This README describes the set of scripts provided in complement to the article
   Efficient and accurate computation of upper bounds of approximation errors
by S. Chevillard, J. Harrison, M. Joldes and Ch. Lauter.

The following files are provided:

  * supnorm.sollya: Sollya script implementing the algorithms of the article
  * unisos.gp: GP script for performing the SOS decomposition
  * sos.sollya: Sollya wrapper around unisos.gp
  * example1.sollya: definition of the example #1 of the article
  * example2.sollya to example10.sollya: idem for the other examples.
  * supnormtest.sollya: a wrapper for conveniently running the examples.

These scripts are provided *as is* and should only be considered as 
an experimental implementation of the algorithms described in the article.

They are meant to be used with the revision 1079 (or higher) of Sollya. In 
particular, please note that a bug in Sollya 2.0, prevents one to
succesfully run these scripts.
The revision 1079 of Sollya can be retrieved with the following command:
  svn co svn://scm.gforge.inria.fr/svn/sollya -r 1079


=======================
How to use the scripts?
=======================

Once you compiled Sollya, simply run "sollya example1.sollya" for instance.

The files example*.sollya provide the definition of the examples. Parameters
can be set by the users:

  * The script is not able to automatically detect removable discontinuities
  inside the expression of f. If f has such a removable discontinuity, 
  please provide it in the list removableDiscontinuitiesOfF
  (see example10.sollya for an example).

  * The variable recLevelInAbsoluteInf sets the depth of the recursion process
  when computing the rigorous lower bound F on |f(x)| in the relative case.
  By default, it is 0 (i.e. if J contains 0, no splitting of I is performed,
  and an error is produced).

  * The verbosity of the algorithms can be increased by manually changing the
  values of verb[*] in supnormtest.sollya.

  * By default, when running the examples, a SOS decomposition is computed.
  This can be time consuming and not really necessary for testing purpose. You
  can disable this by setting PRODUCESOS to false in supnormtest.sollya.

  * By default, the SOS decomposition finally computed is not displayed. You
  can display it by setting DISPLAYSOSINSTANCES to true in supnormtest.sollya.