Related papers: Spectral Factorization of Trigonometric Polynomial…

We prove a theorem on algebraic osculation and we apply our result to the Computer Algebra problem of polynomial factorization. We consider X a smooth completion of the complex plane and D an effective divisor supported on the boundary of…

We formulate several polynomial identities. One side of these identities has a nice simple form. Whereas the other has a form of a polynomial whose coefficients contain binomial coefficients double factorials or (and) rising factorials. The…

This paper derives numerical bounds for and implements the splitting circle method for finding roots of a univariate polynomial in the presence of fixed precision.

A family of polynomials parameterized by the conjugacy classes of a finite Coxeter group is investigated. These polynomials, together with the character table of the group, determine the associated generic degrees. The polynomials are…

Graph polynomials are graph parameters invariant under graph isomorphisms which take values in a polynomial ring with a fixed finite number of indeterminates. We study graph polynomials from a model theoretic point of view. In this paper we…

This paper investigates the p-adic valuation trees of degree-2 and degree-3 polynomials in two variables over any prime p, building upon prior research outlined in [14].

In this paper we investigate polynomial interpolation using orthogonal polynomials. We use weight functions associated with orthogonal polynomials to define a weighted form of Lagrange interpolation. We introduce an upper bound of error…

We study a relation between roots of characteristic polynomials and intersection points of line arrangements. Using these results, we obtain a lot of applications for line arrangements. Namely, we give (i) a generalized addition theorem for…

In this text, we study factorizations of polynomials over the tropical hyperfield and the sign hyperfield, which we call `tropical polynomials' and `sign polynomials', respectively. We classify all irreducible polynomials in either case. We…

The usual methods for root finding of polynomials are based on the iteration of a numerical formula for improvement of successive estimations. The unpredictable nature of the iterations prevents to search roots inside a pre-specified region…

By applying Schmidt's lattice method, we prove results on simultaneous Diophantine approximation modulo 1 for systems of polynomials in a single prime variable provided that certain local conditions are met.

We present an elementary method for proving enumeration formulas which are polynomials in certain parameters if others are fixed and factorize into distinct linear factors over Z. Roughly speaking the idea is to prove such formulas by…

The purpose of this paper is to show how Gelfand's formula and balancing can be used to improve the upper and lower bounds of the spectrum of a companion matrix associated with a given real or complex polynomial. Examples and other related…

In this paper, we propose an algebraic approach to determine whether two non-isomorphic caterpillar trees can have the same symmetric function generalization of the chromatic polynomial. On the set of all composition on integers, we…

We identify a recursive structure among factorizations of polynomial values into two integer factors. Polynomials for which this recursive structure characterizes all non-trivial representations of integer factorizations of the polynomial…

Polynomial factorization in conventional sense is an ill-posed problem due to its discontinuity with respect to coefficient perturbations, making it a challenge for numerical computation using empirical data. As a regularization, this paper…

We enumerate factorisations of the complete graph into spanning regular graphs in several cases, including when the degrees of all the factors except for one or two are small. The resulting asymptotic behaviour is seen to generalise the…

We study matrix three term relations for orthogonal polynomials in two variables constructed from orthogonal polynomials in one variable. Using the three term recurrence relation for the involved univariate orthogonal polynomials, the…

We study functional graphs generated by several quadratic polynomials, acting simultaneously on a finite field of odd characteristic. We obtain several results about the number of leaves in such graphs. In particular, in the case of graphs…

We show factorization formulas for a class of partition functions of rational six vertex model. First we show factorization formulas for partition functions under triangular boundary. Further, by combining the factorization formulas with…