The arithogeometric mean. (English) Zbl 0686.14040

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


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
Full Text: DOI


[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
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