I tried a bunch of different methods, but I didn't have any luck on that system.  For reference, here is the system I reduced it to.  I replaced x[i] with xi and replaced sqrt(3) with _z1 and the imaginary unit I with _z2.  Maybe someone wants to try?

sys := [_z1^2-3, _z2^2+1, x1*x2*x3*_z2*_z1*x4+30*x1^2*x2*x3*x4*x5*_z2*_z1-20*
x1^3*x2*x3*x4*x5*_z2*_z1-12*x1^5*x2*x3*x4*x5*_z2*_z1+x1^6*x2*x3*x4*x5*_z2*_z1+
6*x1^3*x2*x3*_z2*_z1-30*x1^4*x2*x3*_z2*_z1-15*x1^6*x2*x3*_z2*_z1+12*x1^7*x2*x3
*_z2*_z1+6*x1^3*x2*_z2*_z1*x4-30*x1^4*x2*_z2*_z1*x4-15*x1^6*x2*_z2*_z1*x4+6*x1
^3*x3*_z2*_z1*x4-30*x1^4*x3*_z2*_z1*x4-15*x1^6*x3*_z2*_z1*x4+12*x1^7*x3*_z2*
_z1*x4+12*x1^7*x2*_z2*_z1*x4+6*x1^3*x2*_z2*_z1*x5-30*x1^4*x2*_z2*_z1*x5-15*x1^
6*x2*_z2*_z1*x5+6*x1^3*x3*_z2*_z1*x5-30*x1^4*x3*_z2*_z1*x5-15*x1^6*x3*_z2*_z1*
x5+12*x1^7*x3*_z2*_z1*x5+12*x1^7*x2*_z2*_z1*x5+60*x1^3*x2*x3*x4*x5-3*x1^6*x2*
x3*x4*x5+6*x1^3*x4*_z2*_z1*x5-30*x1^4*x4*_z2*_z1*x5-15*x1^6*x4*_z2*_z1*x5+12*
x1^7*x4*_z2*_z1*x5-x1^3*x2*_z2*_z1-30*x1^5*x2*_z2*_z1+20*x1^6*x2*_z2*_z1-x1^3*
x3*_z2*_z1-30*x1^5*x3*_z2*_z1+20*x1^6*x3*_z2*_z1+12*x1^8*x3*_z2*_z1+12*x1^8*x2
*_z2*_z1-3*x1*x2*x3*x4+18*x1^2*x2*x3*x4+60*x1^4*x2*x3*x4-45*x1^5*x2*x3*x4-x1^3
*x4*_z2*_z1-30*x1^5*x4*_z2*_z1+20*x1^6*x4*_z2*_z1+12*x1^8*x4*_z2*_z1-x1^9*x3*
_z2*_z1-x1^9*x2*_z2*_z1-3*x1^7*x2*x3*x4-x1^9*x4*_z2*_z1-3*x1*x2*x3*x5+18*x1^2*
x2*x3*x5+60*x1^4*x2*x3*x5-45*x1^5*x2*x3*x5-3*x1^7*x2*x3*x5-3*x1*x2*x4*x5+18*x1
^2*x2*x4*x5+60*x1^4*x2*x4*x5-45*x1^5*x2*x4*x5-3*x1*x3*x4*x5-3*x2*x3*x4*x5+18*
x1^2*x3*x4*x5+60*x1^4*x3*x4*x5-45*x1^5*x3*x4*x5-3*x1^7*x3*x4*x5-3*x1^7*x2*x4*
x5-x1^3*x5*_z2*_z1-30*x1^5*x5*_z2*_z1+20*x1^6*x5*_z2*_z1+12*x1^8*x5*_z2*_z1-x1
^9*x5*_z2*_z1+18*x1^3*x2*x3-45*x1^6*x2*x3+18*x1^3*x2*x4-45*x1^6*x2*x4+18*x1^3*
x3*x4-45*x1^6*x3*x4+18*x1^3*x2*x5-45*x1^6*x2*x5+18*x1^3*x3*x5-45*x1^6*x3*x5+18
*x1^3*x4*x5-45*x1^6*x4*x5-x1^4*_z2*_z1-6*x1^5*_z2*_z1+20*x1^7*_z2*_z1+15*x1^8*
_z2*_z1+3*x1^3*x2-60*x1^6*x2+3*x1^3*x3-60*x1^6*x3+3*x1^3*x4-60*x1^6*x4+3*x1^9*
x3+3*x1^9*x2+3*x1^9*x4+3*x1^3*x5-60*x1^6*x5+3*x1^9*x5+3*x1^4-18*x1^5-60*x1^7+
45*x1^8+3*x1^10+6*x1^2*x2*x3*_z2*_z1*x4-20*x1^4*x2*x3*_z2*_z1*x4-15*x1^5*x2*x3
*_z2*_z1*x4+x1*x2*x3*_z2*_z1*x5+6*x1^2*x2*x3*_z2*_z1*x5-20*x1^4*x2*x3*_z2*_z1*
x5-15*x1^5*x2*x3*_z2*_z1*x5+x1^7*x2*x3*_z2*_z1*x5+x1*x2*_z2*_z1*x4*x5+6*x1^2*
x2*_z2*_z1*x4*x5-20*x1^4*x2*_z2*_z1*x4*x5-15*x1^5*x2*_z2*_z1*x4*x5+x1*x3*_z2*
