2000) 13. : Solving a system of algebraic equations with symmetries. Journal of Pure and Applied Algebra 177-118, 195–215 (1997) 14. : Computing all nonsingular solutions of cyclic-n polynomial using polyhedral homotopy continuation methods.

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