Algorithms for determining algebraic Lame' equations.

Alexa van der Waall

We consider the Lame' differential equation

  (4z^3-g2*z-g3)y''+(6z^2-g2/2)y'-[n(n+1)z+B]y=0.

The main goal is to determine all values for n, g2, g3 and B such that
the equation only has algebraic functions as solutions.
We give two algorithms that produce an enumeration af all such algebraic
Lame' equations.
The algorithms use invariant theory of finite groups and solving systems
of equations in a few variables.