_z1*x4*x5+x2*x3*_z2*_z1*x4*x5+6*x1^2*x3*_z2*_z1*x4*x5-20*x1^4*x3*_z2*_z1*x4*x5
-15*x1^5*x3*_z2*_z1*x4*x5+x1^7*x3*_z2*_z1*x4*x5+x1^7*x2*_z2*_z1*x4*x5+x1^7*x2*
x3*_z2*_z1*x4-x1^10*_z2*_z1, x1*x2*x3*_z2*_z1*x4-3*x1*x2*x3*x4-3*x1*x2*x3*x5-3
*x1*x2*x4*x5-3*x1*x3*x4*x5-3*x2*x3*x4*x5-x2^3*x1*_z2*_z1-30*x2^5*x1*_z2*_z1+20
*x2^6*x1*_z2*_z1-x2^3*x3*_z2*_z1-30*x2^5*x3*_z2*_z1+20*x2^6*x3*_z2*_z1+12*x2^8
*x3*_z2*_z1+12*x2^8*x1*_z2*_z1+20*x2^6*x4*_z2*_z1+12*x2^8*x4*_z2*_z1-x2^3*x4*
_z2*_z1-30*x2^5*x4*_z2*_z1+60*x2^4*x1*x3*x4-45*x2^5*x1*x3*x4+18*x2^2*x1*x3*x4-
x2^9*x3*_z2*_z1+3*x2^3*x1-60*x2^6*x1+3*x2^3*x3-60*x2^6*x3-60*x2^6*x4+3*x2^3*x4
+3*x2^9*x3+3*x2^9*x1+3*x2^9*x4-60*x2^6*x5+3*x2^9*x5+3*x2^3*x5+x1*x2*x3*_z2*_z1
*x5+x1*x2*_z2*_z1*x4*x5+x1*x3*_z2*_z1*x4*x5+x2*x3*_z2*_z1*x4*x5-20*x2^4*x1*x3*
x4*_z2*_z1-15*x2^5*x1*x3*x4*_z2*_z1+6*x2^2*x1*x3*x4*_z2*_z1+x2^7*x1*x3*x4*_z2*
_z1-20*x2^4*x1*x3*x5*_z2*_z1-15*x2^5*x1*x3*x5*_z2*_z1+6*x2^2*x1*x4*x5*_z2*_z1-\
20*x2^4*x1*x4*x5*_z2*_z1-15*x2^5*x1*x4*x5*_z2*_z1+6*x2^2*x3*x4*x5*_z2*_z1-20*
x2^4*x3*x4*x5*_z2*_z1-15*x2^5*x3*x4*x5*_z2*_z1+x2^7*x3*x4*x5*_z2*_z1+x2^7*x1*
x4*x5*_z2*_z1+x2^7*x1*x3*x5*_z2*_z1+6*x2^2*x1*x3*x5*_z2*_z1-x2^9*x1*_z2*_z1-x2
^9*x4*_z2*_z1-3*x2^7*x1*x3*x4+20*x2^6*x5*_z2*_z1+12*x2^8*x5*_z2*_z1-x2^9*x5*
_z2*_z1-x2^3*x5*_z2*_z1-30*x2^5*x5*_z2*_z1+60*x2^4*x1*x3*x5-45*x2^5*x1*x3*x5+
18*x2^2*x1*x4*x5+60*x2^4*x1*x4*x5-45*x2^5*x1*x4*x5+18*x2^2*x3*x4*x5+60*x2^4*x3
*x4*x5-45*x2^5*x3*x4*x5-3*x2^7*x3*x4*x5-3*x2^7*x1*x4*x5-3*x2^7*x1*x3*x5+18*x2^
2*x1*x3*x5-20*x2^3*x1*x3*x4*x5*_z2*_z1-12*x2^5*x1*x3*x4*x5*_z2*_z1+x2^6*x1*x3*
x4*x5*_z2*_z1+30*x2^2*x1*x3*x4*x5*_z2*_z1+3*x2^10-60*x2^7+45*x2^8+3*x2^4-18*x2
^5-x2^10*_z2*_z1+15*x2^8*_z2*_z1+20*x2^7*_z2*_z1-x2^4*_z2*_z1-6*x2^5*_z2*_z1+
18*x2^3*x1*x3-45*x2^6*x1*x3+18*x2^3*x1*x4-45*x2^6*x1*x4+18*x2^3*x3*x4-45*x2^6*
x3*x4+18*x2^3*x1*x5-45*x2^6*x1*x5+18*x2^3*x3*x5-45*x2^6*x3*x5-45*x2^6*x4*x5+18
*x2^3*x4*x5-15*x2^6*x1*_z2*_z1*x5+6*x2^3*x3*_z2*_z1*x5-30*x2^4*x3*_z2*_z1*x5-\
15*x2^6*x3*_z2*_z1*x5+12*x2^7*x3*_z2*_z1*x5+12*x2^7*x1*_z2*_z1*x5-15*x2^6*x4*
_z2*_z1*x5+12*x2^7*x4*_z2*_z1*x5+6*x2^3*x4*_z2*_z1*x5-30*x2^4*x4*_z2*_z1*x5+60
*x2^3*x1*x3*x4*x5-3*x2^6*x1*x3*x4*x5-15*x2^6*x3*_z2*_z1*x4+12*x2^7*x3*_z2*_z1*
x4+12*x2^7*x1*_z2*_z1*x4+12*x2^7*x1*x3*_z2*_z1+6*x2^3*x1*_z2*_z1*x5-30*x2^4*x1
