grobnerfan := {
[{u1+u2+u3, u4, -u2, -u3}, {x45, x12, x13*x23, x14*x15*x24*x25*x34*x35}, 1/360*
(u2+5+u1+u3)*(u2+4+u1+u3)*(u2+3+u1+u3)*(u2+2+u1+u3)*(u2+1+u1+u3)*(u2+3+u1-2*u3)
], 
[{u1+u3+u4, -u2-u4, u2+u3, -u3}, {x23*x24*x25, x14*x24*x34, x12*x14*x34, x12*
x13*x14, x13*x23, x15*x25*x35*x45, x12*x13*x15*x45, x24*x25*x34*x35, x12*x15*
x35*x45}, 1-5/24*u3*u4^2*u1+3/8*u2^2*u3-1/24*u3^4*u1^2+1/12*u2^2*u3^3-1/6*u3^2*
u4*u1+1/6*u3^3*u4^2+1/24*u3^4*u4+1/12*u3*u4*u1+167/90*u2*u3+7/12*u2*u4*u1-1/18*
u3^3*u4^3-1/12*u3^2*u4^4+29/15*u2+23/15*u3+47/60*u4+1/3*u3^2*u4^2+17/8*u1^2*u3+
1/60*u4^5*u1+1/4*u2^2*u4^3-1/8*u2^2*u4*u1+25/18*u1^3*u2-1/12*u3^2*u4^3*u1+1/6*
u3*u4^3*u1+1/4*u3^2*u4*u2^2+1/120*u1^5*u3+1/120*u3^5*u2+5/24*u3^2*u1+13/36*u1^4
-1/36*u1^3*u3^3+1/8*u4^4+1/6*u2*u4^3*u1+1/6*u1*u4^4+1/12*u1^2*u4^3+1/60*u2*u4^5
-13/12*u1*u4^2-1/24*u2^4-1/4*u3^4-1/30*u3*u4^5+1/20*u4^5-11/12*u2*u4^2+1/4*u3^2
*u4^2*u1+157/60*u1-1/4*u2*u4^2*u1^2+1/24*u2^4*u3+1/12*u2^3*u3^2+1/36*u1^3*u4^3-\
1/12*u1^3*u4^2-11/24*u3*u4^2-1/8*u2^2*u4^2+773/180*u1*u2+529/180*u1*u3+1/6*u2^3
*u3*u4-1/24*u3^4*u2+1/8*u1^4*u3+19/72*u2^3*u1-1/9*u1*u4^3+1/18*u1^3*u4+5/12*u1^
2*u4-25/72*u3^3*u2-23/36*u3^3*u1+53/72*u1^3*u3+1/24*u1^2*u3^2+1/4*u3^2*u4^2*u2+
35/24*u1^2*u2^2-7/72*u2^3*u3+1/24*u3^2*u1*u2+49/24*u1^2*u3*u2+11/12*u2^2*u3*u1-\
1/12*u3^2*u2^2-13/24*u1^2*u4^2+1/6*u3^3*u4*u2-1/24*u3^2*u4*u2-5/72*u3^3*u4-1/6*
u2^2*u3*u4-1/8*u2^3*u4+1/6*u2*u4^4+1/6*u3*u4^3*u2+1/12*u3^2*u4^3+2/9*u3*u4^3-1/
2*u3^3+1/40*u2^5+1/20*u1^5+1/2*u2^2*u3*u1^2+1/2*u2*u3*u1^3-1/3*u2*u3^3*u1-1/30*
u3^5-5/24*u3^4*u1-1/4*u1^2*u3^3+1/6*u2^3*u1^2-11/12*u2*u4^2*u1+5/12*u1^3*u2^2-1
/3*u4^3+1/4*u1^4*u2-3/8*u2^2*u4+949/360*u1^2+31/30*u2^2+1/4*u3^2-1/24*u3*u4^2*
u2+1/4*u3*u4^2*u2^2+43/12*u1^2*u2+25/12*u1*u2^2+1/24*u3*u4^4-3/8*u3^2*u4+1/24*
u2^2*u3^4+1/40*u2^5*u3+1/18*u2^3*u3^3-1/24*u3^2*u2+10/3*u2*u3*u1+4/3*u1^3+1/24*
u2^3-1/4*u2*u3*u4+1/12*u2*u4^3*u1^2+1/24*u1^2*u4^4+1/120*u2^6+1/24*u1^4*u3*u2+1
/12*u2^2*u3*u1^3-1/12*u2*u3^3*u1^2-1/24*u2*u3^4*u1-1/60*u3^5*u1+1/360*u1^6+1/
120*u2^5*u1+1/24*u1^4*u2^2+1/36*u1^3*u2^3+1/4*u2^3*u4^2+1/60*u1^5*u2+1/6*u2*u4*
u1^2+29/60*u2*u4+8/45*u3*u4+91/90*u1*u4-5/8*u4^2+1/24*u2^2*u4^4+1/24*u2^4*u3^2+
1/24*u3^4*u2*u4+1/24*u2^4*u4*u1+1/120*u3^5*u4+1/12*u2^2*u4^3*u1+1/12*u2^4*u3*u4
+1/12*u2^4*u4^2+1/24*u2^5*u4+1/12*u2^3*u4^2*u1+1/12*u2^3*u4^2*u3+1/12*u3^2*u4*
u2^3+1/12*u3^3*u4*u2^2+1/12*u2^3*u4^3+1/12*u2*u4^4*u1-1/24*u3*u4^4*u1+1/8*u2^4*
u4-1/12*u3^2*u4^3*u2-1/24*u2*u4^4*u3], 
[{u1+u3+u4, u2+u3+u4, -u3, -u4}, {x23*x24*x25, x14*x24*x34, x25*x35*x45, x23*
x25*x45, x13*x23, x12*x13*x15*x45, x24*x25*x34*x35, x12*x15*x35*x45, x12*x13*
x14*x15, x12*x14*x34*x15*x35}, 1-5/24*u3*u4^2*u1+1/2*u2^2*u3-1/24*u3^4*u1^2-1/6
*u3^2*u4*u1+1/12*u3^3*u4^2+1/12*u3*u4*u1+9/5*u2*u3+7/12*u2*u4*u1-1/36*u3^3*u4^3
-1/24*u3^2*u4^4+11/6*u2+3/2*u3+41/60*u4+7/24*u3^2*u4^2+17/8*u1^2*u3+1/120*u4^5*
u1+25/18*u1^3*u2-1/12*u3^2*u4^3*u1+1/6*u3*u4^3*u1+1/120*u1^5*u3-1/120*u3^5*u2+5
/24*u3^2*u1+13/36*u1^4-1/36*u1^3*u3^3+1/8*u4^4+1/6*u2*u4^3*u1+1/6*u1*u4^4+1/12*
u1^2*u4^3+1/120*u2*u4^5-13/12*u1*u4^2-17/72*u3^4-1/60*u3*u4^5+1/24*u2*u4^3+1/40
*u4^5-13/24*u2*u4^2+1/4*u3^2*u4^2*u1+157/60*u1-1/4*u2*u4^2*u1^2+1/36*u1^3*u4^3-\
1/12*u1^3*u4^2-1/3*u3*u4^2+767/180*u1*u2+529/180*u1*u3-1/12*u3^4*u2+1/8*u1^4*u3
+11/36*u2^3*u1-5/72*u1*u4^3+1/18*u1^3*u4+5/12*u1^2*u4-7/24*u3^3*u2-23/36*u3^3*
u1+53/72*u1^3*u3+1/24*u1^2*u3^2+35/24*u1^2*u2^2+1/24*u3^2*u1*u2+49/24*u1^2*u3*
u2+11/12*u2^2*u3*u1-1/360*u3^6-13/24*u1^2*u4^2-1/18*u3^3*u4+1/24*u2*u4^4+7/36*
u3*u4^3-11/24*u3^3+1/20*u1^5+1/2*u2^2*u3*u1^2+1/2*u2*u3*u1^3-1/3*u2*u3^3*u1-1/
24*u3^5-5/24*u3^4*u1-1/4*u1^2*u3^3+1/6*u2^3*u1^2-19/24*u2*u4^2*u1+5/12*u1^3*u2^
2-5/24*u4^3+1/4*u1^4*u2+949/360*u1^2+u2^2+43/180*u3^2+43/12*u1^2*u2+25/12*u1*u2
^2-1/4*u3^2*u4+1/12*u3^2*u2+10/3*u2*u3*u1+4/3*u1^3+1/6*u2^3+1/12*u2*u4^3*u1^2+1
/24*u1^2*u4^4+1/24*u1^4*u3*u2+1/12*u2^2*u3*u1^3-1/12*u2*u3^3*u1^2-1/24*u2*u3^4*
u1-1/60*u3^5*u1+1/360*u1^6+1/24*u1^4*u2^2+1/36*u1^3*u2^3+1/60*u1^5*u2+1/6*u2*u4
*u1^2+9/20*u2*u4+7/45*u3*u4+44/45*u1*u4-5/8*u4^2+1/24*u2*u4^4*u1-1/24*u3*u4^4*
u1], 
[{u2, u1+u4, u3+u4, -u2-u4}, {x23*x24*x25, x14*x24*x34, x12*x14*x34, x35*x45, 
x34*x35, x12*x13*x15*x45, x12*x13*x14*x15, x13*x15*x23*x25*x45}, 1-1/8*u2^2*u4*
u1+1/24*u2^4*u4^2+1/120*u2^5*u1+1/24*u2^2*u4^4+1/2*u2^2*u3+1/18*u2^3*u4^3+3/2*
u2*u3+7/12*u2*u4*u1+19/10*u2+u3+2/3*u4+15/8*u1^2*u3+1/40*u4^5*u1+25/18*u1^3*u2+
1/120*u1^5*u3-1/4*u2^2*u4+13/36*u1^4+1/18*u4^4+1/6*u2*u4^3*u1+1/8*u1*u4^4+1/12*
u1^2*u4^3+1/40*u2*u4^5-25/24*u1*u4^2-1/72*u2*u4^3+1/24*u4^5-19/24*u2*u4^2+157/
60*u1-1/4*u2*u4^2*u1^2+1/36*u1^3*u4^3-1/12*u1^3*u4^2+773/180*u1*u2+137/60*u1*u3
+1/8*u1^4*u3+19/72*u2^3*u1-5/72*u1*u4^3-1/72*u2^4+1/18*u1^3*u4-1/12*u2^2*u4^2+5
/12*u1^2*u4+17/24*u1^3*u3+35/24*u1^2*u2^2+47/24*u1^2*u3*u2+11/12*u2^2*u3*u1-13/
24*u1^2*u4^2+1/8*u2*u4^4-1/18*u2^3*u4+1/180*u4^6+1/20*u1^5+1/2*u2^2*u3*u1^2+1/2
*u2*u3*u1^3+1/6*u2^3*u1^2-11/12*u2*u4^2*u1+5/12*u1^3*u2^2-5/24*u4^3+1/4*u1^4*u2
+949/360*u1^2+91/90*u2^2+43/12*u1^2*u2+25/12*u1*u2^2+3*u2*u3*u1+1/6*u2^3*u4^2+4
/3*u1^3+1/12*u2^3+1/360*u2^6+1/6*u2^2*u4^3+1/12*u2^4*u4+1/12*u2*u4^3*u1^2+1/24*
u1^2*u4^4+1/24*u1^4*u3*u2+1/12*u2^2*u3*u1^3+1/12*u2^3*u4^2*u1+1/24*u2^4*u4*u1+1
/60*u2^5*u4+1/12*u2^2*u4^3*u1+1/360*u1^6+1/24*u1^4*u2^2+1/36*u1^3*u2^3+1/60*u1^
5*u2+1/6*u2*u4*u1^2+17/36*u2*u4+173/180*u1*u4-101/180*u4^2+1/60*u2^5+1/12*u2*u4
^4*u1], 
[{u2, u1+u3+u4, -u2-u3, -u2-u4}, {x23*x24*x25, x14*x24*x34, x12*x14*x34, x12*
x13, x13*x23, x15*x25*x35*x45, x12*x15*x35*x45}, 1-1/40*u3^5*u1-35/72*u2^3*u3-1
/8*u2^2*u4*u1+1/6*u3*u4^3*u1+1/12*u2^4*u4^2+1/4*u3^2*u4^2*u1-1/12*u3^2*u2*u1+1/
24*u2^2*u4^4+1/4*u2^2*u3+1/12*u2^3*u4^3+371/180*u2*u3+1/12*u3*u4*u1+7/12*u2*u4*
u1+121/60*u2+97/60*u3+47/60*u4-5/24*u3*u4^2*u1+17/8*u1^2*u3+1/60*u4^5*u1+25/18*
u1^3*u2-1/2*u3^3*u2*u1-1/4*u3^2*u2^2*u1+1/3*u3^2*u4^2-1/12*u3^3*u2*u1^2-1/24*u3
*u4^4*u1+1/120*u1^5*u3-1/3*u2^2*u4-1/180*u3^6-1/12*u3^2*u4^3*u1+13/36*u1^4+1/8*
u4^4+1/6*u2*u4^3*u1+1/6*u1*u4^4+1/12*u1^2*u4^3+1/60*u2*u4^5-13/12*u1*u4^2+41/
180*u3*u4+1/20*u4^5-1/4*u3^4*u1-11/12*u2*u4^2+157/60*u1-1/4*u2*u4^2*u1^2+1/24*
u3^2*u1^2+2/9*u3*u4^3-1/40*u3^5*u2+1/36*u1^3*u4^3-25/72*u3^4-1/12*u1^3*u4^2-1/6
*u3^2*u4*u2-1/24*u3^4*u1^2+391/90*u1*u2+269/90*u1*u3-49/72*u3^3*u1-1/36*u3^3*u1
^3+1/8*u1^4*u3+2/9*u2^3*u1-1/9*u1*u4^3-5/36*u2^4+1/18*u1^3*u4-1/8*u2^2*u4^2+5/
12*u1^2*u4-1/4*u3^3*u1^2+53/72*u1^3*u3-53/72*u3^3*u2-1/12*u3^4*u2*u1+35/24*u1^2
*u2^2+49/24*u1^2*u3*u2+19/24*u2^2*u3*u1-13/24*u1^2*u4^2-3/40*u3^5+1/6*u2*u4^4-2
/3*u3^2*u2^2-1/6*u3^2*u2-1/6*u2^3*u4-7/24*u3*u4*u2^2-13/24*u3^3+1/20*u1^5+1/2*
u2^2*u3*u1^2+1/2*u2*u3*u1^3+1/6*u2^3*u1^2-11/12*u2*u4^2*u1+5/12*u1^3*u2^2-1/3*
u4^3+1/4*u1^4*u2-1/18*u3^3*u2^3+1/4*u3^2*u1-1/24*u3^2*u2^4+949/360*u1^2+409/360
*u2^2-1/120*u2^5*u3-1/6*u3^2*u4*u1+1/4*u3^2*u4^2*u2-1/3*u3^2*u4-11/24*u3*u4^2-1
/24*u2^4*u3*u1+1/24*u2^4*u4*u3-1/24*u3^4*u2^2+43/12*u1^2*u2+17/8*u1*u2^2+1/12*
u3^2*u4^3+41/12*u2*u3*u1+1/4*u2^3*u4^2+4/3*u1^3+1/360*u2^6+1/4*u2^2*u4^3+1/12*
u2^4*u4+1/12*u2*u4^3*u1^2+1/24*u1^2*u4^4+127/360*u3^2+1/24*u1^4*u3*u2+1/12*u2^2
*u3*u1^3+1/12*u2^3*u4^2*u1+1/24*u2^4*u4*u1+1/30*u2^5*u4+1/12*u2^2*u4^3*u1+1/6*
u3*u4^3*u2-1/4*u3^4*u2+1/360*u1^6+1/12*u2^3*u4^2*u3+1/24*u1^4*u2^2+1/36*u1^3*u2
^3+1/60*u1^5*u2+1/6*u2*u4*u1^2-1/12*u3^2*u4^4+8/15*u2*u4-1/18*u3^3*u4^3+91/90*
