Related papers: On Lazard's Valuation and CAD Construction
In this paper, we first introduce the concept of Laurent differentially essential systems and give a criterion for Laurent differentially essential systems in terms of their supports. Then the sparse differential resultant for a Laurent…
Differential lambda-calculus was first introduced by Thomas Ehrhard and Laurent Regnier in 2003. Despite more than 15 years of history, little work has been done on a differential calculus with integration. In this paper, we shall propose a…
We present a new Clifford-valued linear canonical Stockwell transform aimed at providing efficient and focused representation of Clifford-valued functions in high-dimensional time-frequency analysis. This transform improves upon the…
The primary purpose is to introduce and explore projective varieties, $\text{GRASS}_{\bf d}(\Lambda)$, parametrizing the full collection of those modules over a finite dimensional algebra $\Lambda$ which have dimension vector $\bf d$. These…
Least Absolute Deviations (LAD) regression provides a robust alternative to ordinary least squares by minimizing the sum of absolute residuals. However, its widespread use has been limited by the computational cost of existing solvers,…
A multivalued projection is an idempotent linear relation with invariant domain. We characterize multivalued projections that are operator ranges (called semiclosed) and provide several formulae of them. Moreover, we study the…
Canonical Polyadic Decomposition (CPD) represents a third-order tensor as the minimal sum of rank-1 terms. Because of its uniqueness properties the CPD has found many concrete applications in telecommunication, array processing, machine…
Differential measurements of particle collisions or decays can provide stringent constraints on physics beyond the Standard Model of particle physics. In particular, the distributions of the kinematical and angular variables that…
Motivated by Tucker tensor decomposition, this paper imposes low-rank structures to the column and row spaces of coefficient matrices in a multivariate infinite-order vector autoregression (VAR), which leads to a supervised factor model…
We deal with the algebraicity of an iterated Puiseux series in several variables in terms of the properties of its coefficients. Our aim is to generalize to several variables the results from [HM15]. We show that the algebraicity of such a…
Motivated by some recent developments in abstract theories of quadratic forms, we start to develop in this work an expansion of Linear Algebra to multivalued structures (a multialgebraic structure is essentially an algebraic structure but…
We consider systems of Laurent polynomials with support on a fixed point configuration. In the non-defective case, the closure of the locus of coefficients giving a non-degenerate multiple root of the system is defined by a polynomial…
In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…
Canonical correlation analysis (CCA) is a classic statistical method for discovering latent co-variation that underpins two or more observed random vectors. Several extensions and variations of CCA have been proposed that have strengthened…
Our topic is the use of machine learning to improve software by making choices which do not compromise the correctness of the output, but do affect the time taken to produce such output. We are particularly concerned with computer algebra…
The notion of a valuation on convex bodies is very classical. The notion of a valuation on a class of functions was recently introduced and studied by M. Ludwig and others. We study an explicit relation between continuous valuations on…
Recently introduced composition operator for credal sets is an analogy of such operators in probability, possibility, evidence and valuation-based systems theories. It was designed to construct multidimensional models (in the framework of…
An algebraic algorithm is developed for computation of invariants ('generalized Casimir operators') of general Lie algebras over the real or complex number field. Its main tools are the Cartan's method of moving frames and the knowledge of…
In this work we introduce a category $LDP_d$ of discrete-time dynamical systems, that we call discrete Lagrange--D'Alembert--Poincar\'e systems, and study some of its elementary properties. Examples of objects of $LDP_d$ are nonholonomic…
In this article, we study the local behaviour of the multiple polylogarithm functions at integer points, in the $s$-aspect. This is done by writing a Laurent type expansion at integer points, involving certain power series and rational…