*_z2*_z1*x5+6*x2^3*x1*x3*_z2*_z1-30*x2^4*x1*x3*_z2*_z1-15*x2^6*x1*x3*_z2*_z1+6
*x2^3*x1*_z2*_z1*x4-30*x2^4*x1*_z2*_z1*x4-15*x2^6*x1*_z2*_z1*x4+6*x2^3*x3*_z2*
_z1*x4-30*x2^4*x3*_z2*_z1*x4, x1*x2*x3*_z2*_z1*x4-3*x1*x2*x3*x4-3*x1*x2*x3*x5-\
3*x1*x2*x4*x5-3*x1*x3*x4*x5-3*x2*x3*x4*x5+x1*x2*x3*_z2*_z1*x5+x1*x2*_z2*_z1*x4
*x5+x1*x3*_z2*_z1*x4*x5+x2*x3*_z2*_z1*x4*x5+3*x3^10+6*x3^2*x1*x2*_z2*_z1*x5-20
*x3^4*x1*x2*_z2*_z1*x5-15*x3^5*x1*x2*_z2*_z1*x5+x3^7*x1*x2*_z2*_z1*x5+6*x3^2*
x1*x4*_z2*_z1*x5-20*x3^4*x1*x4*_z2*_z1*x5-15*x3^5*x1*x4*_z2*_z1*x5+6*x3^2*x2*
x4*_z2*_z1*x5-20*x3^4*x2*x4*_z2*_z1*x5-15*x3^5*x2*x4*_z2*_z1*x5+x3^7*x2*x4*_z2
*_z1*x5+x3^7*x1*x4*_z2*_z1*x5+x3^7*x1*x2*_z2*_z1*x4+6*x3^2*x1*x2*_z2*_z1*x4-20
*x3^4*x1*x2*_z2*_z1*x4-15*x3^5*x1*x2*_z2*_z1*x4+60*x3^3*x1*x2*x4*x5-3*x3^6*x1*
x2*x4*x5+6*x3^3*x1*x5*_z2*_z1-30*x3^4*x1*x5*_z2*_z1-15*x3^6*x1*x5*_z2*_z1+6*x3
^3*x2*x5*_z2*_z1-30*x3^4*x2*x5*_z2*_z1-15*x3^6*x2*x5*_z2*_z1+12*x3^7*x2*x5*_z2
*_z1+12*x3^7*x1*x5*_z2*_z1-15*x3^6*x4*x5*_z2*_z1+12*x3^7*x4*x5*_z2*_z1+6*x3^3*
x4*x5*_z2*_z1-30*x3^4*x4*x5*_z2*_z1+12*x3^7*x1*x2*_z2*_z1+6*x3^3*x1*x4*_z2*_z1
-30*x3^4*x1*x4*_z2*_z1-15*x3^6*x1*x4*_z2*_z1+6*x3^3*x2*x4*_z2*_z1-30*x3^4*x2*
x4*_z2*_z1-15*x3^6*x2*x4*_z2*_z1+12*x3^7*x2*x4*_z2*_z1+12*x3^7*x1*x4*_z2*_z1+6
*x3^3*x1*x2*_z2*_z1-30*x3^4*x1*x2*_z2*_z1-15*x3^6*x1*x2*_z2*_z1-18*x3^5-60*x3^
7+45*x3^8+3*x3^4-60*x3^6*x5+3*x3^9*x5+3*x3^3*x5+3*x3^9*x2+3*x3^9*x1+3*x3^9*x4+
3*x3^3*x1-60*x3^6*x1+3*x3^3*x2-60*x3^6*x2-60*x3^6*x4+3*x3^3*x4-x3^9*x5*_z2*_z1
-x3^3*x5*_z2*_z1-x3^9*x4*_z2*_z1-x3^9*x2*_z2*_z1-x3^9*x1*_z2*_z1-3*x3^7*x1*x2*
x4+18*x3^2*x1*x2*x5+60*x3^4*x1*x2*x5-45*x3^5*x1*x2*x5+18*x3^2*x1*x4*x5+60*x3^4
*x1*x4*x5-45*x3^5*x1*x4*x5+18*x3^2*x2*x4*x5+60*x3^4*x2*x4*x5-45*x3^5*x2*x4*x5-\
3*x3^7*x2*x4*x5-3*x3^7*x1*x4*x5-3*x3^7*x1*x2*x5-30*x3^5*x1*_z2*_z1+20*x3^6*x1*
_z2*_z1-x3^3*x2*_z2*_z1-30*x3^5*x2*_z2*_z1+20*x3^6*x2*_z2*_z1-30*x3^5*x4*_z2*
_z1+20*x3^6*x4*_z2*_z1+12*x3^8*x4*_z2*_z1-x3^3*x4*_z2*_z1+12*x3^8*x2*_z2*_z1+
12*x3^8*x1*_z2*_z1+18*x3^2*x1*x2*x4+60*x3^4*x1*x2*x4-45*x3^5*x1*x2*x4-30*x3^5*
x5*_z2*_z1+20*x3^6*x5*_z2*_z1+12*x3^8*x5*_z2*_z1-x3^3*x1*_z2*_z1+x3^6*x1*x2*
_z2*_z1*x4*x5+30*x3^2*x1*x2*_z2*_z1*x4*x5-20*x3^3*x1*x2*_z2*_z1*x4*x5-12*x3^5*
x1*x2*_z2*_z1*x4*x5-x3^10*_z2*_z1+15*x3^8*_z2*_z1+20*x3^7*_z2*_z1-x3^4*_z2*_z1
-6*x3^5*_z2*_z1+18*x3^3*x1*x2-45*x3^6*x1*x2+18*x3^3*x1*x4-45*x3^6*x1*x4+18*x3^
