On the Ring of Integer-valued Quasi-polynomials
Nan Li, Sheng Chen
TL;DR
This paper explores the properties of the ring of integer-valued quasi-polynomials, introducing generalized Euclidean division and GCD, and applying these concepts to continued fractions and matrix normal forms.
Contribution
It presents new theoretical frameworks for Euclidean division and GCD in the ring of integer-valued quasi-polynomials, with practical applications.
Findings
Development of generalized Euclidean division and GCD theories
Application to finite simple continued fraction expansion
Derivation of Smith normal form for parameterized matrices
Abstract
The paper studies some properties of the ring of integer-valued quasi-polynomials. On this ring, theory of generalized Euclidean division and generalized GCD are presented. Applications to finite simple continued fraction expansion and Smith normal form of integral matrices with integer parameters are also given.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Iterative Methods for Nonlinear Equations · Polynomial and algebraic computation