The program performs these operations efficiently and provides clean output. It uses an array-based representation to store and manipulate polynomial terms. Please note that the program reads and ...

SOSTOOLS is a free MATLAB toolbox for formulating and solving polynomial optimization programs by searching for a sum-of-squares decompostion of a multivariate polynomial. A sum-of-squares ...

The definition of a Taylor polynomial of order k of a function f at a point xo implies that the degree of this polynomial is at most k, but it can be smaller than k (if f (k)(x0) = 0). It is plain to ...

A polynomial is an algebraic expression involving many terms and can be factorised using long division or synthetic division. Laws of logarithms and exponents Revise what logarithms are and how to use ...

This paper introduces an applied problem-solving task, set in the context of cryptography and embedded in a network of computer-based tools. This designed learning environment engaged students in a ...

Algorithmic complexity, a cornerstone of theoretical computer science, examines the intrinsic resource requirements of computational problems and the limits of what can be efficiently computed. Within ...

In a factorial ring, we can define the p.g.c.d. of two elements (defined to the nearest unit) and the notion of prime elements between them. More generally, Bezout’s identity characterizes two prime ...

ABSTRACT: A new approach for solving polynomial equations is presented in this study. Two techniques for solving quartic equations are described that are based on a new method which was recently ...

Bernstein polynomial estimation provides a robust nonparametric technique for approximating both density and distribution functions. Based on the properties of Bernstein polynomials, which uniformly ...

Mahesh Ramesh Kakde, winner of this year’s Vigyan Yuva Shanti Swarup Bhatnagar award for Mathematics, is a number theorist at the Indian Institute of Science, Bengaluru, who studies polynomial ...