3*x2*x4-45*x3^6*x2*x4+18*x3^3*x1*x5-45*x3^6*x1*x5+18*x3^3*x2*x5-45*x3^6*x2*x5-\
45*x3^6*x4*x5+18*x3^3*x4*x5, x1*x2*x3*_z2*_z1*x4-3*x1*x2*x3*x4-3*x1*x2*x3*x5-3
*x1*x2*x4*x5-3*x1*x3*x4*x5-3*x2*x3*x4*x5+x1*x2*x3*_z2*_z1*x5+x1*x2*_z2*_z1*x4*
x5+x1*x3*_z2*_z1*x4*x5+x2*x3*_z2*_z1*x4*x5+3*x4^9*x3+3*x4^9*x2+3*x4^9*x1+3*x4^
10+3*x4^4-18*x4^5-60*x4^7+45*x4^8-x4^10*_z2*_z1+15*x4^8*_z2*_z1+20*x4^7*_z2*
_z1+18*x4^3*x2*x5-45*x4^6*x2*x5-45*x4^6*x3*x5+18*x4^3*x3*x5+18*x4^3*x1*x5-45*
x4^6*x1*x5-x4^4*_z2*_z1-6*x4^5*_z2*_z1+18*x4^3*x1*x2-45*x4^6*x1*x2+18*x4^3*x2*
x3-45*x4^6*x2*x3+18*x4^3*x1*x3-45*x4^6*x1*x3+12*x4^7*x2*_z2*_z1*x5+12*x4^7*x1*
_z2*_z1*x5-30*x4^4*x3*_z2*_z1*x5-15*x4^6*x3*_z2*_z1*x5+12*x4^7*x3*_z2*_z1*x5+6
*x4^3*x3*_z2*_z1*x5+60*x4^3*x1*x2*x3*x5-3*x4^6*x1*x2*x3*x5+6*x4^3*x1*_z2*_z1*
x5-30*x4^4*x1*_z2*_z1*x5-15*x4^6*x1*_z2*_z1*x5+6*x4^3*x2*_z2*_z1*x5-30*x4^4*x2
*_z2*_z1*x5-15*x4^6*x2*_z2*_z1*x5+6*x4^3*x2*_z2*_z1*x3-30*x4^4*x2*_z2*_z1*x3-\
15*x4^6*x2*_z2*_z1*x3+12*x4^7*x2*_z2*_z1*x3+12*x4^7*x1*_z2*_z1*x3+6*x4^3*x1*x2
*_z2*_z1-30*x4^4*x1*x2*_z2*_z1-15*x4^6*x1*x2*_z2*_z1+12*x4^7*x1*x2*_z2*_z1+6*
x4^3*x1*_z2*_z1*x3-30*x4^4*x1*_z2*_z1*x3-15*x4^6*x1*_z2*_z1*x3-30*x4^5*x5*_z2*
_z1+20*x4^6*x5*_z2*_z1+12*x4^8*x5*_z2*_z1-x4^9*x5*_z2*_z1-x4^3*x5*_z2*_z1+18*
x4^2*x1*x2*x5+60*x4^4*x1*x2*x5-45*x4^5*x1*x2*x5-3*x4^7*x1*x2*x5+18*x4^2*x2*x3*
x5+60*x4^4*x2*x3*x5-45*x4^5*x2*x3*x5-3*x4^7*x2*x3*x5-3*x4^7*x1*x3*x5+18*x4^2*
x1*x3*x5+60*x4^4*x1*x3*x5-45*x4^5*x1*x3*x5-x4^9*x3*_z2*_z1-3*x4^7*x1*x2*x3-x4^
9*x2*_z2*_z1-x4^9*x1*_z2*_z1-x4^3*x1*_z2*_z1-30*x4^5*x1*_z2*_z1+20*x4^6*x1*_z2
*_z1-x4^3*x2*_z2*_z1-30*x4^5*x2*_z2*_z1+20*x4^6*x2*_z2*_z1-30*x4^5*x3*_z2*_z1+
20*x4^6*x3*_z2*_z1+12*x4^8*x3*_z2*_z1-x4^3*x3*_z2*_z1+18*x4^2*x1*x2*x3+60*x4^4
*x1*x2*x3-45*x4^5*x1*x2*x3+12*x4^8*x2*_z2*_z1+12*x4^8*x1*_z2*_z1+x4^7*x1*x2*x3
*_z2*_z1+6*x4^2*x2*x3*x5*_z2*_z1-20*x4^4*x2*x3*x5*_z2*_z1-15*x4^5*x2*x3*x5*_z2
*_z1+x4^7*x2*x3*x5*_z2*_z1+x4^7*x1*x3*x5*_z2*_z1+6*x4^2*x1*x3*x5*_z2*_z1-20*x4
^4*x1*x3*x5*_z2*_z1-15*x4^5*x1*x3*x5*_z2*_z1+6*x4^2*x1*x2*x5*_z2*_z1-20*x4^4*
x1*x2*x5*_z2*_z1-15*x4^5*x1*x2*x5*_z2*_z1+x4^7*x1*x2*x5*_z2*_z1+6*x4^2*x1*x2*
x3*_z2*_z1-20*x4^4*x1*x2*x3*_z2*_z1-15*x4^5*x1*x2*x3*_z2*_z1-60*x4^6*x5+3*x4^9
*x5+3*x4^3*x5+3*x4^3*x2-60*x4^6*x2-60*x4^6*x3+3*x4^3*x3+3*x4^3*x1-60*x4^6*x1+
30*x4^2*x1*x2*x3*x5*_z2*_z1-20*x4^3*x1*x2*x3*x5*_z2*_z1-12*x4^5*x1*x2*x3*x5*
