|description:||TITLE : Butcher's problem
The example has been retrieved from the POSSO test suite, available by anonymous ftp from the site gauss.dm.unipi.it, from the directory pub/posso.
W. Boege, R. Gebauer, and H. Kredel: "Some examples for solving systems of algebraic equations by calculating Groebner bases", J. Symbolic Computation, 2:83-98, 1986.
C. Butcher: "An application of the Runge-Kutta space". BIT, 24, pages 425--440, 1984.
There are 5 regular solutions and two singular solutions The two singular solutions belong to a manifold of solutions: t=-1=w, z=0=y, with u and v arbitrary complex numbers. There are 3 regular real solutions.
|variables:||x > y > z > t > u > v > w|
|equations:||0 1 2 3 4 5 6|
|length of Janet-like basis:||52|
|length of Janet basis:||52|
|length of Gröbner basis||27|
|Hilbert polynomial:||1/2s^3 + 5s^2 - 3/2s + 8|
|Strategy:||degJ highJ lowJ degJL highJL lowJL|