|
The
Factorization
Algorithm
of
Berlekamp
and
Zassenhaus
Title: |
The Factorization Algorithm of Berlekamp and Zassenhaus |
Author: |
Jose Divasón, Sebastiaan Joosten (sebastiaan /dot/ joosten /at/ uibk /dot/ ac /dot/ at), René Thiemann (rene /dot/ thiemann /at/ uibk /dot/ ac /dot/ at) and Akihisa Yamada (akihisa /dot/ yamada /at/ uibk /dot/ ac /dot/ at) |
Submission date: |
2016-10-14 |
Abstract: |
We formalize the Berlekamp-Zassenhaus algorithm for factoring
square-free integer polynomials in Isabelle/HOL. We further adapt an
existing formalization of Yun’s square-free factorization algorithm to
integer polynomials, and thus provide an efficient and certified
factorization algorithm for arbitrary univariate polynomials.
The algorithm first performs a factorization in the prime field GF(p) and
then performs computations in the integer ring modulo p^k, where both
p and k are determined at runtime. Since a natural modeling of these
structures via dependent types is not possible in Isabelle/HOL, we
formalize the whole algorithm using Isabelle’s recent addition of
local type definitions.
Through experiments we verify that our algorithm factors polynomials of degree
100 within seconds.
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BibTeX: |
@article{Berlekamp_Zassenhaus-AFP,
author = {Jose Divasón and Sebastiaan Joosten and René Thiemann and Akihisa Yamada},
title = {The Factorization Algorithm of Berlekamp and Zassenhaus},
journal = {Archive of Formal Proofs},
month = oct,
year = 2016,
note = {\url{http://isa-afp.org/entries/Berlekamp_Zassenhaus.shtml},
Formal proof development},
ISSN = {2150-914x},
}
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License: |
BSD License |
Depends on: |
Containers, Efficient-Mergesort, Jordan_Normal_Form, Native_Word, Polynomial_Factorization, Polynomial_Interpolation, Show, Sqrt_Babylonian |
Used by: |
Algebraic_Numbers |
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. |
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