_z2*_z1+x4^6*x1*x2*x3*x5*_z2*_z1, x1*x2*x3*_z2*_z1*x4-3*x1*x2*x3*x4-3*x1*x2*x3
*x5-3*x1*x2*x4*x5-3*x1*x3*x4*x5-3*x2*x3*x4*x5+x1*x2*x3*_z2*_z1*x5+x1*x2*_z2*
_z1*x4*x5+x1*x3*_z2*_z1*x4*x5+x2*x3*_z2*_z1*x4*x5+3*x5^3*x4-60*x5^6*x4+3*x5^9*
x4+3*x5^3*x3-60*x5^6*x3+3*x5^9*x2+3*x5^9*x1+3*x5^9*x3+3*x5^3*x1-60*x5^6*x1+3*
x5^3*x2-60*x5^6*x2-x5^10*_z2*_z1+15*x5^8*_z2*_z1+20*x5^7*_z2*_z1+18*x5^3*x1*x4
-45*x5^6*x1*x4+18*x5^3*x2*x4-45*x5^6*x2*x4-x5^4*_z2*_z1-6*x5^5*_z2*_z1+18*x5^3
*x1*x2-45*x5^6*x1*x2+18*x5^3*x1*x3-45*x5^6*x1*x3+18*x5^3*x2*x3-45*x5^6*x2*x3+
18*x5^3*x3*x4-45*x5^6*x3*x4+6*x5^3*x1*x2*_z2*_z1-30*x5^4*x1*x2*_z2*_z1-15*x5^6
*x1*x2*_z2*_z1+6*x5^3*x1*x3*_z2*_z1-30*x5^4*x1*x3*_z2*_z1-15*x5^6*x1*x3*_z2*
_z1+30*x5^2*x1*x2*x3*_z2*_z1*x4-20*x5^3*x1*x2*x3*_z2*_z1*x4-12*x5^5*x1*x2*x3*
_z2*_z1*x4+x5^6*x1*x2*x3*_z2*_z1*x4+60*x5^3*x1*x2*x3*x4-3*x5^6*x1*x2*x3*x4+6*
x5^3*x3*x4*_z2*_z1-30*x5^4*x3*x4*_z2*_z1-15*x5^6*x3*x4*_z2*_z1+12*x5^7*x3*x4*
_z2*_z1+6*x5^3*x1*x4*_z2*_z1-30*x5^4*x1*x4*_z2*_z1-15*x5^6*x1*x4*_z2*_z1+6*x5^
3*x2*x4*_z2*_z1-30*x5^4*x2*x4*_z2*_z1-15*x5^6*x2*x4*_z2*_z1+12*x5^7*x2*x4*_z2*
_z1+12*x5^7*x1*x4*_z2*_z1+6*x5^3*x2*x3*_z2*_z1-30*x5^4*x2*x3*_z2*_z1-15*x5^6*
x2*x3*_z2*_z1+12*x5^7*x2*x3*_z2*_z1+12*x5^7*x1*x3*_z2*_z1+12*x5^7*x1*x2*_z2*
_z1+3*x5^10+3*x5^4-18*x5^5-60*x5^7+45*x5^8+x5^7*x1*x2*x3*_z2*_z1-20*x5^4*x2*x3
*x4*_z2*_z1-15*x5^5*x2*x3*x4*_z2*_z1+x5^7*x2*x3*x4*_z2*_z1+x5^7*x1*x3*x4*_z2*
_z1+x5^7*x1*x2*x4*_z2*_z1+6*x5^2*x1*x2*x4*_z2*_z1-20*x5^4*x1*x2*x4*_z2*_z1-15*
x5^5*x1*x2*x4*_z2*_z1+6*x5^2*x1*x3*x4*_z2*_z1-20*x5^4*x1*x3*x4*_z2*_z1-15*x5^5
*x1*x3*x4*_z2*_z1+6*x5^2*x2*x3*x4*_z2*_z1+6*x5^2*x1*x2*x3*_z2*_z1-20*x5^4*x1*
x2*x3*_z2*_z1-15*x5^5*x1*x2*x3*_z2*_z1+18*x5^2*x1*x2*x4+60*x5^4*x1*x2*x4-45*x5
^5*x1*x2*x4+18*x5^2*x1*x3*x4+60*x5^4*x1*x3*x4-45*x5^5*x1*x3*x4+18*x5^2*x2*x3*
x4+60*x5^4*x2*x3*x4-45*x5^5*x2*x3*x4-3*x5^7*x2*x3*x4-3*x5^7*x1*x3*x4-3*x5^7*x1
*x2*x4-x5^3*x4*_z2*_z1-30*x5^5*x4*_z2*_z1+20*x5^6*x4*_z2*_z1+12*x5^8*x4*_z2*
_z1-x5^9*x4*_z2*_z1-3*x5^7*x1*x2*x3-x5^9*x3*_z2*_z1-x5^9*x2*_z2*_z1-x5^9*x1*
_z2*_z1-x5^3*x1*_z2*_z1-30*x5^5*x1*_z2*_z1+20*x5^6*x1*_z2*_z1-x5^3*x2*_z2*_z1-\
30*x5^5*x2*_z2*_z1+20*x5^6*x2*_z2*_z1+18*x5^2*x1*x2*x3+60*x5^4*x1*x2*x3-45*x5^
5*x1*x2*x3-x5^3*x3*_z2*_z1-30*x5^5*x3*_z2*_z1+20*x5^6*x3*_z2*_z1+12*x5^8*x3*
_z2*_z1+12*x5^8*x2*_z2*_z1+12*x5^8*x1*_z2*_z1];

