What is bernina?

Piz Bernina is a 4049-meter peak in Graubunden, in the south-east corner of Switzerland. Its gleaming summit, pictured above, dominates the majestuous Morteratsch and Tschierva glaciers. This page describes however bernina, an interactive interface to the Sum^it library that provides some efficient computations revolving around operators in Q[x,d/dx] or Q(x)[d/dx]. In fact, the main goal of bernina is to provide access to selected functionalities of the Sum^it 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 Q[x,d/dx], including adjoints and left and right gcd's and lcm's.
Symmetric and exterior powers.
Rational kernels, i.e. Ker(L) /\ Q(x) and rational solutions of inhomogeneous equations of the form L(y) = g.
Rational kernels of systems of the form dY/dx = A(x) Y(x).
Radical (resp. exponential) solutions, i.e. the solutions y of L y = 0 such that a positive power of y is in Q(x) (resp. y'/y is in Q(x)).
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 giving it a try.

What is the current version?

The current distributed version is 1.0.0, released September 4, 2002.

How do I get bernina?

You must download first the platform-independent part by clicking here, then download the executable for the operating system(s) and platform(s) you need:

How do I install bernina?

Issue tar -xvzf bernina.tar.gz to install the platform-independent parts. The executables can be installed anywhere. More installation details are in the README file and in the on-line documentation

Are there other Sum^it servers?

Yes, if you are interested in linear ordinary difference equations, you can take a look at the Shasta server, that provides similar functionalities for those equations.

Last update: 25 September 2003