example: butcher8
description: TITLE : 8-variable version of Butcher's problem
REFERENCES :
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.
NOTE :
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.
system: Polynomial
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


examples