To integer programming problems, computational algebraic approaches using Gröbner bases or standard pairs via the discreteness of toric ideals have been studied in recent years. Although these approaches have not given improved time complexity bound compared with existing methods for solving integer programming problems, these give algebraic analysis of their structures. In this paper, we focus...

Universal algebra is often known within computer science in the guise of algebraic specification or equational logic. In 1963, it was given a category theoretic characterisation in terms of what are now called Lawvere theories. Unlike operations and equations, a Lawvere theory is uniquely determined by its category of models. Except for a caveat about nullary operations, the notion of Lawvere t...

Let V be a G-module where G is a complex reductive group. Let Z := V//G denote the categorical quotient and let π : V → Z be the morphism dual to the inclusion O(V ) ⊂ O(V ). Let φ : Z → Z be an algebraic automorphism. Then one can ask if there is an algebraic map Φ: V → V which lifts φ, i.e., π(Φ(v)) = φ(π(v)) for all v ∈ V . In Kuttler [Kut11] the case is treated where V = rg is a multiple of...

The goal of this paper is study closed ideals and annihilators over the class distributive dual weakly complemented lattices(DDWCL's). algebraic structure ideals, dense are shown. connection between andannihilators in obtained.

Let X be an algebraic curve of genus g ≥ 2 defined over a field Fq of characteristic p > 0. From X , under certain conditions, we can construct an algebraic geometry code CX . When this code (or its dual) is self-orthogonal under the symplectic product, a quantum algebraic geometry code QX is constructed. In this paper we study the construction of such codes from curves with automorphisms and t...

Functional programs are merely equations; they may be manipulated by straightforward equational reasoning. In particular, one can use this style of reasoning to calculate programs, in the same way that one calculates numeric values in arithmetic. Many useful theorems for such reasoning derive from an algebraic view of programs, built around datatypes and their operations. Traditional algebraic ...

The aim of this paper is to identify a certain tensor category of perverse sheaves on the real loop Grassmannian GrR of a real form GR of a connected reductive complex algebraic group G with the category of finite-dimensional representations of a reductive complex algebraic subgroup H of the dual group Ǧ. The root system of H is closely related to the restricted root system of GR. The fact that...

We present a construction of bent function fa,S with n = 2m variables for any nonzero vector a ∈ F2 and subset S of F2 satisfying a + S = S. We give the simple expression of the dual bent function of fa,S . We prove that fa,S has optimal algebraic degree m if and only if |S| ≡ 2(mod4). This construction provides series of bent functions with optimal algebraic degree and large symmetric group if...

Toric codes are obtained by evaluating rational functions of a nonsingular toric variety at the algebraic torus. One can extend toric codes to the so called generalized toric codes. This extension consists on evaluating elements of an arbitrary polynomial algebra at the algebraic torus instead of a linear combination of monomials whose exponents are rational points of a convex polytope. We stud...

This paper completes a preceeding paper on the algebraic formulation of elastostatics [Tonti, Zarantonello (2009)]. It shows how to obtain a numerical formulation for elastodynamics by avoiding any process of discretization of differential equations, i.e. PDE-free formulation. To this end, we must analyse in more detail the discretization of time by highlighting the need to introduce a dual sub...