# Project : coprin

## Section: Software

Keywords : constraints solving, optimization, symbolic computation, grid computing.

### ALIAS

Participants : Jean-Pierre Merlet [correspondant], Gilles Chabert, David Daney, Yves Papegay.

The `ALIAS` library
(*Algorithms Library of Interval
Analysis for Systems*)
is a collection of procedures based on interval analysis for systems
solving and optimization. Its development has started in 1998.

`ALIAS` is constituted of two parts:

`ALIAS-C++`: the C++ library (90 000 code lines) which is the core of the algorithms`ALIAS-Maple`: the Maple interface for`ALIAS-C++`(40 000 code lines). This interface allows one to specify a solving problem within Maple and to get the results within the same Maple session. The role of this interface is not only to generate automatically the C++ code, but also to perform an analysis of the problem in order to improve the efficiency of the solver. Furthermore using a distributed implementation of the algorithms is possible directly within the interface

Our effort this year has focused on:

improving the implementation of the 2B filtering method. This method allows one to possibly decrease the size of the ranges of the unknowns by rewriting equations as an equality between a single left term involving only one unknown x and a right term. Such equation has a solution only if the interval evaluations of the left and right term has an intersection and by using the inverse function of the left term we may improve the interval for x. Up to now only algebraic terms of degree 1 and 2 were considered as possible left term. G. Chabert has written an implementation that allows one to deal with almost any expression for the left term.

linear interval system plays an important role in our algorithms and in practical applications. We have implemented an improved linear interval analysis solver (see sectionÂ 6.6.2) that has been incorporated into

`ALIAS`

For dissemination purpose Y. Papegay has also written a web interface for two of our solvers. This on-line service, available since the end of September 2004, allows one to submit a set of up to 5 equations/inequalities to these solvers and to possibly get all the solutions of the system (see http://www-sop.inria.fr/coprin). Approximately 100 systems have been submitted in October 2004.

As mentioned previously our algorithms are well suited for a
distributed implementation. The `ALIAS`-Maple interface already
allows to use our algorithms in that way on a cluster by using the
master-slaves paradigm and the message passing scheme `PVM`. But
this paradigm is limited to a relatively small number of slaves. We
have started a cooperation with the OASIS, APACHE and PARIS projects
for using a grid-computing approach with as application example a
difficult problem in quantum mechanic (see the corresponding
section).

The current version of the `ALIAS` library is available through
the Web page
http://www-sop.inria.fr/coprin/logiciels/ALIAS.