Related papers: Higher discriminants of polynomials
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
The polynomial algebra is a deformed SU(2) algebra. Here, we use polynomial algebra as a method to solve a series of deformed oscillators. Meanwhile, we find a series of physics systems corresponding with polynomial algebra with different…
What polynomial in the coefficients of a system of algebraic equations should be called its discriminant? We prove a package of facts that provide a possible answer. Let us call a system typical, if the homeomorphic type of its set of…
We present a new topological method to study the discriminantal loci of an algebraic variety defined in a product of projective spaces. Our approach relies on an efficient use of groupoid to describe the monodromy. As an example, we treat…
Polynomial algebra offers a standard approach to handle several problems in geometric modeling. A key tool is the discriminant of a univariate polynomial, or of a well-constrained system of polynomial equations, which expresses the…
This paper describes a novel method to approximate the polynomial coefficients of regression functions, with particular interest on multi-dimensional classification. The derivation is simple, and offers a fast, robust classification…
We present an algorithm for computing discriminants and prime ideal decomposition in number fields. The algorithm is a refinement of a p-adic factorization method based on Newton polygons of higher order. The running-time and memory…
We consider polynomial equations, or systems of polynomial equations, with integer coefficients, modulo prime numbers $p$. We offer an elementary approach based on a counting method. The outcome is a weak form of the Lang-Weil lower bound…
It is shown how the dimension of any arbitrary over-determined system of differential equations can be reduced, which makes the system suitable for numerical solution modeling. Specifically, over-determined equations of hydrodynamics are…
In this paper, we introduce the degenerate multiple polyexponential functions which are multiple versions of the degenerate modified polyexponential functions. Then we consider the degenerate multi-poly-Genocchi polynomials which are…
Charlier configurations provide a combinatorial model for Charlier polynomials. We use this model to give a combinatorial proof of a multilinear generating function for Charlier polynomials. As special cases of the multilinear generating…
In this paper, we study linear differential equations arising from $\lambda$- Changhee polynomials (or called degenerate Changhee polynomials) and give some explicit and new identities for the $\lambda$-Changhee polynomials associated with…
I recent years, many mathematicians studied various degenerate version of some spcial polynomials of which quite a few interesting results were discovered. In this paper, we introduce the type 2 degenerate Bernoulli polynomials of the…
The linear complete differential resultant of a finite set of linear ordinary differential polynomials is defined. We study the computation by linear complete differential resultants of the implicit equation of a system of $n$ linear…
We introduce a new approach to constructing derived deformation groupoids, by considering them as parameter spaces for strong homotopy bialgebras. This allows them to be constructed for all classical deformation problems, such as…
Solutions which are quasimodular forms to a second order differential equation attached to a triangular group are explicitly described in terms of certain orthogonal polynomials.
The operational calculus associated with Hermite numbers has been shown to be an effective tool for simplifying the study of special functions. Within this context, Hermite polynomials have been viewed as Newton binomials, with the…
We give an improved polynomial bound on the complexity of the equation solvability problem, or more generally, of finding the value sets of polynomials over finite nilpotent rings. Our proof depends on a result in additive combinatorics,…
We consider linear systems of recurrence equations whose coefficients are given in terms of indefinite nested sums and products covering, e.g., the harmonic numbers, hypergeometric products, $q$-hypergeometric products or their mixed…
In this paper, the result of applying iterative univariate resultant constructions to multivariate polynomials is analyzed. We consider the input polynomials as generic polynomials of a given degree and exhibit explicit decompositions into…