Edit detail for RealClosure revision 4 of 6

Real Algebraic Numbers

Renaud Rioboo:

        LIP6 Case 168, Thème SPI
        Universtité Pierre et Marie Curie
        4 Place Jussieu
        F-75252 Paris CEDEX 05

        Tel : +33 1 4427 3341
        Fax : +33 1 4427 4042
        mailto:Renaud.Rioboo@lip6.fr

http://www.lip6.fr

http://www-spi.lip6.fr/~rr/

Axiom Software

• http://ftp.lip6.fr/lip6/softs/formel/Axiom/RealClosures

  (source code)

• http://www-spi.lip6.fr/~rr/HDR

  (thesis)

• http://doi.acm.org/10.1145/143242.143312

  "Real algebraic closure of an ordered field: implementation in Axiom" Author: Renaud Rioboo, In: Papers from the international symposium on Symbolic and algebraic computation, Berkeley, Pages: 206 - 215, 1992 ISBN:0-89791-489-9.

• http://axiom-portal.newsynthesis.org/refs/articles/axiom-field.pdf

  (same as above)

Real Algebraic Closure of an Ordered Field, Implementation in Axiom

Real algebraic numbers appear in many Computer Algebra problems. For instance the determination of a cylindrical algebraic decomposition for an euclidian space requires computing with real algebraic numbers. This paper describes an implementation for computations with the real roots of a polynomial. This process is designed to be recursively used, so the resulting domain of computation is the set of all real algebraic numbers. An implementation for the real algebraic closure has been done in Axiom (previously called ScratchPad?).

Here is an example of it's usage.

Related Papers

• Infinitesimals and real closure
• Polymorphic Data Types, Objects, Modules and Functors: is it too.much.?