interface(prettyprint,prettyprint=false);

read `gpolyutil.txt`;

delta := (x[1]-x[2])*(x[2]-x[3])*(x[3]-x[1]):
aa[0] := 1:
aa[1] := x[1]+x[2]+x[3]:
aa[2] := x[1]*x[2]+x[2]*x[3]+x[3]*x[1]:
aa[3] := x[1]*x[2]*x[3]:
bb[0] :=
(x[1]*y[2]-x[2]*y[1]-x[3]*y[2]+x[3]*y[1]-x[1]*y[3]+x[2]*y[3])/delta:
bb[1] :=
(x[3]^2*y[2]-x[3]^2*y[1]+x[2]^2*y[1]+y[3]*x[1]^2-y[2]*x[1]^2-y[3]*x[2]
^2)/delta:
bb[2] :=
(-x[2]^2*x[3]*y[1]+x[2]^2*x[1]*y[3]+x[3]^2*x[2]*y[1]-y[3]*x[2]*x[1]^2+
y[2]*x[3]*x[1]^2-x[3]^2*x[1]*y[2])/delta:
F:=x->sum('f[i]*x^i','i'=0..8):
f[8]:=0:
 
kk[0] := aa[0]:
kk[1] := aa[1]:
kk[2] := aa[2]:
kk[3] := aa[3]:
kk[4] := aa[0]*bb[0]^2:
kk[5] := aa[1]*bb[0]^2 + 2*aa[0]*bb[0]*bb[1]:
kk[6] := aa[0]*bb[1]^2  - aa[2]*bb[0]^2:
kk[7] := aa[1]*bb[1]^2 + 2*aa[2]*bb[0]*bb[1] + aa[3]*bb[0]^2:
cc[0]:=naive_reduce_g3(subs(seq(y[i]^2=F(x[i]),i=1..3),expand(kk[4]))):
cc[1]:=naive_reduce_g3(subs(seq(y[i]^2=F(x[i]),i=1..3),expand(kk[5]))):
cc[2]:=naive_reduce_g3(subs(seq(y[i]^2=F(x[i]),i=1..3),expand(kk[6]))):
cc[3]:=naive_reduce_g3(subs(seq(y[i]^2=F(x[i]),i=1..3),expand(kk[7]))):

eqn[1] :=
3*f[7]*a[3]^2-a[3]*c[0]-2*a[3]*a[1]*f[5]+2*a[3]*a[2]*f[6]+a[0]*c[3]-c[1]*a[2]-
c[2]*a[1]+a[2]^2*f[5]:
eqn[2] :=
-2*f[2]*a[3]^2*a[0]*c[2]-4*f[3]*a[3]^2*a[0]*c[3]-2*f[3]*a[3]*a[2]^2*c[2]+2*a[3
]*a[2]*c[3]*c[2]+2*f[3]*a[3]^2*a[1]*c[2]-2*f[1]*a[2]*a[1]^2*c[3]-4*f[1]*a[3]*a
[2]^2*c[0]+2*f[1]*a[2]^2*a[0]*c[3]+2*f[1]*a[3]*a[1]^2*c[2]+4*f[1]*a[3]^2*a[1]*
c[0]+4*f[0]*a[3]*a[1]^2*c[1]+4*f[0]*a[2]*a[1]^2*c[2]-4*f[0]*a[2]^2*a[0]*c[2]+2
*f[2]*a[3]*a[2]^2*c[1]-2*f[2]*a[2]^2*a[1]*c[3]+4*f[2]*a[3]*a[1]^2*c[3]-2*f[2]*
a[3]^2*a[2]*c[0]-4*f[2]*a[3]^2*a[1]*c[1]-4*f[0]*a[3]*a[0]^2*c[3]+a[3]^2*c[2]^2
+4*a[3]^2*c[3]*c[1]-4*f[0]*a[2]^3*c[0]-2*f[3]*a[2]^3*c[3]-4*a[3]*a[1]*c[3]^2+6
*f[7]*f[2]*a[3]^3*a[2]-4*f[0]*a[1]^3*c[3]-4*f[6]*a[3]^3*c[3]+4*f[5]*a[3]^3*c[2
]+a[2]^2*c[3]^2+8*f[0]*a[3]*a[2]*a[1]*c[0]+6*f[3]*a[3]*a[2]*a[1]*c[3]+4*f[0]*a
[2]*a[1]*a[0]*c[3]-2*f[1]*a[3]*a[2]*a[0]*c[2]+4*f[0]*a[3]*a[1]*a[0]*c[2]-2*f[1
]*f[3]*a[3]*a[1]^3+4*a[3]*a[2]*a[1]^2*f[5]*f[0]-2*a[3]*a[2]*a[1]^2*f[3]*f[2]+4
*a[3]^2*a[2]*a[1]*f[5]*f[2]-24*a[3]^2*a[2]*a[1]*f[0]*f[7]-4*a[3]^2*a[2]*a[1]*f
[6]*f[1]-8*a[3]*a[2]^2*a[1]*f[0]*f[6]-2*a[3]*a[2]^2*a[1]*f[3]^2+4*a[3]^3*a[1]*
f[5]*f[3]+4*a[3]^3*a[1]*f[6]*f[2]-12*a[3]^3*a[1]*f[7]*f[1]+12*a[3]*a[2]^3*f[0]
*f[7]+4*a[3]*a[2]^3*f[6]*f[1]-2*a[3]*a[2]^3*f[5]*f[2]+12*a[3]^2*a[2]^2*f[7]*f[
1]+2*a[2]^2*a[1]^2*f[1]*f[3]+4*a[3]^2*a[1]^2*f[5]*f[1]-4*a[3]^2*a[2]^2*f[5]*f[
3]-4*a[3]^2*a[1]^2*f[0]*f[6]+f[1]^2*a[1]^4+2*a[3]*a[2]*a[1]*f[1]*f[3]*a[0]-2*f
[1]^2*a[2]*a[1]^2*a[0]-2*f[1]*f[2]*a[2]^2*a[1]*a[0]-2*f[1]*f[3]*a[2]^3*a[0]-4*
f[5]*f[2]*a[3]^3*a[0]+4*f[5]^2*a[3]^4+2*a[3]^2*a[1]*f[3]*f[2]*a[0]+8*a[3]^2*a[
1]*f[5]*f[0]*a[0]-2*a[3]*a[2]*a[1]*f[2]^2*a[0]-2*f[1]*f[2]*a[3]*a[1]^2*a[0]+f[
2]^2*a[3]^2*a[0]^2+a[3]^2*a[1]^2*f[3]^2+4*a[2]^4*f[0]*f[6]+f[1]^2*a[2]^2*a[0]^
2-8*a[3]*a[2]^2*f[5]*f[0]*a[0]-2*a[3]*a[2]^2*f[3]*f[2]*a[0]-4*f[5]*f[1]*a[3]^2
*a[2]*a[0]+2*f[1]*f[2]*a[3]*a[2]*a[0]^2+a[2]^2*a[1]^2*f[2]^2+a[2]^4*f[3]^2+2*f
[3]*f[2]*a[2]^3*a[1]+2*f[1]*f[2]*a[2]*a[1]^3:
eqn[3] :=
3*f[5]*a[3]*a[2]^2*c[3]-8*f[5]*a[3]^2*a[1]*c[3]+2*f[6]*a[3]^2*a[2]*c[3]+4*f[5]
*a[3]^2*a[2]*c[2]+2*f[2]*a[3]^2*a[1]*c[0]+4*f[2]*a[3]*a[1]^2*c[2]-2*f[2]*a[2]^
2*a[0]*c[3]-2*f[3]*a[3]*a[2]^2*c[1]+2*f[4]*a[3]^2*a[0]*c[3]-2*f[0]*a[2]^2*a[1]
*c[0]+2*f[0]*a[3]*a[1]^2*c[0]-4*f[0]*a[1]^2*a[0]*c[3]-2*f[0]*a[2]^2*a[0]*c[1]+
4*f[0]*a[2]*a[0]^2*c[3]-a[3]^2*c[3]*c[0]-a[3]*a[0]*c[3]^2-f[3]*a[2]^3*c[2]+a[3
]*a[2]*c[2]^2+a[2]^2*c[3]*c[2]+a[3]^2*c[2]*c[1]+f[4]*a[2]^3*c[3]+f[2]*a[2]^3*c
[1]+5*f[7]*a[3]^3*c[3]+2*f[5]*a[3]^3*c[1]-f[1]*a[3]*a[1]^2*c[1]+f[2]*a[3]*a[2]
^2*c[0]+f[1]*a[2]^2*a[0]*c[2]-f[4]*a[3]^2*a[1]*c[2]+f[3]*a[3]^2*a[1]*c[1]-f[2]
*a[3]^2*a[0]*c[1]-3*a[3]*a[1]*c[3]*c[2]-f[1]*a[2]*a[1]^2*c[2]+f[1]*a[3]^2*a[0]
*c[0]+f[1]*a[3]*a[0]^2*c[3]+f[4]*a[3]*a[2]^2*c[2]-f[3]*a[3]^2*a[2]*c[0]-f[1]*a
[2]*a[1]*a[0]*c[3]+3*f[2]*a[3]*a[2]*a[1]*c[1]+3*f[3]*a[3]*a[2]*a[0]*c[3]-3*f[4
]*a[3]*a[2]*a[1]*c[3]+2*f[0]*a[3]*a[1]*a[0]*c[1]-2*f[1]*a[3]*a[2]*a[1]*c[0]-a[
2]^4*f[5]*f[2]+2*a[2]^4*f[7]*f[0]+2*a[3]^2*a[2]^2*f[5]*f[4]-a[2]^4*f[3]*f[4]-4
*a[3]*a[2]*a[1]^2*f[6]*f[0]+a[3]*a[2]*a[1]^2*f[4]*f[2]-a[3]^2*a[2]^2*f[7]*f[2]
+4*a[3]*a[2]^2*a[1]*f[6]*f[1]+2*a[3]*a[2]^2*a[1]*f[7]*f[0]-8*a[3]^3*a[1]*f[7]*
f[2]-4*a[3]*a[2]^2*a[1]*f[5]*f[2]-2*a[3]^3*a[1]*f[5]*f[4]-2*a[3]*a[1]^3*f[5]*f
[0]+a[3]*a[1]^3*f[4]*f[1]+2*a[3]^2*a[2]^2*f[6]*f[3]+2*a[3]*a[2]^2*a[1]*f[3]*f[
4]+10*a[3]^2*a[1]^2*f[5]*f[2]+4*a[3]^2*a[2]*a[1]*f[7]*f[1]-4*a[3]^2*a[2]*a[1]*
f[6]*f[2]-a[3]^2*a[1]^2*f[3]*f[4]-4*a[3]^2*a[1]^2*f[7]*f[0]+3*a[3]^3*a[2]*f[7]
*f[3]+4*a[3]^3*a[2]*f[5]^2-2*a[3]*a[2]^3*f[6]*f[2]-a[3]*a[2]^3*f[3]*f[5]+2*a[3
]*a[2]^3*f[7]*f[1]-a[2]^2*a[1]^2*f[4]*f[1]+2*a[2]^2*a[1]^2*f[5]*f[0]+4*a[2]^3*
a[1]*f[6]*f[0]-a[2]^3*a[1]*f[4]*f[2]+a[2]^2*a[1]*f[3]*f[1]*a[0]+2*f[2]*f[1]*a[
2]*a[1]^2*a[0]+a[2]^2*a[1]*f[2]^2*a[0]+a[2]^3*f[4]*f[1]*a[0]-f[3]*f[1]*a[3]*a[
1]^2*a[0]-3*f[7]*f[1]*a[3]^3*a[0]-f[1]^2*a[2]*a[1]*a[0]^2-f[2]^2*a[3]*a[2]*a[0
]^2-f[4]*f[2]*a[3]^2*a[1]*a[0]+a[3]*a[2]^2*f[4]*f[2]*a[0]-2*f[6]*f[1]*a[3]^2*a
[2]*a[0]-f[2]*f[1]*a[3]*a[1]*a[0]^2+a[3]*a[2]^2*f[5]*f[1]*a[0]-a[3]*a[2]*a[1]*
f[4]*f[1]*a[0]-a[3]*a[2]*a[1]*f[3]*f[2]*a[0]-f[2]*f[1]*a[2]^2*a[0]^2+a[2]^3*f[
3]*f[2]*a[0]+f[1]^2*a[1]^3*a[0]:
eqn[4] :=
-4*a[3]*a[0]*c[3]*c[2]+4*f[4]*a[3]*a[2]^2*c[1]+4*f[5]*a[3]^2*a[2]*c[1]-4*f[0]*
a[2]^2*a[0]*c[0]-4*f[0]*a[1]*a[0]^2*c[3]+4*f[5]*a[3]*a[2]^2*c[2]-12*f[5]*a[3]^
2*a[0]*c[3]+4*f[1]*a[2]^2*a[0]*c[1]-4*f[1]*a[2]*a[0]^2*c[3]+a[2]^2*c[2]^2+a[3]
^2*c[1]^2+2*f[4]*a[2]^3*c[2]+2*f[2]*a[3]*a[0]^2*c[3]-2*f[4]*a[3]^2*a[1]*c[1]+2
*a[3]*a[2]*c[2]*c[1]-2*f[2]*a[3]^2*a[0]*c[0]+2*f[4]*a[3]^2*a[2]*c[0]+2*f[2]*a[
3]*a[1]*a[0]*c[2]-2*f[2]*a[2]^2*a[0]*c[2]-2*f[1]*a[3]*a[1]*a[0]*c[1]+2*f[1]*a[
2]*a[1]*a[0]*c[2]-6*f[4]*a[3]*a[2]*a[0]*c[3]+4*f[0]*a[3]*a[1]*a[0]*c[0]+4*a[3]
^2*a[2]^2*f[5]^2-4*a[3]^2*a[2]^2*f[4]*f[6]-6*f[4]*f[7]*a[3]^3*a[2]+2*f[4]*f[5]
*a[3]*a[2]^3-2*f[4]^2*a[3]*a[2]^2*a[1]+f[4]^2*a[3]^2*a[1]^2+f[4]^2*a[2]^4+4*f[
2]*f[6]*a[3]^2*a[2]*a[0]-12*a[3]^2*a[1]*f[0]*f[7]*a[0]-4*a[3]*a[1]^2*f[0]*f[5]
*a[0]+2*a[3]*a[1]^2*f[4]*f[1]*a[0]-8*a[3]*a[2]*a[1]*f[0]*f[6]*a[0]+8*a[3]^2*a[
1]*f[2]*f[5]*a[0]+2*a[3]*a[2]*a[1]*f[4]*f[2]*a[0]+8*a[2]^3*f[0]*f[6]*a[0]+2*f[
1]*f[2]*a[2]*a[1]*a[0]^2+4*a[2]^2*a[1]*f[0]*f[5]*a[0]-2*a[2]^2*a[1]*f[4]*f[1]*
a[0]-4*a[2]^3*f[1]*f[5]*a[0]-2*a[2]^3*f[4]*f[2]*a[0]-6*a[3]*a[2]^2*f[2]*f[5]*a
[0]+12*a[3]*a[2]^2*f[0]*f[7]*a[0]+6*f[2]*f[7]*a[3]^3*a[0]+8*a[3]*a[2]*a[1]*f[1
]*f[5]*a[0]+f[2]^2*a[2]^2*a[0]^2+f[1]^2*a[1]^2*a[0]^2:
eqn[5] :=
-2*f[3]*f[2]*a[2]^2*a[1]*a[0]-8*a[3]*a[0]*c[3]*c[2]+2*f[4]*a[3]*a[2]^2*c[1]+4*
f[0]*a[2]^2*a[0]*c[0]-8*f[0]*a[1]*a[0]^2*c[3]+6*f[5]*a[3]*a[2]^2*c[2]-16*f[5]*
a[3]^2*a[0]*c[3]-4*f[1]*a[2]^2*a[0]*c[1]+4*a[3]*a[1]*c[3]*c[1]-4*f[3]*a[3]*a[1
]^2*c[2]-4*f[4]*a[3]*a[1]^2*c[3]+8*f[0]*a[2]*a[0]^2*c[2]-4*f[0]*a[2]*a[1]^2*c[
0]+4*f[0]*a[3]*a[0]^2*c[1]-4*f[0]*a[1]^2*a[0]*c[2]-6*f[5]*a[3]^2*a[1]*c[2]+4*f
[3]*a[3]^2*a[0]*c[1]+a[2]^2*c[2]^2-3*a[3]^2*c[1]^2+2*f[4]*a[2]^3*c[2]+2*a[3]^2
*c[2]*c[0]-2*a[2]*a[0]*c[3]^2+2*f[3]*a[2]^3*c[1]+4*f[6]*a[3]^3*c[1]-4*f[7]*a[3
]^3*c[2]+2*f[4]*a[3]^2*a[1]*c[1]+2*f[2]*a[3]^2*a[0]*c[0]+4*f[4]*a[3]^2*a[2]*c[
0]+8*f[2]*a[3]*a[1]*a[0]*c[2]-2*f[2]*a[2]^2*a[0]*c[2]-2*f[1]*a[3]*a[1]*a[0]*c[
1]-4*f[1]*a[2]*a[1]*a[0]*c[2]-6*f[4]*a[3]*a[2]*a[0]*c[3]+4*f[0]*a[3]*a[1]*a[0]
*c[0]+2*a[2]*a[1]*c[3]*c[2]+2*f[5]*a[3]*a[2]*a[1]*c[3]+2*f[2]*a[2]*a[1]*a[0]*c
[3]+2*f[7]*a[3]^2*a[2]*c[3]+2*f[4]*a[3]^2*a[0]*c[2]-2*f[3]*a[3]^2*a[1]*c[0]-2*
f[1]*a[3]*a[1]^2*c[0]+2*f[1]*a[3]*a[0]^2*c[2]+2*f[1]*a[2]*a[1]^2*c[1]-2*f[2]*a
[2]*a[1]^2*c[2]+2*f[4]*a[2]^2*a[1]*c[3]+2*f[3]*a[3]*a[2]^2*c[0]+2*f[3]*a[2]^2*
a[0]*c[3]-6*f[3]*a[3]*a[2]*a[1]*c[1]+6*f[3]*a[3]*a[2]*a[0]*c[2]+2*a[3]*a[2]*a[
1]*f[3]^2*a[0]-2*f[1]*f[2]*a[3]*a[0]^3+12*a[3]^2*a[2]*f[3]*f[5]*a[0]-12*a[3]^3
*a[1]*f[5]^2+8*a[3]^3*a[1]*f[7]*f[3]+2*a[3]*a[2]*f[3]*f[2]*a[0]^2+2*a[3]*a[2]^
2*f[3]*f[4]*a[0]+8*a[3]*a[2]^2*f[6]*f[1]*a[0]-2*a[3]^2*a[2]*f[7]*f[1]*a[0]-2*a
[3]*a[2]*f[1]*f[4]*a[0]^2+4*a[3]*a[2]*a[1]^2*f[6]*f[1]+2*a[3]*a[2]*a[1]^2*f[3]
*f[4]-6*a[3]*a[2]*a[1]^2*f[5]*f[2]+8*a[3]*a[2]*a[1]^2*f[0]*f[7]+4*a[3]*a[2]^2*
a[1]*f[3]*f[5]+4*a[3]*a[2]^2*a[1]*f[7]*f[1]-8*a[3]^2*a[2]^2*f[7]*f[3]+4*a[2]*a
[1]^3*f[0]*f[5]-2*a[2]^4*f[3]*f[5]+2*a[3]^2*a[2]*a[1]*f[7]*f[2]-4*a[3]^2*a[2]*
a[1]*f[4]*f[5]+4*a[3]^2*a[2]*a[1]*f[6]*f[3]-2*f[1]*f[3]*a[3]*a[1]*a[0]^2-2*a[3
]^2*a[1]*f[3]*f[4]*a[0]-4*a[3]^2*a[1]*f[6]*f[1]*a[0]+16*a[3]*a[2]*f[0]*f[5]*a[
0]^2-2*f[1]*f[3]*a[2]*a[1]^2*a[0]+12*a[3]^2*a[2]^2*f[5]^2-4*a[3]^2*a[2]^2*f[4]
*f[6]-12*f[4]*f[7]*a[3]^3*a[2]+4*f[4]*f[5]*a[3]*a[2]^3-2*f[4]^2*a[3]*a[2]^2*a[
