/*******************************************
3/11/2006
Found equation of a Humbert component of discriminant 9 (degree 16)
Ran the following to produce the output:

out:=compareall(16,9,140 :returnkernel:=true,expbounds:=[8,8,8]);

Took 160.047 seconds
********************************************/

h9:=
e1^8*e2^4 - 4*e1^8*e2^3*e3 + 6*e1^8*e2^2*e3^2 - 4*e1^8*e2*e3^3 + e1^8*e3^4 -
    32*e1^7*e2^5*e3^2 + 32*e1^7*e2^5*e3 - 4*e1^7*e2^5 + 32*e1^7*e2^4*e3^3 +
    32*e1^7*e2^4*e3^2 - 52*e1^7*e2^4*e3 + 32*e1^7*e2^3*e3^4 - 128*e1^7*e2^3*e3^3

    + 56*e1^7*e2^3*e3^2 + 32*e1^7*e2^3*e3 - 32*e1^7*e2^2*e3^5 +
    32*e1^7*e2^2*e3^4 + 56*e1^7*e2^2*e3^3 - 64*e1^7*e2^2*e3^2 + 32*e1^7*e2*e3^5

    - 52*e1^7*e2*e3^4 + 32*e1^7*e2*e3^3 - 4*e1^7*e3^5 + 256*e1^6*e2^6*e3^4 -
    512*e1^6*e2^6*e3^3 + 320*e1^6*e2^6*e3^2 - 64*e1^6*e2^6*e3 + 6*e1^6*e2^6 -
    512*e1^6*e2^5*e3^5 + 512*e1^6*e2^5*e3^4 + 480*e1^6*e2^5*e3^3 -
    544*e1^6*e2^5*e3^2 + 56*e1^6*e2^5*e3 + 256*e1^6*e2^4*e3^6 +
    512*e1^6*e2^4*e3^5 - 1344*e1^6*e2^4*e3^4 + 96*e1^6*e2^4*e3^3 +
    426*e1^6*e2^4*e3^2 + 32*e1^6*e2^4*e3 - 512*e1^6*e2^3*e3^6 +
    480*e1^6*e2^3*e3^5 + 96*e1^6*e2^3*e3^4 + 560*e1^6*e2^3*e3^3 -
    544*e1^6*e2^3*e3^2 - 32*e1^6*e2^3*e3 + 320*e1^6*e2^2*e3^6 -
    544*e1^6*e2^2*e3^5 + 426*e1^6*e2^2*e3^4 - 544*e1^6*e2^2*e3^3 +
    320*e1^6*e2^2*e3^2 - 64*e1^6*e2*e3^6 + 56*e1^6*e2*e3^5 + 32*e1^6*e2*e3^4 -
    32*e1^6*e2*e3^3 + 6*e1^6*e3^6 - 32*e1^5*e2^7*e3^2 + 32*e1^5*e2^7*e3 -
    4*e1^5*e2^7 - 512*e1^5*e2^6*e3^5 + 512*e1^5*e2^6*e3^4 + 480*e1^5*e2^6*e3^3 -

    544*e1^5*e2^6*e3^2 + 56*e1^5*e2^6*e3 - 512*e1^5*e2^5*e3^6 +
    4608*e1^5*e2^5*e3^5 - 7104*e1^5*e2^5*e3^4 + 2624*e1^5*e2^5*e3^3 +
    560*e1^5*e2^5*e3^2 - 128*e1^5*e2^5*e3 + 512*e1^5*e2^4*e3^6 -
    7104*e1^5*e2^4*e3^5 + 12672*e1^5*e2^4*e3^4 - 6244*e1^5*e2^4*e3^3 +
    96*e1^5*e2^4*e3^2 + 32*e1^5*e2^4*e3 + 480*e1^5*e2^3*e3^6 +
    2624*e1^5*e2^3*e3^5 - 6244*e1^5*e2^3*e3^4 + 2624*e1^5*e2^3*e3^3 +
    480*e1^5*e2^3*e3^2 - 32*e1^5*e2^2*e3^7 - 544*e1^5*e2^2*e3^6 +
    560*e1^5*e2^2*e3^5 + 96*e1^5*e2^2*e3^4 + 480*e1^5*e2^2*e3^3 -
    512*e1^5*e2^2*e3^2 + 32*e1^5*e2*e3^7 + 56*e1^5*e2*e3^6 - 128*e1^5*e2*e3^5 +

    32*e1^5*e2*e3^4 - 4*e1^5*e3^7 + e1^4*e2^8 + 32*e1^4*e2^7*e3^3 +
    32*e1^4*e2^7*e3^2 - 52*e1^4*e2^7*e3 + 256*e1^4*e2^6*e3^6 +
    512*e1^4*e2^6*e3^5 - 1344*e1^4*e2^6*e3^4 + 96*e1^4*e2^6*e3^3 +
    426*e1^4*e2^6*e3^2 + 32*e1^4*e2^6*e3 + 512*e1^4*e2^5*e3^6 -
    7104*e1^4*e2^5*e3^5 + 12672*e1^4*e2^5*e3^4 - 6244*e1^4*e2^5*e3^3 +
    96*e1^4*e2^5*e3^2 + 32*e1^4*e2^5*e3 - 1344*e1^4*e2^4*e3^6 +
    12672*e1^4*e2^4*e3^5 - 22566*e1^4*e2^4*e3^4 + 12672*e1^4*e2^4*e3^3 -
    1344*e1^4*e2^4*e3^2 + 32*e1^4*e2^3*e3^7 + 96*e1^4*e2^3*e3^6 -
    6244*e1^4*e2^3*e3^5 + 12672*e1^4*e2^3*e3^4 - 7104*e1^4*e2^3*e3^3 +
    512*e1^4*e2^3*e3^2 + 32*e1^4*e2^2*e3^7 + 426*e1^4*e2^2*e3^6 +
    96*e1^4*e2^2*e3^5 - 1344*e1^4*e2^2*e3^4 + 512*e1^4*e2^2*e3^3 +
    256*e1^4*e2^2*e3^2 - 52*e1^4*e2*e3^7 + 32*e1^4*e2*e3^6 + 32*e1^4*e2*e3^5 +
    e1^4*e3^8 - 4*e1^3*e2^8*e3 + 32*e1^3*e2^7*e3^4 - 128*e1^3*e2^7*e3^3 +
    56*e1^3*e2^7*e3^2 + 32*e1^3*e2^7*e3 - 512*e1^3*e2^6*e3^6 +
    480*e1^3*e2^6*e3^5 + 96*e1^3*e2^6*e3^4 + 560*e1^3*e2^6*e3^3 -
    544*e1^3*e2^6*e3^2 - 32*e1^3*e2^6*e3 + 480*e1^3*e2^5*e3^6 +
    2624*e1^3*e2^5*e3^5 - 6244*e1^3*e2^5*e3^4 + 2624*e1^3*e2^5*e3^3 +
    480*e1^3*e2^5*e3^2 + 32*e1^3*e2^4*e3^7 + 96*e1^3*e2^4*e3^6 -
    6244*e1^3*e2^4*e3^5 + 12672*e1^3*e2^4*e3^4 - 7104*e1^3*e2^4*e3^3 +
    512*e1^3*e2^4*e3^2 - 128*e1^3*e2^3*e3^7 + 560*e1^3*e2^3*e3^6 +
    2624*e1^3*e2^3*e3^5 - 7104*e1^3*e2^3*e3^4 + 4608*e1^3*e2^3*e3^3 -
    512*e1^3*e2^3*e3^2 + 56*e1^3*e2^2*e3^7 - 544*e1^3*e2^2*e3^6 +
    480*e1^3*e2^2*e3^5 + 512*e1^3*e2^2*e3^4 - 512*e1^3*e2^2*e3^3 -
    4*e1^3*e2*e3^8 + 32*e1^3*e2*e3^7 - 32*e1^3*e2*e3^6 + 6*e1^2*e2^8*e3^2 -
    32*e1^2*e2^7*e3^5 + 32*e1^2*e2^7*e3^4 + 56*e1^2*e2^7*e3^3 -
    64*e1^2*e2^7*e3^2 + 320*e1^2*e2^6*e3^6 - 544*e1^2*e2^6*e3^5 +
    426*e1^2*e2^6*e3^4 - 544*e1^2*e2^6*e3^3 + 320*e1^2*e2^6*e3^2 -
    32*e1^2*e2^5*e3^7 - 544*e1^2*e2^5*e3^6 + 560*e1^2*e2^5*e3^5 +
    96*e1^2*e2^5*e3^4 + 480*e1^2*e2^5*e3^3 - 512*e1^2*e2^5*e3^2 +
    32*e1^2*e2^4*e3^7 + 426*e1^2*e2^4*e3^6 + 96*e1^2*e2^4*e3^5 -
    1344*e1^2*e2^4*e3^4 + 512*e1^2*e2^4*e3^3 + 256*e1^2*e2^4*e3^2 +
    56*e1^2*e2^3*e3^7 - 544*e1^2*e2^3*e3^6 + 480*e1^2*e2^3*e3^5 +
    512*e1^2*e2^3*e3^4 - 512*e1^2*e2^3*e3^3 + 6*e1^2*e2^2*e3^8 -
    64*e1^2*e2^2*e3^7 + 320*e1^2*e2^2*e3^6 - 512*e1^2*e2^2*e3^5 +
    256*e1^2*e2^2*e3^4 - 4*e1*e2^8*e3^3 + 32*e1*e2^7*e3^5 - 52*e1*e2^7*e3^4 +
    32*e1*e2^7*e3^3 - 64*e1*e2^6*e3^6 + 56*e1*e2^6*e3^5 + 32*e1*e2^6*e3^4 -
    32*e1*e2^6*e3^3 + 32*e1*e2^5*e3^7 + 56*e1*e2^5*e3^6 - 128*e1*e2^5*e3^5 +
    32*e1*e2^5*e3^4 - 52*e1*e2^4*e3^7 + 32*e1*e2^4*e3^6 + 32*e1*e2^4*e3^5 -
    4*e1*e2^3*e3^8 + 32*e1*e2^3*e3^7 - 32*e1*e2^3*e3^6 + e2^8*e3^4 - 4*e2^7*e3^5

    + 6*e2^6*e3^6 - 4*e2^5*e3^7 + e2^4*e3^8
;