cassou -- the system of Pierrette Cassou-Nogu`es

Synopsis

Usage:

cassou(kk)
Inputs:
- kk, a ring, the coefficient ring
Outputs:
- a list, of the polynomials in the system

Description

This system was solved in May 2020, using solveSystem in Macaulay2 v1.15 with an Intel(R) Core(TM) i5-4258U CPU at 2.40GHz

There were 2 solutions found in 39.0405 seconds (with a Bezout bound of 1344).

Reference: Obtained by electronic mail by Carlo Traverso. See the POSSO test suite.

T.Y. Li, Tianjun Wang, Xiaoshen Wang: "Random Product Homotopy with Minimal BKK Bound", in "The Mathematics of Numerical Analysis", Edited by Renegar, J. and Shub, M. and Smale, S., Lectures in Applied Mathematics vol 32, 1996. Proceedings of the AMS-SIAM Summer Seminar in Applied Mathematics, Park City, Utah, July 17-August 11, 1995, Park City, Utah".

See also: http://homepages.math.uic.edu/~jan/Demo/cassou.html

i1 : cassou(RR_53)

        4 3      4 2       4   2     4 3     2 2       2           2 2   
o1 = {6b c  + 21b c d + 15b c*d  + 9b d  - 8b c e - 28b c*d*e + 36b d e -
     ------------------------------------------------------------------------
         2        2           4 4      4 3       4 2 2      4   3      2 3   
     144b c - 648b d - 120, 9b c  + 30b c d + 39b c d  + 18b c*d  - 24b c e -
     ------------------------------------------------------------------------
        2 2         2   2       2 3        2 2       2          2 2      2 2
     16b c d*e + 16b c*d e + 24b d e - 432b c  - 720b c*d - 432b d  + 16c e 
     ------------------------------------------------------------------------
              2      2 2                                       2 3   
     - 32c*d*e  + 16d e  + 576c*e - 576d*e - 240c + 5184, - 15b c e +
     ------------------------------------------------------------------------
        2 2         2 2       2          2 2      2 2          2      2 2  
     15b c d*e - 81b c  + 216b c*d - 162b d  + 40c e  - 80c*d*e  + 40d e  +
     ------------------------------------------------------------------------
                                   2 2     2        2 2
     1008c*e - 1008d*e + 5184, - 4b c  + 4b c*d - 3b d  + 22c*e - 22d*e +
     ------------------------------------------------------------------------
     261}

o1 : List

Ways to use cassou :

cassou(Ring)

For the programmer

The object cassou is a method function.