Interpolation Polynomials (in HOL-Algebra)

 

Title: Interpolation Polynomials (in HOL-Algebra)
Author: Emin Karayel
Submission date: 2022-01-29
Abstract:

A well known result from algebra is that, on any field, there is exactly one polynomial of degree less than n interpolating n points [1, §7].

This entry contains a formalization of the above result, as well as the following generalization in the case of finite fields F: There are |F|m-n polynomials of degree less than m ≥ n interpolating the same n points, where |F| denotes the size of the domain of the field. To establish the result the entry also includes a formalization of Lagrange interpolation, which might be of independent interest.

The formalized results are defined on the algebraic structures from HOL-Algebra, which are distinct from the type-class based structures defined in HOL. Note that there is an existing formalization for polynomial interpolation and, in particular, Lagrange interpolation by Thiemann and Yamada [2] on the type-class based structures in HOL.

BibTeX:
@article{Interpolation_Polynomials_HOL_Algebra-AFP,
  author  = {Emin Karayel},
  title   = {Interpolation Polynomials (in HOL-Algebra)},
  journal = {Archive of Formal Proofs},
  month   = jan,
  year    = 2022,
  note    = {\url{https://isa-afp.org/entries/Interpolation_Polynomials_HOL_Algebra.html},
            Formal proof development},
  ISSN    = {2150-914x},
}
License: BSD License
Used by: Frequency_Moments, Universal_Hash_Families
Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.