** Next:** How do I get
** Up:** Introduction
** Previous:** Introduction
** Contents**
** Index**

Piz Bernina is a 4049-meter peak in Graubünden, in
the south-east corner of Switzerland. Its large summit, which
appears on the cover of this guide,
dominates the majestuous Morteratsch and Tschierva glaciers.
This guide describes however BERNINA, an interactive interface to
the
library that provides some efficient computations revolving
around operators in
or
. In fact, the
main goal of BERNINA is to provide access to selected functionalities
of the
library to other computer algebra systems, or to users
who do not own an `Aldor` compiler, or who feel more confortable with
interactive access to a library. The functionalities currently provided
by BERNINA are the ones that tend to be missing from several commercial
computer algebra systems, namely:
- Basic arithmetic in
, including
adjoints and left and right gcd's and lcm's.
- Symmetric and exterior powers.
- Rational kernels,
*i.e.*
for
,
and rational solutions of inhomogeneous equations of the form
.
- Rational kernels of systems of the form
.
- Radical (resp. exponential) solutions,
*i.e.* the solutions of
such that
for some integer
(resp.
).
- Liouvillian solutions of second-order operators.
- Factorisation and decomposition of second and third-order operators.

If you do not need any of the above computations, then
you probably will not have much use for BERNINA.
Otherwise, since BERNINA provides implementations of several recent
algorithms for those computations, it is worth trying it and
reading further.

** Next:** How do I get
** Up:** Introduction
** Previous:** Introduction
** Contents**
** Index**
Manuel Bronstein
2002-09-04