相关论文: Methods for Computing Normalisations of Affine Rin…

This paper proposes an algorithm for computing regularized solutions to linear rational expectations models. The algorithm allows for regularization cross-sectionally as well as across frequencies. A variety of numerical examples illustrate…

An ideal of a local polynomial ring can be described by calculating a standard basis with respect to a local monomial ordering. However standard basis algorithms are not numerically stable. Instead we can describe the ideal numerically by…

We study the normalization of a monomial ideal, and show how to compute its Hilbert function (using Ehrhart polynomials) if the ideal is zero dimensional. A positive lower bound for the second coefficient of the Hilbert polynomial is shown.

As we know that the normalization is a pre-processing stage of any type problem statement. Especially normalization takes important role in the field of soft computing, cloud computing etc. for manipulation of data like scale down or scale…

In this survey, we describe two different approaches to constructing affine schemes for commutative semirings: one based on prime ideals, and another based on prime kernels (also called subtractive ideals). We then explain how these two…

The main goal of this paper is to give a general method to compute (via computer algebra systems) an explicit set of generators of the ideals of the projective embeddings of some ruled surfaces, namely projective line bundles over curves…

Let B be a ring and $A=B[X,Y]/(aX^2+bXY+cY^2-1)$ where $a,b,c\in B$. We study the smoothness of A over B, and the regularity of B when B is a ring of algebraic integers.

Starting from the parametric representation of a Feynman diagram, we obtain it's well defined value in dimensional regularisation by changing the integrals over parameters into contour integrals. That way we eventually arrive at a…

We characterize the seminormality of an affine semigroup ring in terms of the dualizing complex, and the normality of a Cohen-Macaulay semigroup ring by the "shape" of the canonical module. We also characterize the seminormality of a toric…

Calculation of the log-normalizer is a major computational obstacle in applications of log-linear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical…

We introduce a canonical form for reduced bases of integral closures of discrete valuation rings, and we describe an algorithm for computing a basis in reduced normal form. This normal form has the same applications as the Hermite normal…

Let A \subseteq B be cancellative abelian semigroups, and let R be an integral domain. We show that the semigroup ring R[B] can be decomposed, as an R[A]-module, into a direct sum of R[A]-submodules of the quotient ring of R[A]. In the case…

Here, I present a novel method for normalizing a finite set of numbers, which is studied by the domain of biological vision. Normalizing in this context means searching the maximum and minimum number in a set and then rescaling all numbers…

This paper is devoted to normal forms for x-flat control-affine systems with two inputs. We propose a general triangular normal form which contains several other normal forms discussed in the literature as special cases. We derive…

We present Binomials, a package for the computer algebra system Macaulay2, which specializes well known algorithms to binomial ideals. These come up frequently in algebraic statistics and commutative algebra, and it is shown that…

Ideals in the ring of power series in three variables can be classified based on algebra structures on their minimal free resolutions. The classification is incomplete in the sense that it remains open which algebra structures actually…

We consider a nonlinear representation of a Lie algebra which is regular on an abelian ideal, we define a normal form which generalizes that defined in [D. Arnal, M. Ben Ammar, M. Selmi, {\rm Normalisation d'une repr\'esentation non…

We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…

Normaliz is a program for solving linear systems of inequalities. In this paper we present the algorithms implemented in the program, starting with version 2.0.

In this paper, we present an algorithm for computing a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in several variables. This algorithm is a generalization of a method developed for…