A GAP package for braid orbit computation and applications.
A new source of structured singular value decomposition problems.
A standard basis approach to syzygies of canonical curves.
About the group law for the Jacobi variety of a hyperelliptic curve.
An example of an arithmetic Fuchsian group.
Bouquets of circles for lamination languages and complexities
Laminations are classic sets of disjoint and non-self-crossing curves on surfaces. Lamination languages are languages of two-way infinite words which code laminations by using associated labeled embedded graphs, and which are subshifts. Here, we characterize the possible exact affine factor complexities of these languages through bouquets of circles, i.e. graphs made of one vertex, as representative coding graphs. We also show how to build families of laminations together with corresponding lamination...
Calcolo del conduttore di curve algebriche e ideali di punti
Calcul du nombre de points sur une courbe elliptique dans un corps fini : aspects algorithmiques
Nous décrivons dans cet article les algorithmes nécessaires à une implantation efficace de la méthode de Schoof pour le calcul du nombre de points sur une courbe elliptique dans un corps fini. Nous tentons d’unifier pour cela les idées d’Atkin et d’Elkies. En particulier, nous décrivons le calcul d’équations pour , premier, ainsi que le calcul efficace de facteurs des polynômes de division d’une courbe elliptique.
Calculating Root Numbers of Elliptic curves over Q.
Caractères numériques et fonctions de Macaulay.
The postulation of Aritméticamente Cohen-Macaulay (ACM) subschemes of the projective space PkN is well known in the case of codimension 2. There are many different ways of recording this numerical information: numerical character of Gruson/Peskine, h-vector, postulation character of Martin-Deschamps/Perrin... The first aim of this paper is to show the equivalence of these notions. The second and most important aim, is to study the postulation of codimension 3 ACM subschemes of PN. We use a result...
Cevians as sides of triangles.
Computation of L-series for elliptic curves over function fields.
Computation of Period Matrices of Real Algebraic Curves*
Computing Gröbner fans of toric ideals.
Computing integral points on Mordell's elliptic curves.
Computing periods of cusp forms and modular elliptic curves.
Computing the determinantal representations of hyperbolic forms
The numerical range of an matrix is determined by an degree hyperbolic ternary form. Helton-Vinnikov confirmed conversely that an degree hyperbolic ternary form admits a symmetric determinantal representation. We determine the types of Riemann theta functions appearing in the Helton-Vinnikov formula for the real symmetric determinantal representation of hyperbolic forms for the genus . We reformulate the Fiedler-Helton-Vinnikov formulae for the genus , and present an elementary computation...
Counting points in medium characteristic using Kedlaya's algorithm.
Counting points on elliptic curves over finite fields
We describe three algorithms to count the number of points on an elliptic curve over a finite field. The first one is very practical when the finite field is not too large ; it is based on Shanks's baby-step-giant-step strategy. The second algorithm is very efficient when the endomorphism ring of the curve is known. It exploits the natural lattice structure of this ring. The third algorithm is based on calculations with the torsion points of the elliptic curve [18]. This deterministic polynomial...
Cutting diagram method for systems of plane curves with base points
We develop a new method of proving non-speciality of a linear system with base fat points in general position. Using this method we show that the Hirschowitz-Harbourne conjecture holds for systems with base points of equal multiplicity bounded by 42.