u1*u4-1/24*u1*u2^4-1/12*u3^2*u2^3*u1-1/3*u3^2*u2^3-5/8*u4^2-1/60*u2^5-1/12*u3^3
*u2^2*u1-1/30*u3*u4^5+1/4*u3*u4^2*u2^2-1/6*u2^3*u3*u1-1/12*u3^2*u4^3*u2-1/24*u3
*u4^4*u2-1/6*u2^4*u3-1/6*u3*u4*u2-1/24*u3*u4^2*u2+1/12*u2*u4^4*u1-1/9*u3^3*u4+1
/6*u3^3*u4^2+1/24*u3*u4^4-1/3*u3^3*u2^2], 
[{u3, -u3-u4, u2+u4, u1+u4}, {x23*x24*x25, x14*x24*x34, x25*x35*x45, x23*x25*
x45, x34*x35, x12*x13*x15*x45, x12*x15*x35*x45, x12*x13*x14*x15, x13*x14*x23*
x24}, 1-1/120*u3^5*u1+1/6*u3*u4^3*u1+1/4*u3^2*u4^2*u1+1/2*u2^2*u3+3/2*u2*u3-1/
12*u3*u4*u1+7/12*u2*u4*u1+11/6*u2+13/12*u3+41/60*u4-1/8*u3*u4^2*u1+15/8*u1^2*u3
+1/120*u4^5*u1+25/18*u1^3*u2+1/3*u3^2*u4^2-1/24*u3^4*u4*u1-1/24*u3*u4^4*u1+1/
120*u1^5*u3-1/360*u3^6-1/12*u3^2*u4^3*u1+13/36*u1^4+1/8*u4^4+1/6*u2*u4^3*u1+1/6
*u1*u4^4+1/12*u1^2*u4^3+1/120*u2*u4^5-13/12*u1*u4^2-1/12*u3^3*u4^2*u1+1/24*u2*
u4^3-19/180*u3*u4+1/40*u4^5+1/24*u3^4*u1-13/24*u2*u4^2+157/60*u1-1/4*u2*u4^2*u1
^2+2/9*u3*u4^3+1/36*u1^3*u4^3+1/18*u3^4-1/12*u1^3*u4^2+767/180*u1*u2+7/3*u1*u3-\
1/24*u3^3*u1+1/8*u1^4*u3+11/36*u2^3*u1-5/72*u1*u4^3+1/18*u1^3*u4+5/12*u1^2*u4+
17/24*u1^3*u3+35/24*u1^2*u2^2+47/24*u1^2*u3*u2+11/12*u2^2*u3*u1-13/24*u1^2*u4^2
+1/24*u2*u4^4-1/12*u3^3+1/20*u1^5+1/2*u2^2*u3*u1^2+1/2*u2*u3*u1^3+1/6*u2^3*u1^2
-19/24*u2*u4^2*u1+5/12*u1^3*u2^2-5/24*u4^3+1/4*u1^4*u2-1/24*u3^2*u1+949/360*u1^
2+u2^2-1/8*u3^2*u4*u1-1/4*u3^2*u4-1/4*u3*u4^2+43/12*u1^2*u2+25/12*u1*u2^2+3*u2*
u3*u1+4/3*u1^3+1/6*u2^3+1/12*u2*u4^3*u1^2+1/24*u1^2*u4^4-19/360*u3^2+1/24*u1^4*
u3*u2+1/12*u2^2*u3*u1^3+1/360*u1^6+1/24*u1^4*u2^2+1/36*u1^3*u2^3+1/60*u1^5*u2+1
/6*u2*u4*u1^2-1/24*u3^2*u4^4+9/20*u2*u4-1/18*u3^3*u4^3+44/45*u1*u4+1/6*u3^3*u4*
u1-5/8*u4^2-1/60*u3*u4^5-1/24*u3^4*u4^2+1/24*u2*u4^4*u1-1/60*u3^5*u4+2/9*u3^3*
u4], 
[{u1+u2+u4, u1+u3+u4, -u2-u3-u4, -u1-u4}, {x23*x24*x25, x12*x14*x34, x12*x13*
x14, x34*x35, x24*x34, x15*x25*x35*x45, x12*x15*x35*x45, x13*x15*x23*x25*x45, 
x13*x14*x23*x24}, 1-1/120*u3^5*u1+1/6*u3*u4^3*u1+1/4*u3^2*u4^2*u1+3/8*u2^2*u3+
68/45*u2*u3-1/12*u3*u4*u1+2/3*u2*u4*u1+29/15*u2+67/60*u3+17/20*u4-1/8*u3*u4^2*
u1+15/8*u1^2*u3+97/72*u1^3*u2+5/12*u3^2*u4^2-1/24*u3^4*u4*u1-1/24*u3*u4^4*u1+1/
120*u1^5*u3-1/180*u3^6-1/12*u3^2*u4^3*u1+7/24*u1^4+1/18*u4^4+1/24*u1*u4^4-1/6*
u1^2*u4^3+1/120*u2*u4^5-29/24*u1*u4^2-1/12*u3^3*u4^2*u1-1/60*u1^5*u4-1/24*u2*u4
^3-23/180*u3*u4+1/40*u4^5+1/24*u3^4*u1-7/8*u2*u4^2+161/60*u1-1/2*u2*u4^2*u1^2-1
/8*u1^4*u4+5/18*u3*u4^3-1/36*u1^3*u4^3+5/72*u3^4-1/3*u1^3*u4^2+1/24*u3^4*u2+391
/90*u1*u2+7/3*u1*u3-1/24*u3^3*u1-1/6*u2*u4*u1^3+1/8*u1^4*u3+19/72*u2^3*u1-7/18*
u1*u4^3-2/9*u1^3*u4+1/4*u3^2*u2*u4^2+7/24*u1^2*u4+17/24*u1^3*u3+1/24*u2^2*u4^4+
35/24*u1^2*u2^2+47/24*u1^2*u3*u2+11/12*u2^2*u3*u1-23/24*u1^2*u4^2+1/120*u3^5+1/
8*u2*u4^4-1/8*u3^3+1/40*u1^5+1/2*u2^2*u3*u1^2+1/2*u2*u3*u1^3+1/6*u3^3*u2*u4+1/6
*u2^3*u1^2-25/24*u2*u4^2*u1+5/12*u1^3*u2^2-3/8*u4^3+5/24*u1^4*u2+1/24*u2*u4^2*
u3+1/24*u3^2*u2*u4-1/24*u3^2*u1+1/4*u2^3*u4^2+65/24*u1^2+31/30*u2^2+1/24*u2^4*
u3-1/8*u3^2*u4*u1+1/12*u3^3*u2^2-3/8*u3^2*u4+1/12*u3^2*u2^3+1/8*u2^4*u4+1/4*u2^
2*u4^3+1/4*u3^2*u4*u2^2+1/4*u2^2*u4^2*u3+1/40*u2^5-3/8*u3*u4^2-3/8*u2^2*u4+1/40
*u2^5*u3+1/12*u2^3*u4^3+1/12*u2^4*u4^2-1/24*u1^4*u4^2+1/6*u2^3*u4*u3+29/8*u1^2*
u2+25/12*u1*u2^2-1/24*u2*u4*u1^4+1/12*u3^2*u4^3+3*u2*u3*u1+31/24*u1^3+1/24*u2^3
-1/360*u4^6+1/6*u3*u4^3*u2-1/24*u3^4*u4*u2+1/12*u2^3*u4^2*u1-1/120*u3^5*u2+1/12
*u3*u4^2*u2^3+1/12*u3*u4*u2^4+1/12*u3^2*u4*u2^3-1/24*u4^4*u2*u3+1/24*u3^4*u4+1/
24*u2^4*u1*u4+1/120*u2^6+1/120*u2^5*u1-1/24*u2^4+1/24*u3^2*u2^4+1/36*u3^3*u2^3-\
23/360*u3^2+1/24*u1^4*u3*u2+1/12*u2^2*u3*u1^3-1/12*u3^3*u4^2*u2-1/12*u3^2*u4^3*
u2+1/24*u2^5*u4+1/12*u1*u4^3*u2^2-1/12*u1^3*u4^2*u2+1/24*u1^4*u2^2+1/36*u1^3*u2
^3-1/4*u3*u2*u4-1/8*u3^2*u2+1/120*u1^5*u2+1/24*u2*u4*u1^2-1/12*u3^2*u4^4+8/15*
u2*u4-1/9*u3^3*u4^3+52/45*u1*u4+1/6*u3^3*u4*u1-199/360*u4^2-1/30*u3*u4^5-5/72*
u2^3*u3-1/24*u3^2*u2^2-1/12*u3*u4*u2^2-1/12*u3^4*u4^2-1/8*u2^2*u4*u1+1/24*u2*u4
^4*u1-1/30*u3^5*u4+5/18*u3^3*u4+1/12*u3^3*u4^2+1/72*u3^3*u2+1/24*u3*u4^4-1/8*u2
^3*u4-1/8*u2^2*u4^2], 
[{u2, u3, -u2-u3-u4, u1+u4}, {x23*x24*x25, x14*x24*x34, x12*x14*x34, x12*x13*
x14, x34*x35, x15*x25*x35*x45, x12*x13*x15*x45, x12*x15*x35*x45, x13*x15*x23*
x25*x45, x13*x14*x23*x24}, 1-1/120*u3^5*u1+1/6*u3*u4^3*u1+1/4*u3^2*u4^2*u1+3/8*
u2^2*u3+68/45*u2*u3-1/12*u3*u4*u1+7/12*u2*u4*u1+1/360*u1^6+1/24*u1^2*u4^4+29/15
*u2+67/60*u3+47/60*u4-1/8*u3*u4^2*u1+15/8*u1^2*u3+25/18*u1^3*u2+5/12*u3^2*u4^2-\
1/24*u3^4*u4*u1+1/12*u2*u4^3*u1^2-1/24*u3*u4^4*u1+1/120*u1^5*u3-1/180*u3^6-1/12
*u3^2*u4^3*u1+13/36*u1^4+1/8*u4^4+1/6*u2*u4^3*u1+1/6*u1*u4^4+1/12*u1^2*u4^3+1/
60*u2*u4^5-13/12*u1*u4^2-1/12*u3^3*u4^2*u1-23/180*u3*u4+1/20*u4^5+1/24*u3^4*u1-\
11/12*u2*u4^2+157/60*u1-1/4*u2*u4^2*u1^2+5/18*u3*u4^3+1/36*u1^3*u4^3+5/72*u3^4-\
1/12*u1^3*u4^2+1/24*u3^4*u2+773/180*u1*u2+7/3*u1*u3-1/24*u3^3*u1+1/8*u1^4*u3+19
/72*u2^3*u1-1/9*u1*u4^3+1/18*u1^3*u4+1/4*u3^2*u2*u4^2+5/12*u1^2*u4+17/24*u1^3*
u3+1/24*u2^2*u4^4+35/24*u1^2*u2^2+47/24*u1^2*u3*u2+11/12*u2^2*u3*u1-13/24*u1^2*
u4^2+1/120*u3^5+1/6*u2*u4^4-1/8*u3^3+1/20*u1^5+1/2*u2^2*u3*u1^2+1/2*u2*u3*u1^3+
1/6*u3^3*u2*u4+1/6*u2^3*u1^2-11/12*u2*u4^2*u1+5/12*u1^3*u2^2-1/3*u4^3+1/4*u1^4*
u2+1/24*u2*u4^2*u3+1/24*u3^2*u2*u4-1/24*u3^2*u1+1/4*u2^3*u4^2+949/360*u1^2+31/
30*u2^2+1/24*u2^4*u3-1/8*u3^2*u4*u1+1/12*u3^3*u2^2-3/8*u3^2*u4+1/12*u3^2*u2^3+1
/8*u2^4*u4+1/4*u2^2*u4^3+1/4*u3^2*u4*u2^2+1/4*u2^2*u4^2*u3+1/40*u2^5-3/8*u3*u4^
2-3/8*u2^2*u4+1/40*u2^5*u3+1/12*u2^3*u4^3+1/12*u2^4*u4^2+1/6*u2^3*u4*u3+43/12*
u1^2*u2+25/12*u1*u2^2+1/12*u3^2*u4^3+3*u2*u3*u1+4/3*u1^3+1/24*u2^3+1/6*u3*u4^3*
u2-1/24*u3^4*u4*u2+1/12*u2^3*u4^2*u1-1/120*u3^5*u2+1/12*u3*u4^2*u2^3+1/12*u3*u4
*u2^4+1/12*u3^2*u4*u2^3-1/24*u4^4*u2*u3+1/24*u3^4*u4+1/24*u2^4*u1*u4+1/120*u2^6
+1/120*u2^5*u1-1/24*u2^4+1/24*u3^2*u2^4+1/36*u3^3*u2^3-23/360*u3^2+1/24*u1^4*u3
*u2+1/12*u2^2*u3*u1^3-1/12*u3^3*u4^2*u2-1/12*u3^2*u4^3*u2+1/24*u2^5*u4+1/12*u1*
u4^3*u2^2+1/24*u1^4*u2^2+1/36*u1^3*u2^3-1/4*u3*u2*u4-1/8*u3^2*u2+1/60*u1^5*u2+1
/6*u2*u4*u1^2-1/12*u3^2*u4^4+29/60*u2*u4-1/9*u3^3*u4^3+91/90*u1*u4+1/6*u3^3*u4*
u1-5/8*u4^2-1/30*u3*u4^5+1/60*u4^5*u1-5/72*u2^3*u3-1/24*u3^2*u2^2-1/12*u3*u4*u2
^2-1/12*u3^4*u4^2-1/8*u2^2*u4*u1+1/12*u2*u4^4*u1-1/30*u3^5*u4+5/18*u3^3*u4+1/12
*u3^3*u4^2+1/72*u3^3*u2+1/24*u3*u4^4-1/8*u2^3*u4-1/8*u2^2*u4^2], 
[{u1+u2+u3+u4, -u1-u4, -u2-u4, -u3}, {x12*x14*x34, x12*x13*x14, x13*x23, x23*
x24, x24*x34, x15*x25*x35*x45}, 1/360*(u4+3+u1+u3+u2)*(u4+2+u1+u3+u2)*(u4+1+u1+
u3+u2)*(60+6*u2*u3+9*u3*u4*u1-3*u2*u4*u1+6*u2-14*u3-54*u4+3*u1*u4^2+24*u3*u4+3*
u2*u4^2+56*u1+27*u1*u2-9*u1*u3-9*u1^2*u4-u3^3-9*u3^2*u1+6*u1^2-9*u2^2+3*u3^2*u4
-6*u3*u4^2+6*u2^2*u4+9*u1^2*u2-6*u1*u2^2-2*u1^3+3*u2^3-15*u3^2-6*u3*u2*u4+6*u3^
2*u2-45*u1*u4+9*u4^2)], 
[{u1+u2+u4, -u1-u3-u4, u2+u3+u4, -u2-u4}, {x12*x14*x34, x25*x35*x45, x34*x35, 
x23*x24, x24*x34, x12*x13*x14*x15, x13*x15*x23*x25*x45}, 1-1/12*u1^4*u4^2-1/36*
u3^3*u1^3-11/12*u3*u4*u1^2+1/2*u2^2*u3-1/24*u2*u4*u1^4-1/24*u3^2*u1^4+3/2*u2*u3
-1/2*u3*u4*u1+2/3*u2*u4*u1-1/180*u1^6+19/10*u2+7/6*u3+9/10*u4-11/12*u3*u4^2*u1+
41/24*u1^2*u3-1/2*u3^2*u4*u1^2+97/72*u1^3*u2-1/60*u1^5*u3+7/36*u1^4-1/2*u3*u4*
u1^3-1/72*u4^4-1/3*u1^2*u4^3+1/60*u2*u4^5-17/12*u1*u4^2-1/18*u2*u4^3+1/60*u4^5-\
3/4*u2*u4^2-1/24*u1^5*u4+83/30*u1-1/2*u2*u4^2*u1^2-1/18*u1^3*u4^3-7/12*u1^3*u4^
2+391/90*u1*u2+112/45*u1*u3-11/36*u3^3*u1-1/24*u1^4*u3+19/72*u2^3*u1-47/72*u1*
