# Affine Arithmetic

 Title: Affine Arithmetic Author: Fabian Immler Submission date: 2014-02-07 Abstract: We give a formalization of affine forms as abstract representations of zonotopes. We provide affine operations as well as overapproximations of some non-affine operations like multiplication and division. Expressions involving those operations can automatically be turned into (executable) functions approximating the original expression in affine arithmetic. Change history: [2015-01-31]: added algorithm for zonotope/hyperplane intersection [2017-09-20]: linear approximations for all symbols from the floatarith data type BibTeX: @article{Affine_Arithmetic-AFP, author = {Fabian Immler}, title = {Affine Arithmetic}, journal = {Archive of Formal Proofs}, month = feb, year = 2014, note = {\url{https://isa-afp.org/entries/Affine_Arithmetic.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: Deriving, List-Index, Show Used by: Ordinary_Differential_Equations, Taylor_Models 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.