I tried a bunch of different methods, but I didn't have any luck on that system.  For reference, here is the system I reduced it to.  I replaced x[i] with xi and replaced sqrt(3) with _z1 and the imaginary unit I with _z2.  Maybe someone wants to try?

sys := [_z1^2-3, _z2^2+1, x1*x2*x3*_z2*_z1*x4+30*x1^2*x2*x3*x4*x5*_z2*_z1-20*
x1^3*x2*x3*x4*x5*_z2*_z1-12*x1^5*x2*x3*x4*x5*_z2*_z1+x1^6*x2*x3*x4*x5*_z2*_z1+
6*x1^3*x2*x3*_z2*_z1-30*x1^4*x2*x3*_z2*_z1-15*x1^6*x2*x3*_z2*_z1+12*x1^7*x2*x3
*_z2*_z1+6*x1^3*x2*_z2*_z1*x4-30*x1^4*x2*_z2*_z1*x4-15*x1^6*x2*_z2*_z1*x4+6*x1
^3*x3*_z2*_z1*x4-30*x1^4*x3*_z2*_z1*x4-15*x1^6*x3*_z2*_z1*x4+12*x1^7*x3*_z2*
_z1*x4+12*x1^7*x2*_z2*_z1*x4+6*x1^3*x2*_z2*_z1*x5-30*x1^4*x2*_z2*_z1*x5-15*x1^
6*x2*_z2*_z1*x5+6*x1^3*x3*_z2*_z1*x5-30*x1^4*x3*_z2*_z1*x5-15*x1^6*x3*_z2*_z1*
x5+12*x1^7*x3*_z2*_z1*x5+12*x1^7*x2*_z2*_z1*x5+60*x1^3*x2*x3*x4*x5-3*x1^6*x2*
x3*x4*x5+6*x1^3*x4*_z2*_z1*x5-30*x1^4*x4*_z2*_z1*x5-15*x1^6*x4*_z2*_z1*x5+12*
x1^7*x4*_z2*_z1*x5-x1^3*x2*_z2*_z1-30*x1^5*x2*_z2*_z1+20*x1^6*x2*_z2*_z1-x1^3*
x3*_z2*_z1-30*x1^5*x3*_z2*_z1+20*x1^6*x3*_z2*_z1+12*x1^8*x3*_z2*_z1+12*x1^8*x2
*_z2*_z1-3*x1*x2*x3*x4+18*x1^2*x2*x3*x4+60*x1^4*x2*x3*x4-45*x1^5*x2*x3*x4-x1^3
*x4*_z2*_z1-30*x1^5*x4*_z2*_z1+20*x1^6*x4*_z2*_z1+12*x1^8*x4*_z2*_z1-x1^9*x3*
_z2*_z1-x1^9*x2*_z2*_z1-3*x1^7*x2*x3*x4-x1^9*x4*_z2*_z1-3*x1*x2*x3*x5+18*x1^2*
x2*x3*x5+60*x1^4*x2*x3*x5-45*x1^5*x2*x3*x5-3*x1^7*x2*x3*x5-3*x1*x2*x4*x5+18*x1
^2*x2*x4*x5+60*x1^4*x2*x4*x5-45*x1^5*x2*x4*x5-3*x1*x3*x4*x5-3*x2*x3*x4*x5+18*
x1^2*x3*x4*x5+60*x1^4*x3*x4*x5-45*x1^5*x3*x4*x5-3*x1^7*x3*x4*x5-3*x1^7*x2*x4*
x5-x1^3*x5*_z2*_z1-30*x1^5*x5*_z2*_z1+20*x1^6*x5*_z2*_z1+12*x1^8*x5*_z2*_z1-x1
^9*x5*_z2*_z1+18*x1^3*x2*x3-45*x1^6*x2*x3+18*x1^3*x2*x4-45*x1^6*x2*x4+18*x1^3*
x3*x4-45*x1^6*x3*x4+18*x1^3*x2*x5-45*x1^6*x2*x5+18*x1^3*x3*x5-45*x1^6*x3*x5+18
*x1^3*x4*x5-45*x1^6*x4*x5-x1^4*_z2*_z1-6*x1^5*_z2*_z1+20*x1^7*_z2*_z1+15*x1^8*
_z2*_z1+3*x1^3*x2-60*x1^6*x2+3*x1^3*x3-60*x1^6*x3+3*x1^3*x4-60*x1^6*x4+3*x1^9*
x3+3*x1^9*x2+3*x1^9*x4+3*x1^3*x5-60*x1^6*x5+3*x1^9*x5+3*x1^4-18*x1^5-60*x1^7+
45*x1^8+3*x1^10+6*x1^2*x2*x3*_z2*_z1*x4-20*x1^4*x2*x3*_z2*_z1*x4-15*x1^5*x2*x3
*_z2*_z1*x4+x1*x2*x3*_z2*_z1*x5+6*x1^2*x2*x3*_z2*_z1*x5-20*x1^4*x2*x3*_z2*_z1*
x5-15*x1^5*x2*x3*_z2*_z1*x5+x1^7*x2*x3*_z2*_z1*x5+x1*x2*_z2*_z1*x4*x5+6*x1^2*
x2*_z2*_z1*x4*x5-20*x1^4*x2*_z2*_z1*x4*x5-15*x1^5*x2*_z2*_z1*x4*x5+x1*x3*_z2*
_z1*x4*x5+x2*x3*_z2*_z1*x4*x5+6*x1^2*x3*_z2*_z1*x4*x5-20*x1^4*x3*_z2*_z1*x4*x5
-15*x1^5*x3*_z2*_z1*x4*x5+x1^7*x3*_z2*_z1*x4*x5+x1^7*x2*_z2*_z1*x4*x5+x1^7*x2*
x3*_z2*_z1*x4-x1^10*_z2*_z1, x1*x2*x3*_z2*_z1*x4-3*x1*x2*x3*x4-3*x1*x2*x3*x5-3
*x1*x2*x4*x5-3*x1*x3*x4*x5-3*x2*x3*x4*x5-x2^3*x1*_z2*_z1-30*x2^5*x1*_z2*_z1+20