u4^3-41/72*u1^3*u4+1/8*u1^2*u4+13/36*u1^3*u3+1/24*u2^2*u4^4+35/24*u1^2*u2^2+47/
24*u1^2*u3*u2+11/12*u2^2*u3*u1-17/12*u1^2*u4^2+1/12*u2*u4^4-11/24*u3^2*u1^2-1/6
*u3^3-1/60*u1^5+1/2*u2^2*u3*u1^2+1/2*u2*u3*u1^3+1/6*u2^3*u1^2-25/24*u2*u4^2*u1+
5/12*u1^3*u2^2-5/12*u4^3+5/24*u1^4*u2-1/4*u3^2*u1^3-1/12*u3*u4^2*u1^3-1/12*u3^2
*u1^3*u4-1/4*u3^2*u1-1/6*u3^3*u1^2+1/6*u2^3*u4^2-1/12*u1^3*u4^2*u2+253/90*u1^2+
91/90*u2^2-1/2*u3*u4^2*u1^2-11/12*u3^2*u4*u1-1/2*u3^2*u4-1/12*u3*u4*u1^4+1/12*
u2^4*u4+1/6*u2^2*u4^3+1/360*u4^6+1/60*u2^5-1/2*u3*u4^2-1/4*u2^2*u4+1/18*u2^3*u4
^3+1/24*u2^4*u4^2+29/8*u1^2*u2+25/12*u1*u2^2+3*u2*u3*u1+5/4*u1^3+1/12*u2^3+1/12
*u2^3*u4^2*u1+1/24*u2^4*u1*u4+1/360*u2^6+1/120*u2^5*u1-1/72*u2^4+1/24*u1^4*u3*
u2+1/12*u2^2*u3*u1^3+1/60*u2^5*u4+1/12*u1*u4^3*u2^2-1/6*u2*u4*u1^3+1/24*u1^4*u2
^2+1/36*u1^3*u2^3+1/120*u1^5*u2-7/24*u1^4*u4+1/24*u2*u4*u1^2+47/90*u2*u4+59/45*
u1*u4-22/45*u4^2+1/120*u4^5*u1-1/8*u2^2*u4*u1+1/24*u2*u4^4*u1-1/18*u2^3*u4-1/12
*u2^2*u4^2], 
[{u2, u4, -u2-u3, u1+u3}, {x23*x24*x25, x45, x12*x13, x13*x23, x14*x15*x24*x25*
x34*x35, x12*x14*x34*x15*x35}, 1-1/36*u3^3*u1^3+1/4*u2^2*u3+73/36*u2*u3+1/360*
u1^6+39/20*u2+97/60*u3+17/8*u1^2*u3+25/18*u1^3*u2-1/18*u3^3*u2^3+1/120*u1^5*u3+
13/36*u1^4-1/24*u2^4*u3^2-1/24*u3^4*u1^2+157/60*u1-1/12*u3^3*u2^2*u1-1/12*u3^4*
u1*u2-1/180*u3^6-1/12*u2^3*u3^2*u1-1/12*u3^3*u1^2*u2-1/24*u3^4*u2^2-1/60*u2^5*
u3-1/40*u3^5*u1-1/40*u3^5*u2+194/45*u1*u2+269/90*u1*u3-49/72*u3^3*u1+1/8*u1^4*
u3+19/72*u2^3*u1-1/24*u2^4*u3*u1+53/72*u1^3*u3+35/24*u1^2*u2^2+49/24*u1^2*u3*u2
+19/24*u2^2*u3*u1-1/6*u2^4*u3-1/6*u2^3*u1*u3-1/4*u3^4*u1-1/4*u3^4*u2-1/3*u2^3*
u3^2-1/2*u3^3*u1*u2-1/4*u2^2*u3^2*u1-3/40*u3^5+1/24*u3^2*u1^2-13/24*u3^3+1/20*
u1^5+1/2*u2^2*u3*u1^2+1/2*u2*u3*u1^3+1/6*u2^3*u1^2-1/3*u3^3*u2^2+5/12*u1^3*u2^2
+1/4*u1^4*u2+1/4*u3^2*u1-1/4*u3^3*u1^2+949/360*u1^2+401/360*u2^2-1/6*u2*u3^2-1/
24*u1*u2^4-1/30*u2^5+43/12*u1^2*u2+17/8*u1*u2^2+41/12*u2*u3*u1+4/3*u1^3+1/12*u2
^3-1/360*u2^6-1/120*u2^5*u1-1/9*u2^4+127/360*u3^2+1/24*u1^4*u3*u2+1/12*u2^2*u3*
u1^3+1/24*u1^4*u2^2+1/36*u1^3*u2^3+1/60*u1^5*u2-25/72*u3^4-2/3*u2^2*u3^2-4/9*u2
^3*u3-53/72*u3^3*u2-1/12*u2*u3^2*u1], 
[{u1+u2+u3+u4, -u2, -u3, -u4}, {x14*x24*x34, x12, x13*x23, x15*x25*x35*x45}, 1/
360*(u2-2*u3+u1+3)*(u2+3+u4+u3+u1)*(u2+2+u4+u3+u1)*(u2+1+u4+u3+u1)*(u2^2+2*u2*
u3+9*u2+2*u1*u2-3*u2*u4+9*u3+u1^2+20+9*u1+2*u1*u3+u3^2-3*u3*u4-21*u4-3*u1*u4+6*
u4^2)], 
[{u1+u3+u4, -u2-u3-u4, u2+u4, u2+u3}, {x23*x24*x25, x14*x24*x34, x23*x25*x45, 
x12*x13*x14, x13*x23, x15*x25*x35*x45, x12*x13*x15*x45, x24*x25*x34*x35, x12*
x15*x35*x45, x12*x14*x34*x15*x35}, 1-1/36*u3^3*u1^3+3/8*u2^2*u3+1/6*u1^2*u2*u4-\
19/24*u2*u4^2*u1+1/24*u1^2*u4^4-1/24*u2^2*u4^4+82/45*u2*u3+1/360*u1^6-1/36*u2^3
*u4^3+1/24*u2^2*u4^2+28/15*u2+23/15*u3+43/60*u4+17/8*u1^2*u3+25/18*u1^3*u2-13/
24*u1^2*u4^2-1/60*u4^5*u2-1/4*u4^3+1/18*u3^3*u2^3+1/12*u1^2*u4^3*u2+1/120*u1^5*
u3-1/24*u3*u4^5+11/72*u4^4+13/36*u1^4+7/12*u2*u4*u1+1/18*u1^3*u4-1/24*u3^4*u1^2
-11/24*u3*u4^2-3/8*u3^2*u4+1/24*u1*u4^4*u2-1/12*u3^2*u4^3*u2+157/60*u1-1/24*u3^
4*u1*u2-1/12*u3^3*u1^2*u2+1/24*u3^4*u2^2+1/60*u2^5*u3-1/60*u3^5*u1+1/120*u3^5*
u2-1/72*u2^3*u4-1/12*u3^2*u4^3*u1+767/180*u1*u2+529/180*u1*u3-23/36*u3^3*u1-1/
24*u3*u4^4*u1-1/12*u3*u4^4*u2-1/18*u3^3*u4^3+1/8*u1^4*u3+11/36*u2^3*u1+19/72*u3
*u4^3+53/72*u1^3*u3+35/24*u1^2*u2^2+49/24*u1^2*u3*u2+11/12*u2^2*u3*u1-5/72*u3^3
*u4+1/3*u3^2*u4^2+1/24*u2^4*u3+1/120*u2^5*u4+1/12*u3*u4^2*u2-1/6*u3^2*u4*u1-1/
24*u3^2*u4*u2-5/24*u3^4*u1-1/24*u3^4*u2+1/12*u2^3*u3^2-5/24*u3*u4^2*u1-1/24*u3*
u4*u2^2-1/3*u3^3*u1*u2-1/30*u3^5-2/3*u2*u4^2-1/8*u2^2*u4+1/24*u3^2*u1^2-1/2*u3^
3+1/20*u1^5+1/2*u2^2*u3*u1^2+1/2*u2*u3*u1^3+1/120*u3^5*u4+1/6*u2^3*u1^2+1/12*u3
^3*u2^2+5/12*u1^3*u2^2+1/4*u1^4*u2+1/12*u3^3*u4*u2^2-1/12*u3*u4^3*u2^2+1/24*u3*
u4*u2^4+1/12*u2^3*u3^2*u4+1/24*u3^4*u4*u2+1/24*u2^4*u3^2-1/180*u4^6+5/24*u3^2*
u1-1/4*u3^3*u1^2-13/12*u1*u4^2-1/4*u3*u4*u2+1/12*u3*u4*u1+949/360*u1^2+91/90*u2
^2-1/24*u2*u3^2+1/120*u2^5+43/12*u1^2*u2+25/12*u1*u2^2-233/360*u4^2+10/3*u2*u3*
u1+4/3*u1^3+1/8*u2^3-5/72*u1*u4^3+1/360*u2^6-1/72*u2^4+1/4*u3^2+1/24*u1^4*u3*u2
+1/12*u2^2*u3*u1^3+1/24*u2^4*u4+1/24*u1^4*u2^2+1/36*u1^3*u2^3+1/60*u1^5*u2+1/9*
u2*u4^3+1/24*u3^4*u4+1/6*u2^3*u3*u4+1/4*u3^2*u4*u2^2+1/4*u2^2*u4^2*u3+1/6*u3^3*
u4*u2-1/12*u3^2*u4^4+1/24*u3*u4^4+1/12*u3^2*u4^3-1/4*u3^4-1/12*u1^3*u4^2-1/12*
u2^2*u3^2+5/12*u1^2*u4+1/6*u2*u4^3*u1+1/120*u4^5*u1-1/18*u2^3*u3+1/12*u2^3*u4^2
-25/72*u3^3*u2+1/24*u2*u3^2*u1+13/90*u3*u4+44/45*u1*u4+79/180*u2*u4+1/12*u1^2*
u4^3+1/12*u2^2*u4^3+1/6*u1*u4^4+1/12*u2*u4^4+1/6*u3*u4^3*u1+1/4*u3^2*u4^2*u2+1/
6*u3^3*u4^2+1/4*u3^2*u4^2*u1+1/30*u4^5+1/6*u3*u4^3*u2-1/4*u2*u4^2*u1^2+1/36*u1^
3*u4^3], 
[{u2+u3+u4, -u3-u4, u1+u4, -u2-u4}, {x23*x24*x25, x14*x24*x34, x12*x14*x34, x25
*x35*x45, x34*x35, x12*x13*x15*x45, x12*x15*x35*x45, x12*x13*x14*x15, x13*x15*
x23*x25*x45, x13*x14*x23*x24}, 1+1/2*u2^2*u3+1/6*u1^2*u2*u4-11/12*u2*u4^2*u1+1/
24*u1^2*u4^4+1/24*u2^2*u4^4+3/2*u2*u3+1/360*u1^6+1/18*u2^3*u4^3-1/12*u2^2*u4^2+
19/10*u2+13/12*u3+3/4*u4+15/8*u1^2*u3+25/18*u1^3*u2-13/24*u1^2*u4^2+1/40*u4^5*
u2-7/24*u4^3+1/12*u1^2*u4^3*u2+1/120*u1^5*u3-1/60*u3*u4^5+1/9*u4^4+13/36*u1^4-1
/8*u2^2*u4*u1+7/12*u2*u4*u1+1/18*u1^3*u4-1/4*u3*u4^2-1/4*u3^2*u4+1/12*u1*u4^4*
u2+157/60*u1-1/120*u3^5*u1-1/18*u2^3*u4-1/12*u3^2*u4^3*u1+773/180*u1*u2+7/3*u1*
u3-1/24*u3^3*u1-1/24*u3*u4^4*u1-1/18*u3^3*u4^3+1/8*u1^4*u3+19/72*u2^3*u1+2/9*u3
*u4^3+17/24*u1^3*u3+35/24*u1^2*u2^2+47/24*u1^2*u3*u2+11/12*u2^2*u3*u1+2/9*u3^3*
u4+1/3*u3^2*u4^2+1/60*u2^5*u4-1/8*u3^2*u4*u1+1/24*u3^4*u1-1/8*u3*u4^2*u1+1/6*u3
^3*u4*u1-19/24*u2*u4^2-1/4*u2^2*u4-1/12*u3^3+1/20*u1^5+1/2*u2^2*u3*u1^2+1/2*u2*
u3*u1^3-1/60*u3^5*u4+1/120*u2^5*u1-1/24*u3^4*u4^2+1/6*u2^3*u1^2+5/12*u1^3*u2^2+
1/4*u1^4*u2+1/360*u4^6-1/24*u3^2*u1-13/12*u1*u4^2-1/12*u3*u4*u1+949/360*u1^2+91
/90*u2^2+1/24*u2^4*u4^2+1/60*u2^5+1/24*u2^4*u4*u1-1/12*u3^3*u4^2*u1-1/24*u3^4*
u4*u1-1/360*u3^6+43/12*u1^2*u2+25/12*u1*u2^2-221/360*u4^2+3*u2*u3*u1+4/3*u1^3+1
/12*u2^3+1/12*u2^3*u4^2*u1+1/12*u2^2*u4^3*u1-1/9*u1*u4^3+1/360*u2^6-1/72*u2^4-\
19/360*u3^2+1/24*u1^4*u3*u2+1/12*u2^2*u3*u1^3+1/12*u2^4*u4+1/24*u1^4*u2^2+1/36*
u1^3*u2^3+1/60*u1^5*u2-1/72*u2*u4^3-1/24*u3^2*u4^4+1/18*u3^4-1/12*u1^3*u4^2+5/
12*u1^2*u4+1/6*u2*u4^3*u1+1/60*u4^5*u1+1/6*u2^3*u4^2-19/180*u3*u4+91/90*u1*u4+
17/36*u2*u4+1/12*u1^2*u4^3+1/6*u2^2*u4^3+1/6*u1*u4^4+1/8*u2*u4^4+1/6*u3*u4^3*u1
+1/4*u3^2*u4^2*u1+1/24*u4^5-1/4*u2*u4^2*u1^2+1/36*u1^3*u4^3], 
[{u1+u3+u4, -u1-u4, -u3-u4, u2+u4}, {x23*x24*x25, x25*x35*x45, x23*x25*x45, x34
*x35, x24*x34, x12*x15*x35*x45, x12*x13*x14*x15, x13*x14*x23*x24}, 1+1/2*u2^2*
u3+1/24*u1^2*u2*u4-11/12*u2*u4^2*u1+3/2*u2*u3+11/6*u2+13/12*u3+3/4*u4+15/8*u1^2
*u3+97/72*u1^3*u2-23/24*u1^2*u4^2-1/24*u1^4*u4^2-1/4*u4^3-1/12*u1^3*u4^2*u2+1/
120*u1^5*u3-1/60*u3*u4^5+1/18*u4^4+7/24*u1^4+2/3*u2*u4*u1-2/9*u1^3*u4-1/4*u3*u4
^2-1/4*u3^2*u4+161/60*u1-1/120*u3^5*u1-1/12*u3^2*u4^3*u1+194/45*u1*u2+7/3*u1*u3
-1/24*u3^3*u1-1/24*u3*u4^4*u1-1/18*u3^3*u4^3+1/8*u1^4*u3+11/36*u2^3*u1-1/6*u1^3
*u2*u4+2/9*u3*u4^3+17/24*u1^3*u3+35/24*u1^2*u2^2+47/24*u1^2*u3*u2+11/12*u2^2*u3
*u1+2/9*u3^3*u4+1/3*u3^2*u4^2-1/8*u3^2*u4*u1+1/24*u3^4*u1-1/8*u3*u4^2*u1-1/24*
u1^4*u2*u4-1/60*u1^5*u4+1/6*u3^3*u4*u1-1/2*u2*u4^2-1/12*u3^3+1/40*u1^5+1/2*u2^2
*u3*u1^2+1/2*u2*u3*u1^3-1/60*u3^5*u4-1/24*u3^4*u4^2+1/6*u2^3*u1^2+5/12*u1^3*u2^
2+5/24*u1^4*u2-1/360*u4^6-1/24*u3^2*u1-29/24*u1*u4^2-1/12*u3*u4*u1+65/24*u1^2+
