Related papers: A note about invariant polynomial transformations …

We investigate the representation of symmetric polynomials as a sum of squares. Since this task is solved using semidefinite programming tools we explore the geometric, algebraic, and computational implications of the presence of discrete…

In this note we provide an algorithm for computing the fractional integrals of orthogonal polynomials, which is more stable than that using the expression of the polynomials w.r.t. the canonical basis. This algorithm is aimed at solving…

We introduce the notion of matrices graph, defining continued fraction algorithms where the past and the future are almost independent. We provide an algorithm to convert more general algorithms into matrices graphs. We present an algorithm…

This paper presents an integer decomposition method. The method first writes an integer as a polynomial with 2 as variable that its coefficients are zero or one. Then, suppose that an integer is decomposed into product of such two…

Analyzing and reasoning about safety properties of software systems becomes an especially challenging task for programs with complex flow and, in particular, with loops or recursion. For such programs one needs additional information, for…

We introduce a new numerical method for the computation of the inverse nonlinear Fourier transform and compare its computational complexity and accuracy to those of other methods available in the literature. For a given accuracy, the…

The paper studies constructions of irreducible polynomials over finite fields using polynomial composition method.

In this paper we use Euler-Seidel matrices method to find out some properties of exponential and geometric polynomials and numbers. Some known results are reproved and some new results are obtained.

A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements require the use of projectors,…

In this paper, we investigate new class of sequences related to fully degenerate Bernoulli numbers and polynomials. From those sequences, we derive some formulae for the degenerate Bernoulli and Euler polynomials.

We devise a simple but remarkably accurate iterative routine for calculating the roots of a polynomial of any degree. We demonstrate that our results have significant improvement in accuracy over those obtained by methods used in popular…

These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…

We apply a novel method for the equivalence group and its infinitesimal generators to the investigation of invariants of linear ordinary differential equations. First, a comparative study of this method is illustrated by an example. Next,…

In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…

In this paper we describe a variation of the classical permutation decoding algorithm that can be applied to any affine-invariant code with respect to certain type of information sets. In particular, we can apply it to the family of…

The purpose of this article is to delve into the properties of invariants. The properties, explained in [2], reveal new ways to develop algorithms that allow us to test the primality of a number. In this article, some of these are shown,…

We generalize the notion of the quandle polynomial to the case of singquandles. We show that the singquandle polynomial is an invariant of finite singquandles. We also construct a singular link invariant from the singquandle polynomial and…

This paper presents the concept of digit polynomials, which leads to a deterministic and unconditional integer factorization algorithm with the runtime complexity $\mathcal{O}(N^{1/4+\epsilon})$. Strassen's well known factoring approach is…

This paper presents a program analysis method that generates program summaries involving polynomial arithmetic. Our approach builds on prior techniques that use solvable polynomial maps for summarizing loops. These techniques are able to…

Computation of polynomial relative invariants is a classical tool in algebra. Relative differential invariants are central for the equivalence problem of geometric structures. We address the fundamental problem of finite generation of their…