We consider polynomials of bi-degree (n, 1) over the skew field of quaternions where the indeterminates commute with each other and with all coefficients. Polynomials of this type do not generally ...

We present a randomized quantum algorithm for polynomial factorization over finite fields. For polynomials of degree n over a finite field F_q, the average-case complexity of our algorithm is an ...

Abstract: This paper presents a novel method for calculating a compact order singular value decomposition (SVD) of polynomial matrices, building upon the recently proven existence of an analytic SVD ...

The deterministic factorization algorithm for polynomials over finite fields that was recently introduced by the author is based on a new type of linearization of the factorization problem. The main ...

This code contains three implementations of the polynomials in OCaml. It is intended as a pedagical exercise to demonstrate OCaml. The three implementations are : array_polynomial.ml: an ...

ABSTRACT: Substitution boxes or S-boxes play a significant role in encryption and de-cryption of bit level plaintext and cipher-text respectively. Irreducible Poly-nomials (IPs) have been used to ...

This repository contains code and resources for the paper "Discovering Hidden Algebraic Structures via Transformers with Rank-Aware Beam GRPO". Our research explores the potential of transformer ...