We describe algorithms for polynomial factorization over the binary field F2, and their implementation. They allow polynomials of degree up to 250 000 to be factored in about one day of CPU time, ...

A new algorithm for factoring multivariate polynomials over the integers based on an algorithm by Wang and Rothschild is described. The new algorithm has improved strategies for dealing with the known ...

Matrix polynomials and moment problems are significant areas of study in mathematics, particularly in the fields of control theory, numerical analysis, and probability. Matrix polynomials are ...

If \((x \pm h)\) is a factor of a polynomial, then the remainder will be zero. Conversely, if the remainder is zero, then \((x \pm h)\) is a factor. Often ...

In 2015, the poet-turned-mathematician June Huh helped solve a problem posed about 50 years earlier. The problem was about complex mathematical objects called “matroids” and combinations of points and ...

A polynomial is a chain of algebraic terms with various values of powers. There are some words and phrases to look out for when you're dealing with polynomials: \(6{x^5} - 3{x^2} + 7\) is a polynomial ...

Digital security depends on the difficulty of factoring large numbers. A new proof shows why one method for breaking digital encryption won’t work. My recent story for Quanta explained a newly proved ...