u2^2-1/12*u3^3*u4^2*u1-1/24*u3^4*u4*u1-1/360*u3^6-1/8*u1^4*u4+29/8*u1^2*u2+25/
12*u1*u2^2-199/360*u4^2+3*u2*u3*u1+31/24*u1^3+1/6*u2^3-25/72*u1*u4^3-19/360*u3^
2+1/24*u1^4*u3*u2+1/12*u2^2*u3*u1^3+1/24*u1^4*u2^2+1/36*u1^3*u2^3+1/120*u1^5*u2
-1/24*u3^2*u4^4+1/18*u3^4-1/3*u1^3*u4^2+7/24*u1^2*u4-1/120*u4^5*u1-19/180*u3*u4
+101/90*u1*u4+1/2*u2*u4-1/6*u1^2*u4^3+1/24*u1*u4^4+1/6*u3*u4^3*u1+1/4*u3^2*u4^2
*u1-1/2*u2*u4^2*u1^2-1/36*u1^3*u4^3], 
[{-u1-u3-u4, -u2-u3-u4, u2+u4, u1+u4, u2+u3, u1+u3}, {x14*x24*x34, x23*x25*x45,
x12*x13*x14, x13*x23, x23*x24, x15*x25*x35*x45, x12*x13*x15*x45, x24*x25*x34*
x35, x12*x14*x34*x15*x35}, 1+3/8*u2^2*u3+1/6*u1^2*u2*u4-19/24*u2*u4^2*u1+82/45*
u2*u3+28/15*u2+8/5*u3+47/60*u4+2*u1^2*u3+25/18*u1^3*u2-5/6*u1^2*u4^2-1/3*u4^3-\
17/24*u3*u4*u1^2-1/120*u1^5*u3-1/60*u3*u4^5+1/8*u4^4+7/24*u1^4-1/4*u1^3*u3^2+7/
12*u2*u4*u1-13/72*u1^3*u4-2/3*u3*u4^2-13/24*u3^2*u4-1/3*u1^3*u3*u4+161/60*u1-1/
30*u3^5*u1+1/12*u2*u4^4+1/6*u2*u4^3*u3+767/180*u1*u2+37/12*u1*u3-11/12*u3^3*u1+
1/24*u3*u4^4*u1-1/36*u3^3*u4^3+11/36*u2^3*u1+1/9*u3*u4^3+11/24*u1^3*u3+35/24*u1
^2*u2^2+49/24*u1^2*u3*u2+11/12*u2^2*u3*u1+1/9*u2*u4^3-11/36*u3^3*u4+1/24*u3^2*
u4^2-7/8*u3^2*u4*u1-1/3*u3^4*u1-19/24*u3*u4^2*u1-1/120*u1^5*u4-7/120*u3^5-1/3*
u3^3*u4*u1-2/3*u2*u4^2-13/24*u3^3+1/40*u1^5+1/2*u2^2*u3*u1^2+1/2*u2*u3*u1^3+1/6
*u2^3*u1^2+5/12*u1^3*u2^2+1/4*u1^4*u2+1/12*u3^2*u1-31/24*u1*u4^2-1/2*u3^2*u4*u1
^2-1/4*u3*u4*u1+65/24*u1^2+91/90*u2^2-1/24*u3^2*u2+1/12*u3^3*u2^2-1/24*u3^4*u4*
u1+1/12*u2*u4^2*u3-1/360*u3^6-1/4*u3*u2*u4-1/12*u1^4*u4+43/12*u1^2*u2+25/12*u1*
u2^2-5/8*u4^2+10/3*u2*u3*u1+31/24*u1^3+1/8*u2^3+1/24*u2^4*u4+1/12*u3^2*u2^3-2/9
*u1*u4^3-1/2*u3^3*u1^2+29/90*u3^2+1/24*u1^4*u3*u2+1/12*u2^2*u3*u1^3+1/24*u1^4*
u2^2+1/36*u1^3*u2^3+1/60*u1^5*u2+1/24*u2^2*u4^2+1/12*u2^2*u4^3-1/24*u3^4*u4-1/
18*u2^3*u3-1/72*u2^3*u4+1/24*u3^4*u2^2-1/3*u3^3*u2*u1+1/4*u3^2*u2^2*u4-1/60*u4^
5*u2+1/120*u3^5*u2-1/24*u3^4*u2+1/24*u2^4*u3^2-1/24*u3^2*u4^4-1/8*u2^2*u4+1/12*
u2^3*u4^2+1/4*u3*u2^2*u4^2+1/12*u3*u4^4+1/12*u3^2*u4^3-23/72*u3^4-1/12*u3^4*u1^
2+1/60*u2^5*u3-1/12*u3^2*u2^2-1/6*u1^3*u4^2-1/12*u1^3*u3^3+1/4*u3^2*u4^2*u2+1/6
*u2^3*u4*u3+1/4*u1^2*u4+1/120*u2^5*u4+1/12*u1^2*u4^4+1/12*u1^2*u4^3*u2-1/12*u3^
3*u1^2*u4-1/12*u3^2*u4^3*u2+1/12*u2^3*u3^2*u4-1/12*u3*u4^4*u2-1/24*u2^2*u4^4-1/
24*u1^4*u3*u4+1/24*u2^4*u3*u4-1/24*u3^4*u1*u2+1/24*u1*u4^4*u2+1/24*u3^4*u2*u4-1
/12*u1^3*u3^2*u4+1/12*u1^2*u4^3*u3-1/12*u1^2*u3^3*u2+1/360*u2^6-1/24*u1^4*u3^2+
1/12*u3^3*u2^2*u4-1/36*u2^3*u4^3-1/12*u3*u4^3*u2^2+1/6*u3^3*u4*u2+1/30*u4^5*u1+
1/18*u3^3*u2^3+43/180*u3*u4+193/180*u1*u4+79/180*u2*u4+1/12*u1^2*u4^3-1/24*u2^2
*u3*u4-25/72*u3^3*u2-1/24*u3^2*u2*u4+1/24*u3^2*u1*u2-1/72*u2^4+1/120*u2^5+5/24*
u1*u4^4+1/6*u3*u4^3*u1+1/24*u2^4*u3+1/12*u3^3*u4^2+1/20*u4^5-1/4*u2*u4^2*u1^2+1
/18*u1^3*u4^3-3/8*u1^2*u3^2-1/4*u3*u4^2*u1^2+1/6*u2*u4^3*u1], 
[{u1+u2+u4, u1+u3+u4, u2+u3+u4, -u1-u4, -u3-u4, -u2-u4}, {x23*x24*x25, x12*x14*
x34, x25*x35*x45, x34*x35, x24*x34, x12*x15*x35*x45, x12*x13*x14*x15, x13*x15*
x23*x25*x45, x13*x14*x23*x24}, 1-1/24*u1^4*u4^2+1/24*u2^4*u4^2-1/60*u3^5*u4-1/
24*u3^4*u4^2+1/120*u2^5*u1+1/2*u2^2*u3+1/24*u1^2*u2*u4-25/24*u2*u4^2*u1+3/2*u2*
u3+19/10*u2+13/12*u3+49/60*u4+15/8*u1^2*u3+97/72*u1^3*u2-23/24*u1^2*u4^2-1/3*u4
^3+1/120*u1^5*u3-1/6*u1^3*u2*u4-1/60*u3*u4^5+1/24*u4^4+7/24*u1^4+2/3*u2*u4*u1-2
/9*u1^3*u4-1/4*u3*u4^2-1/4*u3^2*u4+161/60*u1-1/120*u3^5*u1+1/12*u2*u4^4+391/90*
u1*u2+7/3*u1*u3-1/24*u3^3*u1-1/24*u3*u4^4*u1-1/18*u3^3*u4^3+1/8*u1^4*u3+19/72*
u2^3*u1+2/9*u3*u4^3+17/24*u1^3*u3+35/24*u1^2*u2^2+47/24*u1^2*u3*u2+11/12*u2^2*
u3*u1-1/18*u2*u4^3+2/9*u3^3*u4+1/3*u3^2*u4^2-1/8*u3^2*u4*u1+1/24*u3^4*u1-1/8*u3
*u4^2*u1-1/60*u1^5*u4+1/4*u3^2*u4^2*u1+1/6*u3^3*u4*u1-3/4*u2*u4^2-1/12*u3^3+1/
40*u1^5+1/2*u2^2*u3*u1^2+1/2*u2*u3*u1^3+1/6*u2^3*u1^2+5/12*u1^3*u2^2+5/24*u1^4*
u2-1/24*u3^2*u1-29/24*u1*u4^2-1/12*u3*u4*u1+65/24*u1^2+91/90*u2^2-1/24*u3^4*u4*
u1-1/360*u3^6-1/8*u1^4*u4+29/8*u1^2*u2+25/12*u1*u2^2+1/24*u2^4*u1*u4-1/12*u2*u4
^2*u1^3-13/24*u4^2+3*u2*u3*u1+31/24*u1^3+1/12*u2^3+1/12*u2^4*u4-1/12*u3^2*u4^3*
u1-1/12*u3^3*u4^2*u1+1/12*u2^3*u4^2*u1+1/12*u2^2*u4^3*u1-1/24*u1^4*u2*u4-7/18*
u1*u4^3-19/360*u3^2+1/24*u1^4*u3*u2+1/12*u2^2*u3*u1^3+1/24*u1^4*u2^2+1/36*u1^3*
u2^3+1/120*u1^5*u2-1/12*u2^2*u4^2+1/6*u2^2*u4^3-1/18*u2^3*u4+1/60*u4^5*u2-1/8*
u2^2*u4*u1-1/24*u3^2*u4^4-1/4*u2^2*u4+1/6*u2^3*u4^2+1/18*u3^4-1/3*u1^3*u4^2+7/
24*u1^2*u4+1/60*u2^5*u4+1/24*u2^2*u4^4+1/24*u1*u4^4*u2+1/360*u2^6+1/18*u2^3*u4^
3-19/180*u3*u4+52/45*u1*u4+47/90*u2*u4-1/6*u1^2*u4^3-1/72*u2^4+1/60*u2^5+1/24*
u1*u4^4+1/6*u3*u4^3*u1+1/60*u4^5-1/2*u2*u4^2*u1^2-1/36*u1^3*u4^3], 
[{u1+u3+u4, -u2-u3, u2+u4, -u4}, {x23*x24*x25, x14*x24*x34, x23*x25*x45, x12*
x13, x13*x23, x15*x25*x35*x45, x12*x15*x35*x45, x12*x14*x34*x15*x35}, 1-1/12*u2
*u3^2*u1-1/120*u2^5*u1+1/4*u2^2*u3+1/6*u1^2*u2*u4-1/12*u2*u3^3*u1^2-1/12*u2*u3^
4*u1-19/24*u2*u4^2*u1+73/36*u2*u3+39/20*u2+97/60*u3+43/60*u4+17/8*u1^2*u3+1/4*
u3*u4^2*u2^2+25/18*u1^3*u2+1/360*u1^6-13/24*u1^2*u4^2-1/6*u3*u4*u2^2-1/4*u4^3+1
/120*u1^5*u3-53/72*u2*u3^3-1/24*u3*u4^5+11/72*u4^4+13/36*u1^4-1/4*u2^2*u3^2*u1+
7/12*u2*u4*u1+1/18*u1^3*u4-1/6*u2^3*u3*u1-1/2*u2*u3^3*u1-1/6*u3*u4*u2-11/24*u3*
u4^2-1/3*u3^2*u4-2/3*u2^2*u3^2+1/24*u3^2*u1^2-1/24*u3^4*u1^2-1/12*u3^2*u4^3*u2-\
4/9*u2^3*u3+157/60*u1-1/40*u3^5*u1-1/6*u2^4*u3+1/12*u2*u4^4-1/4*u3^3*u1^2-1/36*
u3^3*u1^3+194/45*u1*u2+269/90*u1*u3-49/72*u3^3*u1-1/24*u3*u4^4*u1-1/18*u3^3*u4^
3+1/8*u1^4*u3+19/72*u2^3*u1-1/6*u3^2*u4*u2+19/72*u3*u4^3-1/4*u2*u3^4+53/72*u1^3
*u3+35/24*u1^2*u2^2+49/24*u1^2*u3*u2+19/24*u2^2*u3*u1+1/9*u2*u4^3-1/24*u2^4*u1-\
1/9*u3^3*u4+1/3*u3^2*u4^2-1/6*u3^2*u4*u1-1/4*u3^4*u1-5/24*u3*u4^2*u1+1/4*u3^2*
u4^2*u1-3/40*u3^5-2/3*u2*u4^2-1/6*u2*u3^2-1/3*u2^3*u3^2-13/24*u3^3+1/20*u1^5+1/
4*u3^2*u4^2*u2+1/6*u3*u4^3*u2-1/3*u2^2*u3^3+1/2*u2^2*u3*u1^2+1/2*u2*u3*u1^3+1/6
*u2^3*u1^2+5/12*u1^3*u2^2+1/4*u1^4*u2+1/4*u3^2*u1-13/12*u1*u4^2+1/24*u1^2*u4^4+
1/12*u3*u4*u1+949/360*u1^2+401/360*u2^2-1/180*u4^6-1/12*u3^3*u1*u2^2-1/40*u3^5*
u2-1/60*u2^5*u3+1/120*u4^5*u1-1/24*u3^4*u2^2-1/180*u3^6+1/12*u1^2*u4^3*u2-1/12*
u3*u4^4*u2-1/12*u3*u4^3*u2^2-1/12*u2^3*u3^2*u1-1/18*u2^3*u3^3-1/24*u2^4*u3^2-1/
24*u2^4*u1*u3+43/12*u1^2*u2+17/8*u1*u2^2-233/360*u4^2+1/12*u3*u4^2*u2+41/12*u2*
u3*u1+4/3*u1^3+1/12*u2^3-1/12*u3^2*u4^3*u1-5/72*u1*u4^3+127/360*u3^2+1/24*u1^4*
u3*u2+1/12*u2^2*u3*u1^3+1/24*u1^4*u2^2+1/36*u1^3*u2^3+1/60*u1^5*u2+1/24*u2^2*u4
^2+1/12*u2^2*u4^3-1/18*u2^3*u4-1/60*u4^5*u2-1/12*u3^2*u4^4-1/12*u2^2*u4+1/12*u2
^3*u4^2+1/24*u3*u4^4+1/12*u3^2*u4^3-25/72*u3^4-1/12*u1^3*u4^2+5/12*u1^2*u4-1/24
*u2^2*u4^4+1/24*u1*u4^4*u2-1/360*u2^6-1/36*u2^3*u4^3+7/36*u3*u4+44/45*u1*u4+22/
45*u2*u4+1/12*u1^2*u4^3-1/9*u2^4-1/30*u2^5+1/6*u1*u4^4+1/6*u3*u4^3*u1+1/6*u3^3*
u4^2+1/30*u4^5-1/4*u2*u4^2*u1^2+1/36*u1^3*u4^3+1/6*u2*u4^3*u1], 
[{u4, u2+u3, u1+u3, -u3}, {x23*x24*x25, x45, x13*x23, x24*x25*x34*x35, x12*x13*
x14*x15, x12*x14*x34*x15*x35}, 1+1/24*u2*u3^2*u1+1/2*u2^2*u3-1/12*u2*u3^3*u1^2-\
1/24*u2*u3^4*u1+9/5*u2*u3+11/6*u2+3/2*u3+17/8*u1^2*u3+25/18*u1^3*u2+1/360*u1^6+
1/120*u1^5*u3-7/24*u2*u3^3+13/36*u1^4-1/3*u2*u3^3*u1+1/24*u3^2*u1^2-1/24*u3^4*
u1^2+157/60*u1-1/60*u3^5*u1-1/4*u3^3*u1^2-1/36*u3^3*u1^3+767/180*u1*u2+529/180*
u1*u3-23/36*u3^3*u1+1/8*u1^4*u3+11/36*u2^3*u1-1/12*u2*u3^4+53/72*u1^3*u3+35/24*
u1^2*u2^2+49/24*u1^2*u3*u2+11/12*u2^2*u3*u1-5/24*u3^4*u1-1/24*u3^5+1/12*u2*u3^2