1]+f[4]^2*a[3]^2*a[1]^2+f[4]^2*a[2]^4+2*f[5]*f[1]*a[3]*a[1]^3+4*f[7]*f[5]*a[3]
^4-4*a[3]*a[2]^3*f[6]*f[3]-8*a[3]^2*a[1]*f[0]*f[7]*a[0]-16*a[3]*a[1]^2*f[0]*f[
5]*a[0]+4*a[3]*a[1]^2*f[4]*f[1]*a[0]-16*a[3]*a[2]*a[1]*f[0]*f[6]*a[0]+22*a[3]^
2*a[1]*f[2]*f[5]*a[0]+6*a[3]*a[2]*a[1]*f[4]*f[2]*a[0]+4*f[1]*f[2]*a[2]*a[1]*a[
0]^2+4*a[2]^3*f[1]*f[5]*a[0]-2*a[2]^3*f[4]*f[2]*a[0]-6*a[3]*a[2]^2*f[2]*f[5]*a
[0]-16*a[3]*a[2]^2*f[0]*f[7]*a[0]-8*f[2]*f[7]*a[3]^3*a[0]-6*a[3]*a[2]*a[1]*f[1
]*f[5]*a[0]+f[2]^2*a[2]^2*a[0]^2+3*f[1]^2*a[1]^2*a[0]^2-4*a[3]^3*a[1]*f[4]*f[6
]+8*a[3]^3*a[2]*f[6]*f[5]-2*a[2]*a[1]^3*f[1]*f[4]-2*a[2]^3*a[1]*f[3]*f[4]+4*a[
2]^3*a[1]*f[0]*f[7]+8*a[2]^2*a[1]^2*f[0]*f[6]-2*a[2]^2*a[1]^2*f[5]*f[1]-2*a[2]
^2*a[1]^2*f[2]*f[4]+4*a[3]^2*a[1]^2*f[7]*f[1]-10*a[3]^2*a[1]^2*f[3]*f[5]-2*f[1
]^2*a[2]*a[0]^3-2*a[2]^3*f[3]^2*a[0]+4*a[2]^2*f[1]*f[3]*a[0]^2-2*a[3]^2*f[2]*f
[4]*a[0]^2+4*a[3]^3*f[4]*f[5]*a[0]+4*a[3]^2*f[5]*f[1]*a[0]^2:
eqn[6] :=
2*a[3]*a[0]*c[3]*c[2]-4*f[4]*a[3]*a[2]^2*c[1]-4*f[5]*a[3]^2*a[2]*c[1]+4*f[0]*a
[2]^2*a[0]*c[0]+4*f[0]*a[1]*a[0]^2*c[3]-6*f[5]*a[3]*a[2]^2*c[2]+12*f[5]*a[3]^2
*a[0]*c[3]-4*f[1]*a[2]^2*a[0]*c[1]+4*f[1]*a[2]*a[0]^2*c[3]+4*f[5]*a[3]^2*a[1]*
c[2]-4*f[6]*a[3]^2*a[2]*c[2]-a[2]^2*c[2]^2-a[3]^2*c[1]^2-2*f[4]*a[2]^3*c[2]+2*
a[3]^2*c[2]*c[0]-6*f[7]*a[3]^3*c[2]-2*f[2]*a[3]*a[0]^2*c[3]+2*f[4]*a[3]^2*a[1]
*c[1]+2*f[2]*a[3]^2*a[0]*c[0]-2*f[4]*a[3]^2*a[2]*c[0]-2*f[2]*a[3]*a[1]*a[0]*c[
2]+2*f[2]*a[2]^2*a[0]*c[2]+2*f[1]*a[3]*a[1]*a[0]*c[1]-2*f[1]*a[2]*a[1]*a[0]*c[
2]+6*f[4]*a[3]*a[2]*a[0]*c[3]-4*f[0]*a[3]*a[1]*a[0]*c[0]+2*a[3]*a[1]*c[2]^2-4*
a[3]^2*a[2]^2*f[5]^2+4*a[3]^2*a[2]^2*f[4]*f[6]+6*f[4]*f[7]*a[3]^3*a[2]-2*f[4]*
f[5]*a[3]*a[2]^3+2*f[4]^2*a[3]*a[2]^2*a[1]-f[4]^2*a[3]^2*a[1]^2-f[4]^2*a[2]^4-\
4*f[2]*f[6]*a[3]^2*a[2]*a[0]+12*a[3]^2*a[1]*f[0]*f[7]*a[0]+4*a[3]*a[1]^2*f[0]*
f[5]*a[0]-2*a[3]*a[1]^2*f[4]*f[1]*a[0]+8*a[3]*a[2]*a[1]*f[0]*f[6]*a[0]-8*a[3]^
2*a[1]*f[2]*f[5]*a[0]-2*a[3]*a[2]*a[1]*f[4]*f[2]*a[0]-8*a[2]^3*f[0]*f[6]*a[0]-\
2*f[1]*f[2]*a[2]*a[1]*a[0]^2-4*a[2]^2*a[1]*f[0]*f[5]*a[0]+2*a[2]^2*a[1]*f[4]*f
[1]*a[0]+4*a[2]^3*f[1]*f[5]*a[0]+2*a[2]^3*f[4]*f[2]*a[0]+6*a[3]*a[2]^2*f[2]*f[
5]*a[0]-12*a[3]*a[2]^2*f[0]*f[7]*a[0]-6*f[2]*f[7]*a[3]^3*a[0]-8*a[3]*a[2]*a[1]
*f[1]*f[5]*a[0]-f[2]^2*a[2]^2*a[0]^2-f[1]^2*a[1]^2*a[0]^2:
eqn[7] :=
2*f[3]*f[2]*a[2]^2*a[1]*a[0]+8*a[3]*a[0]*c[3]*c[2]-2*f[4]*a[3]*a[2]^2*c[1]-4*f
[0]*a[2]^2*a[0]*c[0]+8*f[0]*a[1]*a[0]^2*c[3]-6*f[5]*a[3]*a[2]^2*c[2]+16*f[5]*a
[3]^2*a[0]*c[3]+4*f[1]*a[2]^2*a[0]*c[1]-4*a[3]*a[1]*c[3]*c[1]+4*f[3]*a[3]*a[1]
^2*c[2]+4*f[4]*a[3]*a[1]^2*c[3]-8*f[0]*a[2]*a[0]^2*c[2]+4*f[0]*a[2]*a[1]^2*c[0
]-4*f[0]*a[3]*a[0]^2*c[1]+4*f[0]*a[1]^2*a[0]*c[2]+6*f[5]*a[3]^2*a[1]*c[2]-4*f[
3]*a[3]^2*a[0]*c[1]-4*f[6]*a[3]*a[2]^2*c[3]-a[2]^2*c[2]^2+3*a[3]^2*c[1]^2-2*f[
4]*a[2]^3*c[2]-2*a[3]^2*c[2]*c[0]-2*f[3]*a[2]^3*c[1]-4*f[6]*a[3]^3*c[1]+4*f[7]
*a[3]^3*c[2]-2*f[4]*a[3]^2*a[1]*c[1]-2*f[2]*a[3]^2*a[0]*c[0]-4*f[4]*a[3]^2*a[2
]*c[0]-8*f[2]*a[3]*a[1]*a[0]*c[2]+2*f[2]*a[2]^2*a[0]*c[2]+2*f[1]*a[3]*a[1]*a[0
]*c[1]+4*f[1]*a[2]*a[1]*a[0]*c[2]+6*f[4]*a[3]*a[2]*a[0]*c[3]-4*f[0]*a[3]*a[1]*
a[0]*c[0]+2*f[5]*a[3]*a[2]*a[1]*c[3]-2*f[2]*a[2]*a[1]*a[0]*c[3]-8*f[7]*a[3]^2*
a[2]*c[3]-2*f[4]*a[3]^2*a[0]*c[2]+2*f[3]*a[3]^2*a[1]*c[0]+2*f[1]*a[3]*a[1]^2*c
[0]-2*f[1]*a[3]*a[0]^2*c[2]-2*f[1]*a[2]*a[1]^2*c[1]+2*f[2]*a[2]*a[1]^2*c[2]-2*
f[4]*a[2]^2*a[1]*c[3]-2*f[3]*a[3]*a[2]^2*c[0]-2*f[3]*a[2]^2*a[0]*c[3]+6*f[3]*a
[3]*a[2]*a[1]*c[1]-6*f[3]*a[3]*a[2]*a[0]*c[2]-2*f[5]*a[2]^3*c[3]+2*a[2]^2*c[3]
*c[1]+2*a[3]*a[2]*c[3]*c[0]-2*a[3]*a[2]*a[1]*f[3]^2*a[0]+2*f[1]*f[2]*a[3]*a[0]
^3-12*a[3]^2*a[2]*f[3]*f[5]*a[0]+12*a[3]^3*a[1]*f[5]^2-8*a[3]^3*a[1]*f[7]*f[3]
-2*a[3]*a[2]*f[3]*f[2]*a[0]^2-2*a[3]*a[2]^2*f[3]*f[4]*a[0]-8*a[3]*a[2]^2*f[6]*
f[1]*a[0]+2*a[3]^2*a[2]*f[7]*f[1]*a[0]+2*a[3]*a[2]*f[1]*f[4]*a[0]^2-4*a[3]*a[2
]*a[1]^2*f[6]*f[1]-2*a[3]*a[2]*a[1]^2*f[3]*f[4]+6*a[3]*a[2]*a[1]^2*f[5]*f[2]-8
*a[3]*a[2]*a[1]^2*f[0]*f[7]-4*a[3]*a[2]^2*a[1]*f[3]*f[5]-4*a[3]*a[2]^2*a[1]*f[
7]*f[1]+8*a[3]^2*a[2]^2*f[7]*f[3]-4*a[2]*a[1]^3*f[0]*f[5]+2*a[2]^4*f[3]*f[5]-2
*a[3]^2*a[2]*a[1]*f[7]*f[2]+4*a[3]^2*a[2]*a[1]*f[4]*f[5]-4*a[3]^2*a[2]*a[1]*f[
6]*f[3]+2*f[1]*f[3]*a[3]*a[1]*a[0]^2+2*a[3]^2*a[1]*f[3]*f[4]*a[0]+4*a[3]^2*a[1
]*f[6]*f[1]*a[0]-16*a[3]*a[2]*f[0]*f[5]*a[0]^2+2*f[1]*f[3]*a[2]*a[1]^2*a[0]-12
*a[3]^2*a[2]^2*f[5]^2+4*a[3]^2*a[2]^2*f[4]*f[6]+12*f[4]*f[7]*a[3]^3*a[2]-4*f[4
]*f[5]*a[3]*a[2]^3+2*f[4]^2*a[3]*a[2]^2*a[1]-f[4]^2*a[3]^2*a[1]^2-f[4]^2*a[2]^
4-2*f[5]*f[1]*a[3]*a[1]^3-4*f[7]*f[5]*a[3]^4+4*a[3]*a[2]^3*f[6]*f[3]+8*a[3]^2*
a[1]*f[0]*f[7]*a[0]+16*a[3]*a[1]^2*f[0]*f[5]*a[0]-4*a[3]*a[1]^2*f[4]*f[1]*a[0]
+16*a[3]*a[2]*a[1]*f[0]*f[6]*a[0]-22*a[3]^2*a[1]*f[2]*f[5]*a[0]-6*a[3]*a[2]*a[
1]*f[4]*f[2]*a[0]-4*f[1]*f[2]*a[2]*a[1]*a[0]^2-4*a[2]^3*f[1]*f[5]*a[0]+2*a[2]^
3*f[4]*f[2]*a[0]+6*a[3]*a[2]^2*f[2]*f[5]*a[0]+16*a[3]*a[2]^2*f[0]*f[7]*a[0]+8*
f[2]*f[7]*a[3]^3*a[0]+6*a[3]*a[2]*a[1]*f[1]*f[5]*a[0]-f[2]^2*a[2]^2*a[0]^2-3*f
[1]^2*a[1]^2*a[0]^2+4*a[3]^3*a[1]*f[4]*f[6]-8*a[3]^3*a[2]*f[6]*f[5]+2*a[2]*a[1
]^3*f[1]*f[4]+2*a[2]^3*a[1]*f[3]*f[4]-4*a[2]^3*a[1]*f[0]*f[7]-8*a[2]^2*a[1]^2*
f[0]*f[6]+2*a[2]^2*a[1]^2*f[5]*f[1]+2*a[2]^2*a[1]^2*f[2]*f[4]-4*a[3]^2*a[1]^2*
f[7]*f[1]+10*a[3]^2*a[1]^2*f[3]*f[5]+2*f[1]^2*a[2]*a[0]^3+2*a[2]^3*f[3]^2*a[0]
-4*a[2]^2*f[1]*f[3]*a[0]^2+2*a[3]^2*f[2]*f[4]*a[0]^2-4*a[3]^3*f[4]*f[5]*a[0]-4
*a[3]^2*f[5]*f[1]*a[0]^2:
eqn[8] :=
-2*a[1]*a[0]*c[1]*c[0]-12*f[5]*a[3]*a[0]^2*c[0]-4*f[5]*a[2]*a[0]^2*c[1]+2*f[5]
*a[1]^2*a[0]*c[1]-4*f[7]*a[3]*a[1]^2*c[0]-2*f[7]*a[2]^2*a[1]*c[0]+28*f[7]*a[2]
*a[0]^2*c[3]-26*f[7]*a[2]^2*a[0]*c[1]+12*f[7]*a[3]*a[0]^2*c[2]-4*f[7]*a[1]^2*a
[0]*c[3]+8*f[6]*a[2]*a[0]^2*c[2]+12*f[6]*a[2]^2*a[0]*c[0]-4*f[6]*a[2]*a[1]^2*c
[0]-4*f[6]*a[1]^2*a[0]*c[2]+a[0]^2*c[1]^2+a[1]^2*c[0]^2-4*a[0]^2*c[2]*c[0]-2*f
[5]*a[1]^3*c[0]-4*a[2]*a[0]*c[0]^2+8*f[5]*a[2]*a[1]*a[0]*c[0]-24*f[7]*a[2]*a[1
]*a[0]*c[2]+8*f[7]*a[3]*a[1]*a[0]*c[1]+f[5]^2*a[1]^4+4*f[7]*f[5]*a[3]*a[1]^3+8
*f[6]*f[7]*a[3]*a[2]*a[1]^2+4*f[7]^2*a[3]*a[2]^2*a[1]+4*f[7]^2*a[3]^2*a[1]^2+4
*f[5]*f[6]*a[2]*a[1]^3+4*f[6]*f[7]*a[2]^3*a[1]+4*a[2]^2*a[1]^2*f[6]^2+2*a[2]^2
*a[1]^2*f[7]*f[5]+f[7]^2*a[2]^4+4*f[5]^2*a[2]^2*a[0]^2+36*f[7]^2*a[3]^2*a[2]*a
[0]+12*f[6]*f[7]*a[3]*a[2]^2*a[0]+24*f[5]*f[6]*a[3]*a[2]*a[0]^2-12*f[5]*f[6]*a
[3]*a[1]^2*a[0]-72*f[7]*f[5]*a[3]*a[2]*a[1]*a[0]-8*f[5]*f[6]*a[2]^2*a[1]*a[0]+
24*a[2]^3*f[7]*f[5]*a[0]-4*f[5]^2*a[2]*a[1]^2*a[0]+36*f[7]*f[5]*a[3]^2*a[0]^2-\
8*a[2]^3*f[6]^2*a[0]:
eqn[9] :=
-2*a[3]*a[1]*c[2]*c[1]+6*f[5]*a[3]*a[2]^2*c[1]-5*f[5]*a[3]^2*a[1]*c[1]+2*f[6]*
a[3]^2*a[2]*c[1]+2*f[4]*a[3]*a[2]^2*c[0]+2*f[4]*a[3]*a[1]^2*c[2]-a[3]*a[2]*c[1
]^2-a[2]*a[1]*c[2]^2-a[3]^2*c[1]*c[0]+4*f[7]*a[3]^3*c[1]-f[5]*a[3]*a[2]*a[0]*c
[3]+a[2]*a[0]*c[3]*c[2]-f[1]*a[1]*a[0]^2*c[3]+f[1]*a[1]^2*a[0]*c[2]+f[1]*a[3]*
a[0]^2*c[1]-f[4]*a[2]^2*a[0]*c[3]-f[3]*a[3]^2*a[0]*c[0]+f[3]*a[3]*a[0]^2*c[3]+
f[7]*a[3]^2*a[2]*c[2]+f[4]*a[3]^2*a[1]*c[0]+f[4]*a[3]^2*a[0]*c[1]-f[2]*a[2]*a[
0]^2*c[3]+f[1]*a[2]*a[0]^2*c[2]-f[3]*a[2]^2*a[0]*c[2]+f[3]*a[3]*a[1]*a[0]*c[2]
+f[2]*a[2]*a[1]*a[0]*c[2]+2*f[4]*a[2]^3*c[1]+2*a[3]*a[0]*c[2]^2+2*f[0]*a[2]*a[
0]^2*c[1]+10*f[5]*a[3]^2*a[0]*c[2]+5*f[5]*a[3]^2*a[2]*c[0]+4*f[0]*a[1]*a[0]^2*
c[2]-2*f[2]*a[3]*a[0]^2*c[2]+3*f[4]*a[3]*a[2]*a[0]*c[2]+2*f[1]*a[3]*a[1]*a[0]*
c[0]+2*f[0]*a[2]*a[1]*a[0]*c[0]-5*a[3]*a[2]^3*f[5]^2-4*a[3]*a[2]^3*f[6]*f[4]-2
*f[4]*f[5]*a[3]*a[2]^2*a[1]+4*a[3]^2*a[2]*a[1]*f[5]^2-10*a[3]^2*a[2]^2*f[6]*f[
5]-5*a[3]^2*a[2]^2*f[4]*f[7]+5*f[4]*f[5]*a[3]^2*a[1]^2-2*a[3]^2*a[2]*a[1]*f[6]
*f[4]+f[4]^2*a[3]*a[2]*a[1]^2-13*f[7]*f[5]*a[3]^3*a[2]-4*f[4]*f[7]*a[3]^3*a[1]
-f[4]^2*a[2]^3*a[1]-2*f[4]*f[5]*a[2]^4-f[1]^2*a[1]*a[0]^3+f[1]*f[5]*a[3]*a[1]^
2*a[0]-7*a[3]^2*a[1]*f[7]*f[1]*a[0]-2*a[3]*a[1]*f[1]*f[4]*a[0]^2-a[3]^2*a[1]*f
[4]^2*a[0]-f[2]*f[4]*a[3]*a[2]*a[0]^2+2*a[3]*a[2]^2*f[7]*f[1]*a[0]+3*a[3]^3*f[
3]*f[7]*a[0]+a[3]*a[2]^2*f[4]^2*a[0]+12*a[3]*a[1]*f[5]*f[0]*a[0]^2+4*a[3]^2*a[
1]*f[5]*f[3]*a[0]+a[3]*a[2]*a[1]*f[3]*f[4]*a[0]+3*a[3]*a[2]*a[1]*f[2]*f[5]*a[0
]-4*a[3]*a[2]*a[1]*f[6]*f[1]*a[0]-8*a[3]*a[2]*a[1]*f[7]*f[0]*a[0]-3*a[3]*a[2]^
2*f[5]*f[3]*a[0]+2*a[3]^2*a[2]*f[6]*f[3]*a[0]+6*a[3]^2*a[2]*f[4]*f[5]*a[0]+a[3
]^2*a[2]*f[2]*f[7]*a[0]-6*f[2]*f[5]*a[3]^2*a[0]^2+a[2]*a[1]^2*f[1]*f[4]*a[0]-2
*a[2]*a[1]^2*f[5]*f[0]*a[0]+f[3]*f[1]*a[2]*a[1]*a[0]^2+a[2]^2*a[1]*f[2]*f[4]*a
[0]-4*a[2]^2*a[1]*f[6]*f[0]*a[0]-4*a[2]^2*f[5]*f[0]*a[0]^2+a[2]^2*f[1]*f[4]*a[
0]^2+a[2]^2*f[2]*f[3]*a[0]^2-f[1]*f[2]*a[2]*a[0]^3-a[2]^3*f[3]*f[4]*a[0]+2*a[2
]^3*f[7]*f[0]*a[0]+12*a[3]^3*f[5]^2*a[0]:
eqn[10] :=
a[3]*a[1]*c[2]*c[1]+5*f[5]*a[3]*a[2]^2*c[1]+f[5]*a[3]^2*a[1]*c[1]-4*f[6]*a[3]^
