Mora aims to show that solving a polynomial equation really means finding algorithms that help one manipulate roots rather than simply computing them; to that end he also surveys algorithms for ...

We solve polynomials algebraically in order to determine the roots - where a curve cuts the \(x\)-axis. A root of a polynomial function, \(f(x)\), is a value for \(x\) for which \(f(x) = 0\).

This third volume of four finishes the program begun in Volume 1 by describing all the most important techniques, mainly based on Gröbner bases, which allow one to manipulate the roots of the equation ...

Roots can occur in a parabola in 3 different ways as shown in the diagram below: In diagram A, we can see that this parabola has 2 roots, diagram B has 1 root and diagram C has no roots.

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 ...

Having lowered the bar for the sense in which we hope to solve a system of linear equations, one might wonder whether this quantum algorithm 3 offers a real advantage over classical computing at all.

Both algebraic and arithmetic geometry are concerned with the study of solution sets of systems of polynomial equations. Algebraic geometry deals primarily with solutions lying in an algebraically ...

Mathematicians have made lots of recent progress on a question called the Mordell conjecture, which was posed a century ago ...

The book showed how to solve polynomial equations, and algebraic methods of writing an expression in a simpler form, a tactic known as reduction. It also covered key concepts such as moving a ...