Related papers: The Slice Algorithm For Irreducible Decomposition …

We give explicit formulas to compute most of the decomposition numbers of reductions modulo 2 of irreducible spin representations of symmetric groups indexed by partitions with at most 2 parts. In many of the still open cases small upper…

Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…

In this paper we develop a new technique to compute the Betti table of a monomial ideal. We present a prototype implementation of the resulting algorithm and we perform numerical experiments suggesting a very promising efficiency. On the…

Inspired by Faug\`ere and Mou's sparse FGLM algorithm, we show how using linear recurrent multi-dimensional sequences can allow one to perform operations such as the primary decomposition of an ideal, by computing the annihilator of one or…

In present paper we propose seemingly new method for finding solutions of some types of nonlinear PDEs in closed form. The method is based on decomposition of nonlinear operators on sequence of operators of lower orders. It is shown that…

A constructive procedure is given to determine all ideals of a solvable Lie algebra. This is used in determining algorithmically all conjugacy classes of subalgebras of a given solvable Lie algebra.

We develop a new general method for computing the decomposition type of the normal bundle to a projective rational curve. This method is then used to detect and explain an example of a Hilbert scheme that parametrizes all the rational…

Using discrete Morse theory, we give an algorithm that prunes the excess of information in the Taylor resolution and constructs a new cellular free resolution for an arbitrary monomial ideal. The pruned resolution is not simplicial in…

We describe a new software package for computing multiplier ideals in certain cases, including monomial ideals, monomial curves, generic determinantal ideals, and hyperplane arrangements. In these cases we take advantage of combinatorial…

We determine a new technique which allows the computation of the arithmetical rank of certain monomial ideals.

We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive…

Let $J\subset I$ be monomial ideals. We show that the Stanley depth of $I/J$ can be computed in a finite number of steps. We also introduce the $\fdepth$ of a monomial ideal which is defined in terms of prime filtrations and show that it…

Let $\mathcal{A}$ be an abelian variety over a number field, with a good reduction at a prime ideal containing a prime number $p$. Denote by ${\rm A}$ an abelian variety over a finite field of characteristic $p$, obtained by the reduction…

In this paper, we present methods to simplify reducible linear differential systems before solving. Classical integrals appear naturally as solutions of such systems. We will illustrate the methods developed in a previous paper on several…

This paper deals with the index reduction problem for the class of quasi-regular DAE systems. It is shown that any of these systems can be transformed to a generically equivalent first order DAE system consisting of a single purely…

A new algorithm is presented for computing the largest degree invariant factor of the Sylvester matrix (with respect either to $x$ or $y$) associated to two polynomials $a$ and $b$ in $\mathbb F_q[x,y]$ which have no non-trivial common…

We discuss the problem of determining reduction number of a polynomial ideal I in n variables. We present two algorithms based on parametric computations. The first one determines the absolute reduction number of I and requires computation…

We describe a simple algorithm for computing the canonical basis of any finite-dimensional $U_{q}(sp_{2n})$-module.

Functions that are not differentiable in the classical sense have become a central tool in modern mathematical models for imaging, inverse problems, machine learning, and optimal control of differential equations. These models are…

We propose an effective method for primary decomposition of symmetric ideals. Let $K[X]=K[x_1,\ldots,x_n]$ be the $n$-valuables polynomial ring over a field $K$ and $\mathfrak{S}_n$ the symmetric group of order $n$. We consider the…