Computing N-Th Roots Using the Babylonian Method

René Thiemann

3 January 2013

Abstract

We implement the Babylonian method to compute n-th roots of numbers. We provide precise algorithms for naturals, integers and rationals, and offer an approximation algorithm for square roots over linear ordered fields. Moreover, there are precise algorithms to compute the floor and the ceiling of n-th roots.
GNU Lesser General Public License (LGPL)

Change history

[2013-10-16] Added algorithms to compute floor and ceiling of sqrt of integers. [2014-07-11] Moved NthRoot_Impl from Real-Impl to this entry.

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Cite

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@article{Sqrt_Babylonian-AFP,
  author  = {René Thiemann},
  title   = {Computing N-th Roots using the Babylonian Method},
  journal = {Archive of Formal Proofs},
  month   = January,
  year    = 2013,
  note    = {\url{http://isa-afp.org/entries/Sqrt_Babylonian.html},
            Formal proof development},
  ISSN    = {2150-914x},
}
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