2*a[2]*c[1]+4*f[4]*a[3]*a[2]^2*c[0]+f[4]*a[3]*a[1]^2*c[2]+a[3]*a[2]*c[1]^2-a[2
]*a[1]*c[2]^2+3*a[3]^2*c[1]*c[0]-8*f[7]*a[3]^3*c[1]-8*f[5]*a[3]*a[2]*a[0]*c[3]
-2*f[1]*a[1]*a[0]^2*c[3]+3*f[1]*a[1]^2*a[0]*c[2]+f[1]*a[3]*a[0]^2*c[1]-2*f[4]*
a[2]^2*a[0]*c[3]-3*f[3]*a[3]^2*a[0]*c[0]-f[3]*a[3]*a[0]^2*c[3]-4*f[7]*a[3]^2*a
[2]*c[2]-f[4]*a[3]^2*a[1]*c[0]+f[4]*a[3]^2*a[0]*c[1]-2*f[2]*a[2]*a[0]^2*c[3]+f
[3]*a[3]*a[1]*a[0]*c[2]+4*f[2]*a[2]*a[1]*a[0]*c[2]+2*f[4]*a[2]^3*c[1]+3*a[3]*a
[0]*c[2]^2+f[1]*a[1]^3*c[1]-a[1]*a[0]*c[3]^2+a[1]^2*c[3]*c[2]-2*f[0]*a[1]^3*c[
0]+14*f[5]*a[3]^2*a[0]*c[2]+10*f[5]*a[3]^2*a[2]*c[0]+4*f[0]*a[1]*a[0]^2*c[2]-4
*f[2]*a[3]*a[0]^2*c[2]+2*a[3]*a[2]*c[2]*c[0]+2*f[0]*a[1]^2*a[0]*c[1]-4*f[0]*a[
3]*a[0]^2*c[0]+4*f[5]*a[3]*a[1]^2*c[3]+2*f[2]*a[3]*a[1]^2*c[0]+2*f[2]*a[2]^2*a
[0]*c[1]-4*f[6]*a[3]^2*a[0]*c[3]-2*f[6]*a[3]*a[2]^2*c[2]+4*f[4]*a[3]*a[2]*a[0]
*c[2]+5*f[1]*a[3]*a[1]*a[0]*c[0]+8*f[0]*a[2]*a[1]*a[0]*c[0]-a[3]*a[1]*c[3]*c[0
]+f[4]*a[2]*a[1]^2*c[3]+f[7]*a[3]*a[2]^2*c[3]+f[2]*a[2]*a[1]^2*c[1]+f[7]*a[3]^
2*a[1]*c[3]-f[3]*a[3]*a[1]^2*c[1]-f[3]*a[2]*a[1]^2*c[2]+f[3]*a[3]*a[2]*a[1]*c[
0]+2*f[3]*a[2]*a[1]*a[0]*c[3]-3*f[2]*a[3]*a[1]*a[0]*c[1]+2*f[6]*a[3]*a[2]*a[1]
*c[3]-2*a[3]*a[2]^2*a[1]*f[6]*f[3]-6*a[3]*a[2]^3*f[5]^2-6*a[3]*a[2]^3*f[6]*f[4
]-2*f[4]*f[5]*a[3]*a[2]^2*a[1]+4*a[3]^2*a[2]*a[1]*f[5]^2-16*a[3]^2*a[2]^2*f[6]
*f[5]-11*a[3]^2*a[2]^2*f[4]*f[7]+3*f[4]*f[5]*a[3]^2*a[1]^2+f[4]^2*a[3]*a[2]*a[
1]^2-26*f[7]*f[5]*a[3]^3*a[2]+2*f[4]*f[7]*a[3]^3*a[1]-f[4]^2*a[2]^3*a[1]-2*f[4
]*f[5]*a[2]^4-4*a[3]^2*a[1]^2*f[7]*f[2]+a[3]*a[2]*a[1]^2*f[7]*f[1]-2*a[3]^2*a[
2]*a[1]*f[3]*f[7]-3*a[3]*a[2]*a[1]^2*f[5]*f[3]-4*a[3]*a[2]*a[1]^2*f[6]*f[2]-a[
3]*a[2]^2*a[1]*f[7]*f[2]-f[1]^2*a[1]*a[0]^3+5*f[1]*f[5]*a[3]*a[1]^2*a[0]-16*a[
3]^2*a[1]*f[7]*f[1]*a[0]-2*a[3]*a[1]*f[1]*f[4]*a[0]^2-a[3]^2*a[1]*f[4]^2*a[0]-\
2*f[2]*f[4]*a[3]*a[2]*a[0]^2+a[3]*a[2]^2*f[7]*f[1]*a[0]+9*a[3]^3*f[3]*f[7]*a[0
]+a[3]*a[2]^2*f[4]^2*a[0]+12*a[3]*a[1]*f[5]*f[0]*a[0]^2+4*a[3]^2*a[1]*f[5]*f[3
]*a[0]+14*a[3]*a[2]*a[1]*f[2]*f[5]*a[0]-8*a[3]*a[2]*a[1]*f[6]*f[1]*a[0]-24*a[3
]*a[2]*a[1]*f[7]*f[0]*a[0]+a[3]*a[2]^2*f[5]*f[3]*a[0]+6*a[3]^2*a[2]*f[6]*f[3]*
a[0]+8*a[3]^2*a[2]*f[4]*f[5]*a[0]-10*f[2]*f[5]*a[3]^2*a[0]^2+3*a[2]*a[1]^2*f[1
]*f[4]*a[0]-8*a[2]*a[1]^2*f[5]*f[0]*a[0]+2*f[3]*f[1]*a[2]*a[1]*a[0]^2+2*a[2]^2
*a[1]*f[2]*f[4]*a[0]-12*a[2]^2*a[1]*f[6]*f[0]*a[0]-a[2]*a[1]^3*f[2]*f[4]-a[2]*
a[1]^3*f[1]*f[5]+4*a[2]*a[1]^3*f[6]*f[0]+16*a[3]^3*f[5]^2*a[0]+2*a[2]^2*a[1]^2
*f[7]*f[0]-a[2]^2*a[1]^2*f[2]*f[5]-a[2]^2*a[1]^2*f[3]*f[4]+4*a[3]*a[1]^3*f[7]*
f[0]+a[3]*a[1]^3*f[3]*f[4]-a[3]*a[2]^3*f[3]*f[7]-2*a[3]*a[1]^3*f[2]*f[5]+2*a[1
]^4*f[5]*f[0]-a[2]*a[1]^2*f[2]*f[3]*a[0]-a[2]^2*a[1]*f[3]^2*a[0]-2*f[2]*f[5]*a
[2]^3*a[0]-a[2]*a[1]*f[2]^2*a[0]^2-f[3]*f[1]*a[1]^3*a[0]-f[2]*f[1]*a[1]^2*a[0]
^2+f[2]^2*a[3]*a[0]^3-a[1]^4*f[1]*f[4]-4*a[3]*a[1]^2*f[6]*f[0]*a[0]-2*a[3]*a[2
]^2*f[6]*f[2]*a[0]-2*a[3]*a[2]*f[1]*f[5]*a[0]^2+8*a[3]*a[2]*f[6]*f[0]*a[0]^2+
12*a[3]^2*f[7]*f[0]*a[0]^2+2*a[3]*a[1]*f[2]*f[3]*a[0]^2+4*a[3]^2*a[1]*f[6]*f[2
]*a[0]+a[3]*a[1]^2*f[2]*f[4]*a[0]+a[3]*a[1]^2*f[3]^2*a[0]:
eqn[11] :=
-2*a[3]*a[1]*c[2]*c[1]+4*f[5]*a[3]*a[2]^2*c[1]-5*f[5]*a[3]^2*a[1]*c[1]+2*f[6]*
a[3]^2*a[2]*c[1]+2*f[4]*a[3]*a[2]^2*c[0]+2*f[4]*a[3]*a[1]^2*c[2]-a[3]*a[2]*c[1
]^2-a[3]^2*c[1]*c[0]+4*f[7]*a[3]^3*c[1]+f[5]*a[3]*a[2]*a[0]*c[3]-f[1]*a[1]*a[0
]^2*c[3]+f[1]*a[1]^2*a[0]*c[2]+f[1]*a[3]*a[0]^2*c[1]-f[4]*a[2]^2*a[0]*c[3]-f[3
]*a[3]^2*a[0]*c[0]+f[3]*a[3]*a[0]^2*c[3]-2*f[7]*a[3]^2*a[2]*c[2]+f[4]*a[3]^2*a
[1]*c[0]+f[4]*a[3]^2*a[0]*c[1]-f[2]*a[2]*a[0]^2*c[3]+f[1]*a[2]*a[0]^2*c[2]-f[3
]*a[2]^2*a[0]*c[2]+f[3]*a[3]*a[1]*a[0]*c[2]+f[2]*a[2]*a[1]*a[0]*c[2]+2*f[4]*a[
2]^3*c[1]+2*a[3]*a[0]*c[2]^2+a[2]^2*c[2]*c[1]-f[5]*a[2]^3*c[2]+2*f[0]*a[2]*a[0
]^2*c[1]+10*f[5]*a[3]^2*a[0]*c[2]+3*f[5]*a[3]^2*a[2]*c[0]+4*f[0]*a[1]*a[0]^2*c
[2]-2*f[2]*a[3]*a[0]^2*c[2]+a[3]*a[2]*c[2]*c[0]-2*f[6]*a[3]*a[2]^2*c[2]+3*f[4]
*a[3]*a[2]*a[0]*c[2]+2*f[1]*a[3]*a[1]*a[0]*c[0]+2*f[0]*a[2]*a[1]*a[0]*c[0]-3*a
[3]*a[2]^3*f[5]^2-4*a[3]*a[2]^3*f[6]*f[4]-2*f[4]*f[5]*a[3]*a[2]^2*a[1]-6*a[3]^
2*a[2]^2*f[6]*f[5]-5*a[3]^2*a[2]^2*f[4]*f[7]+5*f[4]*f[5]*a[3]^2*a[1]^2-2*a[3]^
2*a[2]*a[1]*f[6]*f[4]+f[4]^2*a[3]*a[2]*a[1]^2-7*f[7]*f[5]*a[3]^3*a[2]-4*f[4]*f
[7]*a[3]^3*a[1]-f[4]^2*a[2]^3*a[1]-2*f[4]*f[5]*a[2]^4-f[1]^2*a[1]*a[0]^3+f[1]*
f[5]*a[3]*a[1]^2*a[0]-7*a[3]^2*a[1]*f[7]*f[1]*a[0]-2*a[3]*a[1]*f[1]*f[4]*a[0]^
2-a[3]^2*a[1]*f[4]^2*a[0]-f[2]*f[4]*a[3]*a[2]*a[0]^2+2*a[3]*a[2]^2*f[7]*f[1]*a
[0]+3*a[3]^3*f[3]*f[7]*a[0]+a[3]*a[2]^2*f[4]^2*a[0]+12*a[3]*a[1]*f[5]*f[0]*a[0
]^2+4*a[3]^2*a[1]*f[5]*f[3]*a[0]+a[3]*a[2]*a[1]*f[3]*f[4]*a[0]+3*a[3]*a[2]*a[1
]*f[2]*f[5]*a[0]-4*a[3]*a[2]*a[1]*f[6]*f[1]*a[0]-8*a[3]*a[2]*a[1]*f[7]*f[0]*a[
0]-3*a[3]*a[2]^2*f[5]*f[3]*a[0]+2*a[3]^2*a[2]*f[6]*f[3]*a[0]+6*a[3]^2*a[2]*f[4
]*f[5]*a[0]+a[3]^2*a[2]*f[2]*f[7]*a[0]-6*f[2]*f[5]*a[3]^2*a[0]^2+a[2]*a[1]^2*f
[1]*f[4]*a[0]-2*a[2]*a[1]^2*f[5]*f[0]*a[0]+f[3]*f[1]*a[2]*a[1]*a[0]^2+a[2]^2*a
[1]*f[2]*f[4]*a[0]-4*a[2]^2*a[1]*f[6]*f[0]*a[0]-4*a[2]^2*f[5]*f[0]*a[0]^2+a[2]
^2*f[1]*f[4]*a[0]^2+a[2]^2*f[2]*f[3]*a[0]^2-f[1]*f[2]*a[2]*a[0]^3-a[2]^3*f[3]*
f[4]*a[0]+2*a[2]^3*f[7]*f[0]*a[0]+12*a[3]^3*f[5]^2*a[0]:
eqn[12] :=
-a[3]*a[1]*c[2]*c[1]-5*f[5]*a[3]*a[2]^2*c[1]-f[5]*a[3]^2*a[1]*c[1]+4*f[6]*a[3]
^2*a[2]*c[1]-4*f[4]*a[3]*a[2]^2*c[0]-f[4]*a[3]*a[1]^2*c[2]-a[3]*a[2]*c[1]^2+a[
2]*a[1]*c[2]^2-3*a[3]^2*c[1]*c[0]+8*f[7]*a[3]^3*c[1]+8*f[5]*a[3]*a[2]*a[0]*c[3
]+2*f[1]*a[1]*a[0]^2*c[3]-3*f[1]*a[1]^2*a[0]*c[2]-f[1]*a[3]*a[0]^2*c[1]+2*f[4]
*a[2]^2*a[0]*c[3]+3*f[3]*a[3]^2*a[0]*c[0]+f[3]*a[3]*a[0]^2*c[3]+4*f[7]*a[3]^2*
a[2]*c[2]+f[4]*a[3]^2*a[1]*c[0]-f[4]*a[3]^2*a[0]*c[1]+2*f[2]*a[2]*a[0]^2*c[3]-
f[3]*a[3]*a[1]*a[0]*c[2]-4*f[2]*a[2]*a[1]*a[0]*c[2]-2*f[4]*a[2]^3*c[1]-3*a[3]*
a[0]*c[2]^2-f[1]*a[1]^3*c[1]+2*f[0]*a[1]^3*c[0]-14*f[5]*a[3]^2*a[0]*c[2]-10*f[
5]*a[3]^2*a[2]*c[0]-4*f[0]*a[1]*a[0]^2*c[2]+4*f[2]*a[3]*a[0]^2*c[2]-2*a[3]*a[2
]*c[2]*c[0]-2*f[0]*a[1]^2*a[0]*c[1]+4*f[0]*a[3]*a[0]^2*c[0]-2*f[5]*a[3]*a[1]^2
*c[3]-2*f[2]*a[3]*a[1]^2*c[0]-2*f[2]*a[2]^2*a[0]*c[1]+4*f[6]*a[3]^2*a[0]*c[3]+
2*f[6]*a[3]*a[2]^2*c[2]-4*f[4]*a[3]*a[2]*a[0]*c[2]-5*f[1]*a[3]*a[1]*a[0]*c[0]-\
8*f[0]*a[2]*a[1]*a[0]*c[0]+2*a[3]*a[1]*c[3]*c[0]-f[4]*a[2]*a[1]^2*c[3]-f[7]*a[
3]*a[2]^2*c[3]-f[2]*a[2]*a[1]^2*c[1]-4*f[7]*a[3]^2*a[1]*c[3]+f[3]*a[3]*a[1]^2*
c[1]+f[3]*a[2]*a[1]^2*c[2]-f[3]*a[3]*a[2]*a[1]*c[0]-2*f[3]*a[2]*a[1]*a[0]*c[3]
+3*f[2]*a[3]*a[1]*a[0]*c[1]-4*f[6]*a[3]*a[2]*a[1]*c[3]+a[2]*a[1]*c[3]*c[1]-f[5
]*a[2]^2*a[1]*c[3]+2*a[3]*a[2]^2*a[1]*f[6]*f[3]+6*a[3]*a[2]^3*f[5]^2+6*a[3]*a[
2]^3*f[6]*f[4]+2*f[4]*f[5]*a[3]*a[2]^2*a[1]-4*a[3]^2*a[2]*a[1]*f[5]^2+16*a[3]^
2*a[2]^2*f[6]*f[5]+11*a[3]^2*a[2]^2*f[4]*f[7]-3*f[4]*f[5]*a[3]^2*a[1]^2-f[4]^2
*a[3]*a[2]*a[1]^2+26*f[7]*f[5]*a[3]^3*a[2]-2*f[4]*f[7]*a[3]^3*a[1]+f[4]^2*a[2]
^3*a[1]+2*f[4]*f[5]*a[2]^4+4*a[3]^2*a[1]^2*f[7]*f[2]-a[3]*a[2]*a[1]^2*f[7]*f[1
]+2*a[3]^2*a[2]*a[1]*f[3]*f[7]+3*a[3]*a[2]*a[1]^2*f[5]*f[3]+4*a[3]*a[2]*a[1]^2
*f[6]*f[2]+a[3]*a[2]^2*a[1]*f[7]*f[2]+f[1]^2*a[1]*a[0]^3-5*f[1]*f[5]*a[3]*a[1]
^2*a[0]+16*a[3]^2*a[1]*f[7]*f[1]*a[0]+2*a[3]*a[1]*f[1]*f[4]*a[0]^2+a[3]^2*a[1]
*f[4]^2*a[0]+2*f[2]*f[4]*a[3]*a[2]*a[0]^2-a[3]*a[2]^2*f[7]*f[1]*a[0]-9*a[3]^3*
f[3]*f[7]*a[0]-a[3]*a[2]^2*f[4]^2*a[0]-12*a[3]*a[1]*f[5]*f[0]*a[0]^2-4*a[3]^2*
a[1]*f[5]*f[3]*a[0]-14*a[3]*a[2]*a[1]*f[2]*f[5]*a[0]+8*a[3]*a[2]*a[1]*f[6]*f[1
]*a[0]+24*a[3]*a[2]*a[1]*f[7]*f[0]*a[0]-a[3]*a[2]^2*f[5]*f[3]*a[0]-6*a[3]^2*a[
2]*f[6]*f[3]*a[0]-8*a[3]^2*a[2]*f[4]*f[5]*a[0]+10*f[2]*f[5]*a[3]^2*a[0]^2-3*a[
2]*a[1]^2*f[1]*f[4]*a[0]+8*a[2]*a[1]^2*f[5]*f[0]*a[0]-2*f[3]*f[1]*a[2]*a[1]*a[
0]^2-2*a[2]^2*a[1]*f[2]*f[4]*a[0]+12*a[2]^2*a[1]*f[6]*f[0]*a[0]+a[2]*a[1]^3*f[
2]*f[4]+a[2]*a[1]^3*f[1]*f[5]-4*a[2]*a[1]^3*f[6]*f[0]-16*a[3]^3*f[5]^2*a[0]-2*
a[2]^2*a[1]^2*f[7]*f[0]+a[2]^2*a[1]^2*f[2]*f[5]+a[2]^2*a[1]^2*f[3]*f[4]-4*a[3]
*a[1]^3*f[7]*f[0]-a[3]*a[1]^3*f[3]*f[4]+a[3]*a[2]^3*f[3]*f[7]+2*a[3]*a[1]^3*f[
2]*f[5]-2*a[1]^4*f[5]*f[0]+a[2]*a[1]^2*f[2]*f[3]*a[0]+a[2]^2*a[1]*f[3]^2*a[0]+
2*f[2]*f[5]*a[2]^3*a[0]+a[2]*a[1]*f[2]^2*a[0]^2+f[3]*f[1]*a[1]^3*a[0]+f[2]*f[1
]*a[1]^2*a[0]^2-f[2]^2*a[3]*a[0]^3+a[1]^4*f[1]*f[4]+4*a[3]*a[1]^2*f[6]*f[0]*a[
0]+2*a[3]*a[2]^2*f[6]*f[2]*a[0]+2*a[3]*a[2]*f[1]*f[5]*a[0]^2-8*a[3]*a[2]*f[6]*
f[0]*a[0]^2-12*a[3]^2*f[7]*f[0]*a[0]^2-2*a[3]*a[1]*f[2]*f[3]*a[0]^2-4*a[3]^2*a
[1]*f[6]*f[2]*a[0]-a[3]*a[1]^2*f[2]*f[4]*a[0]-a[3]*a[1]^2*f[3]^2*a[0]:
eqn[13] :=
a[1]^2*c[2]^2+2*f[5]*a[3]*a[1]^2*c[2]-4*f[6]*a[3]^2*a[0]*c[2]-4*f[5]*a[3]^2*a[
1]*c[0]+2*f[4]*a[2]*a[1]^2*c[2]+2*f[4]*a[3]*a[0]^2*c[3]-4*f[4]*a[3]^2*a[0]*c[0
]-2*f[7]*a[3]^2*a[1]*c[2]-5*f[7]*a[3]^2*a[0]*c[3]-2*f[1]*a[3]*a[0]^2*c[0]+2*f[
1]*a[2]*a[0]^2*c[1]-4*f[3]*a[3]*a[0]^2*c[2]-2*f[3]*a[2]*a[0]^2*c[3]+4*a[3]*a[0
