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 10 solutions found in 0.203 seconds (with a Bezout bound of 24).
Reference: See the PoSSo test suite.
See also: http://homepages.math.uic.edu/~jan/Demo/trinks.html.
i1 : trinks(QQ)
2
o1 = {45y + 35u - 165v - 36, 35y + 25z + 40t - 27u, 25y*u - 165v + 15x - 18z
------------------------------------------------------------------------
3 2
+ 30t, 15y*z + 20t*u - 9x, - 11v + x*y + 2z*t, - 11u*v + 3v + 99x}
o1 : List
|
The object trinks is a method function.