-11/24*u3^3+1/20*u1^5+1/2*u2^2*u3*u1^2+1/2*u2*u3*u1^3+1/6*u2^3*u1^2+5/12*u1^3*
u2^2+1/4*u1^4*u2+5/24*u3^2*u1+949/360*u1^2+u2^2-1/120*u3^5*u2-1/360*u3^6+43/12*
u1^2*u2+25/12*u1*u2^2+10/3*u2*u3*u1+4/3*u1^3+1/6*u2^3+43/180*u3^2+1/24*u1^4*u3*
u2+1/12*u2^2*u3*u1^3+1/24*u1^4*u2^2+1/36*u1^3*u2^3+1/60*u1^5*u2-17/72*u3^4], 

[{u1+u2+u4, u3+u4, -u2, -u4}, {x14*x24*x34, x12, x35*x45, x34*x35, x13*x15*x23*
x25*x45, x13*x23*x14*x24*x15*x25}, 1+13/36*u2^4+1/40*u4^5*u2+1/120*u2^5*u3+1/24
*u4^4*u2^2+1/36*u4^3*u2^3+1/24*u4^4*u1^2+1/40*u4^5*u1+1/36*u4^3*u1^3+15/8*u2^2*
u3+1/6*u1^2*u2*u4+1/6*u2^2*u4*u1+137/60*u2*u3+157/60*u2+u3+2/3*u4+15/8*u1^2*u3+
1/2*u2^3*u3*u1+1/24*u4^5+13/9*u1^3*u2+1/360*u1^6+1/120*u1^5*u3+13/36*u1^4+1/180
*u4^6+1/12*u4^3*u2^2+1/8*u2^4*u3+1/12*u4^3*u1^2+1/6*u4^3*u1*u2+1/8*u4^4*u1+17/
24*u2^3*u3+1/20*u2^5-1/4*u2^2*u4^2*u1+1/18*u1^3*u4+1/4*u2^4*u1+157/60*u1+949/
180*u1*u2+137/60*u1*u3+1/8*u1^4*u3+13/9*u2^3*u1+1/18*u2^3*u4+17/24*u1^3*u3-25/
24*u2*u4^2+13/6*u1^2*u2^2+17/8*u1^2*u3*u2+17/8*u2^2*u3*u1+1/360*u2^6+1/20*u1^5+
3/4*u2^2*u3*u1^2+1/2*u2*u3*u1^3+1/2*u2^3*u1^2+1/2*u1^3*u2^2+1/4*u1^4*u2+5/6*u2*
u4*u1+5/12*u2^2*u4+949/360*u1^2+949/360*u2^2-25/24*u1*u4^2-1/12*u1^3*u4^2+5/12*
u1^2*u4-101/180*u4^2+1/8*u4^4*u2+173/180*u2*u4+4*u1^2*u2+4*u1*u2^2+15/4*u2*u3*
u1+4/3*u1^3+4/3*u2^3+1/60*u2^5*u1+1/24*u1^4*u3*u2+1/12*u2^2*u3*u1^3+1/24*u2^4*
u1^2-5/72*u4^3*u1-5/72*u4^3*u2-1/12*u2^3*u4^2+1/24*u1^4*u2^2+1/18*u1^3*u2^3+1/
60*u1^5*u2-5/24*u4^3+1/24*u2^4*u3*u1+1/12*u2^3*u3*u1^2+1/18*u4^4+1/12*u4^3*u1*
u2^2+1/12*u4^4*u1*u2+1/12*u4^3*u1^2*u2-13/24*u1^2*u4^2-13/24*u2^2*u4^2-13/12*u2
*u4^2*u1+173/180*u1*u4-1/4*u2*u4^2*u1^2], 
[{u2+u4, u1+u4, u3+u4, -u4}, {x23*x24*x25, x14*x24*x34, x23*x25*x45, x35*x45, 
x34*x35, x12*x13*x15*x45, x12*x13*x14*x15}, 1+1/120*u4^5*u2+1/24*u4^4*u1^2+1/60
*u4^5*u1+1/36*u4^3*u1^3+1/2*u2^2*u3+1/6*u1^2*u2*u4+3/2*u2*u3+11/6*u2+u3+3/5*u4+
15/8*u1^2*u3+1/40*u4^5+25/18*u1^3*u2+1/360*u1^6+1/120*u1^5*u3+13/36*u1^4+1/360*
u4^6+1/12*u4^3*u1^2+1/6*u4^3*u1*u2+1/8*u4^4*u1+1/18*u1^3*u4+157/60*u1+767/180*
u1*u2+137/60*u1*u3+1/8*u1^4*u3+11/36*u2^3*u1+17/24*u1^3*u3-13/24*u2*u4^2+35/24*
u1^2*u2^2+47/24*u1^2*u3*u2+11/12*u2^2*u3*u1+1/20*u1^5+1/2*u2^2*u3*u1^2+1/2*u2*
u3*u1^3+1/6*u2^3*u1^2+5/12*u1^3*u2^2+1/4*u1^4*u2+7/12*u2*u4*u1+949/360*u1^2+u2^
2-25/24*u1*u4^2-1/12*u1^3*u4^2+5/12*u1^2*u4-103/180*u4^2+1/24*u4^4*u2+9/20*u2*
u4+43/12*u1^2*u2+25/12*u1*u2^2+3*u2*u3*u1+4/3*u1^3+1/6*u2^3+1/24*u1^4*u3*u2+1/
12*u2^2*u3*u1^3-1/36*u4^3*u1+1/24*u4^3*u2+1/24*u1^4*u2^2+1/36*u1^3*u2^3+1/60*u1
^5*u2-1/8*u4^3+5/72*u4^4+1/24*u4^4*u1*u2+1/12*u4^3*u1^2*u2-13/24*u1^2*u4^2-19/
24*u2*u4^2*u1+167/180*u1*u4-1/4*u2*u4^2*u1^2], 
[{-u1-u3-u4, u2+u3+u4, u1+u4, u1+u3}, {x14*x24*x34, x25*x35*x45, x23*x25*x45, 
x13*x23, x23*x24, x12*x13*x15*x45, x24*x25*x34*x35, x12*x13*x14*x15, x12*x14*
x34*x15*x35}, 1+1/12*u3^2*u2+1/12*u3^2*u1+1/120*u4^5*u2+1/12*u4^4*u1^2+1/30*u4^
5*u1+1/18*u4^3*u1^3+1/2*u2^2*u3+1/6*u1^2*u2*u4+9/5*u2*u3-13/24*u3*u4^2-5/12*u3^
2*u4-1/2*u3^3+11/6*u2+47/30*u3+3/4*u4+2*u1^2*u3+1/24*u4^5-19/24*u3*u4^2*u1+25/
18*u1^3*u2+1/120*u4^5*u3-1/120*u3^5*u2-1/120*u1^5*u3-1/120*u3^5*u4-7/8*u3^2*u4*
u1+7/24*u1^4+1/180*u4^6-1/4*u3*u4*u1+1/12*u4^3*u1^2+1/6*u4^3*u1*u2+5/24*u4^4*u1
-17/24*u3*u4*u1^2+1/24*u4^4*u1*u3-1/12*u3^3*u1^2*u4-1/180*u3^6-1/12*u3^2*u1^3*
u4-1/24*u3^4*u1*u2-1/24*u3^4*u1*u4-1/24*u1^4*u3*u4-1/12*u3^3*u1^3+1/12*u4^3*u1^
2*u3-1/12*u3^3*u1^2*u2-1/24*u1^4*u3^2-1/30*u3^5*u1+1/24*u3*u4^3-1/2*u3^2*u4*u1^
2-13/72*u1^3*u4-1/4*u3*u4^2*u1^2-3/8*u3^2*u1^2+161/60*u1-1/120*u1^5*u4-1/12*u1^
4*u4+767/180*u1*u2+37/12*u1*u3+11/36*u2^3*u1+1/4*u3*u4+14/45*u3^2+11/24*u1^3*u3
-13/24*u2*u4^2+35/24*u1^2*u2^2+49/24*u1^2*u3*u2+11/12*u2^2*u3*u1-1/12*u3^4*u1^2
-1/15*u3^5+1/40*u1^5-1/12*u3^4*u4+1/2*u2^2*u3*u1^2+1/2*u2*u3*u1^3+1/6*u2^3*u1^2
+5/12*u1^3*u2^2+1/4*u1^4*u2+7/12*u2*u4*u1-1/3*u3*u4*u1^3+65/24*u1^2+u2^2-31/24*
u1*u4^2-1/6*u1^3*u4^2+1/4*u1^2*u4-217/360*u4^2+1/24*u4^4*u2-1/4*u3^2*u1^3+9/20*
u2*u4+43/12*u1^2*u2+25/12*u1*u2^2+10/3*u2*u3*u1+31/24*u1^3+1/6*u2^3-11/12*u3^3*
u1-7/24*u3^3*u2+1/24*u3^2*u2*u1-7/24*u3^3*u4-11/36*u3^4-1/12*u3^4*u2+1/24*u1^4*
u3*u2+1/12*u2^2*u3*u1^3-2/9*u4^3*u1+1/24*u4^3*u2+1/24*u1^4*u2^2+1/36*u1^3*u2^3+
1/60*u1^5*u2-7/24*u4^3+7/72*u4^4+1/24*u4^4*u1*u2-1/2*u3^3*u1^2-1/3*u3^4*u1+1/6*
u3*u4^3*u1+1/24*u4^4*u3-1/3*u3^3*u2*u1-1/3*u3^3*u1*u4+1/12*u4^3*u1^2*u2-5/6*u1^
2*u4^2-19/24*u2*u4^2*u1+193/180*u1*u4-1/4*u2*u4^2*u1^2], 
[{-u1-u3-u4, u1+u4, -u2-u4, u2+u3}, {x14*x24*x34, x12*x14*x34, x12*x13*x14, x13
*x23, x23*x24, x15*x25*x35*x45, x12*x13*x15*x45, x24*x25*x34*x35}, 1-1/24*u3^2*
u2+1/12*u3^2*u1+1/60*u4^5*u2+1/12*u4^4*u1^2+1/24*u4^5*u1+1/18*u4^3*u1^3+3/8*u2^
2*u3+1/6*u1^2*u2*u4-1/8*u2^2*u4*u1-1/12*u2^2*u3^2+167/90*u2*u3-2/3*u3*u4^2-13/
24*u3^2*u4-13/24*u3^3+29/15*u2+8/5*u3+17/20*u4+2*u1^2*u3+1/15*u4^5-19/24*u3*u4^
2*u1+25/18*u1^3*u2-1/120*u4^5*u3+1/120*u3^5*u2-1/120*u1^5*u3-7/8*u3^2*u4*u1-1/8
*u2^2*u4^2+7/24*u1^4-1/24*u3^2*u4*u2-1/6*u3*u4*u2^2+1/180*u4^6-1/4*u3*u4*u1+1/
12*u4^3*u1^2+1/6*u4^3*u1*u2+5/24*u4^4*u1-17/24*u3*u4*u1^2+1/24*u4^4*u1*u3-1/12*
u3^3*u1^2*u4-1/360*u3^6-1/12*u3^2*u1^3*u4-1/24*u3^4*u1*u2-1/24*u3^4*u1*u4-1/24*
u1^4*u3*u4-1/12*u3^3*u1^3+1/12*u4^3*u1^2*u3-1/12*u3^3*u1^2*u2-1/24*u1^4*u3^2-1/
30*u3^5*u1+5/72*u3*u4^3-1/2*u3^2*u4*u1^2+1/12*u3^2*u4^3-13/72*u1^3*u4-1/4*u3*u4
^2*u1^2-3/8*u3^2*u1^2+161/60*u1-1/120*u1^5*u4-1/12*u1^4*u4+1/6*u3*u4^3*u2+773/
180*u1*u2+37/12*u1*u3+19/72*u2^3*u1+49/180*u3*u4+29/90*u3^2-7/72*u2^3*u3+11/24*
u1^3*u3-1/24*u3*u4^2*u2-11/12*u2*u4^2+35/24*u1^2*u2^2+49/24*u1^2*u3*u2+11/12*u2
^2*u3*u1-1/12*u3^4*u1^2-1/24*u4^4*u3^2+1/24*u3^4*u2^2+1/24*u2^5*u4+1/24*u4^4*u2
^2+1/120*u2^5*u1+1/24*u2^4*u3^2-1/36*u3^3*u4^3-7/120*u3^5+1/18*u2^3*u3^3+1/40*
u1^5-1/24*u3^4*u4+1/2*u2^2*u3*u1^2+1/2*u2*u3*u1^3+1/6*u2^3*u1^2+5/12*u1^3*u2^2+
1/4*u1^4*u2+7/12*u2*u4*u1+1/12*u3*u4*u2^4-1/24*u4^4*u2*u3+1/12*u3^2*u4*u2^3+1/
12*u3*u4^2*u2^3+1/24*u2^4*u1*u4-1/12*u3^2*u4^3*u2+1/12*u3^3*u4*u2^2+1/120*u2^6+
1/12*u2^3*u4^2*u1+1/24*u3^4*u4*u2+1/12*u2^3*u4^3+1/40*u2^5*u3-1/24*u2^4+1/12*u2
^4*u4^2-1/3*u3*u4*u1^3-1/8*u2^3*u4+65/24*u1^2+31/30*u2^2-31/24*u1*u4^2+1/12*u3^
2*u2^3+1/24*u2^4*u3-1/6*u1^3*u4^2+1/4*u1^2*u4-217/360*u4^2+1/12*u3^3*u4^2+1/8*
u2^4*u4+1/12*u2^2*u4^3*u1+1/6*u4^4*u2-1/4*u3^2*u1^3+29/60*u2*u4+43/12*u1^2*u2+
25/12*u1*u2^2+1/12*u3^3*u2^2+10/3*u2*u3*u1+31/24*u1^3+1/24*u2^3+1/6*u3^3*u2*u4+
1/4*u3^2*u2^2*u4+1/4*u2^3*u4^2+1/40*u2^5+1/4*u3*u4^2*u2^2+1/4*u3^2*u4^2*u2+1/6*
u2^3*u4*u3-1/4*u3*u4*u2-11/12*u3^3*u1-25/72*u3^3*u2+1/24*u3^2*u2*u1-11/36*u3^3*
u4-23/72*u3^4+1/24*u3^2*u4^2-1/24*u3^4*u2+1/24*u1^4*u3*u2+1/12*u2^2*u3*u1^3-19/
72*u4^3*u1+1/24*u1^4*u2^2+1/36*u1^3*u2^3+1/60*u1^5*u2-5/12*u4^3+7/72*u4^4-3/8*
u2^2*u4+1/12*u4^4*u1*u2-1/2*u3^3*u1^2-1/3*u3^4*u1+1/6*u3*u4^3*u1+1/12*u4^4*u3-1
/3*u3^3*u2*u1-1/3*u3^3*u1*u4+1/12*u4^3*u1^2*u2-5/6*u1^2*u4^2-11/12*u2*u4^2*u1+
199/180*u1*u4-1/4*u2*u4^2*u1^2+1/4*u2^2*u4^3], 
[{u2+u3+u4, -u1-u4, u1+u3, -u3}, {x25*x35*x45, x23*x25*x45, x13*x23, x23*x24, 
x24*x34, x12*x13*x14*x15, x12*x14*x34*x15*x35}, 1+1/12*u3^2*u2+1/12*u3^2*u1-1/
18*u4^3*u1^3+1/2*u2^2*u3+1/24*u1^2*u2*u4-1/24*u1^4*u2*u4+9/5*u2*u3-1/120*u3^5*
u4-1/2*u3*u4^2-5/12*u3^2*u4-1/2*u3^3+11/6*u2+47/30*u3+5/6*u4+49/24*u1^2*u3-11/
12*u3*u4^2*u1+97/72*u1^3*u2-1/120*u3^5*u2-1/60*u1^5*u3-7/8*u3^2*u4*u1+7/36*u1^4
