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Linear Recurrences
| Title: | Linear Recurrences |
| Author: | Manuel Eberl |
| Submission date: | 2017-10-12 |
| Abstract: |
Linear recurrences with constant coefficients are an interesting class of recurrence equations that can be solved explicitly. The most famous example are certainly the Fibonacci numbers with the equation f(n) = f(n-1) + f(n - 2) and the quite non-obvious closed form (φn - (-φ)-n) / √5 where φ is the golden ratio. In this work, I build on existing tools in Isabelle – such as formal power series and polynomial factorisation algorithms – to develop a theory of these recurrences and derive a fully executable solver for them that can be exported to programming languages like Haskell. |
| BibTeX: |
@article{Linear_Recurrences-AFP,
author = {Manuel Eberl},
title = {Linear Recurrences},
journal = {Archive of Formal Proofs},
month = oct,
year = 2017,
note = {\url{http://isa-afp.org/entries/Linear_Recurrences.html},
Formal proof development},
ISSN = {2150-914x},
}
|
| License: | BSD License |
| Depends on: | Count_Complex_Roots, Polynomial_Factorization |
| 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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