example: cyclic8
description: TITLE : cyclic n-roots problem
See G\"oran Bj\"orck and Ralf Fr\"oberg: `A faster way to count the solutions of inhomogeneous systems of algebraic equations, with applications to cyclic n-roots', in J. Symbolic Computation (1991) 12, pp 329--336.
Backelin, J. and Froeberg, R.: "How we proved that there are exactly 924 cyclic 7-roots" , Proceedings of ISSAC-91, pp 103-111, ACM, New York, 1991.
G. Bj\"orck and R. Fr\"oberg, R.: "Methods to ``divide out'' certain solutions from systems of algebraic equations, applied to find all cyclic 8-roots " , In: Analysis, Algebra and Computers in Math. research, M. Gyllenberg and L.E.Persson eds., Lect. Notes in Applied Math. vol. 564, pp 57-70, Dekker, 1994.
J. Canny and P. Pedersen. An algorithm for the Newton resultant. Technical Report 1394, Comp. Science Dept., Cornell University, 1993.
I.Z. Emiris and J.F. Canny. Efficient incremental algorithms for the sparse resultant and the mixed volume. J. Symbolic Computation, 20(2):117-149, August 1995.
L. Pottier. Bounds for degree of the n-cyclic system. INRIA Sophia-Antipolis, Manuscript, 1995.
From the FRISCO test suite, see http://www.inria.fr/safir/POL/index.html.
system: Polynomial
variables: x1 > x2 > x3 > x4 > x5 > x6 > x7 > x8
equations: 0 1 2 3 4 5 6 7
length of Janet-like basis: 383
length of Janet basis: 384
length of Gröbner basis 372
Hilbert polynomial: 144s + 760
Strategy: degJ highJ lowJ degJL highJL lowJL