]*c[2]*c[1]-4*f[0]*a[2]*a[0]^2*c[0]+12*f[5]*a[3]^2*a[0]*c[1]-4*f[0]*a[0]^3*c[2
]-f[5]*a[2]^2*a[0]*c[3]+a[3]*a[0]*c[3]*c[0]-a[1]*a[0]*c[3]*c[2]+a[2]*a[0]*c[3]
*c[1]+2*f[3]*a[2]*a[1]*a[0]*c[2]-4*f[5]*a[3]*a[2]*a[0]*c[2]-2*f[6]*a[3]*a[2]*a
[0]*c[3]-4*f[5]*a[3]*a[2]*a[1]*c[1]-6*f[4]*a[3]*a[1]*a[0]*c[2]-2*f[4]*a[2]*a[1
]*a[0]*c[3]-2*a[3]^2*a[2]*a[1]*f[7]*f[4]+8*a[3]^2*a[2]*a[1]*f[6]*f[5]+6*f[4]*f
[5]*a[3]*a[2]*a[1]^2+6*f[7]*f[5]*a[3]^3*a[1]+4*f[5]^2*a[3]*a[2]^2*a[1]+f[5]^2*
a[3]^2*a[1]^2+f[7]^2*a[3]^4+f[1]^2*a[0]^4+f[4]^2*a[2]^2*a[1]^2-4*a[2]^2*a[1]*f
[0]*f[7]*a[0]-2*a[2]*a[1]*f[1]*f[4]*a[0]^2-2*f[3]*f[1]*a[2]*a[0]^3+4*a[2]^2*f[
0]*f[6]*a[0]^2-2*a[2]^2*f[1]*f[5]*a[0]^2+4*a[2]*a[1]*f[0]*f[5]*a[0]^2-14*f[4]*
f[5]*a[3]^2*a[1]*a[0]+a[2]^2*f[3]^2*a[0]^2+2*a[3]*f[1]*f[4]*a[0]^3+2*a[2]^2*a[
1]*f[3]*f[4]*a[0]+2*a[3]^2*a[2]*f[7]*f[3]*a[0]+16*a[3]*a[2]*f[0]*f[7]*a[0]^2+a
[3]^2*f[4]^2*a[0]^2+6*a[3]*a[2]*a[1]*f[5]*f[3]*a[0]+4*a[3]^2*a[2]*f[4]*f[6]*a[
0]-2*a[3]*a[2]*f[3]*f[4]*a[0]^2-2*a[3]*a[2]*a[1]*f[4]^2*a[0]+2*f[1]*f[5]*a[3]*
a[1]*a[0]^2-4*a[3]*a[2]*a[1]*f[7]*f[1]*a[0]-12*a[3]^2*a[2]*f[5]^2*a[0]-12*a[3]
^3*f[6]*f[5]*a[0]-12*a[3]^2*f[5]*f[3]*a[0]^2+8*a[3]^2*f[7]*f[1]*a[0]^2-12*a[3]
*f[0]*f[5]*a[0]^3+14*a[3]^3*f[7]*f[4]*a[0]:
eqn[14] :=
-14*a[1]^2*c[2]^2-26*f[5]*a[3]*a[1]^2*c[2]+44*f[6]*a[3]^2*a[0]*c[2]+54*f[5]*a[
3]^2*a[1]*c[0]-26*f[4]*a[2]*a[1]^2*c[2]-30*f[4]*a[3]*a[0]^2*c[3]+40*f[4]*a[3]^
2*a[0]*c[0]+30*f[7]*a[3]^2*a[1]*c[2]+4*f[7]*a[3]^2*a[0]*c[3]+10*f[1]*a[3]*a[0]
^2*c[0]-24*f[1]*a[2]*a[0]^2*c[1]+44*f[3]*a[3]*a[0]^2*c[2]+18*f[3]*a[2]*a[0]^2*
c[3]-50*a[3]*a[0]*c[2]*c[1]+28*f[0]*a[2]*a[0]^2*c[0]-144*f[5]*a[3]^2*a[0]*c[1]
+8*f[0]*a[1]^2*a[0]*c[0]-8*f[0]*a[1]*a[0]^2*c[1]-4*f[1]*a[1]*a[0]^2*c[2]-2*f[1
]*a[1]^2*a[0]*c[1]-4*f[3]*a[1]^2*a[0]*c[3]+6*f[3]*a[2]^2*a[0]*c[1]+2*f[3]*a[3]
*a[1]^2*c[0]+2*f[2]*a[1]^2*a[0]*c[2]-2*f[2]*a[2]*a[1]^2*c[0]-4*f[4]*a[3]*a[1]^
2*c[1]-8*f[6]*a[3]*a[2]^2*c[1]-4*f[6]*a[2]^2*a[1]*c[3]-8*f[6]*a[3]^2*a[2]*c[0]
+4*f[4]*a[2]^2*a[0]*c[2]+10*f[7]*a[3]^2*a[2]*c[1]+14*f[7]*a[3]*a[2]^2*c[2]-6*f
[2]*a[1]*a[0]^2*c[3]+6*f[2]*a[3]*a[0]^2*c[1]+4*f[6]*a[3]^2*a[1]*c[1]+2*a[2]*a[
1]*c[3]*c[0]-2*f[3]*a[2]^2*a[1]*c[0]-6*f[5]*a[2]*a[1]^2*c[3]-12*f[5]*a[3]*a[2]
^2*c[0]+44*f[0]*a[0]^3*c[2]+4*f[6]*a[2]^3*c[2]-4*a[2]^2*c[2]*c[0]-6*f[5]*a[2]^
3*c[1]+4*a[1]^2*c[3]*c[1]-2*f[7]*a[2]^3*c[3]-4*f[4]*a[2]^3*c[0]-4*f[4]*a[1]^3*
c[3]-2*f[1]*a[1]^3*c[0]+3*a[2]^2*c[1]^2+18*f[5]*a[2]^2*a[0]*c[3]+18*a[1]*a[0]*
c[3]*c[2]-16*a[2]*a[0]*c[3]*c[1]+a[3]^2*c[0]^2-18*f[3]*a[2]*a[1]*a[0]*c[2]+52*
f[5]*a[3]*a[2]*a[0]*c[2]+12*f[6]*a[3]*a[2]*a[0]*c[3]+54*f[5]*a[3]*a[2]*a[1]*c[
1]+70*f[4]*a[3]*a[1]*a[0]*c[2]+30*f[4]*a[2]*a[1]*a[0]*c[3]+4*f[2]*a[2]^2*a[0]*
c[0]-4*f[2]*a[2]*a[0]^2*c[2]+4*f[4]*a[3]*a[2]*a[1]*c[0]-2*f[3]*a[3]*a[1]*a[0]*
c[1]+6*f[1]*a[2]*a[1]*a[0]*c[0]-4*f[2]*a[3]*a[1]*a[0]*c[0]+4*a[2]^3*f[4]^2*a[0
]+4*a[2]*f[2]^2*a[0]^3+4*a[2]*a[1]^2*f[2]*f[4]*a[0]-2*a[2]*a[1]^2*f[1]*f[5]*a[
0]-16*a[2]*a[1]^2*f[0]*f[6]*a[0]+22*a[3]^2*a[1]*f[2]*f[7]*a[0]-4*a[3]*a[1]^2*f
[1]*f[6]*a[0]+10*a[3]*a[1]^2*f[2]*f[5]*a[0]-4*a[2]^3*f[2]*f[6]*a[0]-2*a[2]^3*f
[1]*f[7]*a[0]-32*a[3]*a[1]^2*f[0]*f[7]*a[0]-8*a[2]^3*f[3]*f[5]*a[0]-8*a[2]^2*f
[2]*f[4]*a[0]^2+4*a[2]*a[1]*f[3]*f[2]*a[0]^2+4*f[3]*f[1]*a[1]^2*a[0]^2+4*f[1]*
f[2]*a[1]*a[0]^3+4*a[1]^3*f[1]*f[4]*a[0]-8*a[1]^3*f[5]*f[0]*a[0]-8*a[2]^2*a[1]
*f[1]*f[6]*a[0]-2*a[2]^2*a[1]*f[2]*f[5]*a[0]+4*a[3]*a[1]^2*f[3]*f[4]*a[0]+24*a
[3]*a[2]*f[1]*f[6]*a[0]^2-16*a[3]*a[2]*f[2]*f[5]*a[0]^2-18*a[3]*a[2]^2*f[2]*f[
7]*a[0]+12*a[3]*a[2]^2*f[4]*f[5]*a[0]+4*a[3]*a[1]*f[2]*f[4]*a[0]^2+4*a[3]*a[2]
*a[1]*f[2]*f[6]*a[0]+6*a[3]^2*a[2]*a[1]*f[7]*f[4]-108*a[3]^2*a[2]*a[1]*f[6]*f[
5]-74*f[4]*f[5]*a[3]*a[2]*a[1]^2-80*f[7]*f[5]*a[3]^3*a[1]-54*f[5]^2*a[3]*a[2]^
2*a[1]-7*f[5]^2*a[3]^2*a[1]^2-20*f[7]^2*a[3]^4-11*f[1]^2*a[0]^4-15*f[4]^2*a[2]
^2*a[1]^2+52*a[2]^2*a[1]*f[0]*f[7]*a[0]+18*a[2]*a[1]*f[1]*f[4]*a[0]^2+22*f[3]*
f[1]*a[2]*a[0]^3-12*a[2]^2*f[0]*f[6]*a[0]^2+26*a[2]^2*f[1]*f[5]*a[0]^2-28*a[2]
*a[1]*f[0]*f[5]*a[0]^2+162*f[4]*f[5]*a[3]^2*a[1]*a[0]-11*a[2]^2*f[3]^2*a[0]^2-\
22*a[3]*f[1]*f[4]*a[0]^3-26*a[2]^2*a[1]*f[3]*f[4]*a[0]-22*a[3]^2*a[2]*f[7]*f[3
]*a[0]-128*a[3]*a[2]*f[0]*f[7]*a[0]^2-11*a[3]^2*f[4]^2*a[0]^2-50*a[3]*a[2]*a[1
]*f[5]*f[3]*a[0]-36*a[3]^2*a[2]*f[4]*f[6]*a[0]+22*a[3]*a[2]*f[3]*f[4]*a[0]^2+
18*a[3]*a[2]*a[1]*f[4]^2*a[0]-30*f[1]*f[5]*a[3]*a[1]*a[0]^2+32*a[3]*a[2]*a[1]*
f[7]*f[1]*a[0]+148*a[3]^2*a[2]*f[5]^2*a[0]+132*a[3]^3*f[6]*f[5]*a[0]+132*a[3]^
2*f[5]*f[3]*a[0]^2-52*a[3]^2*f[7]*f[1]*a[0]^2+132*a[3]*f[0]*f[5]*a[0]^3-142*a[
3]^3*f[7]*f[4]*a[0]+2*f[1]*f[5]*a[1]^4+12*f[7]*f[6]*a[3]^3*a[2]+3*a[2]^4*f[5]^
2+34*a[3]^2*a[2]^2*f[7]*f[5]+2*a[2]^4*f[3]*f[7]+4*a[2]^4*f[4]*f[6]+12*a[3]^2*a
[2]^2*f[6]^2+16*a[3]*a[2]^3*f[7]*f[4]+20*a[3]*a[2]^3*f[6]*f[5]-4*a[3]^2*a[1]^2
*f[4]*f[6]-4*a[3]^2*a[1]^2*f[3]*f[7]+2*a[3]*a[2]^2*a[1]*f[3]*f[7]-2*a[3]*a[1]^
3*f[3]*f[5]+4*a[3]*a[1]^3*f[1]*f[7]+4*a[2]^3*a[1]*f[3]*f[6]+2*a[2]^3*a[1]*f[2]
*f[7]+4*a[3]*a[1]^3*f[4]^2-4*a[3]*a[2]*a[1]^2*f[3]*f[6]+4*a[3]*a[2]*a[1]^2*f[2
]*f[7]+2*a[2]^2*a[1]^2*f[3]*f[5]+4*a[2]^2*a[1]^2*f[2]*f[6]+2*a[2]^2*a[1]^2*f[1
]*f[7]+4*a[2]*a[1]^3*f[1]*f[6]+2*a[2]*a[1]^3*f[2]*f[5]:
eqn[15] :=
7*a[1]^2*c[2]^2+13*f[5]*a[3]*a[1]^2*c[2]-24*f[6]*a[3]^2*a[0]*c[2]-28*f[5]*a[3]
^2*a[1]*c[0]+14*f[4]*a[2]*a[1]^2*c[2]+16*f[4]*a[3]*a[0]^2*c[3]-22*f[4]*a[3]^2*
a[0]*c[0]-13*f[7]*a[3]^2*a[1]*c[2]-6*f[7]*a[3]^2*a[0]*c[3]-6*f[1]*a[3]*a[0]^2*
c[0]+13*f[1]*a[2]*a[0]^2*c[1]-24*f[3]*a[3]*a[0]^2*c[2]-10*f[3]*a[2]*a[0]^2*c[3
]+27*a[3]*a[0]*c[2]*c[1]-16*f[0]*a[2]*a[0]^2*c[0]+78*f[5]*a[3]^2*a[0]*c[1]-4*f
[0]*a[1]^2*a[0]*c[0]+4*f[0]*a[1]*a[0]^2*c[1]+2*f[1]*a[1]*a[0]^2*c[2]+f[1]*a[1]
^2*a[0]*c[1]+2*f[3]*a[1]^2*a[0]*c[3]-3*f[3]*a[2]^2*a[0]*c[1]-f[3]*a[3]*a[1]^2*
c[0]-f[2]*a[1]^2*a[0]*c[2]+f[2]*a[2]*a[1]^2*c[0]+2*f[4]*a[3]*a[1]^2*c[1]+2*f[6
]*a[3]*a[2]^2*c[1]+2*f[6]*a[2]^2*a[1]*c[3]+2*f[6]*a[3]^2*a[2]*c[0]-2*f[4]*a[2]
^2*a[0]*c[2]-5*f[7]*a[3]^2*a[2]*c[1]-7*f[7]*a[3]*a[2]^2*c[2]+3*f[2]*a[1]*a[0]^
2*c[3]-3*f[2]*a[3]*a[0]^2*c[1]-2*f[6]*a[3]^2*a[1]*c[1]-a[2]*a[1]*c[3]*c[0]+f[3
]*a[2]^2*a[1]*c[0]+3*f[5]*a[2]*a[1]^2*c[3]+5*f[5]*a[3]*a[2]^2*c[0]-24*f[0]*a[0
]^3*c[2]-2*f[6]*a[2]^3*c[2]+2*a[2]^2*c[2]*c[0]+2*f[5]*a[2]^3*c[1]-2*a[1]^2*c[3
]*c[1]+f[7]*a[2]^3*c[3]+2*f[4]*a[2]^3*c[0]+2*f[4]*a[1]^3*c[3]+f[1]*a[1]^3*c[0]
-a[2]^2*c[1]^2-9*f[5]*a[2]^2*a[0]*c[3]-9*a[1]*a[0]*c[3]*c[2]+8*a[2]*a[0]*c[3]*
c[1]+10*f[3]*a[2]*a[1]*a[0]*c[2]-28*f[5]*a[3]*a[2]*a[0]*c[2]-6*f[6]*a[3]*a[2]*
a[0]*c[3]-28*f[5]*a[3]*a[2]*a[1]*c[1]-38*f[4]*a[3]*a[1]*a[0]*c[2]-16*f[4]*a[2]
*a[1]*a[0]*c[3]-2*f[2]*a[2]^2*a[0]*c[0]+2*f[2]*a[2]*a[0]^2*c[2]-2*f[4]*a[3]*a[
2]*a[1]*c[0]+f[3]*a[3]*a[1]*a[0]*c[1]-3*f[1]*a[2]*a[1]*a[0]*c[0]+2*f[2]*a[3]*a
[1]*a[0]*c[0]+a[3]*a[2]*c[1]*c[0]-2*a[2]^3*f[4]^2*a[0]-2*a[2]*f[2]^2*a[0]^3-2*
a[2]*a[1]^2*f[2]*f[4]*a[0]+a[2]*a[1]^2*f[1]*f[5]*a[0]+8*a[2]*a[1]^2*f[0]*f[6]*
a[0]-11*a[3]^2*a[1]*f[2]*f[7]*a[0]+2*a[3]*a[1]^2*f[1]*f[6]*a[0]-5*a[3]*a[1]^2*
f[2]*f[5]*a[0]+2*a[2]^3*f[2]*f[6]*a[0]+a[2]^3*f[1]*f[7]*a[0]+16*a[3]*a[1]^2*f[
0]*f[7]*a[0]+4*a[2]^3*f[3]*f[5]*a[0]+4*a[2]^2*f[2]*f[4]*a[0]^2-2*a[2]*a[1]*f[3
]*f[2]*a[0]^2-2*f[3]*f[1]*a[1]^2*a[0]^2-2*f[1]*f[2]*a[1]*a[0]^3-2*a[1]^3*f[1]*
f[4]*a[0]+4*a[1]^3*f[5]*f[0]*a[0]+4*a[2]^2*a[1]*f[1]*f[6]*a[0]+a[2]^2*a[1]*f[2
]*f[5]*a[0]-2*a[3]*a[1]^2*f[3]*f[4]*a[0]-12*a[3]*a[2]*f[1]*f[6]*a[0]^2+8*a[3]*
a[2]*f[2]*f[5]*a[0]^2+9*a[3]*a[2]^2*f[2]*f[7]*a[0]-6*a[3]*a[2]^2*f[4]*f[5]*a[0
]-2*a[3]*a[1]*f[2]*f[4]*a[0]^2-2*a[3]*a[2]*a[1]*f[2]*f[6]*a[0]-4*a[3]^2*a[2]*a
[1]*f[7]*f[4]+56*a[3]^2*a[2]*a[1]*f[6]*f[5]+40*f[4]*f[5]*a[3]*a[2]*a[1]^2+46*f
[7]*f[5]*a[3]^3*a[1]+28*f[5]^2*a[3]*a[2]^2*a[1]+4*f[5]^2*a[3]^2*a[1]^2+6*f[7]^
2*a[3]^4+6*f[1]^2*a[0]^4+8*f[4]^2*a[2]^2*a[1]^2-28*a[2]^2*a[1]*f[0]*f[7]*a[0]-\
10*a[2]*a[1]*f[1]*f[4]*a[0]^2-12*f[3]*f[1]*a[2]*a[0]^3+8*a[2]^2*f[0]*f[6]*a[0]
^2-14*a[2]^2*f[1]*f[5]*a[0]^2+16*a[2]*a[1]*f[0]*f[5]*a[0]^2-88*f[4]*f[5]*a[3]^
2*a[1]*a[0]+6*a[2]^2*f[3]^2*a[0]^2+12*a[3]*f[1]*f[4]*a[0]^3+14*a[2]^2*a[1]*f[3
]*f[4]*a[0]+12*a[3]^2*a[2]*f[7]*f[3]*a[0]+72*a[3]*a[2]*f[0]*f[7]*a[0]^2+6*a[3]
^2*f[4]^2*a[0]^2+28*a[3]*a[2]*a[1]*f[5]*f[3]*a[0]+20*a[3]^2*a[2]*f[4]*f[6]*a[0
]-12*a[3]*a[2]*f[3]*f[4]*a[0]^2-10*a[3]*a[2]*a[1]*f[4]^2*a[0]+16*f[1]*f[5]*a[3
]*a[1]*a[0]^2-18*a[3]*a[2]*a[1]*f[7]*f[1]*a[0]-80*a[3]^2*a[2]*f[5]^2*a[0]-72*a
[3]^3*f[6]*f[5]*a[0]-72*a[3]^2*f[5]*f[3]*a[0]^2+30*a[3]^2*f[7]*f[1]*a[0]^2-72*
a[3]*f[0]*f[5]*a[0]^3+78*a[3]^3*f[7]*f[4]*a[0]-f[1]*f[5]*a[1]^4-6*f[7]*f[6]*a[
3]^3*a[2]-a[2]^4*f[5]^2-17*a[3]^2*a[2]^2*f[7]*f[5]-a[2]^4*f[3]*f[7]-2*a[2]^4*f
[4]*f[6]-4*a[3]^2*a[2]^2*f[6]^2-8*a[3]*a[2]^3*f[7]*f[4]-8*a[3]*a[2]^3*f[6]*f[5
