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 46 solutions found in 0.111 seconds (with a Bezout bound of 49).
Reference: PoSSo test suite.
See also: http://homepages.math.uic.edu/~jan/Demo/sendra.html.
i1 : sendra(QQ)
4 3 4 3 7 6 5 2 4 3
o1 = {- 270x y - 314x*y - 689x*y + 1428, 36x + 417x y - 422x y - 270x y
------------------------------------------------------------------------
3 4 2 5 6 6 5 4 2 3 3
+ 1428x y - 1475x y + 510x*y - 200x - 174x y - 966x y + 529x y +
------------------------------------------------------------------------
2 4 5 6 4 2 3 4 5 4
269x y + 49x*y - 267y + 529x y + 1303x y - 314x*y + 262y + 36x -
------------------------------------------------------------------------
2 2 3 4
788x y - 689x*y + 177y }
o1 : List
|
The object sendra is a method function.