Efficient Generic Quotients Using Exact Arithmetic

Autor:	Watt, Stephen M.
Rok vydání:	2023
Předmět:	Computer Science - Symbolic Computation
Druh dokumentu:	Working Paper
Popis:	The usual formulation of efficient division uses Newton iteration to compute an inverse in a related domain where multiplicative inverses exist. On one hand, Newton iteration allows quotients to be calculated using an efficient multiplication method. On the other hand, working in another domain is not always desirable and can lead to a library structure where arithmetic domains are interdependent. This paper uses the concept of a whole shifted inverse and modified Newton iteration to compute quotients efficiently without leaving the original domain. The iteration is generic to domains having a suitable shift operation, such as integers or polynomials with coefficients that do not necessarily commute. Comment: Reformat of v3
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2304.01753 Zobrazit plný text záznamu View this record from Arxiv