ku10 -- a 10-dimensional system of Ku

Synopsis

Usage:

ku10(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) i5-5250U CPU at 1.60GHz.

There were 4 solutions found in 2.266 seconds (with a Bezout bound of 1024).

We point out that this system is difficult for homotopy continuation (without multi-homogenization), yet an easy system for elimination.

Reference: "Die numeriese oplos van stelsels polinoomvergelykings" by M.C. Steenkamp.

See also: http://homepages.math.uic.edu/~jan/Demo/ku10.html.

i1 : ku10(QQ)

o1 = {5x x  + 5x  + 3x  + 55, 7x x  + 9x  + 9x  + 19, 3x x  + 6x  + 5x  - 4,
        1 2     1     2         2 3     2     3         3 4     3     4     
     ------------------------------------------------------------------------
     6x x  + 6x  + 7x  + 118, x x  + 3x  + 9x  + 27, 6x x  + 7x  + x  + 72,
       4 5     4     5         5 6     5     6         6 7     6    7      
     ------------------------------------------------------------------------
     9x x  + 7x  + x  + 35, 4x x  + 4x  + 6x  + 16, 8x x   + 4x  + 3x   - 51,
       7 8     7    8         8 9     8     9         9 10     9     10      
     ------------------------------------------------------------------------
     3x x   - 6x  + x   + 5}
       1 10     1    10

o1 : List

Ways to use ku10 :

ku10(Ring)

For the programmer

The object ku10 is a method function.