The basic facts about separable extensions of discrete fields and factoring polynomials are developed in the constructive spirit of Errett Bishop. The ability to factor polynomials is shown to be ...

Researchers introduced new concepts and arithmetic functions that could play a significant role in the quantum factorization problem. The Factorization Ensemble is the main one; it allows us to bind ...

In this paper we present the implementation of simultaneous method for the determination of polynomial roots on a distributed memory multicomputer. The total cost of such a parallelization per ...

Uncertainty quantification (UQ) is increasingly critical for modelling complex systems in which input parameters or environmental conditions vary unpredictably. Polynomial chaos methods offer a ...

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 ...