
Online 3rd order linear ODE solver now available
Online demos are available:
What is bernina?
Piz Bernina is a 4049meter peak in Graubunden, in the southeast 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 secondorder operators.

Factorisation and decomposition of second and thirdorder 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 platformindependent 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 platformindependent parts.
The executables can be installed anywhere.
More installation details are in the
README
file and in the
online 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