Related papers: Optimal Normal Bases Over Finite Fields
Using the notion of multivariate lower set interpolation, we construct nodal basis functions for the serendipity family of finite elements, of any order and any dimension. For the purpose of computation, we also show how to express these…
We present a sufficient condition for irreducibility of forcing algebras and study the (non)-reducedness phenomenon. Furthermore, we prove a criterion for normality for forcing algebras over a polynomial base ring with coefficients in a…
Given a number field $K$, a finite abelian group $G$ and finitely many elements $\alpha_1,\ldots,\alpha_t\in K$, we construct abelian extensions $L/K$ with Galois group $G$ that realise all of the elements $\alpha_1,\ldots,\alpha_t$ as…
In this paper, two nonconforming finite element schemes that use piecewise cubic and piecewise quartic polynomials respectively are constructed for the planar biharmonic equation with optimal convergence rates on general shape-regular…
Optimizing an implicational base of a closure system consists in turning this implicational base into an equivalent one with premises and conclusions as small as possible. This task is known to be hard in general but tractable for a number…
The concept of additive basis has been investigated in the literature for several mathematicians which works with number theorem. Recently, the concept of finitely stable additive basis was introduced. In this note we provide a…
Projecting fields between different meshes commonly arises in computational physics. This operation requires a supermesh construction and its computational cost is proportional to the number of cells of the supermesh $n$. Given any two…
Gr\"obner bases can be used for computing the Hilbert basis of a numerical submonoid. By using these techniques, we provide an algorithm that calculates a basis of a subspace of a finite-dimensional vector space over a finite prime field…
An algorithm to generate a minimal comprehensive Gr\"obner\, basis of a parametric polynomial system from an arbitrary faithful comprehensive Gr\"obner\, system is presented. A basis of a parametric polynomial ideal is a comprehensive…
We introduce two constructions of additive codes over finite fields. Both constructions start with a linear code over a field with $q$ elements and give additive codes over the field with $q^h$ elements whose minimum distance is…
This paper investigates the normal bases of algebras with low growth.
The number of linear independent algebraic relations among elementary symmetric polynomial functions over finite fields is computed. An algorithm able to find all such relations is described. It is proved that the basis of the ideal of…
In this paper, we survey and refine several results -- some previously established in the literature -- that facilitate the construction of exponential bases on planar domains with explicit control over the associated frame bounds. We apply…
For $q=3^r$ ($r>0$), denote by $\mathbb{F}_q$ the finite field of order $q$ and for a positive integer $m\geq2$, let $\mathbb{F}_{q^m}$ be its extension field of degree $m$. We establish a sufficient condition for existence of a primitive…
The finite basis optimized effective potential (OEP) method within density functional theory is examined as an ill-posed problem. It is shown that the generation of nonphysical potentials is a controllable manifestation of the use of…
In recent decades, the defect of finite extensions of valued fields has emerged as the main obstacle in several fundamental problems in algebraic geometry such as the local uniformization problem. Hence, it is important to identify…
This paper presents a novel boundary-optimized fast Fourier extension algorithm for efficient approximation of non-periodic functions. The proposed methodology constructs periodic extensions through strategic utilization of boundary…
We show how to construct all the extensions of left braces by ideals with trivial structure. This is useful to find new examples of left braces. But, to do so, we must know the basic blocks for extensions: the left braces with no ideals…
We construct standard resolutions for analytic local modules on complex hypersurfaces using standard basis methods, with extensions to complete intersections. The algebraic version over arbitrary infinite fields is also suggested.…
A number of constructions in function field arithmetic involve extensions from linear objects using digit expansions. This technique is described here as a method of constructing orthonormal bases in spaces of continuous functions. We…