*x2^6*x1*_z2*_z1-x2^3*x3*_z2*_z1-30*x2^5*x3*_z2*_z1+20*x2^6*x3*_z2*_z1+12*x2^8
*x3*_z2*_z1+12*x2^8*x1*_z2*_z1+20*x2^6*x4*_z2*_z1+12*x2^8*x4*_z2*_z1-x2^3*x4*
_z2*_z1-30*x2^5*x4*_z2*_z1+60*x2^4*x1*x3*x4-45*x2^5*x1*x3*x4+18*x2^2*x1*x3*x4-
x2^9*x3*_z2*_z1+3*x2^3*x1-60*x2^6*x1+3*x2^3*x3-60*x2^6*x3-60*x2^6*x4+3*x2^3*x4
+3*x2^9*x3+3*x2^9*x1+3*x2^9*x4-60*x2^6*x5+3*x2^9*x5+3*x2^3*x5+x1*x2*x3*_z2*_z1
*x5+x1*x2*_z2*_z1*x4*x5+x1*x3*_z2*_z1*x4*x5+x2*x3*_z2*_z1*x4*x5-20*x2^4*x1*x3*
x4*_z2*_z1-15*x2^5*x1*x3*x4*_z2*_z1+6*x2^2*x1*x3*x4*_z2*_z1+x2^7*x1*x3*x4*_z2*
_z1-20*x2^4*x1*x3*x5*_z2*_z1-15*x2^5*x1*x3*x5*_z2*_z1+6*x2^2*x1*x4*x5*_z2*_z1-\
20*x2^4*x1*x4*x5*_z2*_z1-15*x2^5*x1*x4*x5*_z2*_z1+6*x2^2*x3*x4*x5*_z2*_z1-20*
x2^4*x3*x4*x5*_z2*_z1-15*x2^5*x3*x4*x5*_z2*_z1+x2^7*x3*x4*x5*_z2*_z1+x2^7*x1*
x4*x5*_z2*_z1+x2^7*x1*x3*x5*_z2*_z1+6*x2^2*x1*x3*x5*_z2*_z1-x2^9*x1*_z2*_z1-x2
^9*x4*_z2*_z1-3*x2^7*x1*x3*x4+20*x2^6*x5*_z2*_z1+12*x2^8*x5*_z2*_z1-x2^9*x5*
_z2*_z1-x2^3*x5*_z2*_z1-30*x2^5*x5*_z2*_z1+60*x2^4*x1*x3*x5-45*x2^5*x1*x3*x5+
18*x2^2*x1*x4*x5+60*x2^4*x1*x4*x5-45*x2^5*x1*x4*x5+18*x2^2*x3*x4*x5+60*x2^4*x3
*x4*x5-45*x2^5*x3*x4*x5-3*x2^7*x3*x4*x5-3*x2^7*x1*x4*x5-3*x2^7*x1*x3*x5+18*x2^
2*x1*x3*x5-20*x2^3*x1*x3*x4*x5*_z2*_z1-12*x2^5*x1*x3*x4*x5*_z2*_z1+x2^6*x1*x3*
x4*x5*_z2*_z1+30*x2^2*x1*x3*x4*x5*_z2*_z1+3*x2^10-60*x2^7+45*x2^8+3*x2^4-18*x2
^5-x2^10*_z2*_z1+15*x2^8*_z2*_z1+20*x2^7*_z2*_z1-x2^4*_z2*_z1-6*x2^5*_z2*_z1+
18*x2^3*x1*x3-45*x2^6*x1*x3+18*x2^3*x1*x4-45*x2^6*x1*x4+18*x2^3*x3*x4-45*x2^6*
x3*x4+18*x2^3*x1*x5-45*x2^6*x1*x5+18*x2^3*x3*x5-45*x2^6*x3*x5-45*x2^6*x4*x5+18
*x2^3*x4*x5-15*x2^6*x1*_z2*_z1*x5+6*x2^3*x3*_z2*_z1*x5-30*x2^4*x3*_z2*_z1*x5-\
15*x2^6*x3*_z2*_z1*x5+12*x2^7*x3*_z2*_z1*x5+12*x2^7*x1*_z2*_z1*x5-15*x2^6*x4*
_z2*_z1*x5+12*x2^7*x4*_z2*_z1*x5+6*x2^3*x4*_z2*_z1*x5-30*x2^4*x4*_z2*_z1*x5+60
*x2^3*x1*x3*x4*x5-3*x2^6*x1*x3*x4*x5-15*x2^6*x3*_z2*_z1*x4+12*x2^7*x3*_z2*_z1*
x4+12*x2^7*x1*_z2*_z1*x4+12*x2^7*x1*x3*_z2*_z1+6*x2^3*x1*_z2*_z1*x5-30*x2^4*x1
*_z2*_z1*x5+6*x2^3*x1*x3*_z2*_z1-30*x2^4*x1*x3*_z2*_z1-15*x2^6*x1*x3*_z2*_z1+6
*x2^3*x1*_z2*_z1*x4-30*x2^4*x1*_z2*_z1*x4-15*x2^6*x1*_z2*_z1*x4+6*x2^3*x3*_z2*
_z1*x4-30*x2^4*x3*_z2*_z1*x4, x1*x2*x3*_z2*_z1*x4-3*x1*x2*x3*x4-3*x1*x2*x3*x5-\
3*x1*x2*x4*x5-3*x1*x3*x4*x5-3*x2*x3*x4*x5+x1*x2*x3*_z2*_z1*x5+x1*x2*_z2*_z1*x4
*x5+x1*x3*_z2*_z1*x4*x5+x2*x3*_z2*_z1*x4*x5+3*x3^10+6*x3^2*x1*x2*_z2*_z1*x5-20
*x3^4*x1*x2*_z2*_z1*x5-15*x3^5*x1*x2*_z2*_z1*x5+x3^7*x1*x2*_z2*_z1*x5+6*x3^2*
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That's a nice app.  I thought about adding radix sort (MSB/inplace) which looks like quicksort but with more buckets.  I didn't want to try it in Maple.  Here it is in C for integers, along with the famous paper by McIlroy and Bostic:

