Abstract: The general number field sieve (GNFS) is asymptotically the fastest algorithm known for factoring large integers. One of the most important steps of GNFS is to select a good polynomial pair.

1 Warwick Mathematics Institute, The University of Warwick, Coventry, United Kingdom 2 School of Computer and Information Engineering, Luoyang Institute of Science and Technology, Luoyang, China To ...

An algorithm for finding the symbolic factors of a multivariate polynomial with integer coefficients is presented. The algorithm is an extension of a technique used by Kronecker in a proof that the ...

Two mathematicians have used a new geometric approach in order to address a very old problem in algebra. In school, we often learn how to multiply out and factor polynomial equations like (x² – 1) or ...

Two mathematicians have used a new geometric approach in order to address a very old problem in algebra. In school, we often learn how to multiply out and factor polynomial equations like (x² – 1) or ...

Emily Long is a freelance writer based in Salt Lake City. After graduating from Duke University, she spent several years reporting on the federal workforce for Government Executive, a publication of ...

New research details an intriguing new way to solve "unsolvable" algebra problems that go beyond the fourth degree – something that has generally been deemed impossible using traditional methods for ...

A UNSW Sydney mathematician has discovered a new method to tackle algebra's oldest challenge—solving higher polynomial equations. Polynomials are equations involving a variable raised to powers, such ...

Methods of polynomial factorization which find the zeros one at a time require the division of the polynomial by the accepted factor. It is shown how the accuracy of this division may be increased by ...

This appendix provides an example on how to apply the k-prototypes clustering algorithm in R, which is an open-source programming language that is mainly used for data processing and statistical ...