]+2*a[3]^2*a[1]^2*f[4]*f[6]+2*a[3]^2*a[1]^2*f[3]*f[7]-a[3]*a[2]^2*a[1]*f[3]*f[
7]+a[3]*a[1]^3*f[3]*f[5]-2*a[3]*a[1]^3*f[1]*f[7]-2*a[2]^3*a[1]*f[3]*f[6]-a[2]^
3*a[1]*f[2]*f[7]-2*a[3]*a[1]^3*f[4]^2+2*a[3]*a[2]*a[1]^2*f[3]*f[6]-2*a[3]*a[2]
*a[1]^2*f[2]*f[7]-a[2]^2*a[1]^2*f[3]*f[5]-2*a[2]^2*a[1]^2*f[2]*f[6]-a[2]^2*a[1
]^2*f[1]*f[7]-2*a[2]*a[1]^3*f[1]*f[6]-a[2]*a[1]^3*f[2]*f[5]:
eqn[16] :=
-7*a[1]^2*c[2]^2-13*f[5]*a[3]*a[1]^2*c[2]+24*f[6]*a[3]^2*a[0]*c[2]+28*f[5]*a[3
]^2*a[1]*c[0]-14*f[4]*a[2]*a[1]^2*c[2]-16*f[4]*a[3]*a[0]^2*c[3]+22*f[4]*a[3]^2
*a[0]*c[0]+13*f[7]*a[3]^2*a[1]*c[2]+6*f[7]*a[3]^2*a[0]*c[3]+6*f[1]*a[3]*a[0]^2
*c[0]-13*f[1]*a[2]*a[0]^2*c[1]+24*f[3]*a[3]*a[0]^2*c[2]+10*f[3]*a[2]*a[0]^2*c[
3]-27*a[3]*a[0]*c[2]*c[1]+16*f[0]*a[2]*a[0]^2*c[0]-78*f[5]*a[3]^2*a[0]*c[1]+4*
f[0]*a[1]^2*a[0]*c[0]-4*f[0]*a[1]*a[0]^2*c[1]-2*f[1]*a[1]*a[0]^2*c[2]-f[1]*a[1
]^2*a[0]*c[1]-2*f[3]*a[1]^2*a[0]*c[3]+3*f[3]*a[2]^2*a[0]*c[1]+f[3]*a[3]*a[1]^2
*c[0]+f[2]*a[1]^2*a[0]*c[2]-f[2]*a[2]*a[1]^2*c[0]-2*f[4]*a[3]*a[1]^2*c[1]-4*f[
6]*a[3]*a[2]^2*c[1]-2*f[6]*a[2]^2*a[1]*c[3]-2*f[6]*a[3]^2*a[2]*c[0]+2*f[4]*a[2
]^2*a[0]*c[2]+2*f[7]*a[3]^2*a[2]*c[1]+7*f[7]*a[3]*a[2]^2*c[2]-3*f[2]*a[1]*a[0]
^2*c[3]+3*f[2]*a[3]*a[0]^2*c[1]+2*f[6]*a[3]^2*a[1]*c[1]+a[2]*a[1]*c[3]*c[0]-f[
3]*a[2]^2*a[1]*c[0]-3*f[5]*a[2]*a[1]^2*c[3]-5*f[5]*a[3]*a[2]^2*c[0]+24*f[0]*a[
0]^3*c[2]+2*f[6]*a[2]^3*c[2]-2*a[2]^2*c[2]*c[0]-3*f[5]*a[2]^3*c[1]+2*a[1]^2*c[
3]*c[1]-f[7]*a[2]^3*c[3]-2*f[4]*a[2]^3*c[0]-2*f[4]*a[1]^3*c[3]-f[1]*a[1]^3*c[0
]+2*a[2]^2*c[1]^2+9*f[5]*a[2]^2*a[0]*c[3]+9*a[1]*a[0]*c[3]*c[2]-9*a[2]*a[0]*c[
3]*c[1]-10*f[3]*a[2]*a[1]*a[0]*c[2]+28*f[5]*a[3]*a[2]*a[0]*c[2]+6*f[6]*a[3]*a[
2]*a[0]*c[3]+30*f[5]*a[3]*a[2]*a[1]*c[1]+38*f[4]*a[3]*a[1]*a[0]*c[2]+16*f[4]*a
[2]*a[1]*a[0]*c[3]+2*f[2]*a[2]^2*a[0]*c[0]-2*f[2]*a[2]*a[0]^2*c[2]+2*f[4]*a[3]
*a[2]*a[1]*c[0]-f[3]*a[3]*a[1]*a[0]*c[1]+3*f[1]*a[2]*a[1]*a[0]*c[0]-2*f[2]*a[3
]*a[1]*a[0]*c[0]+a[2]*a[1]*c[2]*c[1]+2*a[2]^3*f[4]^2*a[0]+2*a[2]*f[2]^2*a[0]^3
+2*a[2]*a[1]^2*f[2]*f[4]*a[0]-a[2]*a[1]^2*f[1]*f[5]*a[0]-8*a[2]*a[1]^2*f[0]*f[
6]*a[0]+11*a[3]^2*a[1]*f[2]*f[7]*a[0]-2*a[3]*a[1]^2*f[1]*f[6]*a[0]+5*a[3]*a[1]
^2*f[2]*f[5]*a[0]-2*a[2]^3*f[2]*f[6]*a[0]-a[2]^3*f[1]*f[7]*a[0]-16*a[3]*a[1]^2
*f[0]*f[7]*a[0]-4*a[2]^3*f[3]*f[5]*a[0]-4*a[2]^2*f[2]*f[4]*a[0]^2+2*a[2]*a[1]*
f[3]*f[2]*a[0]^2+2*f[3]*f[1]*a[1]^2*a[0]^2+2*f[1]*f[2]*a[1]*a[0]^3+2*a[1]^3*f[
1]*f[4]*a[0]-4*a[1]^3*f[5]*f[0]*a[0]-4*a[2]^2*a[1]*f[1]*f[6]*a[0]-a[2]^2*a[1]*
f[2]*f[5]*a[0]+2*a[3]*a[1]^2*f[3]*f[4]*a[0]+12*a[3]*a[2]*f[1]*f[6]*a[0]^2-8*a[
3]*a[2]*f[2]*f[5]*a[0]^2-9*a[3]*a[2]^2*f[2]*f[7]*a[0]+6*a[3]*a[2]^2*f[4]*f[5]*
a[0]+2*a[3]*a[1]*f[2]*f[4]*a[0]^2+2*a[3]*a[2]*a[1]*f[2]*f[6]*a[0]+4*a[3]^2*a[2
]*a[1]*f[7]*f[4]-56*a[3]^2*a[2]*a[1]*f[6]*f[5]-40*f[4]*f[5]*a[3]*a[2]*a[1]^2-\
46*f[7]*f[5]*a[3]^3*a[1]-28*f[5]^2*a[3]*a[2]^2*a[1]-4*f[5]^2*a[3]^2*a[1]^2-6*f
[7]^2*a[3]^4-6*f[1]^2*a[0]^4-8*f[4]^2*a[2]^2*a[1]^2+28*a[2]^2*a[1]*f[0]*f[7]*a
[0]+10*a[2]*a[1]*f[1]*f[4]*a[0]^2+12*f[3]*f[1]*a[2]*a[0]^3-8*a[2]^2*f[0]*f[6]*
a[0]^2+14*a[2]^2*f[1]*f[5]*a[0]^2-16*a[2]*a[1]*f[0]*f[5]*a[0]^2+88*f[4]*f[5]*a
[3]^2*a[1]*a[0]-6*a[2]^2*f[3]^2*a[0]^2-12*a[3]*f[1]*f[4]*a[0]^3-14*a[2]^2*a[1]
*f[3]*f[4]*a[0]-12*a[3]^2*a[2]*f[7]*f[3]*a[0]-72*a[3]*a[2]*f[0]*f[7]*a[0]^2-6*
a[3]^2*f[4]^2*a[0]^2-28*a[3]*a[2]*a[1]*f[5]*f[3]*a[0]-20*a[3]^2*a[2]*f[4]*f[6]
*a[0]+12*a[3]*a[2]*f[3]*f[4]*a[0]^2+10*a[3]*a[2]*a[1]*f[4]^2*a[0]-16*f[1]*f[5]
*a[3]*a[1]*a[0]^2+18*a[3]*a[2]*a[1]*f[7]*f[1]*a[0]+80*a[3]^2*a[2]*f[5]^2*a[0]+
72*a[3]^3*f[6]*f[5]*a[0]+72*a[3]^2*f[5]*f[3]*a[0]^2-30*a[3]^2*f[7]*f[1]*a[0]^2
+72*a[3]*f[0]*f[5]*a[0]^3-78*a[3]^3*f[7]*f[4]*a[0]+f[1]*f[5]*a[1]^4+6*f[7]*f[6
]*a[3]^3*a[2]+a[2]^4*f[5]^2+17*a[3]^2*a[2]^2*f[7]*f[5]+a[2]^4*f[3]*f[7]+2*a[2]
^4*f[4]*f[6]+4*a[3]^2*a[2]^2*f[6]^2+8*a[3]*a[2]^3*f[7]*f[4]+8*a[3]*a[2]^3*f[6]
*f[5]-2*a[3]^2*a[1]^2*f[4]*f[6]-2*a[3]^2*a[1]^2*f[3]*f[7]+a[3]*a[2]^2*a[1]*f[3
]*f[7]-a[3]*a[1]^3*f[3]*f[5]+2*a[3]*a[1]^3*f[1]*f[7]+2*a[2]^3*a[1]*f[3]*f[6]+a
[2]^3*a[1]*f[2]*f[7]+2*a[3]*a[1]^3*f[4]^2-2*a[3]*a[2]*a[1]^2*f[3]*f[6]+2*a[3]*
a[2]*a[1]^2*f[2]*f[7]+a[2]^2*a[1]^2*f[3]*f[5]+2*a[2]^2*a[1]^2*f[2]*f[6]+a[2]^2
*a[1]^2*f[1]*f[7]+2*a[2]*a[1]^3*f[1]*f[6]+a[2]*a[1]^3*f[2]*f[5]:
eqn[17] :=
8*a[1]^2*c[2]^2+15*f[5]*a[3]*a[1]^2*c[2]-24*f[6]*a[3]^2*a[0]*c[2]-28*f[5]*a[3]
^2*a[1]*c[0]+14*f[4]*a[2]*a[1]^2*c[2]+16*f[4]*a[3]*a[0]^2*c[3]-22*f[4]*a[3]^2*
a[0]*c[0]-16*f[7]*a[3]^2*a[1]*c[2]-6*f[7]*a[3]^2*a[0]*c[3]-6*f[1]*a[3]*a[0]^2*
c[0]+13*f[1]*a[2]*a[0]^2*c[1]-24*f[3]*a[3]*a[0]^2*c[2]-10*f[3]*a[2]*a[0]^2*c[3
]+27*a[3]*a[0]*c[2]*c[1]-16*f[0]*a[2]*a[0]^2*c[0]+78*f[5]*a[3]^2*a[0]*c[1]-4*f
[0]*a[1]^2*a[0]*c[0]+4*f[0]*a[1]*a[0]^2*c[1]+2*f[1]*a[1]*a[0]^2*c[2]+f[1]*a[1]
^2*a[0]*c[1]+2*f[3]*a[1]^2*a[0]*c[3]-3*f[3]*a[2]^2*a[0]*c[1]-f[3]*a[3]*a[1]^2*
c[0]-f[2]*a[1]^2*a[0]*c[2]+f[2]*a[2]*a[1]^2*c[0]+2*f[4]*a[3]*a[1]^2*c[1]+6*f[6
]*a[3]*a[2]^2*c[1]+2*f[6]*a[2]^2*a[1]*c[3]+4*f[6]*a[3]^2*a[2]*c[0]-2*f[4]*a[2]
^2*a[0]*c[2]-2*f[7]*a[3]^2*a[2]*c[1]-7*f[7]*a[3]*a[2]^2*c[2]+3*f[2]*a[1]*a[0]^
2*c[3]-3*f[2]*a[3]*a[0]^2*c[1]-2*f[6]*a[3]^2*a[1]*c[1]-a[2]*a[1]*c[3]*c[0]+f[3
]*a[2]^2*a[1]*c[0]+3*f[5]*a[2]*a[1]^2*c[3]+6*f[5]*a[3]*a[2]^2*c[0]-24*f[0]*a[0
]^3*c[2]-2*f[6]*a[2]^3*c[2]+2*a[2]^2*c[2]*c[0]+4*f[5]*a[2]^3*c[1]-2*a[1]^2*c[3
]*c[1]+f[7]*a[2]^3*c[3]+2*f[4]*a[2]^3*c[0]+2*f[4]*a[1]^3*c[3]+f[1]*a[1]^3*c[0]
-2*a[2]^2*c[1]^2-10*f[5]*a[2]^2*a[0]*c[3]-10*a[1]*a[0]*c[3]*c[2]+9*a[2]*a[0]*c
[3]*c[1]+10*f[3]*a[2]*a[1]*a[0]*c[2]-28*f[5]*a[3]*a[2]*a[0]*c[2]-8*f[6]*a[3]*a
[2]*a[0]*c[3]-30*f[5]*a[3]*a[2]*a[1]*c[1]-38*f[4]*a[3]*a[1]*a[0]*c[2]-16*f[4]*
a[2]*a[1]*a[0]*c[3]-2*f[2]*a[2]^2*a[0]*c[0]+2*f[2]*a[2]*a[0]^2*c[2]-2*f[4]*a[3
]*a[2]*a[1]*c[0]+f[3]*a[3]*a[1]*a[0]*c[1]-3*f[1]*a[2]*a[1]*a[0]*c[0]+2*f[2]*a[
3]*a[1]*a[0]*c[0]+a[3]*a[1]*c[2]*c[0]-2*a[2]^3*f[4]^2*a[0]-2*a[2]*f[2]^2*a[0]^
3-2*a[2]*a[1]^2*f[2]*f[4]*a[0]+a[2]*a[1]^2*f[1]*f[5]*a[0]+8*a[2]*a[1]^2*f[0]*f
[6]*a[0]-11*a[3]^2*a[1]*f[2]*f[7]*a[0]+2*a[3]*a[1]^2*f[1]*f[6]*a[0]-5*a[3]*a[1
]^2*f[2]*f[5]*a[0]+2*a[2]^3*f[2]*f[6]*a[0]+a[2]^3*f[1]*f[7]*a[0]+16*a[3]*a[1]^
2*f[0]*f[7]*a[0]+4*a[2]^3*f[3]*f[5]*a[0]+4*a[2]^2*f[2]*f[4]*a[0]^2-2*a[2]*a[1]
*f[3]*f[2]*a[0]^2-2*f[3]*f[1]*a[1]^2*a[0]^2-2*f[1]*f[2]*a[1]*a[0]^3-2*a[1]^3*f
[1]*f[4]*a[0]+4*a[1]^3*f[5]*f[0]*a[0]+4*a[2]^2*a[1]*f[1]*f[6]*a[0]+a[2]^2*a[1]
*f[2]*f[5]*a[0]-2*a[3]*a[1]^2*f[3]*f[4]*a[0]-12*a[3]*a[2]*f[1]*f[6]*a[0]^2+8*a
[3]*a[2]*f[2]*f[5]*a[0]^2+9*a[3]*a[2]^2*f[2]*f[7]*a[0]-6*a[3]*a[2]^2*f[4]*f[5]
*a[0]-2*a[3]*a[1]*f[2]*f[4]*a[0]^2-2*a[3]*a[2]*a[1]*f[2]*f[6]*a[0]-4*a[3]^2*a[
2]*a[1]*f[7]*f[4]+60*a[3]^2*a[2]*a[1]*f[6]*f[5]+40*f[4]*f[5]*a[3]*a[2]*a[1]^2+
46*f[7]*f[5]*a[3]^3*a[1]+30*f[5]^2*a[3]*a[2]^2*a[1]+4*f[5]^2*a[3]^2*a[1]^2+6*f
[7]^2*a[3]^4+6*f[1]^2*a[0]^4+8*f[4]^2*a[2]^2*a[1]^2-28*a[2]^2*a[1]*f[0]*f[7]*a
[0]-10*a[2]*a[1]*f[1]*f[4]*a[0]^2-12*f[3]*f[1]*a[2]*a[0]^3+8*a[2]^2*f[0]*f[6]*
a[0]^2-14*a[2]^2*f[1]*f[5]*a[0]^2+16*a[2]*a[1]*f[0]*f[5]*a[0]^2-88*f[4]*f[5]*a
[3]^2*a[1]*a[0]+6*a[2]^2*f[3]^2*a[0]^2+12*a[3]*f[1]*f[4]*a[0]^3+14*a[2]^2*a[1]
*f[3]*f[4]*a[0]+12*a[3]^2*a[2]*f[7]*f[3]*a[0]+72*a[3]*a[2]*f[0]*f[7]*a[0]^2+6*
a[3]^2*f[4]^2*a[0]^2+28*a[3]*a[2]*a[1]*f[5]*f[3]*a[0]+20*a[3]^2*a[2]*f[4]*f[6]
*a[0]-12*a[3]*a[2]*f[3]*f[4]*a[0]^2-10*a[3]*a[2]*a[1]*f[4]^2*a[0]+16*f[1]*f[5]
*a[3]*a[1]*a[0]^2-18*a[3]*a[2]*a[1]*f[7]*f[1]*a[0]-80*a[3]^2*a[2]*f[5]^2*a[0]-\
72*a[3]^3*f[6]*f[5]*a[0]-72*a[3]^2*f[5]*f[3]*a[0]^2+30*a[3]^2*f[7]*f[1]*a[0]^2
-72*a[3]*f[0]*f[5]*a[0]^3+78*a[3]^3*f[7]*f[4]*a[0]-f[1]*f[5]*a[1]^4-12*f[7]*f[
6]*a[3]^3*a[2]-2*a[2]^4*f[5]^2-20*a[3]^2*a[2]^2*f[7]*f[5]-a[2]^4*f[3]*f[7]-2*a
[2]^4*f[4]*f[6]-8*a[3]^2*a[2]^2*f[6]^2-8*a[3]*a[2]^3*f[7]*f[4]-12*a[3]*a[2]^3*
f[6]*f[5]+2*a[3]^2*a[1]^2*f[4]*f[6]+2*a[3]^2*a[1]^2*f[3]*f[7]-a[3]*a[2]^2*a[1]
*f[3]*f[7]+a[3]*a[1]^3*f[3]*f[5]-2*a[3]*a[1]^3*f[1]*f[7]-2*a[2]^3*a[1]*f[3]*f[
6]-a[2]^3*a[1]*f[2]*f[7]-2*a[3]*a[1]^3*f[4]^2+2*a[3]*a[2]*a[1]^2*f[3]*f[6]-2*a
[3]*a[2]*a[1]^2*f[2]*f[7]-a[2]^2*a[1]^2*f[3]*f[5]-2*a[2]^2*a[1]^2*f[2]*f[6]-a[
2]^2*a[1]^2*f[1]*f[7]-2*a[2]*a[1]^3*f[1]*f[6]-a[2]*a[1]^3*f[2]*f[5]:
eqn[18] :=
a[1]^2*c[2]^2+a[0]^2*c[3]^2-4*f[6]*a[3]^2*a[0]*c[2]-6*f[5]*a[3]^2*a[1]*c[0]+2*
f[4]*a[2]*a[1]^2*c[2]+2*f[4]*a[3]*a[0]^2*c[3]-4*f[4]*a[3]^2*a[0]*c[0]-2*f[7]*a
[3]^2*a[1]*c[2]-2*f[7]*a[3]^2*a[0]*c[3]-2*f[1]*a[3]*a[0]^2*c[0]+2*f[1]*a[2]*a[
0]^2*c[1]-4*f[3]*a[3]*a[0]^2*c[2]-2*f[3]*a[2]*a[0]^2*c[3]+4*a[3]*a[0]*c[2]*c[1
]-4*f[0]*a[2]*a[0]^2*c[0]+12*f[5]*a[3]^2*a[0]*c[1]-4*f[0]*a[0]^3*c[2]-2*a[1]*a
[0]*c[3]*c[2]+2*f[3]*a[2]*a[1]*a[0]*c[2]-4*f[5]*a[3]*a[2]*a[0]*c[2]-6*f[5]*a[3
]*a[2]*a[1]*c[1]-6*f[4]*a[3]*a[1]*a[0]*c[2]-2*f[4]*a[2]*a[1]*a[0]*c[3]-2*a[3]^
2*a[2]*a[1]*f[7]*f[4]+12*a[3]^2*a[2]*a[1]*f[6]*f[5]+6*f[4]*f[5]*a[3]*a[2]*a[1]
^2+12*f[7]*f[5]*a[3]^3*a[1]+6*f[5]^2*a[3]*a[2]^2*a[1]-3*f[5]^2*a[3]^2*a[1]^2+f
[7]^2*a[3]^4+f[1]^2*a[0]^4+f[4]^2*a[2]^2*a[1]^2-4*a[2]^2*a[1]*f[0]*f[7]*a[0]-2
*a[2]*a[1]*f[1]*f[4]*a[0]^2-2*f[3]*f[1]*a[2]*a[0]^3+4*a[2]^2*f[0]*f[6]*a[0]^2-\
2*a[2]^2*f[1]*f[5]*a[0]^2+4*a[2]*a[1]*f[0]*f[5]*a[0]^2-14*f[4]*f[5]*a[3]^2*a[1
]*a[0]+a[2]^2*f[3]^2*a[0]^2+2*a[3]*f[1]*f[4]*a[0]^3+2*a[2]^2*a[1]*f[3]*f[4]*a[
0]+2*a[3]^2*a[2]*f[7]*f[3]*a[0]+16*a[3]*a[2]*f[0]*f[7]*a[0]^2+a[3]^2*f[4]^2*a[
0]^2+6*a[3]*a[2]*a[1]*f[5]*f[3]*a[0]+4*a[3]^2*a[2]*f[4]*f[6]*a[0]-2*a[3]*a[2]*
f[3]*f[4]*a[0]^2-2*a[3]*a[2]*a[1]*f[4]^2*a[0]+2*f[1]*f[5]*a[3]*a[1]*a[0]^2-4*a
[3]*a[2]*a[1]*f[7]*f[1]*a[0]-12*a[3]^2*a[2]*f[5]^2*a[0]-12*a[3]^3*f[6]*f[5]*a[
0]-12*a[3]^2*f[5]*f[3]*a[0]^2+8*a[3]^2*f[7]*f[1]*a[0]^2-12*a[3]*f[0]*f[5]*a[0]
^3+14*a[3]^3*f[7]*f[4]*a[0]:
eqn[19] :=
5*a[1]^2*c[2]^2+7*f[5]*a[3]*a[1]^2*c[2]-16*f[6]*a[3]^2*a[0]*c[2]-22*f[5]*a[3]^
2*a[1]*c[0]+8*f[4]*a[2]*a[1]^2*c[2]+11*f[4]*a[3]*a[0]^2*c[3]-15*f[4]*a[3]^2*a[
0]*c[0]-9*f[7]*a[3]^2*a[1]*c[2]-4*f[7]*a[3]^2*a[0]*c[3]-4*f[1]*a[3]*a[0]^2*c[0
]+9*f[1]*a[2]*a[0]^2*c[1]-16*f[3]*a[3]*a[0]^2*c[2]-8*f[3]*a[2]*a[0]^2*c[3]+18*
a[3]*a[0]*c[2]*c[1]-12*f[0]*a[2]*a[0]^2*c[0]+52*f[5]*a[3]^2*a[0]*c[1]-2*f[0]*a
[1]^2*a[0]*c[0]+2*f[0]*a[1]*a[0]^2*c[1]+f[1]*a[1]*a[0]^2*c[2]+2*f[3]*a[1]^2*a[
0]*c[3]-f[3]*a[2]^2*a[0]*c[1]-f[3]*a[3]*a[1]^2*c[0]+f[2]*a[2]*a[1]^2*c[0]+4*f[
6]*a[3]*a[2]^2*c[1]+2*f[6]*a[2]^2*a[1]*c[3]+2*f[6]*a[3]^2*a[2]*c[0]-f[7]*a[3]^
2*a[2]*c[1]-6*f[7]*a[3]*a[2]^2*c[2]+2*f[2]*a[1]*a[0]^2*c[3]-2*f[2]*a[3]*a[0]^2
*c[1]-2*f[6]*a[3]^2*a[1]*c[1]-a[2]*a[1]*c[3]*c[0]+f[3]*a[2]^2*a[1]*c[0]+3*f[5]
*a[2]*a[1]^2*c[3]+6*f[5]*a[3]*a[2]^2*c[0]-16*f[0]*a[0]^3*c[2]-2*f[6]*a[2]^3*c[
2]+2*a[2]^2*c[2]*c[0]+4*f[5]*a[2]^3*c[1]-2*a[1]^2*c[3]*c[1]+f[7]*a[2]^3*c[3]+2
*f[4]*a[2]^3*c[0]+2*f[4]*a[1]^3*c[3]+f[1]*a[1]^3*c[0]-2*a[2]^2*c[1]^2-8*f[5]*a
[2]^2*a[0]*c[3]-7*a[1]*a[0]*c[3]*c[2]+7*a[2]*a[0]*c[3]*c[1]+7*f[3]*a[2]*a[1]*a
[0]*c[2]-14*f[5]*a[3]*a[2]*a[0]*c[2]-6*f[6]*a[3]*a[2]*a[0]*c[3]-23*f[5]*a[3]*a
[2]*a[1]*c[1]-26*f[4]*a[3]*a[1]*a[0]*c[2]-11*f[4]*a[2]*a[1]*a[0]*c[3]-2*f[2]*a
[2]^2*a[0]*c[0]-3*f[4]*a[3]*a[2]*a[1]*c[0]-3*f[1]*a[2]*a[1]*a[0]*c[0]+f[2]*a[3
]*a[1]*a[0]*c[0]+a[3]*a[1]*c[1]^2+a[2]*a[0]*c[2]^2-a[2]^3*f[4]^2*a[0]-a[2]*f[2
]^2*a[0]^3+2*a[3]*a[2]^2*a[1]*f[4]*f[6]-a[2]*a[1]^2*f[2]*f[4]*a[0]+2*a[2]*a[1]
^2*f[1]*f[5]*a[0]+4*a[2]*a[1]^2*f[0]*f[6]*a[0]-6*a[3]^2*a[1]*f[2]*f[7]*a[0]+2*
a[3]*a[1]^2*f[1]*f[6]*a[0]-a[3]*a[1]^2*f[2]*f[5]*a[0]+2*a[2]^3*f[2]*f[6]*a[0]+
a[2]^3*f[1]*f[7]*a[0]+8*a[3]*a[1]^2*f[0]*f[7]*a[0]+2*a[2]^3*f[3]*f[5]*a[0]+2*a
[2]^2*f[2]*f[4]*a[0]^2-a[2]*a[1]*f[3]*f[2]*a[0]^2-f[3]*f[1]*a[1]^2*a[0]^2-f[1]
*f[2]*a[1]*a[0]^3-a[1]^3*f[1]*f[4]*a[0]+2*a[1]^3*f[5]*f[0]*a[0]+4*a[2]^2*a[1]*
f[1]*f[6]*a[0]+a[2]^2*a[1]*f[2]*f[5]*a[0]-a[3]*a[1]^2*f[3]*f[4]*a[0]-8*a[3]*a[
2]*f[1]*f[6]*a[0]^2+2*a[3]*a[2]*f[2]*f[5]*a[0]^2+8*a[3]*a[2]^2*f[2]*f[7]*a[0]-
a[3]*a[2]^2*f[4]*f[5]*a[0]-a[3]*a[1]*f[2]*f[4]*a[0]^2+2*a[3]^2*a[2]*a[1]*f[7]*
f[4]+44*a[3]^2*a[2]*a[1]*f[6]*f[5]+25*f[4]*f[5]*a[3]*a[2]*a[1]^2+40*f[7]*f[5]*
a[3]^3*a[1]+22*f[5]^2*a[3]*a[2]^2*a[1]-2*f[5]^2*a[3]^2*a[1]^2+4*f[7]^2*a[3]^4+
4*f[1]^2*a[0]^4+5*f[4]^2*a[2]^2*a[1]^2-18*a[2]^2*a[1]*f[0]*f[7]*a[0]-7*a[2]*a[
1]*f[1]*f[4]*a[0]^2-8*f[3]*f[1]*a[2]*a[0]^3+8*a[2]^2*f[0]*f[6]*a[0]^2-10*a[2]^
2*f[1]*f[5]*a[0]^2+12*a[2]*a[1]*f[0]*f[5]*a[0]^2-60*f[4]*f[5]*a[3]^2*a[1]*a[0]
+4*a[2]^2*f[3]^2*a[0]^2+8*a[3]*f[1]*f[4]*a[0]^3+9*a[2]^2*a[1]*f[3]*f[4]*a[0]+8
*a[3]^2*a[2]*f[7]*f[3]*a[0]+52*a[3]*a[2]*f[0]*f[7]*a[0]^2+4*a[3]^2*f[4]^2*a[0]
^2+20*a[3]*a[2]*a[1]*f[5]*f[3]*a[0]+14*a[3]^2*a[2]*f[4]*f[6]*a[0]-8*a[3]*a[2]*
f[3]*f[4]*a[0]^2-7*a[3]*a[2]*a[1]*f[4]^2*a[0]+10*f[1]*f[5]*a[3]*a[1]*a[0]^2-9*
a[3]*a[2]*a[1]*f[7]*f[1]*a[0]-48*a[3]^2*a[2]*f[5]^2*a[0]-48*a[3]^3*f[6]*f[5]*a
[0]-48*a[3]^2*f[5]*f[3]*a[0]^2+20*a[3]^2*f[7]*f[1]*a[0]^2-48*a[3]*f[0]*f[5]*a[
0]^3+53*a[3]^3*f[7]*f[4]*a[0]-f[1]*f[5]*a[1]^4-6*f[7]*f[6]*a[3]^3*a[2]-2*a[2]^
4*f[5]^2-18*a[3]^2*a[2]^2*f[7]*f[5]-a[2]^4*f[3]*f[7]-2*a[2]^4*f[4]*f[6]-4*a[3]
^2*a[2]^2*f[6]^2-7*a[3]*a[2]^3*f[7]*f[4]-10*a[3]*a[2]^3*f[6]*f[5]+2*a[3]^2*a[1
]^2*f[4]*f[6]+2*a[3]^2*a[1]^2*f[3]*f[7]-a[3]*a[2]^2*a[1]*f[3]*f[7]+a[3]*a[1]^3
*f[3]*f[5]-2*a[3]*a[1]^3*f[1]*f[7]-2*a[2]^3*a[1]*f[3]*f[6]-a[2]^3*a[1]*f[2]*f[
7]-a[3]*a[1]^3*f[4]^2+2*a[3]*a[2]*a[1]^2*f[3]*f[6]-2*a[3]*a[2]*a[1]^2*f[2]*f[7
]-a[2]^2*a[1]^2*f[3]*f[5]-2*a[2]^2*a[1]^2*f[2]*f[6]-a[2]^2*a[1]^2*f[1]*f[7]-2*
a[2]*a[1]^3*f[1]*f[6]-a[2]*a[1]^3*f[2]*f[5]:
eqn[20] :=
a[3]*a[0]*c[1]^2+f[7]*a[2]^3*c[2]+a[2]*a[1]*c[1]^2-f[5]*a[2]^3*c[0]-f[1]*a[0]^
3*c[2]+a[3]*a[2]*c[0]^2+a[2]^2*c[1]*c[0]-2*f[0]*a[0]^3*c[1]+2*a[1]^2*c[2]*c[1]
-2*f[6]*a[2]^3*c[1]+2*a[1]*a[0]*c[2]^2-2*f[6]*a[3]^2*a[0]*c[1]-16*f[7]*a[3]^2*
a[0]*c[2]+16*f[5]*a[3]^2*a[0]*c[0]-2*f[2]*a[1]*a[0]^2*c[2]+2*f[1]*a[2]*a[0]^2*
c[0]-2*f[5]*a[3]*a[0]^2*c[3]-2*f[7]*a[3]*a[2]^2*c[1]-2*f[3]*a[3]*a[0]^2*c[1]+3
*f[4]*a[2]*a[0]^2*c[3]-2*f[4]*a[1]^2*a[0]*c[3]+2*f[4]*a[2]*a[1]^2*c[1]-3*f[4]*
a[2]^2*a[0]*c[1]-2*f[3]*a[2]^2*a[0]*c[0]+2*f[4]*a[3]*a[1]^2*c[0]+2*f[0]*a[1]*a
[0]^2*c[0]-2*f[7]*a[3]^2*a[1]*c[1]-2*f[6]*a[2]^2*a[0]*c[3]-6*f[7]*a[3]^2*a[2]*
c[0]-4*f[6]*a[3]*a[2]^2*c[0]-2*f[3]*a[1]^2*a[0]*c[2]+6*f[5]*a[3]*a[1]^2*c[1]-f
[1]*a[1]^2*a[0]*c[0]-f[5]*a[2]^2*a[0]*c[2]-f[4]*a[3]*a[0]^2*c[2]-f[4]*a[2]^2*a
[1]*c[0]+f[3]*a[2]*a[0]^2*c[2]-f[2]*a[3]*a[0]^2*c[0]+f[5]*a[3]*a[2]*a[1]*c[0]+
a[2]*a[0]*c[3]*c[0]+5*a[3]*a[0]*c[2]*c[0]-f[2]*a[2]*a[1]*a[0]*c[0]+f[3]*a[3]*a
[1]*a[0]*c[0]+f[5]*a[2]*a[1]^2*c[2]-2*f[4]*a[3]*a[1]*a[0]*c[1]+11*f[5]*a[3]*a[
1]*a[0]*c[2]-4*f[7]*a[3]*a[2]*a[0]*c[3]-8*f[6]*a[3]*a[2]*a[0]*c[2]-4*f[5]*a[2]
*a[1]*a[0]*c[3]+a[2]^4*f[4]*f[7]+2*a[2]^4*f[5]*f[6]-4*a[3]*a[2]*a[1]^2*f[4]*f[
6]-2*a[3]*a[2]^2*a[1]*f[5]*f[6]+2*a[3]*a[2]^2*a[1]*f[4]*f[7]+2*a[2]^3*a[1]*f[4
]*f[6]+a[3]*a[2]*a[1]^2*f[5]^2+4*a[3]*a[2]^3*f[6]^2-a[2]^3*a[1]*f[5]^2+5*a[3]*
a[2]^3*f[5]*f[7]-4*f[4]*f[7]*a[3]^2*a[1]^2+12*f[6]*f[7]*a[3]^2*a[2]^2-f[5]*f[7
]*a[3]^2*a[2]*a[1]-2*f[4]*f[5]*a[3]*a[1]^3+8*f[7]^2*a[3]^3*a[2]-f[4]^2*a[2]*a[
1]^3-f[4]*f[5]*a[2]^2*a[1]^2-4*a[3]^2*a[1]*f[3]*f[7]*a[0]-5*a[3]*a[1]*f[5]*f[2
]*a[0]^2-7*a[3]*a[1]^2*f[3]*f[5]*a[0]+6*a[3]*a[1]^2*f[1]*f[7]*a[0]+a[3]*a[1]^2
*f[4]^2*a[0]-8*a[3]*a[1]*f[7]*f[0]*a[0]^2-4*a[3]*a[2]^2*f[5]^2*a[0]-a[3]*a[2]*
f[4]^2*a[0]^2+f[1]*f[2]*a[0]^4-7*a[3]*a[2]*f[1]*f[7]*a[0]^2+5*a[3]*a[2]^2*f[3]
*f[7]*a[0]+6*a[3]*a[2]*f[3]*f[5]*a[0]^2+2*a[3]*a[2]^2*f[4]*f[6]*a[0]+2*a[3]*a[
2]*a[1]*f[2]*f[7]*a[0]+4*a[3]*a[2]*a[1]*f[4]*f[5]*a[0]-24*a[3]^2*a[2]*f[5]*f[6
]*a[0]-2*a[3]^2*f[4]*f[5]*a[0]^2+14*a[3]^2*a[1]*f[5]^2*a[0]-2*a[3]^2*a[2]*f[4]
*f[7]*a[0]-a[2]*a[1]*f[4]*f[2]*a[0]^2+4*a[2]*f[0]*f[5]*a[0]^3+a[2]^2*f[4]*f[3]
*a[0]^2-4*a[2]^2*f[1]*f[6]*a[0]^2-2*a[2]^2*f[7]*f[0]*a[0]^2+2*a[2]^3*f[4]*f[5]
*a[0]-a[2]^3*f[2]*f[7]*a[0]+4*a[2]^3*f[3]*f[6]*a[0]-2*a[1]^2*f[0]*f[5]*a[0]^2+
2*a[2]^2*a[1]*f[3]*f[5]*a[0]+a[2]*a[1]^2*f[5]*f[2]*a[0]-a[2]*f[3]*f[2]*a[0]^3-
a[2]^2*a[1]*f[1]*f[7]*a[0]-2*a[2]*a[1]^2*f[4]*f[3]*a[0]+2*a[2]*a[1]^2*f[1]*f[6
]*a[0]-a[2]*f[4]*f[1]*a[0]^3+4*a[3]^2*f[2]*f[7]*a[0]^2-50*f[5]*f[7]*a[3]^3*a[0
]-a[2]*a[1]*f[3]^2*a[0]^2+a[2]^2*a[1]*f[4]^2*a[0]+4*a[2]*a[1]^2*f[7]*f[0]*a[0]
-2*a[3]*a[2]*a[1]*f[3]*f[6]*a[0]+a[3]*f[4]*f[2]*a[0]^3-2*a[3]*f[5]*f[1]*a[0]^3
+a[1]^2*f[4]*f[1]*a[0]^2+a[2]^2*f[5]*f[2]*a[0]^2-a[2]*a[1]*f[5]*f[1]*a[0]^2+2*
a[2]^2*a[1]*f[2]*f[6]*a[0]+a[3]*a[1]*f[4]*f[3]*a[0]^2+2*a[3]^2*a[1]*f[4]*f[6]*
a[0]+2*a[3]*a[1]*f[1]*f[6]*a[0]^2+f[5]*f[1]*a[1]^3*a[0]+f[1]*f[3]*a[1]*a[0]^3:
eqn[21] :=
-2*a[3]*a[0]*c[1]^2+a[2]*a[1]*c[1]^2+f[1]*a[0]^3*c[2]+2*f[0]*a[0]^3*c[1]-a[1]*
a[0]*c[2]^2+2*f[6]*a[3]^2*a[0]*c[1]+7*f[7]*a[3]^2*a[0]*c[2]-10*f[5]*a[3]^2*a[0
]*c[0]+8*f[5]*a[3]*a[0]^2*c[3]+f[7]*a[3]*a[2]^2*c[1]+2*f[3]*a[3]*a[0]^2*c[1]-f
[4]*a[2]*a[0]^2*c[3]-2*f[4]*a[2]*a[1]^2*c[1]+2*f[4]*a[2]^2*a[0]*c[1]-f[4]*a[3]
*a[1]^2*c[0]-2*f[0]*a[1]*a[0]^2*c[0]-2*f[7]*a[3]^2*a[1]*c[1]+f[7]*a[3]^2*a[2]*
c[0]+2*f[3]*a[1]^2*a[0]*c[2]-f[5]*a[3]*a[1]^2*c[1]-2*f[3]*a[1]*a[0]^2*c[3]+f[4
]*a[3]*a[0]^2*c[2]-f[3]*a[2]*a[0]^2*c[2]+f[2]*a[3]*a[0]^2*c[0]+f[5]*a[3]*a[2]*
a[1]*c[0]-2*a[3]*a[0]*c[2]*c[0]+f[3]*a[3]*a[1]*a[0]*c[0]+2*f[5]*a[2]*a[1]^2*c[
2]+3*f[4]*a[3]*a[1]*a[0]*c[1]-9*f[5]*a[3]*a[1]*a[0]*c[2]-2*f[7]*a[3]*a[2]*a[0]
*c[3]+2*f[6]*a[3]*a[2]*a[0]*c[2]-2*f[5]*a[2]*a[1]*a[0]*c[3]+a[0]^2*c[3]*c[2]-2
*f[6]*a[3]*a[2]*a[1]*c[1]+a[3]*a[1]*c[1]*c[0]+f[1]*a[1]*a[0]^2*c[1]-f[2]*a[2]*
a[0]^2*c[1]+2*a[3]*a[2]*a[1]^2*f[4]*f[6]-2*a[3]*a[2]^2*a[1]*f[5]*f[6]-a[3]*a[2
]^2*a[1]*f[4]*f[7]+5*a[3]*a[2]*a[1]^2*f[5]^2-a[2]^3*a[1]*f[5]^2-a[3]*a[2]^3*f[
5]*f[7]+2*f[4]*f[7]*a[3]^2*a[1]^2-2*f[6]*f[7]*a[3]^2*a[2]^2-5*f[5]*f[7]*a[3]^2
