Computation of L-series for elliptic curves over function fields.
Computation of Period Matrices of Real Algebraic Curves*
Computation of the distance to semi-algebraic sets
Computation of the distance to semi-algebraic sets
This paper is devoted to the computation of distance to set, called S, defined by polynomial equations. First we consider the case of quadratic systems. Then, application of results stated for quadratic systems to the quadratic equivalent of polynomial systems (see [5]), allows us to compute distance to semi-algebraic sets. Problem of computing distance can be viewed as non convex minimization problem: , where u is in . To have, at least, lower approximation of distance, we consider the dual...
Computation of the Selmer groups of certain parametrized elliptic curves
Computer-aided serendipity
Computerbilder von Aufblasungen.
Computing amoebas.
Computing Gauss-Manin systems for complete intersection singularities .
Computing Gröbner fans of toric ideals.
Computing Igusa's local zeta functions of univariate polynomials, and linear feedback shift registers.
Computing integral points on Mordell's elliptic curves.
Computing limit linear series with infinitesimal methods
Alexander and Hirschowitz determined the Hilbert function of a generic union of fat points in a projective space when the number of fat points is much bigger than the greatest multiplicity of the fat points. Their method is based on a lemma which determines the limit of a linear system depending on fat points approaching a divisor.Other Hilbert functions were computed previously by Nagata. In connection with his counter-example to Hilbert’s fourteenth problem, Nagata determined the Hilbert function...
Computing periods of cusp forms and modular elliptic curves.
Computing special values of motivic -functions.
Computing the cardinality of CM elliptic curves using torsion points
Let be an elliptic curve having complex multiplication by a given quadratic order of an imaginary quadratic field . The field of definition of is the ring class field of the order. If the prime splits completely in , then we can reduce modulo one the factors of and get a curve defined over . The trace of the Frobenius of is known up to sign and we need a fast way to find this sign, in the context of the Elliptic Curve Primality Proving algorithm (ECPP). For this purpose, we propose...
Computing the characteristic polynomials of a class of hyperelliptic curves for cryptographic applications.
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...
Computing the dimension of a semi-algebraic set.
Computing the level of a modular rigid Calabi-Yau threefold.