相关论文: A generating algorithm for ribbon tableaux and spi…
In this article, we give a numerical algorithm to compute braid groups of curves, hyperplane arrangements, and parameterized system of polynomial equations. Our main result is an algorithm that determines the cross-locus and the generators…
We give a simple and practical algorithm to compute the link polynomials, which are defined according to the skein relations. Our method is based on a new total order on the set of all braid representatives. As by-product a new complete…
In recent years it has been shown that for many linear algebra operations it is possible to create families of algorithms following a very systematic procedure. We do not refer to the fine tuning of a known algorithm, but to a methodology…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
A large class of MDS linear codes is constructed. These codes are endowed with an efficient decoding algorithm. Both the definition of the codes and the design of their decoding algorithm only require from Linear Algebra methods, making…
We use cyclotomy to design new classes of permutation polynomials over finite fields. This allows us to generate many classes of permutation polynomials in an algorithmic way. Many of them are permutation polynomials of large indices.
Conditional neural text generation models generate high-quality outputs, but often concentrate around a mode when what we really want is a diverse set of options. We present a search algorithm to construct lattices encoding a massive number…
This paper proposes a set of techniques to develop correctly rounded math libraries for 32-bit float and posit types. It enhances our RLibm approach that frames the problem of generating correctly rounded libraries as a linear programming…
Algorithms to generate various combinatorial structures find tremendous importance in computer science. In this paper, we begin by reviewing an algorithm proposed by Rohl that generates all unique permutations of a list of elements which…
We generalize the notion of cyclic codes by using generator polynomials in (non commutative) skew polynomial rings. Since skew polynomial rings are left and right euclidean, the obtained codes share most properties of cyclic codes. Since…
In this article, we present a new algorithm for computing a generating set of a lattice ideal. This algorithm is based on a project-and-lift approach and is implemented in 4ti2. We also include a computational comparison of several existing…
We extend the existing skew polynomial representations of matrix algebras which are direct sum of matrix spaces over division rings. In this representation, the sum-rank distance between two tuples of matrices is captured by a weight…
Two distinct algorithms are presented to extract (schemata of) resolution proofs from closed tableaux for propositional schemata. The first one handles the most efficient version of the tableau calculus but generates very complex…
We describe an algorithm for fast multiplication of skew polynomials. It is based on fast modular multiplication of such skew polynomials, for which we give an algorithm relying on evaluation and interpolation on normal bases. Our…
The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…
We speed up existing decoding algorithms for three code classes in different metrics: interleaved Gabidulin codes in the rank metric, lifted interleaved Gabidulin codes in the subspace metric, and linearized Reed-Solomon codes in the…
Different approaches to construct linear codes using skew polynomials can be unified by using the nonassociative algebras built from skew-polynomial rings by Petit.
In this paper, we introduce a new family of codes relevent for rank and sum-rank metrics. These codes are based on an effective Chinese remainders theorem for linearized polynomials over finite fields. We propose a decoding algorithm for…
We develop a new characterization of potential maximal cliques of a triconnected planar graph and, using this characterization, give a polynomial delay algorithm generating all potential maximal cliques of a given triconnected planar graph.…
Ouroboros functions have shown some interesting properties when subjected to conventional operations. The aim of this paper is to continue our investigation and prove some additional properties of these functions. Using algebraic methods,…