For a computable field F, the splitting set S is the set of polynomials p(X) ∈ F[X] which factor over F, and the root set R is the set of polynomials with roots in F. Work by Frohlich and Shepherdson ...

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 ...

Arxiv – Pretending to factor large numbers on a quantum computer – Shor’s algorithm for factoring in polynomial time on a quantum computer gives an enormous advantage over all known classical ...