RAGlib
A library for real solving polynomial systems of equations and inequalities


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RAGlib is distributed as a gzipped archive file. It has to be unpacked inside in a repository containing an installations of the FGb library and its interface to Maple.
See README file for the installation instructions (tar zxvf the download file).

A development version containing improved algorithms and more functionalities can be obtained by contacting me (mohab.safey[at]lip6.fr).

  • RAGlib release 3.3 (December 2016)   
    Standard release: [Download] (requires the installation of FGb)
    Standalone release: [Download] (can be used directly with Maple release not older than 16 -- has some internal limitations)
    • Performance improvements for functions dealing with systems with inequalities
    • Several bugs fixed
    • This release can not be used with Maple release older than 16.

  • RAGlib release 3.23 (March 2015)   
    Standard release: [Download] (requires the installation of FGb)
    Standalone release: [Download] (can be used directly with Maple release not older than 14 -- has some internal limitations)
    • Important speed-ups for HasRealSolutions

  • RAGlib release 3.22 (January 2014)   
    Standard release: [Download] (requires the installation of FGb)
    Standalone release: [Download] (can be used directly with Maple release not older than 14 -- has some internal limitations)
    • Important speed-ups improvements of the function UnivariateSumOfSquaresDec that decomposes non-negative univariate polynomials into sum of squares
      Warning: the output specification has changed
    • Bugs fixed and important speed-ups for HasRealSolutions and PointsPerComponents

  • RAGlib release 3.21 (July 2013)   
    Standard release: [Download] (requires the installation of FGb)
    Standalone release: [Download] (can be used directly with Maple release not older than 14 -- has some internal limitations)
    • Practical improvement of the function UnivariateSumOfSquaresDec that decomposes non-negative univariate polynomials into sum of squares
    • Bug fixed in the functions HasRealSolutions and PointsPerComponents

  • RAGlib release 3.20 (May 2013)   
    Standard release: [Download] (requires the installation of FGb)
    Standalone release: [Download] (can be used directly with Maple release not older than 14 -- has some internal limitations)
    • New function:UnivariateSumOfSquaresDec that decomposes non-negative univariate polynomials into sum of squares
      This is an implementation of Markus Schweighofer's algorithm described in his master's thesis
      Algorithmische Beweise fur Nichtnegativ une Positivstellensatze (Univ. Passau, 1999)
    • Practical improvements for HasRealSolutions and PointsPerComponents

  • RAGlib release 3.19.4 (October 2012)   
    Standalone release: [Download] (can be used directly with Maple release not older than 3.14)
    Standard release: [Download] (requires the installation of FGb)
    • Practical performances improved (especially for systems of polynomial inequalities)
    • Some bugs have been fixed.

  • RAGlib release 3.18 (July 2012)   
    Standard release: [Download]
    Standalone release: [Download]
    Release notes:
    • See the README file for installation instructions
    • Standalone release uses FGb functionalities integrated in Maple 15 (written by J.-C. Faugere)
      This has internal limitations (size of matrices built by FGb) but does not require a direct installation of FGb.
      The standard release needs you to install FGb but may be able to handle larger systems.
    • Warning:Names of functions and calling sequences have changed since release 3.1.
      HasRealSolutions(syst, vars) and PointsPerComponents(syst, vars)
      where syst is a list of equations and/or strict inequalities/inequations and
      vars is the list of variables appearing in syst.
    • RAGlib handles mixed systems of equations and inequalities
    • Warning: In the case of mixed systems, equations should satisfy genericity assumptions (checked by RAGlib).
      The next release will deal with mixed systems where equations don't satisfy these assumptions
    • Practical improvements for both functions
    • Several bugs have been fixed
  • RAGlib release 3.1 (October 2011)    [Download]
    Release notes:
    • Warning:Names of functions and calling sequences have changed.
      HasRealSolutions(syst, vars) and PointsPerComponents(syst, vars)
      where syst is a list of equations and/or inequalities/inequations and
      vars is the list of variables appearing in syst.
    • Now, RAGlib handles mixed systems of equations and inequalities
    • Warning: In the case of mixed systems, equations should satisfy genericity assumptions (checked by RAGlib).
    • New algorithms are now implemented and used by the above functions
    • Several bugs have been fixed
  • RAGlib Release 2.36 (July, 2009 -- no more maintained)    [Download]
    Release notes:
    • Pre-treatment of the input that may improve computation times of sampling_points and is_empty
    • Bugs fixed in the function sampling_inequations
    • sampling_inequations and sampling_inequalities have been improved (stronger improvements in the next release)
    • Warning: The functions sampling_positive (and sampling_negative) can be substituted by the functions sampling_inequalitites and sampling_inequations. The next release won't contain sampling_positive (and sampling_negative).
  • RAGlib Release 2.35 (January, 2009)    [Download]
    Release notes:
    • Bugs fixed in the function is_empty (in the case of singular varieties).
    • Bugs fixed in the function sampling_inequalities
    • Warning: The functions sampling_positive (and sampling_negative) can be substituted by the functions sampling_inequalitites and sampling_inequations. The next release won't contain sampling_positive (and sampling_negative).
  • RAGlib Release 2.32 (June, 2008)    [Download]
    Release notes:
    • Bugs fixed in the function sampling_points (in the case of singular varieties).
    • Bug fixed in the function sampling_inequations
    • Warning: The functions sampling_positive (and sampling_negative) can be substituted by the functions sampling_inequalitites and sampling_inequations. The next release won't contain sampling_positive (and sampling_negative).
  • RAGlib Release 2.30 (April, 23-th 2008 -- Current)    [Download]
    Release notes:
    • New functionality: sampling_inequations for computing sampling points in semi-algebraic sets defined by polynomial systems of inequalities and inequations.
    • Improvements of the function sampling_inequalities
    • A bug has been fixed in the function sampling_positive
  • RAGlib Release 2.24 (November, 22-th 2007)    [Download]
    Release notes:
    • New functionality: sampling_inequalities for computaing sampling points in semi-algebraic sets defined by polynomial systems of inequalities.
    • Improvements of the functions sampling_positive, sampling_negative, is_empty_regular
    • Improvements of the functions sampling_points in the case of a single equation.
    • A bug has been fixed in the function sampling_points (in singular situations)
  • RAGlib Release 2.21 (June, 12-th 2007)    [Download]
    Release notes:
    • Control of the verbosity.
    • Now, RAG uses exclusively FGb and RS
    • The function is_empty_regular has been improved.
    • Some bugs have been fixed in the function sampling_points
  • RAGlib Release 2.20 (May 2007)    [Download]
    Release notes :
    • Full compatibility with the new Gb/FGb and RS interfaces with Maple.
    • Improvement of the decomposition of polynomial ideals and the computation of sampling points of the real solution set of a polynomial system of equations.
    • The function is_empty_regular is a new provided functionality.
  • Earlier versions of the RAGlib Maple package are no more maintained.



© Copyright 2007, Mohab Safey El Din (Mohab.Safey@lip6.fr).  All rights reserved.