example: |
butcher |

description: |
TITLE : Butcher's problem REFERENCES : 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. See also 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: 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. |

system: |
Polynomial |

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 |

examples