http://www.cecm.sfu.ca/~rpearcea/radix4.c

http://static.usenix.org/publications/compsystems/1993/win_mcilroy.pdf

I'm just grateful this is not referring to code.

@muffinman123 Try making a new worksheet.  Does your document show a red Maple prompt?  If not, try creating a new worksheet and check if it is in Maple notation or 2D math.  To convert an existing document you would have to select the Maple commands and set it to "Maple Notation".

@muffinman123 Try making a new worksheet.  Does your document show a red Maple prompt?  If not, try creating a new worksheet and check if it is in Maple notation or 2D math.  To convert an existing document you would have to select the Maple commands and set it to "Maple Notation".

I just want to point out that cpu times on hyperthreaded processors are generally nonsense.  When the operating system runs two threads per core it bills all the cpu cycles to both threads, effectively double counting resources.  I bet if you run that example with 8 threads on a hyperthreaded Core i7 you'll get a strange cpu time like 16 seconds, and a faster real time maybe 2 seconds.  You should use hyperthreading on the Core i7 and Atom.

We should just make e = exp(1), and while we're at it, make pi = Pi and i = imaginary unit.  People obviously expect this.  Local variables in procedures shouldn't be affected.  Just get rid of these weird things once and for all.  If we'd done it 10 years ago it would be over by now, and people would be happier and Maple would be easier to use.  These problems are like zombies: they suck your brain and never die.

We should just make e = exp(1), and while we're at it, make pi = Pi and i = imaginary unit.  People obviously expect this.  Local variables in procedures shouldn't be affected.  Just get rid of these weird things once and for all.  If we'd done it 10 years ago it would be over by now, and people would be happier and Maple would be easier to use.  These problems are like zombies: they suck your brain and never die.

@LijiH You're out of memory and swapping.  It will run 1000x slower under those condtions, and because it is using so much memory it is unlikely that it can ever compute the answer.  A better algorithm is needed here.

@LijiH You're out of memory and swapping.  It will run 1000x slower under those condtions, and because it is using so much memory it is unlikely that it can ever compute the answer.  A better algorithm is needed here.

I still find the site a little slow when you have multiple tabs open.  Please consider:

http://www.codinghorror.com/blog/2011/06/performance-is-a-feature.html

Is there any chance of getting modern 3d in Maple?  Those plots look like they were produced in 1992.  Let me fire up my 386SX.  It looks like nothing happened in computer graphics in the last 20 years.  We should have scientific visualization geared towards large data sets.  Take a look at  http://en.wikipedia.org/wiki/VTK  and note that it is BSD licensed, specifically to encourage commercial adoption.

@Christopher2222 I don't expect Laurent to tip his hand :)  High end GPUs actually have about 512 cores (shaders), organized into blocks of 16-48 cores (per streaming multiprocessor).  All cores in a multiprocessor should be executing the same code.  The multiprocessors interleave up to 32 threads, so 16384 simultaneous threads are about the maximum today.

The GPUs in notebooks and most desktops are considerably less powerful at the moment.  For example, my notebook has a GeForce 320M (MCP89) with 48 cores.  It does about 120 GFLOPs single precision, whereas a Core i7 would do around 90.  The newer mobile GPUs are twice as fast, and you can see the performance is starting to pull away from CPUs.

The catch is that you have to use single precision floats (24-bit mantissa) to get good performance.  There's a strong case for moving floating point algorithms to GPUs now and using iterative methods to gain precision.  For general computer algebra there is a slightly longer window because CPUs are doing 64-bit integer arithmetic.

That's only for the algorithms where GPUs make sense however.  Basically, dense algorithms.  Dense polynomials and linear algebra, graphs, simulations, etc.  For anything sparse or structured GPUs are hard to use, and you want threads on a multicore cpu.  The multithreading going into Maple now is focused on those cases because it's a good investment now and it won't be obsolete later, although I expect GPUs to push the applicability of dense algorithms out very far.  I'm sure in 10 years we'll be shocked by what we can compute.  We'll be there.

Any graphical changes?  One thing I would really like is a little more breathing space in the layout.  I understand it's set to 1000 pixels wide.  I agree that's an acceptable minimum, but it looks extremely cramped.  How about adding space between the columns and expanding the right column when you resize?  I would prefer everything to be resizable, actually, but I think there was an argument about that.

Also, could you please provide a setting to turn email notifications off by default?  Email is sacrosanct.  I would like a message at the top of MaplePrimes directing me to any replies or new posts in topics where I have posted.