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 40 solutions found in 3.740 seconds (with a Bezout bound of 576).
Reference: generated by Fabrice Rouillier, as a deformation of a system found in Innocenti.
See also: http://homepages.math.uic.edu/~jan/Demo/rbpl24s.html.
i1 : rbpl24s(RR_53)
2 2 2 2 2 2 2 2
o1 = {.902353x + .506753y + 1.1541z - 1.89489, .547653x + .401593y + .914601z - 1.374x - 3.61818, 1.26481x + .299954y +
1 1 1 2 2 2 2 3 3
----------------------------------------------------------------------------------------------------------------------------
2
1.20376z + .346368x - 3.03447y - 2.08335, 1.01543x x + .651627y y + 1.48404z z - 1.3475x + .75575, 1.4913x x +
3 3 3 1 2 1 2 1 2 2 1 3
----------------------------------------------------------------------------------------------------------------------------
.544239y y + 1.64533z z + .1979x - 1.73377y - 2.1825, 3.63357x x + 1.51527y y + 4.58093z z - 4.97527x + .45581x -
1 3 1 3 3 3 2 3 2 3 2 3 2 3
----------------------------------------------------------------------------------------------------------------------------
3.99328y - .00437819, 1.74298x y z - .991213x y z - 1.74298x y z + 1.13265x y z + 1.31579x y z - 1.50355x y z -
3 3 2 1 2 3 1 3 1 2 1 3 2 2 1 3 1 2 3
----------------------------------------------------------------------------------------------------------------------------
3.35742x y + 3.07591x y + 3.83651x y - 3.71822x y - 1.99884x y + 2.11451x y - .0493297x z + .0451934x z - 1.2983y z
2 1 3 1 1 2 3 2 1 3 2 3 2 1 3 1 2 1
----------------------------------------------------------------------------------------------------------------------------
+ .67642y z + .0563687x z - .0546307x z + 1.2983y z - .817669y z - .0389852x z + .0412412x z - .897916y z +
3 1 1 2 3 2 1 2 3 2 1 3 2 3 1 3
----------------------------------------------------------------------------------------------------------------------------
1.08542y z - 9.85984x + 1.09273x + 7.70206x + .240411y + .0363213y - 10.5808y - 37.2647z - 5.62995z + 21.2116z -
2 3 1 2 3 1 2 3 1 2 3
----------------------------------------------------------------------------------------------------------------------------
.695579, - .981142x y z + .557965x y z + .981142x y z - .637583x y z - .740673x y z + .846363x y z - 1.88369x y +
3 2 1 2 3 1 3 1 2 1 3 2 2 1 3 1 2 3 2 1
----------------------------------------------------------------------------------------------------------------------------
1.72575x y + 2.15249x y - 2.08612x y - 1.12146x y + 1.18635x y - 2.14929x z + 1.96908x z - 1.39179y z + .725132y z
3 1 1 2 3 2 1 3 2 3 2 1 3 1 2 1 3 1
----------------------------------------------------------------------------------------------------------------------------
+ 2.45598x z - 2.38026x z + 1.39179y z - .876553y z - 1.69859x z + 1.79688x z - .962579y z + 1.16358y z + .527434x
1 2 3 2 1 2 3 2 1 3 2 3 1 3 2 3 1
----------------------------------------------------------------------------------------------------------------------------
+ .943204x + .344042x - .522684y - .543486y + .0767906y + 1.04328z + 1.0848z + .649757z + .838949, 1.4167x +
2 3 1 2 3 1 2 3 2
----------------------------------------------------------------------------------------------------------------------------
.705867}
o1 : List
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The object rbpl24s is a method function.