-1/6*u1^3*u2*u4-1/6*u3*u4*u1-1/12*u1^4*u4^2-1/3*u4^3*u1^2-5/6*u3*u4*u1^2-1/12*
u3^3*u1^2*u4-1/180*u3^6-1/12*u3^2*u1^3*u4-1/24*u3^4*u1*u2-1/24*u3^4*u1*u4-1/12*
u1^4*u3*u4-1/12*u3^3*u1^3-1/12*u3^3*u1^2*u2-1/24*u1^4*u3^2-1/30*u3^5*u1-1/2*u3^
2*u4*u1^2-41/72*u1^3*u4-1/2*u3*u4^2*u1^2-3/8*u3^2*u1^2+83/30*u1-1/24*u1^5*u4-7/
24*u1^4*u4+194/45*u1*u2+47/15*u1*u3-1/24*u1^4*u3+11/36*u2^3*u1+3/10*u3*u4+14/45
*u3^2+5/12*u1^3*u3-1/2*u2*u4^2+35/24*u1^2*u2^2+49/24*u1^2*u3*u2+11/12*u2^2*u3*
u1-1/12*u3^4*u1^2-1/15*u3^5-1/60*u1^5-1/12*u3^4*u4+1/2*u2^2*u3*u1^2+1/2*u2*u3*
u1^3+1/6*u2^3*u1^2+5/12*u1^3*u2^2+5/24*u1^4*u2+2/3*u2*u4*u1-1/2*u3*u4*u1^3+253/
90*u1^2+u2^2-17/12*u1*u4^2-1/12*u1^3*u4^2*u2-7/12*u1^3*u4^2+1/8*u1^2*u4-1/2*u4^
2-1/4*u3^2*u1^3+1/2*u2*u4+29/8*u1^2*u2+25/12*u1*u2^2+10/3*u2*u3*u1+5/4*u1^3+1/6
*u2^3-11/12*u3^3*u1-7/24*u3^3*u2+1/24*u3^2*u2*u1-7/24*u3^3*u4-11/36*u3^4-1/12*
u3^4*u2+1/24*u1^4*u3*u2+1/12*u2^2*u3*u1^3-11/18*u4^3*u1+1/24*u1^4*u2^2+1/36*u1^
3*u2^3+1/120*u1^5*u2-1/3*u4^3-1/2*u3^3*u1^2-1/3*u3^4*u1-1/3*u3^3*u2*u1-1/3*u3^3
*u1*u4-17/12*u1^2*u4^2-11/12*u2*u4^2*u1+23/18*u1*u4-1/180*u1^6-1/12*u3*u4^2*u1^
3-1/2*u2*u4^2*u1^2], 
[{u3, u4, u1+u2, -u2}, {x45, x12, x34*x35, x13*x23*x14*x24*x15*x25}, 1/360*(u2+
u1+3)*(u2+2+u1)*(u2+1+u1)*(u2+5+u1)*(u2+4+u1)*(u2+3+u1+3*u3)], 
[{u1+u2+u4, u3, -u3-u4, -u2}, {x14*x24*x34, x12, x34*x35, x15*x25*x35*x45, x13*
x15*x23*x25*x45, x13*x14*x23*x24}, 1+17/24*u2^3*u3+5/6*u2*u4*u1+15/8*u2^2*u3-13
/12*u2*u4^2*u1+1/6*u2*u4*u1^2+7/3*u2*u3+157/60*u2+67/60*u3+47/60*u4+15/8*u1^2*
u3+13/9*u1^3*u2+1/6*u2^2*u4*u1+1/120*u1^5*u3+13/36*u1^4+5/12*u1^2*u4+5/12*u2^2*
u4+13/36*u2^4-13/24*u4^2*u1^2-13/24*u2^2*u4^2+157/60*u1+1/18*u2^3*u4-1/120*u3^5
*u2+949/180*u1*u2+7/3*u1*u3+1/8*u1^4*u3+13/9*u2^3*u1+17/24*u1^3*u3-1/8*u3^2*u4*
u2-1/8*u3^2*u4*u1-1/8*u3*u4^2*u1-1/8*u3*u4^2*u2+5/72*u3^4+1/6*u4^4*u1+5/12*u3^2
*u4^2-1/24*u3^3*u1-1/24*u3^3*u2+5/18*u3^3*u4+13/6*u1^2*u2^2+17/8*u1^2*u3*u2+17/
8*u2^2*u3*u1+1/6*u2*u4^4+1/12*u2^3*u3*u1^2+1/24*u2^4*u3*u1+1/120*u2^5*u3+1/20*
u1^5+3/4*u2^2*u3*u1^2+1/2*u2*u3*u1^3-1/9*u4^3*u1+1/360*u2^6+1/2*u2^3*u1^2+1/2*
u1^3*u2^2+1/4*u1^4*u2+1/12*u2^2*u4^3+1/8*u4^4+1/24*u1^2*u2^4+949/360*u1^2+949/
360*u2^2+1/60*u2^5*u1+1/12*u3^3*u4^2-1/9*u2*u4^3+1/8*u2^4*u3+1/24*u3^4*u1-3/8*
u3^2*u4-3/8*u3*u4^2-1/24*u3^2*u2+4*u1^2*u2+4*u1*u2^2+1/12*u3^2*u4^3+15/4*u2*u3*
u1-13/12*u2*u4^2+1/2*u2^3*u3*u1+4/3*u1^3+4/3*u2^3-1/12*u3*u4*u1-1/12*u3*u4*u2-1
/24*u3^2*u1-1/8*u3^3+1/24*u3^4*u2+1/18*u1^3*u4+1/4*u1*u2^4+1/20*u2^5+1/24*u1^4*
u3*u2+1/12*u2^2*u3*u1^3+1/24*u1^4*u2^2+1/18*u1^3*u2^3+1/60*u1^5*u2+1/6*u3^3*u1*
u4+1/4*u3^2*u4^2*u2+1/4*u3^2*u4^2*u1+1/6*u3^3*u2*u4+1/6*u3*u4^3*u2+1/6*u3*u4^3*
u1+1/24*u3^4*u4+1/120*u3^5+1/24*u3*u4^4-13/12*u4^2*u1+1/6*u2*u4^3*u1+5/18*u3*u4
^3+1/20*u4^5+1/24*u2^2*u4^4+1/24*u4^4*u1^2-1/12*u3^2*u4^4-1/9*u3^3*u4^3-1/30*u3
*u4^5-1/30*u3^5*u4-1/12*u3^4*u4^2-1/3*u4^3+1/12*u4^3*u1^2*u2+1/60*u4^5*u2-1/180
*u3^6-1/120*u3^5*u1+1/60*u4^5*u1+1/36*u4^3*u1^3+1/36*u2^3*u4^3-1/12*u3^3*u4^2*
u2-1/24*u3*u4^4*u1-1/24*u3^4*u4*u2-1/12*u3^3*u4^2*u1-1/24*u3*u4^4*u2-1/12*u3^2*
u4^3*u2-1/12*u3^2*u4^3*u1+1/12*u2^2*u4^3*u1+1/12*u2*u4^4*u1-1/24*u3^4*u4*u1+1/
12*u4^3*u1^2+1/360*u1^6-1/4*u2*u4^2*u1^2-23/360*u3^2-5/8*u4^2-23/180*u3*u4+91/
90*u2*u4+91/90*u1*u4-1/4*u2^2*u4^2*u1-1/12*u2^3*u4^2-1/12*u1^3*u4^2], 
[{u1+u2+u4, -u1-u3-u4, u3, -u2-u3-u4}, {x12*x14*x34, x12*x13*x14, x34*x35, x23*
x24, x24*x34, x15*x25*x35*x45, x13*x15*x23*x25*x45}, 1-5/72*u2^3*u3-1/24*u3^2*
u1^4-1/36*u3^3*u1^3+2/3*u2*u4*u1+1/24*u2^5*u4+1/36*u2^3*u3^3+1/12*u2^4*u4^2+1/
24*u2^4*u3^2-1/12*u4^2*u1^4+3/8*u2^2*u3-25/24*u2*u4^2*u1+1/24*u2*u4*u1^2+68/45*
u2*u3+29/15*u2+6/5*u3+14/15*u4+41/24*u1^2*u3-1/2*u3*u4*u1^3+97/72*u1^3*u2-1/8*
u2^2*u4*u1-1/60*u1^5*u3+7/36*u1^4-1/24*u2*u4*u1^4+1/8*u1^2*u4-3/8*u2^2*u4-7/24*
u1^4*u4-1/24*u2^4-17/12*u4^2*u1^2-1/24*u2^2*u3^2-1/8*u2^2*u4^2+83/30*u1-1/12*u2
^2*u3*u4-1/8*u2^3*u4-1/120*u3^5*u2+391/90*u1*u2+112/45*u1*u3-1/24*u1^4*u3+19/72
*u2^3*u1+13/36*u1^3*u3+1/24*u3^2*u4*u2-11/12*u3^2*u4*u1-11/12*u3*u4^2*u1+1/24*
u3*u4^2*u2+1/72*u3^4+1/12*u3^2*u4^2-11/36*u3^3*u1+1/72*u3^3*u2+1/18*u3^3*u4+35/
24*u1^2*u2^2+47/24*u1^2*u3*u2+11/12*u2^2*u3*u1-1/6*u3^3*u1^2+1/8*u2*u4^4-1/4*u3
^2*u1^3+1/40*u2^5*u3-1/2*u3^2*u1^2*u4+1/4*u3*u4^2*u2^2+1/6*u2^3*u3*u4+1/4*u3^2*
u4*u2^2+1/12*u2^3*u3^2+1/12*u3^3*u2^2-1/60*u1^5+1/2*u2^2*u3*u1^2+1/2*u2*u3*u1^3
-1/2*u3*u4^2*u1^2-1/12*u3*u4^2*u1^3+1/12*u2^4*u3*u4-47/72*u4^3*u1+1/120*u2^6+1/
12*u2^3*u3^2*u4+1/6*u2^3*u1^2+5/12*u1^3*u2^2-1/12*u4^2*u1^3*u2+1/24*u2^4*u1*u4+
5/24*u1^4*u2+1/12*u2^3*u4^2*u1+1/4*u2^2*u4^3+1/12*u2^3*u3*u4^2-1/12*u3*u4*u1^4-\
1/12*u3^2*u1^3*u4-11/24*u3^2*u1^2+253/90*u1^2+31/30*u2^2+1/120*u2^5*u1+1/12*u3^
3*u4^2-1/24*u2*u4^3+1/24*u2^4*u3-5/8*u3^2*u4-5/8*u3*u4^2-1/8*u3^2*u2-1/6*u2*u4*
u1^3+29/8*u1^2*u2+25/12*u1*u2^2+1/12*u3^2*u4^3+3*u2*u3*u1-7/8*u2*u4^2+5/4*u1^3+
1/24*u2^3-1/2*u3*u4*u1-1/4*u3*u4*u2-1/4*u3^2*u1-5/24*u3^3+1/24*u3^4*u2-11/12*u3
*u4*u1^2-41/72*u1^3*u4+1/40*u2^5+1/24*u1^4*u3*u2+1/12*u2^2*u3*u1^3+1/24*u1^4*u2
^2+1/36*u1^3*u2^3+1/120*u1^5*u2+1/4*u3^2*u4^2*u2+1/6*u3^3*u2*u4+1/6*u3*u4^3*u2+
1/24*u3^4*u4+1/120*u3^5+1/24*u3*u4^4-17/12*u4^2*u1+1/18*u3*u4^3+1/40*u4^5+1/24*
u2^2*u4^4-1/24*u3^2*u4^4-1/18*u3^3*u4^3-1/60*u3*u4^5-1/60*u3^5*u4-1/24*u3^4*u4^
2-11/24*u4^3+1/120*u4^5*u2-1/360*u3^6+1/120*u4^5*u1-1/18*u4^3*u1^3-1/24*u1^5*u4
+1/12*u2^3*u4^3-1/12*u3^3*u4^2*u2-1/24*u3^4*u4*u2-1/24*u3*u4^4*u2-1/12*u3^2*u4^
3*u2+1/12*u2^2*u4^3*u1+1/24*u2*u4^4*u1-1/3*u4^3*u1^2+1/8*u2^4*u4-1/180*u1^6-1/2
*u2*u4^2*u1^2-1/90*u3^2-1/2*u4^2-1/45*u3*u4+8/15*u2*u4+59/45*u1*u4+1/4*u2^3*u4^
2-7/12*u1^3*u4^2], 
[{-u1-u3-u4, u3, u2+u4, u1}, {x25*x35*x45, x23*x25*x45, x34*x35, x23*x24, x24*
x34, x12*x13*x14*x15}, 1/360*(u1+3)*(u1+2)*(u1+1)*(60-15*u2*u4*u1+30*u2^2*u3+90
*u2*u3+110*u2+70*u3+50*u4-6*u1^2*u3-15*u1^2*u4+56*u1+57*u1*u2+21*u1*u3+6*u1^2+
60*u2^2-30*u3^2*u4-30*u3*u4^2+3*u1^2*u2+15*u1*u2^2+15*u2*u3*u1-30*u2*u4^2-2*u1^
3+10*u2^3-30*u3*u4*u1-15*u3^2*u1-10*u3^3-30*u4^2*u1-20*u4^3-30*u4^2+30*u2*u4-15
*u1*u4)], 
[{-u2-u3-u4, -u1-u4, u2+u4, u1+u3}, {x23*x25*x45, x12*x13*x14, x13*x23, x23*x24
, x24*x34, x15*x25*x35*x45, x12*x14*x34*x15*x35}, 1-1/24*u3^2*u1^4-1/12*u3^3*u1
^3+2/3*u2*u4*u1-1/12*u4^2*u1^4+3/8*u2^2*u3-11/12*u2*u4^2*u1+1/24*u2*u4*u1^2+82/
45*u2*u3+28/15*u2+8/5*u3+13/15*u4+49/24*u1^2*u3-1/2*u3*u4*u1^3+97/72*u1^3*u2-1/
60*u1^5*u3+7/36*u1^4-1/24*u2*u4*u1^4+1/8*u1^2*u4-7/24*u1^4*u4-17/12*u4^2*u1^2+
83/30*u1+194/45*u1*u2+47/15*u1*u3-1/24*u1^4*u3+11/36*u2^3*u1+5/12*u1^3*u3-1/8*
u2^2*u4-7/8*u3^2*u4*u1-11/12*u3*u4^2*u1-11/12*u3^3*u1+35/24*u1^2*u2^2+49/24*u1^
2*u3*u2+11/12*u2^2*u3*u1-1/2*u3^3*u1^2-1/4*u3^2*u1^3-1/2*u3^2*u1^2*u4-1/60*u1^5
+1/2*u2^2*u3*u1^2+1/2*u2*u3*u1^3-1/2*u3*u4^2*u1^2-1/12*u3*u4^2*u1^3-11/18*u4^3*
u1+1/6*u2^3*u1^2+5/12*u1^3*u2^2-1/12*u4^2*u1^3*u2+5/24*u1^4*u2-1/12*u3*u4*u1^4-\
1/12*u3^2*u1^3*u4-3/8*u3^2*u1^2+253/90*u1^2+91/90*u2^2+1/36*u4^4-13/24*u3^2*u4-\
5/8*u3*u4^2-1/6*u2*u4*u1^3+29/8*u1^2*u2+25/12*u1*u2^2+10/3*u2*u3*u1-5/8*u2*u4^2
+5/4*u1^3+1/8*u2^3-1/6*u3*u4*u1+1/12*u3^2*u1-13/24*u3^3-5/6*u3*u4*u1^2-41/72*u1
^3*u4+1/24*u1^4*u3*u2+1/12*u2^2*u3*u1^3+1/24*u1^4*u2^2+1/36*u1^3*u2^3+1/120*u1^
5*u2-17/12*u4^2*u1+1/24*u2^4*u3+1/12*u2^3*u4^2+1/12*u2^3*u3^2+1/12*u3^3*u4^2+1/
12*u2^2*u4^3-3/8*u4^3-1/18*u4^3*u1^3+1/24*u2^4*u4-1/24*u1^5*u4+1/12*u3^3*u2^2+1
/24*u3^2*u2^4-7/120*u3^5+1/24*u4^2*u2^2+1/24*u3^2*u4^2-11/36*u3^3*u4-1/3*u4^3*
