|description:||TITLE : 8-variable version of Butcher's problem
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.
The system has 16 regular solutions. Four paths converged to highly singular solutions, which indicates that the system probably has an infinite component of solutions.
|variables:||A > a32 > B > b1 > b2 > b3 > c2 > c3|
|equations:||0 1 2 3 4 5 6 7|
|length of Janet-like basis:||64|
|length of Janet basis:||64|
|length of Gröbner basis||54|
|Hilbert polynomial:||1/2s^3 + 5/2s^2 + 4s + 14|
|Strategy:||degJ highJ lowJ degJL highJL lowJL|