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.