u1^2-1/180*u1^6-1/2*u2*u4^2*u1^2-1/24*u4^4*u2^2+29/90*u3^2-47/90*u4^2+13/45*u3*
u4+22/45*u2*u4+23/18*u1*u4-1/36*u3^3*u4^3-7/12*u1^3*u4^2-1/18*u2^3*u3-1/24*u4^4
*u3^2+1/120*u2^5*u4+1/24*u4^4*u3+1/24*u3^4*u2^2-1/12*u3^4*u1^2-1/36*u4^3*u2^3-1
/40*u4^5*u3-1/30*u3^5*u1+1/120*u3^5*u2+1/24*u4^4*u2-1/3*u3^4*u1+1/360*u2^6+1/60
*u2^5*u3-1/24*u3^4*u4-1/360*u3^6-1/24*u3^4*u2-1/180*u4^6-1/24*u3^4*u4*u1-1/12*
u4^4*u3*u2-1/12*u4^3*u3^2*u2-1/24*u3^4*u1*u2+1/18*u3^3*u2^3+1/24*u3^4*u4*u2-1/
40*u4^5*u2-1/12*u3^2*u2^2+1/12*u3^3*u4*u2^2-1/12*u3^3*u4*u1^2-1/12*u3^3*u2*u1^2
-1/12*u3*u4^3*u2^2+1/24*u2^4*u3*u4+1/12*u2^3*u3^2*u4-1/72*u2^3*u4-1/72*u2^4-23/
72*u3^4+5/72*u4^3*u2-1/24*u2^2*u3*u4+1/12*u3*u4^2*u2-1/24*u3^2*u4*u2+1/24*u3^2*
u1*u2+5/72*u3*u4^3-25/72*u3^3*u2+1/120*u4^5+1/6*u3*u4^3*u2+1/4*u3*u2^2*u4^2+1/6
*u3^3*u4*u2+1/4*u3^2*u4^2*u2-1/3*u3^3*u4*u1-1/3*u3^3*u2*u1+1/4*u3^2*u2^2*u4+1/
12*u3^2*u4^3+1/6*u2^3*u3*u4+1/120*u2^5-1/4*u3*u2*u4-1/24*u3^2*u2], 
[{u2, u3, u4, u1}, {x23*x24*x25, x45, x34*x35, x12*x13*x14*x15}, 1/360*(u1+3)*(
u1+2)*(u1+1)*(u1^2+5*u1*u2+9*u1+20+10*u2^2+30*u2)*(u2+u1+3*u3+3)], 
[{u2, u1+u3+u4, -u1-u2-u4, -u2-u3-u4}, {x23*x24*x25, x34, x12*x13*x14, x15*x25*
x35*x45, x12*x15*x35*x45, x13*x14*x23*x24}, 1+1/6*u3*u4^3*u1+1/6*u3^3*u4*u1+3/8
*u2^2*u3-1/8*u3*u4^2*u1-1/12*u3^2*u4^3*u1-1/12*u3^3*u4^2*u1+1/24*u3*u4^4+1/24*
u3^4*u4+68/45*u2*u3+11/5*u2+67/60*u3+67/60*u4+15/8*u1^2*u3+41/18*u1^3*u2-1/8*u3
^2*u4*u1-1/24*u3^4*u4*u1-1/24*u3*u4^4*u1+5/72*u4^4-1/24*u4^3*u1+1/120*u1^5*u3+1
/4*u3^2*u4^2*u1+5/72*u3^4+43/72*u1^4+15/8*u1^2*u4-1/12*u2*u3^3*u4^2+47/24*u2*u4
*u1^2+5/18*u3*u4^3+1/72*u2*u3^3+5/18*u3^3*u4-1/120*u3^5*u1+17/24*u1^3*u4-1/12*
u3^4*u4^2+1/2*u2*u4*u1^3+5/12*u3^2*u4^2-1/30*u3*u4^5-1/30*u3^5*u4+1/120*u4^5-1/
12*u2^2*u4*u3+11/12*u2^2*u4*u1+59/20*u1-1/120*u2*u4^5+1/8*u1^4*u4+1/12*u3^3*u4^
2+497/90*u1*u2+7/3*u1*u3+1/120*u3^5+1/8*u1^4*u3+11/18*u2^3*u1-1/120*u2*u3^5+17/
24*u1^3*u3+29/12*u1^2*u2^2+47/24*u1^2*u3*u2+11/12*u2^2*u3*u1-1/24*u3^2*u1-3/8*
u3^2*u4-1/8*u3^3+1/120*u1^5*u4-1/24*u4^2*u1-1/4*u2*u3*u4-1/12*u3*u4*u1-1/24*u3^
4*u2*u4-1/8*u4^3+3*u2*u4*u1-1/24*u4^4*u2*u3-1/180*u3^6-1/180*u4^6-1/8*u2*u3^2+
11/120*u1^5+1/72*u4^3*u2-1/24*u3^3*u1+1/24*u4^4*u1+1/2*u2^2*u3*u1^2+1/2*u2*u3*
u1^3+1/3*u2^3*u1^2+3/4*u1^3*u2^2-3/8*u3*u4^2-1/8*u2*u4^2+11/24*u1^4*u2+1/24*u3^
4*u1+1/40*u2^5*u3-1/12*u3^2*u4^4+1/40*u2^5*u4+1/24*u4^4*u2+1223/360*u1^2+137/90
*u2^2+1/24*u2^4*u4^2-23/360*u4^2-23/360*u3^2+1/36*u2^3*u4^3+1/12*u2^2*u1^3*u4+1
/12*u2^3*u3*u4^2+1/12*u2^3*u3^2*u4+1/12*u2^4*u3*u4+1/24*u2^4*u3^2+1/180*u2^6+7/
3*u1*u4-23/180*u3*u4+68/45*u2*u4+125/24*u1^2*u2+13/4*u1*u2^2+3*u2*u3*u1+1/4*u2^
2*u4^2*u3+1/12*u2^2*u3^3+1/6*u2^3*u3*u4+1/4*u2^2*u3^2*u4+1/12*u2^3*u4^2+1/2*u2^
2*u4*u1^2+1/120*u2^5+1/12*u2^3*u3^2+1/12*u2^2*u4^3+47/24*u1^3+7/24*u2^3+1/24*u2
^4*u4+1/24*u2^4*u3+1/12*u3^2*u4^3+1/24*u1^4*u3*u2+1/12*u2^2*u3*u1^3+1/36*u2^3*
u3^3+1/6*u3^3*u4*u2+1/12*u1^4*u2^2+1/18*u1^3*u2^3+1/4*u3^2*u4^2*u2+1/6*u3*u4^3*
u2+1/24*u3^4*u2+1/30*u1^5*u2+1/24*u3*u4^2*u2+1/24*u2*u3^2*u4+1/180*u1^6+1/24*u2
*u4*u1^4-1/12*u2*u3^2*u4^3-1/9*u3^3*u4^3-1/120*u4^5*u1-1/24*u2^2*u3^2-5/72*u2^3
*u4-5/72*u2^3*u3-1/24*u2^2*u4^2+3/8*u2^2*u4-1/36*u2^4], 
[{-u1-u4, u2+u4, u3+u4, u1}, {x23*x24*x25, x23*x25*x45, x35*x45, x34*x35, x24*
x34, x12*x13*x14*x15}, 1/360*(u1+3)*(u1+2)*(u1+1)*(3*u1^2*u3-6*u1^2*u4+9*u1^2+3
*u1^2*u2+51*u1+57*u1*u2+15*u1*u2^2-9*u1*u4-15*u4^2*u1+27*u1*u3-15*u2*u4*u1+15*
u2*u3*u1+30*u2*u4+60+60*u3+60*u2^2+40*u4+90*u2*u3-30*u4^2+110*u2-10*u4^3+30*u2^
2*u3+10*u2^3-30*u2*u4^2)], 
[{-u1-u3-u4, u1+u2+u3+u4, -u2-u3, -u2-u4}, {x14*x24*x34, x12*x14*x34, x12*x13,
x13*x23, x23*x24, x15*x25*x35*x45}, 1/360*(u1+3+u2+u4+u3)*(u1+2+u2+u4+u3)*(u1+
u2+u4+u3+1)*(60-3*u3^3-6*u2^2*u3+11*u2-9*u3-59*u4-3*u1^2*u3-6*u1*u3^2-3*u1^2*u4
+51*u1+3*u3*u4*u1-9*u3*u4^2+27*u1*u2-9*u1*u3+9*u2^2*u4+6*u3^2*u4+9*u4^2*u1+2*u4
^3-9*u2*u4*u1-18*u3^2+24*u3*u4+9*u1^2-12*u2^2+12*u4^2-39*u1*u4+6*u1^2*u2-3*u1*
u2^2+6*u2*u3*u1+u2^3)], 
[{u1+u2+u4, -u1-u4, u3+u4, -u2-u4}, {x23*x24*x25, x12*x14*x34, x35*x45, x34*x35
, x24*x34, x12*x13*x14*x15, x13*x15*x23*x25*x45}, 1+1/6*u2^2*u4^3+1/6*u2^3*u4^2
+1/12*u2^4*u4+1/2*u2^2*u3+3/2*u2*u3+19/10*u2+u3+11/15*u4+15/8*u1^2*u3+97/72*u1^
3*u2-1/6*u2*u4*u1^3-25/72*u4^3*u1+1/120*u1^5*u3+7/24*u1^4+7/24*u1^2*u4+1/24*u2*
u4*u1^2-2/9*u1^3*u4+161/60*u1-1/3*u1^3*u4^2-1/8*u1^4*u4+1/60*u2^5+391/90*u1*u2+
137/60*u1*u3-1/4*u2^2*u4+1/8*u1^4*u3+19/72*u2^3*u1+17/24*u1^3*u3+35/24*u1^2*u2^
2+47/24*u1^2*u3*u2+11/12*u2^2*u3*u1-25/24*u2*u4^2*u1-1/60*u1^5*u4-1/24*u1^4*u4^
2-7/6*u4^2*u1-1/4*u4^3-1/24*u1^4*u2*u4-1/12*u1^3*u4^2*u2+1/120*u2^5*u1+2/3*u2*
u4*u1+1/40*u1^5+1/2*u2^2*u3*u1^2+1/2*u2*u3*u1^3+1/6*u2^3*u1^2+5/12*u1^3*u2^2-3/
4*u2*u4^2+5/24*u1^4*u2-1/2*u1^2*u4^2*u2+65/24*u1^2+91/90*u2^2+1/24*u2^4*u4^2-22
/45*u4^2+1/24*u4^4*u2^2+1/18*u2^3*u4^3-1/8*u2^2*u1*u4-1/72*u2^4-1/12*u2^2*u4^2+
1/360*u2^6-1/18*u2^3*u4+1/60*u2^5*u4+199/180*u1*u4+47/90*u2*u4-1/6*u1^2*u4^3+1/
120*u4^5*u1+29/8*u1^2*u2+25/12*u1*u2^2+3*u2*u3*u1+1/60*u4^5*u2+31/24*u1^3+1/12*
u2^3+1/12*u4^3*u1*u2^2+1/24*u4^4*u1*u2+1/24*u2^4*u1*u4+1/360*u4^6+1/12*u2^3*u4^
2*u1+1/24*u1^4*u3*u2+1/12*u2^2*u3*u1^3-23/24*u1^2*u4^2+1/24*u1^4*u2^2+1/36*u1^3
*u2^3+1/120*u1^5*u2+1/60*u4^5+1/12*u2*u4^4-1/72*u4^4-1/18*u2*u4^3-1/36*u1^3*u4^
3], 
[{-u1-u3-u4, -u2-u3, u2+u4, u1+u3}, {x14*x24*x34, x23*x25*x45, x12*x13, x13*x23
, x23*x24, x15*x25*x35*x45, x12*x14*x34*x15*x35}, 1+1/12*u2^2*u4^3-1/24*u2^4*u1
-1/6*u3*u4*u2^2-7/8*u3^2*u4*u1+1/9*u3*u4^3+1/12*u2^3*u4^2+1/4*u2^2*u3-1/3*u2^3*
u3^2+73/36*u2*u3+39/20*u2+101/60*u3+47/60*u4+2*u1^2*u3+25/18*u1^3*u2-2/9*u4^3*
u1-1/120*u1^5*u3-1/4*u2^2*u3^2*u1+7/24*u1^4-1/3*u3^3*u4*u1+1/4*u1^2*u4-1/6*u2^3
*u3*u1+1/6*u2*u4*u1^2-1/3*u1^3*u4*u3+1/8*u3^2*u1-23/24*u3^3*u1-13/72*u1^3*u4-53
/72*u2*u3^3+161/60*u1-1/6*u1^3*u4^2-1/2*u3^3*u1^2-1/12*u1^4*u4-1/30*u2^5-1/3*u2
^2*u3^3-1/4*u3^2*u1^3+194/45*u1*u2+47/15*u1*u3-1/12*u2^2*u4+19/72*u2^3*u1-1/10*
u3^5-1/4*u3^4*u2+11/24*u1^3*u3-19/24*u3*u4^2*u1+1/12*u3*u4^2*u2+1/24*u3^2*u4^2+
35/24*u1^2*u2^2+49/24*u1^2*u3*u2+19/24*u2^2*u3*u1-1/12*u2*u3^2*u1+1/6*u2*u4^3*
u1-19/24*u2*u4^2*u1-1/120*u1^5*u4-31/24*u4^2*u1-5/12*u3^4-1/3*u4^3-1/120*u2^5*
u1+7/12*u2*u4*u1-1/4*u3*u4*u1-1/6*u3*u4*u2-2/3*u3*u4^2-1/2*u3^2*u4+1/40*u1^5+1/
2*u2^2*u3*u1^2+1/2*u2*u3*u1^3-1/60*u4^5*u3-1/36*u3^3*u4^3+1/6*u2^3*u1^2-1/120*
u3^5*u4+5/12*u1^3*u2^2-1/24*u4^4*u3^2-2/3*u2*u4^2+1/4*u1^4*u2-1/4*u1^2*u4^2*u2-\
1/12*u3^3*u1^3-1/24*u3^5*u1-1/18*u2^3*u3^3-1/24*u2^4*u3^2-1/6*u2*u3^2-1/12*u3^4
*u1^2+5/24*u4^4*u1-17/24*u3*u4*u1^2-25/72*u3^3*u4+65/24*u1^2+401/360*u2^2+1/12*
u4^4*u1^2-1/24*u1^4*u3^2-1/24*u3^4*u2^2-1/120*u3^6-5/8*u4^2-2/3*u2^2*u3^2-1/12*
u4^4*u3*u2-1/24*u3^4*u1*u4-1/12*u2^3*u3^2*u1-1/12*u3^4*u1*u2-1/12*u3^3*u1^2*u2-\
1/12*u3^3*u1*u2^2-1/12*u3^2*u4^3*u2-1/12*u3^2*u1^3*u4+1/24*u4^4*u3*u1-1/12*u3^3
*u1^2*u4-1/40*u3^5*u2-1/24*u2^4*u3*u1-1/24*u1^4*u3*u4+1/12*u4^3*u1^2*u2+1/12*u4
^3*u1^2*u3-1/60*u2^5*u3-1/12*u2^2*u4^3*u3-3/8*u3^2*u1^2-1/24*u4^4*u2^2-1/36*u2^
3*u4^3-1/9*u2^4+1/24*u2^2*u4^2-1/360*u2^6-1/18*u2^3*u4-4/9*u2^3*u3+193/180*u1*
u4+22/45*u2*u4+1/12*u1^2*u4^3+1/30*u4^5*u1+43/12*u1^2*u2+17/8*u1*u2^2+41/12*u2*
u3*u1-1/60*u4^5*u2+31/24*u1^3+1/12*u2^3+1/24*u4^4*u1*u2-3/8*u3^4*u1+1/24*u1^4*
u3*u2+1/12*u2^2*u3*u1^3-5/6*u1^2*u4^2-1/6*u2^4*u3+1/24*u1^4*u2^2+1/36*u1^3*u2^3
-1/2*u2*u3^3*u1+1/60*u1^5*u2-7/12*u3^3+1/20*u4^5+1/12*u2*u4^4+1/8*u4^4-1/6*u2*
