# Elimination for coefficients of special characteristic polynomials
# Wilhelm Plesken, Daniel Robertz
# Janet basis for I_(3,3) over the rationals Q restricted to determinant 1:
#
v := [c7 = 7, c6 = 6, c5 = 5, c4 = 4, c3 = 3, c2 = 2, c1 = 1]:
J := [c4*c3*c2-c5*c3*c1+c3*c2*c1+c4*c1^3*c8+c5*c4+
c3*c1^3-c2^3+c4*c2-c5*c1+2*c2*c1+4*c2^2*c1^2-4*c2*c1
^4-2*c1*c8+c1^6-c5*c1^4-2*c4*c1^2-c4*c2*c1*c8-c4^2*c1+
c6*c1^3-c6*c2*c1+2*c5*c2*c1^2+3*c2*c1^2*c8-3*c3*c1
*c8+c4*c3*c8-c3^2*c1*c8-2*c2^2*c8-c1^4*c8+2*c4*c8+c7*
c3*c2-c7*c4*c1+c7*c2-c5*c2^2, c8*c7-c8*c6*c1+c7*
c5-2*c4*c8+c3*c1*c8-c4*c2+2*c5*c1-c2*c1, 2*c5*c8+
c4*c1^3-c4*c2*c1-c3*c2*c8-2*c8*c6*c2-c7^2*c1^2+c7*
c2*c1+c7^2*c2-c5*c4*c1-c7*c1^3-2*c5*c1^2-c7*c5*c1-
c6*c2^2-c2*c8-c2*c1^3*c8+c6*c2*c1^2+c2^2*c1*c8+c1^
2*c8+2*c8*c6*c1^2+c3*c1^2*c8-c2^2+c1^4+c3*c5*c8+c5
^2, 3*c3*c2^2*c1+c5*c1^3-c1^5-c2^4+6*c2^2*c1-c2*c1^3-c1^
3*c8+c4*c3*c2^2-2*c6*c2^2*c1-3*c7*c2*c1^2+2*c5*c2^2*
c1^2+3*c6*c2*c1^3-c5*c2*c1^4+5*c4*c2*c1^2-3*c5*c2*c1
-4*c2^2*c1^4-3*c3*c2*c1*c8+4*c2^3*c1^2+c2*c1^6-c8*c4*c2^
2*c1-3*c2*c1*c8-c3^2*c2*c1*c8-2*c8*c2^3+c7*c3*c2
^2-c5*c3*c1^3-c6*c1^5-3*c4*c1^4+c3*c1^5-2*c3*c2*c1^3-c3*
c1^3*c8+2*c2^2*c1^2*c8+c5*c1^4*c8+3*c7*c2^2-c5*c2^
3+2*c7*c1^4-c7^2*c2*c1+c7^2*c1^3+c8*c4*c2*c1^3+2*c1*c6*
c2*c8-2*c1^3*c8*c6-2*c8*c5*c2*c1^2+c8*c5*c2^2, c3
*c2^2*c1+c5*c1^3-c3*c1^2+c1^2-2*c1^5+4*c4*c3*c1+2*c4*c1+
2*c2^2*c1+3*c2*c1^3-2*c1^3*c8+c5*c1*c8+c1^6*c8-c5*
c4*c2-c6*c4*c1-3*c7*c3*c1-c6*c2^2*c1+2*c6*c2*c1^3+
2*c4*c2*c1^2-4*c5*c2*c1-3*c7*c1-c3*c2*c1*c8+c2*c1*
c8+c7*c4*c3-c7*c5*c2-c7*c3^2*c1-c7*c5*c1^2+c7*c4
*c1^3-c6*c1^5-c4*c1^4+c4^2*c3-2*c3^2*c1^2-2*c4*c1^2*c8
+c3*c1^3*c8+2*c2^2*c1^2*c8-3*c2*c1^4*c8-c4^2*c1*c8+c7*
c4+c7*c2^2+c5^2*c1+c7*c1^4-c7^2+c7^2*c2*c1+c7*c6*c1+
c8*c5*c4-c7^2*c3, c4*c3*c2+3*c3*c2*c1-c3*c1^4*c8+
3*c4*c1^3*c8-2*c3*c1^3-c1^3-c2^3-3*c5*c1+6*c2*c1+5*c2^
2*c1^2-3*c2*c1^4-3*c1*c8+c1^6-3*c5*c1^4+3*c4*c1^2+c4*
c2*c1^3-c4*c2*c1*c8+c6*c1^3-2*c6*c2*c1+2*c5*c2*c1^
2+3*c2*c1^2*c8-3*c3*c1*c8-c3^2*c1*c8-2*c2^2*c8-c1^4*c8-
2*c5*c1^2*c8-c7*c5*c1^3+c7*c3*c2+3*c7*c2-c5*c2^2-4*
c7*c1^2-c7*c3*c1^2-c7^2*c1+c8*c5*c2+c1^4*c8*c6+2*c8*
c6*c1, c5*c3*c1-c3*c1^3+c1^3+c2^3-2*c4*c2-c5*c1+
c2^2*c1^2+c4*c2^2*c1-c3*c2*c1^2*c8+c1*c8+3*c4*c1^2-c7*
c5*c2*c1+2*c4*c2*c1*c8+c6*c1^3-2*c6*c2*c1-2*c5*c2*
c1^2-c2*c1^2*c8+c3*c1*c8+c2^2*c8-c5*c1^2*c8-c7*c3*
c2-c7*c2-2*c7*c1^2-c7^2*c1+c2*c8*c6*c1^2+2*c8*c6
*c1, -c4*c3*c2-c3*c2*c1-2*c4*c1^3*c8-2*c5*c4-2*c3*c1^
3+3*c1^3+2*c2^3-2*c4*c2-c5*c1-7*c2*c1-8*c2^2*c1^2+8*c2*
c1^4-c7*c5*c3+6*c1*c8-2*c1^6+2*c5*c1^4+5*c4*c1^2+2*c4*
c2*c1*c8+2*c4^2*c1-c6*c1^3+c6*c2*c1-4*c5*c2*c1^2-4
*c2*c1^2*c8+5*c3*c1*c8+c3^2*c1*c8+3*c2^2*c8+c1^4*c8-2*
c7*c3*c2+c7*c4*c1-c7*c5-4*c7*c2+2*c5*c2^2-c7*c1^
2-c7^2*c1+c8*c6*c3*c1+2*c8*c6*c1, 2*c4*c3*c2-3*c5*c3*
c1+4*c3*c2*c1-3*c3*c1^4*c8+2*c4*c1^3*c8-c2^3*c1*c8+
c2^2*c1^3*c8-4*c5*c4-5*c3*c1^3-2*c2^3+4*c4*c2-4*c5*c1-
2*c2*c1-c3*c2^3+c3^2*c1^3-12*c2^2*c1^2+13*c2*c1^4-2*c7
*c5*c3-c7*c4*c2*c1^2-4*c4*c2^2*c1+5*c3*c2*c1^2*c8+2*
c1*c8-c3*c2^2*c8-3*c1^6-3*c4*c3*c1^2+4*c4*c1^2+3*c7*c5*
c2*c1+c7*c3^2*c2+4*c4*c2*c1^3-2*c4*c2*c1*c8+4*c4^
2*c1-4*c6*c1^3-c4*c1^5+6*c6*c2*c1+c5*c2*c1^2+5*c2*c1
^2*c8-c3*c1*c8-c3^2*c1*c8-2*c2^2*c8-c5*c3^2*c1-c1^4*
c8-2*c5*c1^2*c8-c7*c5*c1^3-c6*c3*c1^3+3*c7*c3*c2+2*c7*
c4*c1-2*c7*c2^2*c1+2*c6*c3*c2*c1-2*c7*c5-c5^2*c1
^2+c7*c1^5+2*c7*c2+2*c5*c2^2-2*c7*c1^2+c5*c4*c1^3-2*c7
*c2*c1^3-2*c7^2*c2*c1^2+c7^2*c1^4+2*c8*c5*c2+c3*c1*c7^
2, -6*c3*c2^2*c1^2-2*c4*c3*c2-3*c3^2*c2*c1-6*c3*c2*c1-
4*c3*c1^4*c8+6*c4*c1^3*c8+c3^3*c1*c8+4*c2^3*c1*c8-10
*c2^2*c1^3*c8+4*c3*c1^3-2*c1^3-3*c2^3+4*c4*c2+2*c5*c1+2*
c3*c2^3+c3^2*c1^3-3*c2*c1^4-c7*c3*c2^2*c1+2*c7*c4*c2
*c1^2+c7*c3*c2*c1^3-4*c4*c2^2*c1+4*c3*c2*c1^2*c8-2*c1*
c8+8*c2*c1^5*c8+c4*c1^6*c8+2*c3*c2^2*c8+2*c1^6-c5*c1^
7-5*c2^3*c1^3-2*c5*c1^4-5*c2*c1^7-c3^2*c1^4*c8+c1^9-6*c4*
c1^2-2*c1^7*c8+2*c7*c5*c2*c1-2*c7*c3^2*c2+4*c4*c2*
c1^3+c4*c2^2*c1^2*c8-10*c4*c2*c1*c8-c4*c3^2*c2+2*c6*
c1^6+c2^4*c1-2*c6*c1^3-2*c4*c1^5-2*c4*c2*c1^4*c8+4*c6*
c2*c1+6*c5*c2*c1^2+4*c3*c2*c1^4+4*c2*c1^2*c8+2*c3*c1
*c8+4*c3^2*c1*c8-3*c2^2*c8+c5*c3^2*c1-c1^4*c8+c7*c3^
2*c1^2-2*c7*c4*c1^4+c3^2*c2*c1^2*c8-2*c7*c3*c2+c5*c3
*c2^2+2*c7*c2^2*c1+c5*c2^3*c1-2*c5*c4*c2*c1-c4*c3*c2^
2*c1-c5*c3*c2*c1^2+c4*c3*c2*c1^3+c5^2*c2-c6*c2^3-
c5^2*c1^2-c4^2*c1^4+2*c7*c2+4*c7*c1^2+8*c2^2*c1^5+2*c7*c3*
c1^2+c4^2*c2*c1^2+4*c6*c2^2*c1^2+2*c5*c4*c1^3-2*c7*c2*
c1^3-3*c5*c2^2*c1^3-5*c6*c2*c1^4+3*c5*c2*c1^5+2*c7^2
*c1+c7^2*c2^2-c7^2*c2*c1^2+2*c8*c5*c2-2*c8*c6*c2^2-4*c8*
c6*c1, -3*c2*c1-2*c7*c2+c2*c8^2-c4*c2+c1^3+c5*c1
+c7*c1^2+2*c1*c8-c1^2*c8^2+c3*c1*c8, 21*c3*c2^2*c1^2-6
*c4*c3*c2+2*c3^2*c2*c1+9*c5*c3*c1+2*c3*c2*c1+19*c3*c1^
4*c8-14*c4*c1^3*c8-c3^3*c1*c8-c2^3*c1*c8+15*c2^2*c1^
3*c8+12*c5*c4+12*c3*c1^3-2*c1^3+6*c2^3-12*c4*c2+12*c5*c1+
6*c2*c1+c3*c2^3+5*c3^2*c1^3+22*c2^2*c1^2-36*c2*c1^4+8*c7*
c5*c3+c7*c4*c3*c2*c1^2-5*c7*c4*c3*c1-2*c6*c3^2*c2*
c1+3*c7*c3*c2^2*c1-c6*c5*c2*c1^2+c7*c4*c2*c1^2-2
*c5*c4*c3*c1^3+2*c6*c4*c2*c1^3-3*c7*c3*c2*c1^3+16*c4
*c2^2*c1-16*c3*c2*c1^2*c8-6*c1*c8-16*c2*c1^5*c8-4*c4*c1^
6*c8-c3*c2^2*c8+8*c1^6+3*c5*c1^7+4*c5*c1^4+11*c2*c1^
7+4*c3^2*c1^4*c8-3*c1^9-5*c4*c3*c1^2-16*c4*c1^2+4*c1^7*c8-
10*c7*c5*c2*c1-2*c7*c3^2*c2-c3^2*c2^2*c1^2-2*c4*c2^3
*c1^2-20*c4*c2*c1^3+c3^2*c2^3-2*c4*c2^2*c1^2*c8+14*c4*c2*
c1*c8+c3*c2^3*c1*c8-c4^2*c3^2*c1-6*c4^2*c3*c1-c4*
c3^2*c1^2+c3^3*c1^3-2*c6*c1^6-12*c4^2*c1-2*c2^4*c1+12*c6
*c1^3+11*c4*c1^5+6*c4*c2*c1^4*c8+c5*c3^3*c1-18*c6*c2*c1-
3*c5*c2*c1^2-25*c3*c2*c1^4+c7*c4^2*c1^3-c7*c4*c3*c1^
4-13*c2*c1^2*c8-7*c3*c1*c8-4*c3^2*c1*c8+6*c2^2*c8+4*
c5*c3^2*c1+11*c1^4*c8+c3^2*c2^2*c8+6*c5*c1^2*c8+c4^3*c1^
3-c7*c1^8+c5^2*c4*c1-c5^2*c2^2*c1-2*c5*c4^2*c1^2+3*c7*
c3^2*c1^2+2*c7*c2^3*c1^2+6*c7*c5*c1^3+c6*c3^2*c1^3+c5^
2*c2*c1^3+3*c7*c4*c1^4-7*c7*c2^2*c1^4-c6*c4*c1^5-c7*
c3*c1^5+5*c7*c2*c1^6+2*c5*c4*c3*c2*c1+7*c6*c3*c1^3
-5*c3^2*c2*c1^2*c8+4*c5*c4*c3-3*c7*c3*c2-4*c5*c3*c2^
2-8*c7*c4*c1+2*c7*c2^2*c1+c5*c2^3*c1-c5*c4*c2*c1-12*
c6*c3*c2*c1+4*c4*c3*c2^2*c1+4*c5*c3*c2*c1^2-5*c4*c3*
c2*c1^3+6*c7*c5+2*c5^2*c1^2+3*c4^2*c1^4-3*c7*c1^5-6*c7
*c2-6*c5*c2^2+12*c7*c1^2-8*c2^2*c1^5+2*c3*c1^6+2*c6*c4*c1^
2+7*c7*c3*c1^2+3*c4^2*c2*c1^2+4*c6*c2^2*c1^2-7*c5*c4
*c1^3+3*c5*c2^2*c1^3+c4*c2^2*c1^4-6*c5*c2*c1^5+c7*c3^3
*c1^2+2*c7*c5*c3*c1^3-c7*c6*c1^5+c7*c5*c1^6-3*c7*c5*
c2*c1^4-2*c7*c6*c1^2+c6*c4*c3*c1^2+2*c7^2*c1+2*c7*c5
*c3^2-c7*c3^3*c2+2*c7^2*c2*c1^2-2*c7^2*c1^4-6*c8*c5*c2
-c7*c4*c3^2*c1-c7*c5*c4*c1^2-c7*c6*c3*c1^2+2*c7*c5
*c2^2*c1^2-3*c7*c5*c3*c2*c1+2*c7*c6*c2*c1^3, -c3*c2^
2*c1^2+3*c4*c3*c2-2*c5*c3*c1+4*c3*c2*c1-c3*c1^4*c8+7
*c4*c1^3*c8-2*c2^2*c1^3*c8+c4^2*c1^2*c8+4*c5*c4+7*c3*c1^
3-6*c1^3-5*c2^3+4*c4*c2-c5*c1+17*c2*c1+2*c3^2*c1^3+18*
c2^2*c1^2-23*c2*c1^4+c7*c5*c3-c7*c4*c3*c1-13*c1*c8+3
*c2*c1^5*c8+7*c1^6-5*c5*c1^4-3*c4*c3*c1^2-14*c4*c1^2-c1^
7*c8+c7*c5*c2*c1-2*c4*c2*c1^3-4*c4*c2*c1*c8-c4^2*c3*
c1+c6*c1^6-6*c4^2*c1+3*c6*c1^3+c4*c1^5-2*c6*c2*c1+
11*c5*c2*c1^2+9*c2*c1^2*c8-11*c3*c1*c8-2*c3^2*c1*c8-8*
c2^2*c8-c1^4*c8+c4*c8-2*c5*c1^2*c8+c7*c3^2*c1^2+c7*c5*
c1^3-c7*c4*c1^4-c5*c4*c3-c6*c4*c2+5*c7*c3*c2+c6*
c5*c1-3*c7*c4*c1-c7*c2^2*c1+c5*c4*c2*c1+c6*c3*c2*
c1+c7*c5+c5^2*c2-2*c5^2*c1^2-c7*c1^5+9*c7*c2-4*c5*c2^
2+4*c7*c1^2+c6*c4*c1^2+2*c7*c3*c1^2+c6*c2^2*c1^2-2*c6*
c2*c1^4-c7*c6*c1^2+2*c7^2*c1+c7^2*c4-c7^2*c2*c1^2+
2*c8*c5*c2-2*c8*c6*c1-2*c8*c6*c4, 3*c3*c2^2*c1^2+11*c4*
c3*c2-12*c5*c3*c1+31*c3*c2*c1-11*c3*c1^4*c8+5*c4*c1^
3*c8-4*c2^3*c1*c8+12*c2^2*c1^3*c8-2*c4^2*c1^2*c8-20*c5*
c4-34*c3*c1^3+3*c1^3-13*c2^3+20*c4*c2-23*c5*c1+2*c2*c1
-4*c3*c2^3-6*c3^2*c1^3-42*c2^2*c1^2+72*c2*c1^4-8*c7*c5*c3+
4*c7*c4*c3*c1-c6*c5*c2*c1^2-5*c7*c4*c2*c1^2-c6*c4*
c2*c1^3+c7*c3*c2*c1^3-18*c4*c2^2*c1+24*c3*c2*c1^2*c8+
c1*c8-14*c2*c1^5*c8-4*c3*c2^2*c8-23*c1^6-c5*c1^7-2*c2^
3*c1^3-5*c2*c1^7+c1^9+6*c4*c3*c1^2+31*c4*c1^2+5*c1^7*c8+
11*c7*c5*c2*c1+4*c7*c3^2*c2+22*c4*c2*c1^3-13*c4*c2*
c1*c8+6*c4^2*c3*c1-c4*c3^2*c1^2-3*c6*c1^6+20*c4^2*c1-15*
c6*c1^3-7*c4*c1^5+22*c6*c2*c1-2*c5*c2*c1^2-c3*c2*c1^
4-c7*c4^2*c1^3+45*c2*c1^2*c8-17*c3*c1*c8-9*c3^2*c1*c8-
16*c2^2*c8-4*c5*c3^2*c1-21*c1^4*c8-10*c5*c1^2*c8-5*c7
*c3^2*c1^2-8*c7*c5*c1^3-c6*c3^2*c1^3+3*c7*c4*c1^4+c6*c4*
c1^5-4*c6*c3*c1^3+2*c5*c4*c3+17*c7*c3*c2+8*c7*c4*c1-
4*c7*c2^2*c1+c5*c2^3*c1-6*c5*c4*c2*c1+6*c6*c3*c2
*c1-c4*c3*c2^2*c1+c4*c3*c2*c1^3-4*c7*c5-2*c5^2*c2+c5^
2*c1^2-c4^2*c1^4+9*c7*c1^5+19*c7*c2+5*c5*c2^2-32*c7*c1^
2+7*c2^2*c1^5+c3*c1^6-4*c6*c4*c1^2-15*c7*c3*c1^2-c6*c2^
2*c1^2+6*c5*c4*c1^3-8*c7*c2*c1^3-3*c5*c2^2*c1^3+c5*c3*
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