On the computation of Hermite-Humbert constants: the algorithm of Cohn revisited
نویسنده
چکیده
We develop an algorithm for calculating Hermite-Humbert constants of real quadratic fields K with class number one. It reduces the necessary amount of computations considerably and could therefore be used for the calculation of two new Hermite-Humbert constants of the fields Q( √ 6), Q( √ 21), respectively. 2000 Mathematics Subject Classification: 11Y40; 11H55; 11R11
منابع مشابه
On the computation of Hermite-Humbert constants for real quadratic number fields
We present algorithms for the computation of extreme binary Humbert forms in real quadratic number fields. With these algorithms we are able to compute extreme Humbert forms for the number fields Q( √ 13) and Q( √ 17). Finally we compute the Hermite-Humbert constant for the number field Q( √ 13).
متن کاملSweep Line Algorithm for Convex Hull Revisited
Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and imp...
متن کاملHermite's Constant for Quadratic Number Fields
CONTENTS We develop a method to compute the Hermite-Humbert con1 . Introduction stants 7 K n of a real quadratic number field K, the analogue of the 2. Bounds for Minimal Vectors of Humbert Forms classical Hermite constant 7 n when Q is replaced by a quadratic 3. Examples extension. In the case n = 2, the problem is equivalent to the deReferences termination of lowest points of fundamental doma...
متن کاملHIERARCHICAL COMPUTATION OF HERMITE SPHERICAL INTERPOLANT
In this paper, we propose to extend the hierarchical bivariateHermite Interpolant to the spherical case. Let $T$ be an arbitraryspherical triangle of the unit sphere $S$ and let $u$ be a functiondefined over the triangle $T$. For $kin mathbb{N}$, we consider aHermite spherical Interpolant problem $H_k$ defined by some datascheme $mathcal{D}_k(u)$ and which admits a unique solution $p_k$in the ...
متن کاملGenetic Algorithm-based Optimization Procedures to Find the Constants of Johnson-Cook Constitutive Equation
Johnson-Cook constitutive equation is one of the most famous constitutive equations that have ever been developed to model the hot deformation flow curves of different materials. This equation is a predefined model in the traditional finite element codes to describe the material behavior in applications such as simulating the manufacturing processes. In this work, two different genetic algorith...
متن کامل