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