bellido -- Bellido system

Synopsis

Usage:

bellido(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) i5-8250U CPU at 1.60GHz.

There were 40 solutions found in 0.546875 seconds (with a Bezout bound of 64).

Reference: Bellido A.M. "Construction of iteration functions for the simultaneous computation of the solutions of equations and algebraic systems." Numerical Algorithms, 6(3-4):315-351, 1992.

See also: http://www-sop.inria.fr/coprin/logiciels/ALIAS/Benches/node1.html#SECTION00012000000000000000

i1 : bellido(QQ)

       2    2    2               2    2    2               2    2    2
o1 = {z  + z  + z  - 12z  - 68, z  + z  + z  - 12z  - 68, z  + z  + z  - 24z 
       1    2    3      1        4    5    6      5        7    8    9      8
     ------------------------------------------------------------------------
     - 12z  + 100, z z  + z z  + z z  - 6z  - 6z  - 52, z z  + z z  + z z  -
          9         1 4    2 5    3 6     1     5        1 7    2 8    3 9  
     ------------------------------------------------------------------------
     6z  - 12z  - 6z  + 64, z z  + z z  + z z  - 6z  - 12z  - 6z  + 32, 2z  +
       1      8     9        4 7    5 8    6 9     5      8     9         2  
     ------------------------------------------------------------------------
     2z  - z  - z  - 2z  - z  - z  + 18, z  + z  + 2z  + 2z  + 2z  - 2z  + z 
       3    4    5     6    7    9        1    2     3     4     6     7    8
     ------------------------------------------------------------------------
     - z  - 38, z  + z  - 2z  + z  - z  + 2z  - 2z  + 8}
        9        1    3     4    5    6     7     8

o1 : List

Ways to use bellido :

bellido(Ring)

For the programmer

The object bellido is a method function.