Changes http://page.axiom-developer.org/zope/mathaction/RealNumbers/diff -- There is apparently a lot of work on this subject.
Some History http://www.rbjones.com/rbjpub/cs/cs006.htm > The lazy digit sequence approach (similar to lazy power series) has, > for example, been implemented by Michael Stoll in Common Lisp, 1988. http://www.haible.de/bruno/MichaelStoll/reals.html XR - Exact Real Arithmetic Overview This is an implementation of exact (or constructive) real arithmetic, including python and C++ versions. It is an alternative to multiple- precision floating-point codes. An important distinction is that in multiple-precision floating-point one sets the precision before starting a computation, and then one cannot be sure of the final result. Interval arithmetic is an improvement on this, but still not an ideal solution because if the final interval is larger than desired, there is no simple way to restart the computation at higher precision. By constrast, in XR no precision level is set in advance, and no computation takes place until a final request takes place for some output. http://more.btexact.com/people/briggsk2/XR.html Others A Calculator for Exact Real Number Computation Abstract The most usual approach to real arithmetic on computers consists of using floating point approximations. Unfortunately, floating point arithmetic can sometimes produce wildly erroneous results. One alternative approach is to use exact real arithmetic. Exact real arithmetic allows exact real number computation to be performed without the roundoff errors characteristic of other methods. http://www.dcs.ed.ac.uk/home/mhe/plume Formalising exact Arithmetic ... deals with exact rational and real arithmetic in constructive type theory. Parts of the thesis are formalised in Coq. The thesis can be downloaded at the following URL: http://www.cs.ru.nl/~milad/proefschrift/thesis.pdf -- forwarded from http://page.axiom-developer.org/zope/mathaction/[EMAIL PROTECTED] _______________________________________________ Axiom-developer mailing list Axiom-developer@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-developer