*a[2]*a[1]+f[4]*f[5]*a[3]*a[1]^3-2*f[7]^2*a[3]^3*a[2]+f[4]^2*a[2]*a[1]^3+2*f[4
]*f[5]*a[2]^2*a[1]^2-2*a[3]^2*a[1]*f[3]*f[7]*a[0]-a[3]*a[1]*f[5]*f[2]*a[0]^2+5
*a[3]*a[1]^2*f[3]*f[5]*a[0]-2*a[3]*a[1]^2*f[1]*f[7]*a[0]-a[3]*a[1]^2*f[4]^2*a[
0]+8*a[3]*a[1]*f[7]*f[0]*a[0]^2+2*a[3]*a[2]^2*f[5]^2*a[0]+a[3]*a[2]*f[4]^2*a[0
]^2-f[1]*f[2]*a[0]^4+a[3]*a[2]*f[1]*f[7]*a[0]^2+a[3]*a[2]^2*f[3]*f[7]*a[0]-6*a
[3]*a[2]*f[3]*f[5]*a[0]^2-2*a[3]*a[2]^2*f[4]*f[6]*a[0]+2*a[3]*a[2]*a[1]*f[2]*f
[7]*a[0]-4*a[3]*a[2]*a[1]*f[4]*f[5]*a[0]+12*a[3]^2*a[2]*f[5]*f[6]*a[0]+2*a[3]^
2*f[4]*f[5]*a[0]^2-14*a[3]^2*a[1]*f[5]^2*a[0]+2*a[3]^2*a[2]*f[4]*f[7]*a[0]+a[2
]*a[1]*f[4]*f[2]*a[0]^2-4*a[2]*f[0]*f[5]*a[0]^3-a[2]^2*f[4]*f[3]*a[0]^2+2*a[2]
^2*f[7]*f[0]*a[0]^2-2*a[2]^3*f[4]*f[5]*a[0]+2*a[1]^2*f[0]*f[5]*a[0]^2+a[2]*f[3
]*f[2]*a[0]^3+2*a[2]*a[1]^2*f[4]*f[3]*a[0]+a[2]*f[4]*f[1]*a[0]^3-4*a[3]^2*f[2]
*f[7]*a[0]^2+32*f[5]*f[7]*a[3]^3*a[0]+a[2]*a[1]*f[3]^2*a[0]^2-a[2]^2*a[1]*f[4]
^2*a[0]-4*a[2]*a[1]^2*f[7]*f[0]*a[0]-2*a[3]*a[2]*a[1]*f[3]*f[6]*a[0]-a[3]*f[4]
*f[2]*a[0]^3+2*a[3]*f[5]*f[1]*a[0]^3-a[1]^2*f[4]*f[1]*a[0]^2+a[2]^2*f[5]*f[2]*
a[0]^2-a[2]*a[1]*f[5]*f[1]*a[0]^2-a[3]*a[1]*f[4]*f[3]*a[0]^2-2*a[3]^2*a[1]*f[4
]*f[6]*a[0]-2*a[3]*a[1]*f[1]*f[6]*a[0]^2-f[1]*f[3]*a[1]*a[0]^3:
eqn[22] :=
-a[3]*a[0]*c[1]^2-f[7]*a[2]^3*c[2]-a[2]*a[1]*c[1]^2+f[1]*a[0]^3*c[2]+2*f[0]*a[
0]^3*c[1]-2*a[1]^2*c[2]*c[1]+2*f[6]*a[2]^3*c[1]-2*a[1]*a[0]*c[2]^2+2*f[6]*a[3]
^2*a[0]*c[1]+16*f[7]*a[3]^2*a[0]*c[2]-16*f[5]*a[3]^2*a[0]*c[0]+2*f[2]*a[1]*a[0
]^2*c[2]-2*f[1]*a[2]*a[0]^2*c[0]+2*f[5]*a[3]*a[0]^2*c[3]+2*f[7]*a[3]*a[2]^2*c[
1]+2*f[3]*a[3]*a[0]^2*c[1]-3*f[4]*a[2]*a[0]^2*c[3]+2*f[4]*a[1]^2*a[0]*c[3]-2*f
[4]*a[2]*a[1]^2*c[1]+3*f[4]*a[2]^2*a[0]*c[1]+2*f[3]*a[2]^2*a[0]*c[0]-2*f[4]*a[
3]*a[1]^2*c[0]-2*f[0]*a[1]*a[0]^2*c[0]+2*f[7]*a[3]^2*a[1]*c[1]+2*f[6]*a[2]^2*a
[0]*c[3]+3*f[7]*a[3]^2*a[2]*c[0]+2*f[6]*a[3]*a[2]^2*c[0]+2*f[3]*a[1]^2*a[0]*c[
2]-6*f[5]*a[3]*a[1]^2*c[1]+f[1]*a[1]^2*a[0]*c[0]+f[5]*a[2]^2*a[0]*c[2]+f[4]*a[
3]*a[0]^2*c[2]+f[4]*a[2]^2*a[1]*c[0]-f[3]*a[2]*a[0]^2*c[2]+f[2]*a[3]*a[0]^2*c[
0]+f[5]*a[3]*a[2]*a[1]*c[0]-2*a[2]*a[0]*c[3]*c[0]-5*a[3]*a[0]*c[2]*c[0]+f[2]*a
[2]*a[1]*a[0]*c[0]-f[3]*a[3]*a[1]*a[0]*c[0]-f[5]*a[2]*a[1]^2*c[2]+2*f[4]*a[3]*
a[1]*a[0]*c[1]-11*f[5]*a[3]*a[1]*a[0]*c[2]+4*f[7]*a[3]*a[2]*a[0]*c[3]+8*f[6]*a
[3]*a[2]*a[0]*c[2]+4*f[5]*a[2]*a[1]*a[0]*c[3]+a[2]*a[1]*c[2]*c[0]-a[2]^4*f[4]*
f[7]-2*a[2]^4*f[5]*f[6]+4*a[3]*a[2]*a[1]^2*f[4]*f[6]+2*a[3]*a[2]^2*a[1]*f[5]*f
[6]-2*a[3]*a[2]^2*a[1]*f[4]*f[7]-2*a[2]^3*a[1]*f[4]*f[6]-a[3]*a[2]*a[1]^2*f[5]
^2-4*a[3]*a[2]^3*f[6]^2+a[2]^3*a[1]*f[5]^2-5*a[3]*a[2]^3*f[5]*f[7]+4*f[4]*f[7]
*a[3]^2*a[1]^2-12*f[6]*f[7]*a[3]^2*a[2]^2+f[5]*f[7]*a[3]^2*a[2]*a[1]+2*f[4]*f[
5]*a[3]*a[1]^3-8*f[7]^2*a[3]^3*a[2]+f[4]^2*a[2]*a[1]^3+f[4]*f[5]*a[2]^2*a[1]^2
+4*a[3]^2*a[1]*f[3]*f[7]*a[0]+5*a[3]*a[1]*f[5]*f[2]*a[0]^2+7*a[3]*a[1]^2*f[3]*
f[5]*a[0]-6*a[3]*a[1]^2*f[1]*f[7]*a[0]-a[3]*a[1]^2*f[4]^2*a[0]+8*a[3]*a[1]*f[7
]*f[0]*a[0]^2+4*a[3]*a[2]^2*f[5]^2*a[0]+a[3]*a[2]*f[4]^2*a[0]^2-f[1]*f[2]*a[0]
^4+7*a[3]*a[2]*f[1]*f[7]*a[0]^2-5*a[3]*a[2]^2*f[3]*f[7]*a[0]-6*a[3]*a[2]*f[3]*
f[5]*a[0]^2-2*a[3]*a[2]^2*f[4]*f[6]*a[0]-2*a[3]*a[2]*a[1]*f[2]*f[7]*a[0]-4*a[3
]*a[2]*a[1]*f[4]*f[5]*a[0]+24*a[3]^2*a[2]*f[5]*f[6]*a[0]+2*a[3]^2*f[4]*f[5]*a[
0]^2-14*a[3]^2*a[1]*f[5]^2*a[0]+2*a[3]^2*a[2]*f[4]*f[7]*a[0]+a[2]*a[1]*f[4]*f[
2]*a[0]^2-4*a[2]*f[0]*f[5]*a[0]^3-a[2]^2*f[4]*f[3]*a[0]^2+4*a[2]^2*f[1]*f[6]*a
[0]^2+2*a[2]^2*f[7]*f[0]*a[0]^2-2*a[2]^3*f[4]*f[5]*a[0]+a[2]^3*f[2]*f[7]*a[0]-\
4*a[2]^3*f[3]*f[6]*a[0]+2*a[1]^2*f[0]*f[5]*a[0]^2-2*a[2]^2*a[1]*f[3]*f[5]*a[0]
-a[2]*a[1]^2*f[5]*f[2]*a[0]+a[2]*f[3]*f[2]*a[0]^3+a[2]^2*a[1]*f[1]*f[7]*a[0]+2
*a[2]*a[1]^2*f[4]*f[3]*a[0]-2*a[2]*a[1]^2*f[1]*f[6]*a[0]+a[2]*f[4]*f[1]*a[0]^3
-4*a[3]^2*f[2]*f[7]*a[0]^2+50*f[5]*f[7]*a[3]^3*a[0]+a[2]*a[1]*f[3]^2*a[0]^2-a[
2]^2*a[1]*f[4]^2*a[0]-4*a[2]*a[1]^2*f[7]*f[0]*a[0]+2*a[3]*a[2]*a[1]*f[3]*f[6]*
a[0]-a[3]*f[4]*f[2]*a[0]^3+2*a[3]*f[5]*f[1]*a[0]^3-a[1]^2*f[4]*f[1]*a[0]^2-a[2
]^2*f[5]*f[2]*a[0]^2+a[2]*a[1]*f[5]*f[1]*a[0]^2-2*a[2]^2*a[1]*f[2]*f[6]*a[0]-a
[3]*a[1]*f[4]*f[3]*a[0]^2-2*a[3]^2*a[1]*f[4]*f[6]*a[0]-2*a[3]*a[1]*f[1]*f[6]*a
[0]^2-f[5]*f[1]*a[1]^3*a[0]-f[1]*f[3]*a[1]*a[0]^3:
eqn[23] :=
-2*a[3]*a[0]*c[1]^2+a[2]*a[1]*c[1]^2+f[1]*a[0]^3*c[2]+2*f[0]*a[0]^3*c[1]+2*f[6
]*a[3]^2*a[0]*c[1]+4*f[7]*a[3]^2*a[0]*c[2]-10*f[5]*a[3]^2*a[0]*c[0]+8*f[5]*a[3
]*a[0]^2*c[3]+f[7]*a[3]*a[2]^2*c[1]+2*f[3]*a[3]*a[0]^2*c[1]-f[4]*a[2]*a[0]^2*c
[3]-2*f[4]*a[2]*a[1]^2*c[1]+2*f[4]*a[2]^2*a[0]*c[1]-f[4]*a[3]*a[1]^2*c[0]-2*f[
0]*a[1]*a[0]^2*c[0]-2*f[7]*a[3]^2*a[1]*c[1]+f[7]*a[3]^2*a[2]*c[0]+2*f[3]*a[1]^
2*a[0]*c[2]-f[5]*a[3]*a[1]^2*c[1]-2*f[3]*a[1]*a[0]^2*c[3]-f[5]*a[2]^2*a[0]*c[2
]+f[4]*a[3]*a[0]^2*c[2]-f[3]*a[2]*a[0]^2*c[2]+f[2]*a[3]*a[0]^2*c[0]+f[5]*a[3]*
a[2]*a[1]*c[0]-a[3]*a[0]*c[2]*c[0]+f[3]*a[3]*a[1]*a[0]*c[0]+2*f[5]*a[2]*a[1]^2
*c[2]+3*f[4]*a[3]*a[1]*a[0]*c[1]-7*f[5]*a[3]*a[1]*a[0]*c[2]-2*f[7]*a[3]*a[2]*a
[0]*c[3]-2*f[5]*a[2]*a[1]*a[0]*c[3]-2*f[6]*a[3]*a[2]*a[1]*c[1]+a[3]*a[1]*c[1]*
c[0]+f[1]*a[1]*a[0]^2*c[1]-f[2]*a[2]*a[0]^2*c[1]+a[2]*a[0]*c[2]*c[1]+2*a[3]*a[
2]*a[1]^2*f[4]*f[6]-2*a[3]*a[2]^2*a[1]*f[5]*f[6]-a[3]*a[2]^2*a[1]*f[4]*f[7]+5*
a[3]*a[2]*a[1]^2*f[5]^2-a[2]^3*a[1]*f[5]^2-a[3]*a[2]^3*f[5]*f[7]+2*f[4]*f[7]*a
[3]^2*a[1]^2-2*f[6]*f[7]*a[3]^2*a[2]^2-5*f[5]*f[7]*a[3]^2*a[2]*a[1]+f[4]*f[5]*
a[3]*a[1]^3-2*f[7]^2*a[3]^3*a[2]+f[4]^2*a[2]*a[1]^3+2*f[4]*f[5]*a[2]^2*a[1]^2-\
2*a[3]^2*a[1]*f[3]*f[7]*a[0]-a[3]*a[1]*f[5]*f[2]*a[0]^2+5*a[3]*a[1]^2*f[3]*f[5
]*a[0]-2*a[3]*a[1]^2*f[1]*f[7]*a[0]-a[3]*a[1]^2*f[4]^2*a[0]+8*a[3]*a[1]*f[7]*f
[0]*a[0]^2+2*a[3]*a[2]^2*f[5]^2*a[0]+a[3]*a[2]*f[4]^2*a[0]^2-f[1]*f[2]*a[0]^4+
a[3]*a[2]*f[1]*f[7]*a[0]^2+a[3]*a[2]^2*f[3]*f[7]*a[0]-6*a[3]*a[2]*f[3]*f[5]*a[
0]^2-2*a[3]*a[2]^2*f[4]*f[6]*a[0]+2*a[3]*a[2]*a[1]*f[2]*f[7]*a[0]-4*a[3]*a[2]*
a[1]*f[4]*f[5]*a[0]+12*a[3]^2*a[2]*f[5]*f[6]*a[0]+2*a[3]^2*f[4]*f[5]*a[0]^2-14
*a[3]^2*a[1]*f[5]^2*a[0]+2*a[3]^2*a[2]*f[4]*f[7]*a[0]+a[2]*a[1]*f[4]*f[2]*a[0]
^2-4*a[2]*f[0]*f[5]*a[0]^3-a[2]^2*f[4]*f[3]*a[0]^2+2*a[2]^2*f[7]*f[0]*a[0]^2-2
*a[2]^3*f[4]*f[5]*a[0]+2*a[1]^2*f[0]*f[5]*a[0]^2+a[2]*f[3]*f[2]*a[0]^3+2*a[2]*
a[1]^2*f[4]*f[3]*a[0]+a[2]*f[4]*f[1]*a[0]^3-4*a[3]^2*f[2]*f[7]*a[0]^2+32*f[5]*
f[7]*a[3]^3*a[0]+a[2]*a[1]*f[3]^2*a[0]^2-a[2]^2*a[1]*f[4]^2*a[0]-4*a[2]*a[1]^2
*f[7]*f[0]*a[0]-2*a[3]*a[2]*a[1]*f[3]*f[6]*a[0]-a[3]*f[4]*f[2]*a[0]^3+2*a[3]*f
[5]*f[1]*a[0]^3-a[1]^2*f[4]*f[1]*a[0]^2+a[2]^2*f[5]*f[2]*a[0]^2-a[2]*a[1]*f[5]
*f[1]*a[0]^2-a[3]*a[1]*f[4]*f[3]*a[0]^2-2*a[3]^2*a[1]*f[4]*f[6]*a[0]-2*a[3]*a[
1]*f[1]*f[6]*a[0]^2-f[1]*f[3]*a[1]*a[0]^3:
eqn[24] :=
-2*a[1]^2*c[1]^2-5*f[4]*a[1]*a[0]^2*c[3]+7*f[4]*a[1]^2*a[0]*c[2]-4*f[5]*a[3]*a
[1]^2*c[0]+2*f[5]*a[3]*a[0]^2*c[2]+3*f[5]*a[2]*a[1]^2*c[1]+14*f[5]*a[2]*a[0]^2
*c[3]+2*f[6]*a[2]*a[1]^2*c[2]+2*f[3]*a[1]*a[0]^2*c[2]+2*f[7]*a[2]^2*a[0]*c[3]+
31*f[7]*a[3]^2*a[0]*c[1]-2*f[4]*a[2]*a[0]^2*c[2]-2*f[6]*a[2]^2*a[0]*c[2]+4*f[2
]*a[1]*a[0]^2*c[1]-2*f[2]*a[2]*a[0]^2*c[0]+3*f[7]*a[3]^2*a[1]*c[0]+8*f[3]*a[3]
*a[0]^2*c[0]+4*f[3]*a[1]^2*a[0]*c[1]-10*a[3]*a[0]*c[1]*c[0]-3*a[1]*a[0]*c[2]*c
[1]-10*f[6]*a[3]^2*a[0]*c[0]+4*f[7]*a[3]*a[1]^2*c[2]+18*f[6]*a[3]*a[0]^2*c[3]+
2*a[2]*a[0]*c[2]*c[0]+f[1]*a[0]^3*c[1]-f[7]*a[2]^3*c[1]-a[1]^2*c[2]*c[0]+a[0]^
2*c[3]*c[1]+4*f[4]*a[1]^3*c[1]+8*f[0]*a[0]^3*c[0]+2*f[2]*a[0]^3*c[2]-f[3]*a[2]
*a[1]*a[0]*c[0]-f[3]*a[2]*a[0]^2*c[1]+2*f[4]*a[2]^2*a[0]*c[0]-16*f[5]*a[2]^2*a
[0]*c[1]-f[7]*a[3]*a[2]^2*c[0]+f[4]*a[3]*a[0]^2*c[1]-f[4]*a[2]*a[1]^2*c[0]-f[1
]*a[1]*a[0]^2*c[0]+a[1]*a[0]*c[3]*c[0]-2*f[7]*a[3]*a[2]*a[1]*c[1]-2*f[6]*a[2]*
a[1]*a[0]*c[3]-10*f[7]*a[3]*a[2]*a[0]*c[2]-14*f[5]*a[2]*a[1]*a[0]*c[2]+12*f[4]
*a[3]*a[1]*a[0]*c[0]-14*f[6]*a[3]*a[1]*a[0]*c[2]-3*f[5]*a[3]*a[1]*a[0]*c[1]-2*
f[4]^2*a[1]^4+2*a[2]^2*a[1]^2*f[4]*f[6]+8*a[3]*a[2]*a[1]^2*f[6]*f[5]+6*a[3]*a[
2]*a[1]^2*f[4]*f[7]-a[2]^2*a[1]^2*f[5]^2+3*f[7]*f[5]*a[3]*a[2]^2*a[1]+12*f[7]*
f[5]*a[3]^2*a[1]^2-6*f[6]*f[7]*a[3]^2*a[2]*a[1]+2*f[6]*f[7]*a[3]*a[2]^3-8*f[7]
^2*a[3]^3*a[1]+f[5]^2*a[3]*a[1]^3-3*f[4]*f[5]*a[2]*a[1]^3+f[7]*f[5]*a[2]^4+f[4
]*f[7]*a[2]^3*a[1]-2*f[2]^2*a[0]^4-2*a[2]^2*a[1]*f[7]*f[2]*a[0]+4*a[2]*a[1]*f[
4]*f[3]*a[0]^2-2*a[2]*a[1]*f[2]*f[5]*a[0]^2+2*a[2]^2*a[1]*f[6]*f[3]*a[0]-2*a[2
]*a[1]^2*f[7]*f[1]*a[0]-8*a[2]*a[1]*f[0]*f[7]*a[0]^2-a[2]^2*a[1]*f[4]*f[5]*a[0
]+8*a[1]^2*f[0]*f[6]*a[0]^2-4*a[1]^2*f[2]*f[4]*a[0]^2+30*f[6]*f[7]*a[3]^3*a[0]
-2*a[2]*f[1]*f[5]*a[0]^3+4*a[2]*f[2]*f[4]*a[0]^3-16*a[2]*f[0]*f[6]*a[0]^3+2*a[
2]^2*f[6]*f[2]*a[0]^2-3*a[2]*a[1]^2*f[5]*f[3]*a[0]-2*a[2]^2*f[4]^2*a[0]^2-8*a[
3]*a[1]^2*f[7]*f[2]*a[0]-2*a[2]^3*f[4]*f[6]*a[0]-a[2]^3*f[7]*f[3]*a[0]+2*a[2]^
2*f[5]*f[3]*a[0]^2+a[2]^2*f[7]*f[1]*a[0]^2-32*f[5]*f[6]*a[3]^2*a[1]*a[0]+2*a[3
]*a[1]*f[5]*f[3]*a[0]^2+4*a[3]^2*f[5]^2*a[0]^2-24*a[3]*f[0]*f[7]*a[0]^3+4*a[3]
*a[1]*f[7]*f[1]*a[0]^2-8*a[3]*a[1]*f[6]*f[2]*a[0]^2-35*a[3]^2*a[1]*f[4]*f[7]*a
[0]+13*a[3]*a[1]^2*f[4]*f[5]*a[0]-11*a[3]*a[2]^2*f[4]*f[7]*a[0]+12*a[3]*a[2]*f
[7]*f[2]*a[0]^2-24*a[3]^2*f[7]*f[3]*a[0]^2-4*a[3]*a[2]*f[4]*f[5]*a[0]^2+20*f[6
]^2*a[3]^2*a[2]*a[0]-8*f[5]*f[7]*a[3]^2*a[2]*a[0]+2*a[3]*f[2]*f[5]*a[0]^3+26*f
[5]*f[6]*a[3]*a[2]^2*a[0]-16*a[3]*a[2]*f[6]*f[3]*a[0]^2-32*f[5]^2*a[3]*a[2]*a[
1]*a[0]-18*a[3]*a[2]*a[1]*f[4]*f[6]*a[0]-4*f[2]*f[3]*a[1]*a[0]^3+a[1]^2*f[1]*f
[5]*a[0]^2-4*a[1]^3*f[4]*f[3]*a[0]+8*a[1]^3*f[0]*f[7]*a[0]+16*f[5]^2*a[2]^3*a[
0]-2*a[1]^2*f[3]^2*a[0]^2+4*a[2]*a[1]^2*f[4]^2*a[0]:
eqn[25] :=
a[1]^2*c[1]^2+a[0]^2*c[2]^2+2*f[4]*a[1]*a[0]^2*c[3]-4*f[4]*a[1]^2*a[0]*c[2]+4*
f[5]*a[3]*a[0]^2*c[2]-2*f[5]*a[2]*a[1]^2*c[1]-4*f[5]*a[2]*a[0]^2*c[3]-2*f[3]*a
[1]*a[0]^2*c[2]-12*f[7]*a[3]^2*a[0]*c[1]+2*f[4]*a[2]*a[0]^2*c[2]-2*f[2]*a[1]*a
[0]^2*c[1]-4*f[7]*a[3]^2*a[1]*c[0]-4*f[3]*a[3]*a[0]^2*c[0]-2*f[3]*a[1]^2*a[0]*
c[1]+4*a[3]*a[0]*c[1]*c[0]+2*a[1]*a[0]*c[2]*c[1]+4*f[6]*a[3]^2*a[0]*c[0]-4*f[7
]*a[3]*a[1]^2*c[2]-8*f[6]*a[3]*a[0]^2*c[3]-2*f[4]*a[1]^3*c[1]-4*f[0]*a[0]^3*c[
0]-2*f[2]*a[0]^3*c[2]+4*f[5]*a[2]^2*a[0]*c[1]-2*f[7]*a[3]*a[2]*a[1]*c[1]+2*f[7
]*a[3]*a[2]*a[0]*c[2]+2*f[5]*a[2]*a[1]*a[0]*c[2]-6*f[4]*a[3]*a[1]*a[0]*c[0]+4*
f[6]*a[3]*a[1]*a[0]*c[2]+4*f[5]*a[3]*a[1]*a[0]*c[1]+2*a[3]*a[2]*a[1]*f[3]*f[7]
*a[0]+f[7]^2*a[3]^2*a[2]^2+f[4]^2*a[1]^4-2*a[3]*a[2]*a[1]^2*f[4]*f[7]+a[2]^2*a
[1]^2*f[5]^2+2*f[7]*f[5]*a[3]*a[2]^2*a[1]-8*f[7]*f[5]*a[3]^2*a[1]^2+8*f[6]*f[7
]*a[3]^2*a[2]*a[1]+12*f[7]^2*a[3]^3*a[1]+2*f[4]*f[5]*a[2]*a[1]^3+f[2]^2*a[0]^4
-2*a[2]*a[1]*f[4]*f[3]*a[0]^2+2*a[2]*a[1]*f[2]*f[5]*a[0]^2+4*a[2]*a[1]*f[0]*f[
7]*a[0]^2-4*a[1]^2*f[0]*f[6]*a[0]^2+2*a[1]^2*f[2]*f[4]*a[0]^2-12*f[6]*f[7]*a[3
]^3*a[0]-2*a[2]*f[2]*f[4]*a[0]^3+8*a[2]*f[0]*f[6]*a[0]^3+2*a[2]*a[1]^2*f[5]*f[
3]*a[0]+a[2]^2*f[4]^2*a[0]^2+4*a[3]*a[1]^2*f[7]*f[2]*a[0]+8*f[5]*f[6]*a[3]^2*a
[1]*a[0]-4*a[3]*a[1]*f[5]*f[3]*a[0]^2+4*a[3]^2*f[5]^2*a[0]^2+12*a[3]*f[0]*f[7]
*a[0]^3+4*a[3]*a[1]*f[6]*f[2]*a[0]^2+18*a[3]^2*a[1]*f[4]*f[7]*a[0]-8*a[3]*a[1]
^2*f[4]*f[5]*a[0]+2*a[3]*a[2]^2*f[4]*f[7]*a[0]-2*a[3]*a[2]*f[7]*f[2]*a[0]^2+12
*a[3]^2*f[7]*f[3]*a[0]^2+4*a[3]*a[2]*f[4]*f[5]*a[0]^2-8*f[6]^2*a[3]^2*a[2]*a[0
]+4*f[5]*f[7]*a[3]^2*a[2]*a[0]-4*a[3]*f[2]*f[5]*a[0]^3-8*f[5]*f[6]*a[3]*a[2]^2
*a[0]+8*a[3]*a[2]*f[6]*f[3]*a[0]^2+4*f[5]^2*a[3]*a[2]*a[1]*a[0]+8*a[3]*a[2]*a[
1]*f[4]*f[6]*a[0]+2*f[2]*f[3]*a[1]*a[0]^3+2*a[1]^3*f[4]*f[3]*a[0]-4*a[1]^3*f[0
]*f[7]*a[0]-4*f[5]^2*a[2]^3*a[0]+a[1]^2*f[3]^2*a[0]^2-2*a[2]*a[1]^2*f[4]^2*a[0
]:
eqn[26] :=
6*f[6]*a[2]^2*a[0]*c[1]+2*f[5]*a[2]*a[0]^2*c[2]-3*a[2]*a[0]*c[1]*c[0]+3*f[5]*a
[1]*a[0]^2*c[3]-2*f[5]*a[3]*a[0]^2*c[1]-4*f[5]*a[1]^2*a[0]*c[2]-2*f[4]*a[3]*a[
0]^2*c[0]-2*f[6]*a[2]*a[1]^2*c[1]-2*f[6]*a[2]*a[0]^2*c[3]-16*f[7]*a[3]^2*a[0]*
c[0]+3*f[5]*a[2]^2*a[0]*c[0]+5*f[7]*a[3]*a[0]^2*c[3]-2*f[7]*a[3]*a[1]^2*c[1]+2
*f[3]*a[2]*a[0]^2*c[0]-f[4]*a[1]^3*c[0]-a[1]*a[0]*c[1]^2-a[0]^2*c[2]*c[1]-f[5]
*a[1]^3*c[1]+f[2]*a[0]^3*c[1]+a[0]^2*c[3]*c[0]+a[3]*a[0]*c[0]^2+a[1]^2*c[1]*c[
0]-2*f[1]*a[0]^3*c[0]+f[7]*a[2]*a[1]*a[0]*c[3]+f[4]*a[1]^2*a[0]*c[1]-f[2]*a[1]
*a[0]^2*c[0]-5*f[5]*a[3]*a[1]*a[0]*c[0]+2*f[6]*a[2]*a[1]*a[0]*c[2]+3*f[4]*a[2]
*a[1]*a[0]*c[0]+2*f[6]*a[3]*a[1]*a[0]*c[1]+2*f[7]*a[3]*a[2]*a[1]*c[0]-f[7]*a[2
]^2*a[0]*c[2]+f[7]*a[2]*a[1]^2*c[2]+f[3]*a[1]*a[0]^2*c[1]-f[3]*a[1]^2*a[0]*c[0
]-f[5]*a[2]*a[1]^2*c[0]-f[4]*a[2]*a[0]^2*c[1]-9*f[7]*a[3]*a[1]*a[0]*c[2]+f[4]*
f[5]*a[1]^4+a[2]^2*a[1]^2*f[4]*f[7]+2*a[2]^2*a[1]^2*f[5]*f[6]+2*a[2]*a[1]^3*f[
4]*f[6]+2*f[4]*f[7]*a[3]*a[1]^3-4*f[6]*f[7]*a[3]*a[2]^2*a[1]-5*f[7]^2*a[3]^2*a
[2]*a[1]-f[7]^2*a[3]*a[2]^3+a[2]*a[1]^3*f[5]^2+3*f[7]*f[5]*a[3]*a[2]*a[1]^2-4*
a[2]^2*f[3]*f[6]*a[0]^2+2*a[2]*a[1]^2*f[3]*f[6]*a[0]+6*f[1]*f[7]*a[3]*a[0]^3+6
*f[4]*f[7]*a[3]^2*a[0]^2+4*f[2]*f[7]*a[3]*a[1]*a[0]^2-4*f[6]^2*a[3]*a[2]^2*a[0
]-3*f[7]*f[5]*a[3]^2*a[1]*a[0]+4*a[3]*a[1]^2*f[3]*f[7]*a[0]-2*a[3]*a[1]^2*f[4]
*f[6]*a[0]+39*f[7]^2*a[3]^3*a[0]+4*a[3]*a[2]*f[4]*f[6]*a[0]^2-6*a[3]*a[2]*f[3]
*f[7]*a[0]^2-8*a[3]*a[2]*a[1]*f[4]*f[7]*a[0]-8*a[3]*a[1]^2*f[5]^2*a[0]-6*f[6]*
f[5]*a[2]^3*a[0]-a[2]^3*f[4]*f[7]*a[0]-4*a[2]^2*a[1]*f[4]*f[6]*a[0]+a[2]^2*a[1
]*f[5]^2*a[0]-2*a[2]*f[2]*f[5]*a[0]^3+4*a[2]*f[1]*f[6]*a[0]^3-a[2]^2*a[1]*f[3]
*f[7]*a[0]+2*a[2]*a[1]*f[1]*f[7]*a[0]^2-2*a[1]^3*f[1]*f[7]*a[0]+a[1]^3*f[3]*f[
5]*a[0]-2*a[1]^2*f[1]*f[6]*a[0]^2+a[1]^2*f[2]*f[5]*a[0]^2+10*f[6]*f[5]*a[3]*a[
2]*a[1]*a[0]-a[3]*a[2]^2*f[7]*f[5]*a[0]+20*f[6]*f[7]*a[3]^2*a[2]*a[0]+4*a[3]*a
[2]*f[5]^2*a[0]^2+a[2]^2*f[2]*f[7]*a[0]^2-2*a[2]*a[1]*f[3]*f[5]*a[0]^2+2*a[2]^
2*f[4]*f[5]*a[0]^2-3*a[2]*a[1]^2*f[4]*f[5]*a[0]-2*a[2]*a[1]^2*f[2]*f[7]*a[0]:
eqn[27] :=
-2*a[1]^2*c[1]^2-5*f[4]*a[1]*a[0]^2*c[3]+7*f[4]*a[1]^2*a[0]*c[2]-2*f[5]*a[3]*a
[1]^2*c[0]+2*f[5]*a[3]*a[0]^2*c[2]+3*f[5]*a[2]*a[1]^2*c[1]+14*f[5]*a[2]*a[0]^2
*c[3]+2*f[6]*a[2]*a[1]^2*c[2]+2*f[3]*a[1]*a[0]^2*c[2]+2*f[7]*a[2]^2*a[0]*c[3]+
31*f[7]*a[3]^2*a[0]*c[1]-2*f[4]*a[2]*a[0]^2*c[2]-2*f[6]*a[2]^2*a[0]*c[2]+4*f[2
]*a[1]*a[0]^2*c[1]-2*f[2]*a[2]*a[0]^2*c[0]+8*f[3]*a[3]*a[0]^2*c[0]+4*f[3]*a[1]
^2*a[0]*c[1]-10*a[3]*a[0]*c[1]*c[0]-3*a[1]*a[0]*c[2]*c[1]-10*f[6]*a[3]^2*a[0]*
c[0]+4*f[7]*a[3]*a[1]^2*c[2]+18*f[6]*a[3]*a[0]^2*c[3]+2*a[2]*a[0]*c[2]*c[0]+f[
1]*a[0]^3*c[1]-f[7]*a[2]^3*c[1]+a[0]^2*c[3]*c[1]+4*f[4]*a[1]^3*c[1]+8*f[0]*a[0
]^3*c[0]+2*f[2]*a[0]^3*c[2]-f[3]*a[2]*a[1]*a[0]*c[0]-f[3]*a[2]*a[0]^2*c[1]+2*f
[4]*a[2]^2*a[0]*c[0]-16*f[5]*a[2]^2*a[0]*c[1]-f[7]*a[3]*a[2]^2*c[0]+f[4]*a[3]*
a[0]^2*c[1]-f[4]*a[2]*a[1]^2*c[0]-f[1]*a[1]*a[0]^2*c[0]-2*f[7]*a[3]*a[2]*a[1]*
c[1]-2*f[6]*a[2]*a[1]*a[0]*c[3]-10*f[7]*a[3]*a[2]*a[0]*c[2]-14*f[5]*a[2]*a[1]*
a[0]*c[2]+12*f[4]*a[3]*a[1]*a[0]*c[0]-14*f[6]*a[3]*a[1]*a[0]*c[2]-3*f[5]*a[3]*
a[1]*a[0]*c[1]+a[3]*a[1]*c[0]^2-f[5]*a[2]^2*a[1]*c[0]+a[2]*a[1]*c[1]*c[0]-2*f[
6]*a[3]*a[2]*a[1]*c[0]-2*f[4]^2*a[1]^4+2*a[2]^2*a[1]^2*f[4]*f[6]+8*a[3]*a[2]*a
[1]^2*f[6]*f[5]+6*a[3]*a[2]*a[1]^2*f[4]*f[7]-a[2]^2*a[1]^2*f[5]^2+3*f[7]*f[5]*
a[3]*a[2]^2*a[1]+12*f[7]*f[5]*a[3]^2*a[1]^2-6*f[6]*f[7]*a[3]^2*a[2]*a[1]+2*f[6
]*f[7]*a[3]*a[2]^3-8*f[7]^2*a[3]^3*a[1]+f[5]^2*a[3]*a[1]^3-3*f[4]*f[5]*a[2]*a[
1]^3+f[7]*f[5]*a[2]^4+f[4]*f[7]*a[2]^3*a[1]-2*f[2]^2*a[0]^4-2*a[2]^2*a[1]*f[7]
*f[2]*a[0]+4*a[2]*a[1]*f[4]*f[3]*a[0]^2-2*a[2]*a[1]*f[2]*f[5]*a[0]^2+2*a[2]^2*
a[1]*f[6]*f[3]*a[0]-2*a[2]*a[1]^2*f[7]*f[1]*a[0]-8*a[2]*a[1]*f[0]*f[7]*a[0]^2-
a[2]^2*a[1]*f[4]*f[5]*a[0]+8*a[1]^2*f[0]*f[6]*a[0]^2-4*a[1]^2*f[2]*f[4]*a[0]^2
+30*f[6]*f[7]*a[3]^3*a[0]-2*a[2]*f[1]*f[5]*a[0]^3+4*a[2]*f[2]*f[4]*a[0]^3-16*a
[2]*f[0]*f[6]*a[0]^3+2*a[2]^2*f[6]*f[2]*a[0]^2-3*a[2]*a[1]^2*f[5]*f[3]*a[0]-2*
a[2]^2*f[4]^2*a[0]^2-8*a[3]*a[1]^2*f[7]*f[2]*a[0]-2*a[2]^3*f[4]*f[6]*a[0]-a[2]
^3*f[7]*f[3]*a[0]+2*a[2]^2*f[5]*f[3]*a[0]^2+a[2]^2*f[7]*f[1]*a[0]^2-32*f[5]*f[
6]*a[3]^2*a[1]*a[0]+2*a[3]*a[1]*f[5]*f[3]*a[0]^2+4*a[3]^2*f[5]^2*a[0]^2-24*a[3
]*f[0]*f[7]*a[0]^3+4*a[3]*a[1]*f[7]*f[1]*a[0]^2-8*a[3]*a[1]*f[6]*f[2]*a[0]^2-\
35*a[3]^2*a[1]*f[4]*f[7]*a[0]+13*a[3]*a[1]^2*f[4]*f[5]*a[0]-11*a[3]*a[2]^2*f[4
]*f[7]*a[0]+12*a[3]*a[2]*f[7]*f[2]*a[0]^2-24*a[3]^2*f[7]*f[3]*a[0]^2-4*a[3]*a[
2]*f[4]*f[5]*a[0]^2+20*f[6]^2*a[3]^2*a[2]*a[0]-8*f[5]*f[7]*a[3]^2*a[2]*a[0]+2*
a[3]*f[2]*f[5]*a[0]^3+26*f[5]*f[6]*a[3]*a[2]^2*a[0]-16*a[3]*a[2]*f[6]*f[3]*a[0
]^2-32*f[5]^2*a[3]*a[2]*a[1]*a[0]-18*a[3]*a[2]*a[1]*f[4]*f[6]*a[0]-4*f[2]*f[3]
*a[1]*a[0]^3+a[1]^2*f[1]*f[5]*a[0]^2-4*a[1]^3*f[4]*f[3]*a[0]+8*a[1]^3*f[0]*f[7
]*a[0]+16*f[5]^2*a[2]^3*a[0]-2*a[1]^2*f[3]^2*a[0]^2+4*a[2]*a[1]^2*f[4]^2*a[0]:

for i from 1 to 27 do
expand(subs(c[0] = t*c[0], c[1]=t*c[1], c[2] = t*c[2], c[3] = t*c[3], eqn[i])):
eqn[i,2] := coeff(%,t^2):
eqn[i,1] := coeff(%%,t):
eqn[i,0] := subs(t=0,%%%):
od:

subs1 := [a[0]=aa[0], a[1]=aa[1], a[2]=aa[2], a[3]=aa[3],
          c[0]=cc[0], c[1]=cc[1], c[2]=cc[2], c[3]=cc[3]]:

for i from 1 to 27 do
eqn[i] := subs(op(subs1),eqn[i]):
eqn[i,0] := subs(op(subs1),eqn[i,0]):
eqn[i,1] := subs(op(subs1),eqn[i,1]):
eqn[i,2] := subs(op(subs1),eqn[i,2]):
eqn[i,0] := 
  normal(subs(seq(y[i]^2=F(x[i]),i=1..3),simplify(normal(eqn[i,0],expanded))),expanded):
eqn[i,1] := 
  normal(subs(seq(y[i]^2=F(x[i]),i=1..3),simplify(normal(eqn[i,1],expanded))),expanded):
eqn[i,2] := 
  normal(subs(seq(y[i]^2=F(x[i]),i=1..3),simplify(normal(eqn[i,2],expanded))),expanded):
eqn[i,12] :=
 normal(subs(seq(y[i]^2=F(x[i]),i=1..3),simplify(normal(eqn[i,1]+eqn[i,2],expanded))),expanded):
check[i] :=
normal(subs(seq(y[i]^2=F(x[i]),i=1..3),simplify(normal(eqn[i,0]+eqn[i,12],expanded))),expanded):
print(i): 
print(check[i]):
od: