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 |
The object ku10 is a method function.