Grayson, Daniel R. The arithogeometric mean. (English) Zbl 0686.14040 Arch. Math. 52, No. 5, 507-512 (1989). The article is based upon the arithogeometric mean method of Gauss. It explains a method to compute the periods of an elliptic curve and it provides a way to compute elliptic functions. These algorithms can be used to perform very accurate machine computations. The reader, familiar with the theory of elliptic curves, gets a clear survey of the methods. The algorithms are presented in a scheme that can be implemented immediately. Reviewer: G.Molenbergh Cited in 1 ReviewCited in 2 Documents MSC: 14H45 Special algebraic curves and curves of low genus 14-04 Software, source code, etc. for problems pertaining to algebraic geometry 33E05 Elliptic functions and integrals 68W30 Symbolic computation and algebraic computation 14H52 Elliptic curves Keywords:arithogeometric mean; periods of an elliptic curve; compute elliptic functions; machine computations; algorithms Software:EllipticIntegrals PDF BibTeX XML Cite \textit{D. R. Grayson}, Arch. Math. 52, No. 5, 507--512 (1989; Zbl 0686.14040) Full Text: DOI References: [1] D. Cox, The arithmetic-geometric mean of Gauss. Enseign. Math.30, 275-330 (1984). · Zbl 0583.33002 [2] J.Silverman, The arithmetic of Elliptic Curves. Berlin-Heidelberg-New York 1985. · Zbl 0613.14029 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.