Polynomial equations are fundamental concepts in mathematics that define relationships between numbers and variables in a structured manner. In mathematics, various equations are composed using ...

The intertwined study of orthogonal polynomials and Painlevé equations continues to be a fertile area of research at the confluence of mathematical analysis and theoretical physics. Orthogonal ...

Over the centuries, mathematicians have developed a variety of methods of solving equations. Using the capabilities of modern computers, they have explored in detail how these age-old recipes ...

Equations, like numbers, cannot always be split into simpler elements. Researchers have now proved that such “prime” equations become ubiquitous as equations grow larger. Prime numbers get all the ...

Chebyshev polynomials, a central class of orthogonal polynomials, have long been pivotal in numerical analysis, approximation theory and the solution of differential equations. Their inherent ...

A mathematician has uncovered a way of answering some of algebra's oldest problems. University of New South Wales Honorary Professor Norman Wildberger, has revealed a potentially game-changing ...

Vesselin Dimitrov’s proof of the Schinzel-Zassenhaus conjecture quantifies the way special values of polynomials push each other apart. In the physical world, objects often push each other apart in an ...

Three researchers from Bristol University are seeking to develop methods for analysing the distribution of integer solutions to polynomial equations. How do you know when a polynomial equation has ...

Polynomial equations are a cornerstone of modern science, providing a mathematical basis for celestial mechanics, computer graphics, market growth predictions and much more. But although most high ...