u4*u3^2+1/9*u2*u4^3+1/18*u1^3*u4^3-1/12*u3^4*u4+1/12*u3^3*u4^2+1/12*u3^2*u4^3+1
/4*u3*u4^2*u2^2-1/4*u3*u4^2*u1^2+1/6*u3*u4^3*u1+1/6*u3*u4^3*u2+1/4*u3^2*u4^2*u2
-1/2*u3^2*u4*u1^2+1/12*u4^4*u3+17/40*u3^2+13/45*u3*u4], 
[{-u1-u2-u4, u1+u2+u3+u4, -u3-u4, -u2}, {x12, x34, x15*x25*x35*x45, x13*x14*x23
*x24}, 1/360*(u2+u4+u3+3+u1)*(u2+2+u4+u3+u1)*(u2+1+u4+u3+u1)*(u2+4-u4-u3+u1)*(2
*u2^2+13*u2+4*u1*u2-u2*u4-u2*u3+15+13*u1-u1*u3+2*u1^2-7*u3-7*u4-u1*u4+2*u4^2+4*
u3*u4+2*u3^2)], 
[{u1+u3+u4, -u1-u2-u4, u2+u3+u4, -u3-u4}, {x23*x24*x25, x34, x25*x35*x45, x12*
x15*x35*x45, x12*x13*x14*x15, x13*x14*x23*x24}, 1-1/8*u3^2*u4*u1+2/9*u3*u4^3+1/
2*u2^2*u3+3/2*u2*u3+13/6*u2+13/12*u3+13/12*u4+15/8*u1^2*u3+41/18*u1^3*u2-1/24*
u4^3*u1+1/120*u1^5*u3+11/12*u2^2*u4*u1+43/72*u1^4+1/6*u3^3*u4*u1+15/8*u1^2*u4+
47/24*u2*u4*u1^2-1/24*u3^2*u1-1/24*u3^3*u1+17/24*u1^3*u4+59/20*u1+1/8*u1^4*u4+
497/90*u1*u2+7/3*u1*u3+1/2*u2^2*u4+1/8*u1^4*u3+11/18*u2^3*u1+17/24*u1^3*u3-1/8*
u3*u4^2*u1+1/3*u3^2*u4^2+29/12*u1^2*u2^2+47/24*u1^2*u3*u2+11/12*u2^2*u3*u1+1/
120*u1^5*u4-1/24*u4^2*u1+1/2*u2*u4*u1^3+1/2*u2^2*u4*u1^2+1/18*u3^4-1/12*u4^3+3*
u2*u4*u1-1/12*u3*u4*u1-1/4*u3*u4^2-1/4*u3^2*u4+11/120*u1^5+1/2*u2^2*u3*u1^2+1/2
*u2*u3*u1^3-1/60*u4^5*u3-1/18*u3^3*u4^3+1/3*u2^3*u1^2-1/60*u3^5*u4+3/4*u1^3*u2^
2-1/24*u4^4*u3^2+11/24*u1^4*u2-1/120*u3^5*u1-1/12*u3^3*u4^2*u1+1/24*u4^4*u1+2/9
*u3^3*u4+1223/360*u1^2+3/2*u2^2-1/360*u3^6-19/360*u4^2-1/24*u3^4*u1*u4-1/24*u4^
4*u3*u1+7/3*u1*u4+3/2*u2*u4-1/120*u4^5*u1+125/24*u1^2*u2+13/4*u1*u2^2+3*u2*u3*
u1+47/24*u1^3+1/3*u2^3+1/24*u3^4*u1+1/24*u1^4*u3*u2+1/12*u2^2*u3*u1^3+1/12*u1^4
*u2^2+1/18*u1^3*u2^3+1/30*u1^5*u2-1/12*u3^3+1/18*u4^4+1/4*u3^2*u4^2*u1+1/24*u1^
4*u4*u2-1/24*u3^4*u4^2+1/12*u2^2*u4*u1^3-1/360*u4^6-1/12*u3^2*u4^3*u1+1/6*u3*u4
^3*u1-19/360*u3^2-19/180*u3*u4+1/180*u1^6], 
[{u1+u2+u3, u4, -u2-u3, -u1-u3}, {x45, x23, x12*x13, x14*x15*x24*x25*x34*x35},
-1/360*(u2-3+u3-2*u1)*(u2+5+u3+u1)*(u2+4+u3+u1)*(u2+3+u3+u1)*(u2+2+u3+u1)*(u2+1
+u3+u1)], 
[{u2+u3+u4, -u1-u4, u1, -u1-u3}, {x23, x25*x35*x45, x24*x34, x12*x13*x14*x15},
1/360*(u1+3)*(u1+2)*(u1+1)*(u3-2*u4+u2+3)*(10*u2^2+30*u2+15*u1*u2+20*u2*u3+20*
u2*u4+20+15*u1*u4+30*u3+30*u4+15*u1*u3+6*u1^2+10*u4^2+10*u3^2+24*u1+20*u3*u4)],

[{u4, u2+u3, u1, -u1-u3}, {x45, x23, x24*x25*x34*x35, x12*x13*x14*x15}, 1/360*(
u1+3)*(u1+2)*(u1+1)*(u1+4+2*u2+2*u3)*(5*u2^2+5*u1*u2+10*u2*u3+20*u2+13*u1+5*u1*
u3+20*u3+2*u1^2+5*u3^2+15)], 
[{u2+u3+u4, u1+u4, -u4, -u1-u3}, {x14*x24*x34, x23, x25*x35*x45, x12*x13*x15*
x45, x24*x25*x34*x35, x12*x13*x14*x15}, 1-19/24*u3*u4^2*u1+7/12*u3*u4*u1+1/2*u2
^2*u3+11/12*u1*u2*u3^2+229/180*u1*u4+9/20*u2*u4+9/20*u3*u4-1/4*u3*u4^2*u1^2-1/4
*u2*u4^2*u1^2+7/12*u2*u4*u1+2*u2*u3-19/24*u2*u4^2*u1+11/6*u2+11/6*u3+3/4*u4+4*
u1^2*u3+121/72*u1^3*u2+1/6*u2*u4*u1^2+1/40*u1^5*u3+1/24*u3*u4^3+43/72*u1^4-31/
24*u4^2*u1-1/6*u4^2*u1^3+1/6*u3*u4*u1^2-5/6*u4^2*u1^2+1/9*u1^3*u4+25/12*u3^2*u1
+11/36*u3^3*u1-2/9*u4^3*u1-217/360*u4^2-13/24*u3*u4^2+59/20*u1-13/24*u2*u4^2+1/
24*u2*u4^3+803/180*u1*u2+803/180*u1*u3+7/72*u4^4+1/3*u1^4*u3+11/36*u2^3*u1+121/
72*u1^3*u3+35/24*u1^2*u2^2+35/12*u1^2*u3*u2+11/12*u2^2*u3*u1+1/36*u1^3*u3^3+1/
12*u1^3*u3^2*u2+1/24*u1^4*u3^2+35/24*u1^2*u3^2+11/120*u1^5+1/2*u2^2*u3*u1^2+5/6
*u2*u3*u1^3+2/3*u1^2*u4+1/6*u2^3*u1^2+5/12*u1^3*u2^2+1/3*u1^4*u2+1/12*u4^3*u1^2
+1223/360*u1^2+u2^2+1/24*u4^5+1/12*u4^3*u1^2*u3+1/24*u4^4*u3-7/24*u4^3+4*u1^2*
u2+25/12*u1*u2^2+1/120*u4^5*u3+1/12*u4^4*u1^2+1/120*u4^5*u2+1/24*u4^4*u2+25/6*
u2*u3*u1+5/24*u4^4*u1+1/30*u4^5*u1+47/24*u1^3+1/6*u2^3+1/6*u3*u4^3*u1+1/6*u2*u4
^3*u1+1/180*u1^6+1/12*u1^4*u3*u2+1/12*u2^2*u3*u1^3+1/24*u1^4*u2^2+1/36*u1^3*u2^
3+1/18*u4^3*u1^3+1/40*u1^5*u2+1/24*u1*u2*u4^4+1/24*u1*u3*u4^4+1/12*u4^3*u1^2*u2
+1/180*u4^6+1/6*u3^3+1/2*u1^2*u2*u3^2+5/12*u1^3*u3^2+1/6*u1^2*u3^3+u3^2+1/2*u3^
2*u2], 
[{-u2-u3-u4, u1+u4, u2+u3, -u1-u3}, {x14*x24*x34, x23, x12*x13*x14, x15*x25*x35
*x45, x12*x13*x15*x45, x24*x25*x34*x35}, 1+1/60*u2^5*u3+1/18*u3^3*u2^3-1/24*u3^
2*u4^4-1/24*u2^2*u4^4+1/120*u3^5*u4+1/60*u3^5*u2+1/360*u2^6+1/12*u3^2*u4^3-19/
24*u3*u4^2*u1+1/360*u3^6-1/36*u3^3*u4^3+7/12*u3*u4*u1+1/24*u3^2*u2^4+1/120*u2^5
*u4-1/36*u2^3*u4^3+1/24*u3^4*u2^2+3/8*u2^2*u3+11/12*u1*u2*u3^2+229/180*u1*u4+79
/180*u2*u4+79/180*u3*u4-1/4*u3*u4^2*u1^2-1/4*u2*u4^2*u1^2+7/12*u2*u4*u1+91/45*
u2*u3-19/24*u2*u4^2*u1+28/15*u2+28/15*u3+47/60*u4+4*u1^2*u3+121/72*u1^3*u2+1/6*
u2*u4*u1^2+1/40*u1^5*u3+1/9*u3*u4^3+43/72*u1^4+1/24*u2^2*u4^2-31/24*u4^2*u1-1/6
*u4^2*u1^3+1/6*u3*u4^3*u2+1/6*u3*u4*u1^2-5/6*u4^2*u1^2+1/9*u1^3*u4+25/12*u3^2*
u1+11/36*u3^3*u1-2/9*u4^3*u1-5/8*u4^2-2/3*u3*u4^2+59/20*u1-2/3*u2*u4^2+1/9*u2*
u4^3+803/180*u1*u2+803/180*u1*u3+1/8*u4^4-1/72*u3^3*u4+1/3*u1^4*u3+11/36*u2^3*
u1+1/24*u3^2*u4^2+1/12*u2^2*u4^3-1/18*u3^3*u2-1/18*u2^3*u3-1/12*u3^2*u2^2-1/72*
u2^3*u4+121/72*u1^3*u3+35/24*u1^2*u2^2-1/72*u3^4+35/12*u1^2*u3*u2+11/12*u2^2*u3
*u1-1/72*u2^4+1/36*u1^3*u3^3-1/24*u2^2*u3*u4-1/24*u3^2*u2*u4+1/12*u1^3*u3^2*u2+
1/12*u4^2*u3*u2+1/24*u1^4*u3^2+35/24*u1^2*u3^2+1/24*u3^4*u4+11/120*u1^5+1/24*u2
^4*u4+1/12*u3^3*u4^2+1/24*u2^4*u3+1/24*u3^4*u2+1/2*u2^2*u3*u1^2+5/6*u2*u3*u1^3+
1/12*u3^2*u2^3*u4+2/3*u1^2*u4+1/12*u3^3*u2^2+1/6*u2^3*u1^2+5/12*u1^3*u2^2+1/3*
u1^4*u2+1/12*u4^3*u1^2+1/4*u3^2*u2*u4^2+1/12*u3^2*u2^3+1/6*u3^3*u4*u2+1/4*u2^2*
u3*u4^2+1/4*u3^2*u2^2*u4+1/6*u2^3*u4*u3+1/120*u3^5+1/12*u2^3*u4^2+1/120*u2^5+1/
24*u3^4*u4*u2-1/12*u2^2*u4^3*u3+1223/360*u1^2+91/90*u2^2+1/20*u4^5+1/12*u4^3*u1
^2*u3+1/12*u4^4*u3-1/3*u4^3-1/12*u3^2*u4^3*u2+4*u1^2*u2+25/12*u1*u2^2-1/60*u4^5
*u3+1/12*u4^4*u1^2-1/60*u4^5*u2+1/12*u4^4*u2+25/6*u2*u3*u1+5/24*u4^4*u1+1/30*u4
^5*u1+47/24*u1^3+1/8*u2^3+1/6*u3*u4^3*u1+1/6*u2*u4^3*u1+1/180*u1^6+1/12*u1^4*u3
*u2+1/12*u2^2*u3*u1^3+1/24*u2^4*u4*u3+1/24*u1^4*u2^2+1/36*u1^3*u2^3+1/18*u4^3*
u1^3+1/40*u1^5*u2+1/24*u1*u2*u4^4+1/24*u1*u3*u4^4+1/12*u4^3*u1^2*u2+1/8*u3^3+1/
12*u3^3*u4*u2^2+1/2*u1^2*u2*u3^2+5/12*u1^3*u3^2+1/6*u1^2*u3^3-1/12*u3*u4^4*u2-1
/8*u2^2*u4-1/8*u3^2*u4-1/4*u2*u3*u4+91/90*u3^2+3/8*u3^2*u2], 
[{u1+u2+u3+u4, -u2-u3, -u4, -u1-u3}, {x14*x24*x34, x23, x12*x13, x15*x25*x35*
x45}, -1/360*(-3+u3+u2-2*u1)*(u2+3+u1+u3+u4)*(u2+2+u1+u3+u4)*(u2+1+u1+u3+u4)*(
u2^2+2*u2*u3+2*u1*u2+9*u2-3*u2*u4+9*u3+2*u1*u3+9*u1+u3^2+20+u1^2-3*u3*u4-3*u1*
u4-21*u4+6*u4^2)], 
[{-u1-u2-u4, u3+u4, u1+u2, -u2}, {x12, x34, x35*x45, x13*x23*x14*x24*x15*x25},
1/360*(u2+1+u1)*(u2+5+u1)*(u2+4+u1)*(u2+3+u1)*(u2+2+u1)*(2*u2+2*u1+3*u4+3+3*u3)
], 
[{u1+u2+u3+u4, -u2-u3-u4, -u1-u4, -u1-u3}, {x23, x12*x13*x14, x24*x34, x15*x25*
x35*x45}, 1/360*(u3+3-2*u4+u2)*(u2+1+u4+u1+u3)*(u2+u4+u1+3+u3)*(u2+2+u4+u1+u3)*
(u2^2+2*u2*u4+2*u2*u3-6*u2-3*u1*u2+20+u4^2+2*u3*u4+u3^2-6*u4-3*u1*u4-6*u3-3*u1*
u3+24*u1+6*u1^2)], 
[{u2, -u1-u2-u4, u3+u4, u1}, {x23*x24*x25, x34, x35*x45, x12*x13*x14*x15}, 1/
360*(u1+3)*(u1+2)*(u1+1)*(u1^2+5*u1*u2+9*u1+20+10*u2^2+30*u2)*(2*u2+2*u1+3+3*u4
+3*u3)], 
[{-u1-u3-u4, -u1-u2-u4, u2+u3+u4, u1}, {x34, x25*x35*x45, x23*x24, x12*x13*x14*
x15}, 1/360*(u1+3)*(u1+2)*(u1+1)*(-u4+3-u3+2*u2)*(10*u2^2+30*u2+20*u2*u3+15*u1*
u2+20*u2*u4+20+30*u3+24*u1+15*u1*u3+30*u4+15*u1*u4+6*u1^2+20*u3*u4+10*u3^2+10*
u4^2)], 
[{-u1-u3-u4, -u1-u2-u4, u1+u2+u3+u4, -u2-u3-u4}, {x34, x12*x13*x14, x23*x24, 
x15*x25*x35*x45}, 1/360*(-u3+3-u4+2*u2)*(u2+2+u1+u3+u4)*(u2+1+u1+u3+u4)*(u2+3+
u1+u3+u4)*(u2^2+2*u2*u4+2*u2*u3-6*u2-3*u1*u2+20+u3^2+u4^2+2*u3*u4-6*u4-3*u1*u4-\
6*u3-3*u1*u3+24*u1+6*u1^2)]}: