-----------------------------------------------------------------------------
Loading  GBNP 1.0.1 (Non-commutative Gröbner bases)
by A.M. Cohen (http://www.win.tue.nl/~amc) and
   J.W. Knopper (J.W.Knopper@tue.nl).
-----------------------------------------------------------------------------
Computing Grobner...
Ready Grobner
Computing Grobner...
We compute lambda(z)-z otimes 1- g otimes z and take U=1:
 -L2g0^2g1^3y0x2x1x0 + L2g0^2g1^3y0x0x2x1 + L1g0^2g1^3y0x0x1x2 + L1g0^2g1^3y0x\
0x1x0 + L2g0^3g2^2y2x2x1x0 + -L1g0^3g2^2y2x1x2x1 + -L2g0^3g2^2y2x1x0x2 + -L1g0\
^3g2^2y2x0x1x2 + L1g0^3g1^2y1x1x2x1 + L2g0^3g1^2y1x1x0x2 + -L2g0^3g1^2y1x0x2x1\
 + -L1g0^3g1^2y1x0x1x0 + -L2g0^3g1^3x2x1x0x2 + -L2g0^3g1^3x1x0x2x1 + -L2g0^3g1\
^3x0x2x1x0 + L2g0^2g3^2x1x0x2x1 + L2g0^2g3^2y2y3x1x2 + L2g0^2g3^2y2y3x1x0 + L1\
g0^2g3^2y2y3x0x2 + L2g0^2g3^2y2y3x0x1 + L2g0^2g3^2y0y2x2x1 + L2g0^2g3^2y0y2x1x\
2 + L1g0^2g3^2y0y2x0x2 + L2g0^2g3^2y0y2x0x1 + -L1g0^2g2^2y1y2x1x2 + -2*L1g0^2g\
2^2y1y2x0x1 + L1g0^2g2^2y0y1x1x2 + -L1g0^2g2^2y0y1x0x1 + L2g0^2g1g3x0x2x1x0 + \
L1g0^2g1g3y2y1x2x1 + -L2g0^2g1g3y2y1x1x2 + L2g0^2g1g3y2y1x1x0 + L1g0^2g1g3y1y3\
x2x1 + -L2g0^2g1g3y1y3x1x2 + L2g0^2g1g3y1y3x0x2 + L2g0^2g1^2x2x1x0x2 + L1g0^2g\
1^2y1y0x1x0 + L2g0^2g1^2y1y0x0x2 + -L2g0^2g1^2y1y0x0x1 + L2g0^2g1^2y0y3x2x1 + \
L1g0^2g1^2y0y3x1x0 + -L2g0^2g1^2y0y3x0x1 + L1^2g0^2g1^3y0x2 + L2g0^2g1^3y0x2x1\
x0 + -L1*L2g0^2g1^3y0x0 + -L2g0^2g1^3y0x0x2x1 + -L1g0^2g1^3y0x0x1x2 + -L1g0^2g\
1^3y0x0x1x0 + -L2g0^3g2^2y2x2x1x0 + L1*L2g0^3g2^2y2x1 + L1g0^3g2^2y2x1x2x1 + L\
2g0^3g2^2y2x1x0x2 + -L1^2g0^3g2^2y2x0 + L1g0^3g2^2y2x0x1x2 + -L1^2g0^3g1^2y1x2\
 + -L1*L2g0^3g1^2y1x1 + -L1g0^3g1^2y1x1x2x1 + -L2g0^3g1^2y1x1x0x2 + L1^2+L1*L2\
g0^3g1^2y1x0 + L2g0^3g1^2y1x0x2x1 + L1g0^3g1^2y1x0x1x0 + -L1^2-2*L1*L2+2*L2^2g\
0^3g1^3x2x1 + -L1^2-2*L1*L2+2*L2^2g0^3g1^3x1x0 + -L1^2-2*L1*L2+2*L2^2g0^3g1^3x\
0x2 + -L1*L2g0^3g1^3x0x1 + L1g0g3^2y0y1y2x2 + -L1g0g3^2y0y1y2x0 + L1g0g2^2y0y1\
y0x1 + -L1g0g2^2y0y1y0x0 + L2g0g1g3y2x2x1x0 + -L2g0g1g3y2x1x0x2 + L2g0g1g3y1x1\
x0x2 + -L2g0g1g3y1x0x2x1 + -L2g0g1g3y0x2x1x0 + L2g0g1g3y0x0x2x1 + -L2g0g1^2y3x\
1x2x1 + L2g0g1^2y0x1x2x1 + -L2g0g1^2y0y2y3x2 + L2g0g1^2y0y2y3x1 + 2*L1*L2g0g1^\
3x2x1 + 2*L1^2g0g1^3x1x2 + -L2g0^2g3y3x0x1x0 + L2g0^2g3y2x0x1x0 + -L2g0^2g3y2y\
1y3x1 + L2g0^2g3y2y1y3x0 + -L2^2g0^2g3^2x2x1 + -L2^2g0^2g3^2x1x2 + -L2^2g0^2g3\
^2x1x0 + -L2^2g0^2g3^2x0x1 + -L2^2g0^2g3^2y2y3 + -L2g0^2g3^2y2y3x1x2 + -L2g0^2\
g3^2y2y3x1x0 + -L1g0^2g3^2y2y3x0x2 + -L2g0^2g3^2y2y3x0x1 + -L2^2g0^2g3^2y0y2 +\
 -L2g0^2g3^2y0y2x2x1 + -L2g0^2g3^2y0y2x1x2 + -L1g0^2g3^2y0y2x0x2 + -L2g0^2g3^2\
y0y2x0x1 + L1g0^2g2y1y2y1x2 + -L1g0^2g2y1y2y1x1 + L1*L2g0^2g2^2x0x1 + L1*L2g0^\
2g2^2y1y2 + L1g0^2g2^2y1y2x1x2 + 2*L1g0^2g2^2y1y2x0x1 + -L1g0^2g2^2y0y1x1x2 + \
L1g0^2g2^2y0y1x0x1 + L2g0^2g1y3x0x1x2 + -L2g0^2g1y1x0x1x2 + L2g0^2g1y1y0y3x2 +\
 -L2g0^2g1y1y0y3x0 + L2^2g0^2g1g3x1x2 + -L2^2g0^2g1g3x1x0 + -L2^2g0^2g1g3x0x2 \
+ -L1g0^2g1g3y2y1x2x1 + L2g0^2g1g3y2y1x1x2 + -L2g0^2g1g3y2y1x1x0 + -L1g0^2g1g3\
y1y3x2x1 + L2g0^2g1g3y1y3x1x2 + -L2g0^2g1g3y1y3x0x2 + -L2^2g0^2g1^2x2x1 + -L2^\
2g0^2g1^2x0x2 + L2^2g0^2g1^2x0x1 + -L1g0^2g1^2y1y0x1x0 + -L2g0^2g1^2y1y0x0x2 +\
 L2g0^2g1^2y1y0x0x1 + -L2g0^2g1^2y0y3x2x1 + -L1g0^2g1^2y0y3x1x0 + L2g0^2g1^2y0\
y3x0x1 + -L1^2-L1*L2+L2^2g0^2g1^3y0x2 + L1*L2-L2^2g0^2g1^3y0x1 + L1*L2g0^2g1^3\
y0x0 + L1^2g0^3g3x2x1 + L1^2g0^3g3x1x0 + L1^2g0^3g3x0x2 + -L1^2g0^3g3^2y3x2 + \
L1^2g0^3g3^2y3x0 + 2*L1*L2g0^3g2x1x0 + 2*L1^2g0^3g2x0x1 + L1*L2g0^3g2^2y2x2 + \
-2*L1*L2+L2^2g0^3g2^2y2x1 + L1^2-L2^2g0^3g2^2y2x0 + -2*L1^2g0^3g1x1x2 + 2*L1*L\
2g0^3g1x0x2 + -2*L1^2g0^3g1x0x1 + L1^2+L1*L2-L2^2g0^3g1^2y1x2 + L1*L2g0^3g1^2y\
1x1 + -L1^2-2*L1*L2+L2^2g0^3g1^2y1x0 + 4*L1^2*L2-L1*L2^2-L2^3g0^3g1^3 + L1^2+L\
1*L2-L2^2g0^3g1^3x2x1 + L1^2+L1*L2-L2^2g0^3g1^3x1x0 + L1^2+L1*L2-L2^2g0^3g1^3x\
0x2 + L1*L2g0^3g1^3x0x1 + -L2g1g3y1y2x2x1 + L2g1g3y0y2x2x1 + -L2g1g3y0y1x2x1 +\
 L2g0g3y2y1x1x0 + L2g0g3y1y2x1x0 + -2*L1^2g0g3^2y3x2 + L1^2g0g3^2y1x2 + L1^2g0\
g3^2y1x0 + -L1g0g3^2y0y1y2x2 + L1g0g3^2y0y1y2x0 + L2g0g2y1y0x0x2 + L2g0g2y0y1x\
0x2 + -2*L1^2g0g2^2y3x0 + 2*L1^2g0g2^2y2x1 + -L1*L2g0g2^2y0x1 + L1*L2g0g2^2y0x\
0 + -L1g0g2^2y0y1y0x1 + L1g0g2^2y0y1y0x0 + L2g0g1y2y3x1x2 + 2*L2g0g1y2y3x0x1 +\
 -L2g0g1y2y1x1x2 + -L2g0g1y2y1x0x1 + -2*L2g0g1y1y3x1x2 + -L2g0g1y1y3x0x1 + L2g\
0g1y1y0x1x2 + L2g0g1y0y3x1x2 + -L2g0g1y0y3x0x1 + L2g0g1y0y2x0x1 + L2^2g0g1^2y3\
x1 + -L1*L2g0g1^2y3x0 + -2*L1*L2g0g1^2y2x2 + 2*L1*L2g0g1^2y2x1 + 2*L1*L2g0g1^2\
y1x2 + -2*L1*L2g0g1^2y1x1 + -L2^2g0g1^2y0x1 + L1*L2g0g1^2y0x0 + L2g0g1^2y0y2y3\
x2 + -L2g0g1^2y0y2y3x1 + -2*L1^2*L2g0g1^3 + -2*L1*L2g0g1^3x2x1 + -2*L1^2g0g1^3\
x1x2 + -L1*L2g0^2g3y3x2 + L2^2g0^2g3y3x0 + L1*L2g0^2g3y2x2 + -L2^2g0^2g3y2x0 +\
 L2g0^2g3y2y1y3x1 + -L2g0^2g3y2y1y3x0 + -2*L1*L2g0^2g3y1x1 + 2*L1*L2g0^2g3y1x0\
 + 2*L1*L2g0^2g3y0x1 + -2*L1*L2g0^2g3y0x0 + L1^2*L2+L2^3g0^2g3^2 + 2*L2^2g0^2g\
3^2x1x2 + L2^2g0^2g3^2x1x0 + -L1*L2g0^2g3^2x0x2 + L2^2g0^2g3^2x0x1 + -L1^2+L2^\
2g0^2g3^2y2y3 + -L1^2+L2^2g0^2g3^2y0y2 + -2*L1^2g0^2g2y3x1 + -L1*L2g0^2g2y1x2 \
+ L1*L2g0^2g2y1x1 + -L1g0^2g2y1y2y1x2 + L1g0^2g2y1y2y1x1 + 2*L1^2g0^2g2y0x2 + \
-L1*L2g0^2g2^2x0x1 + -L1*L2g0^2g2^2y1y2 + -2*L1*L2g0^2g1y2x2 + 2*L1*L2g0^2g1y2\
x0 + -L2g0^2g1y1y0y3x2 + L2g0^2g1y1y0y3x0 + 2*L1*L2g0^2g1y0x2 + -2*L1*L2g0^2g1\
y0x0 + L1^2*L2g0^2g1g3 + -L1*L2g0^2g1g3x2x1 + -L2^2g0^2g1g3x1x2 + L2^2g0^2g1g3\
x1x0 + L2^2g0^2g1g3x0x2 + L2^2g0^2g1g3x0x1 + -L1^2g0^2g1g3y2y1 + -L1^2g0^2g1g3\
y1y3 + L1^2*L2g0^2g1^2 + L2^2g0^2g1^2x2x1 + -L2^2g0^2g1^2x1x2 + -L1*L2g0^2g1^2\
x1x0 + L2^2g0^2g1^2x0x2 + -2*L2^2g0^2g1^2x0x1 + -L1^2g0^2g1^2y1y0 + -L1^2g0^2g\
1^2y0y3 + L1*L2-L2^2g0^2g1^3y0x2 + -L1*L2+L2^2g0^2g1^3y0x1 + -3*L1^2*L2+L1*L2^\
2g0^3g3 + -L1^2g0^3g3x2x1 + -L1^2g0^3g3x1x0 + -L1^2g0^3g3x0x2 + L1^2g0^3g3^2y3\
x2 + -L1^2g0^3g3^2y3x0 + -2*L1^2*L2g0^3g2 + -2*L1*L2g0^3g2x1x0 + -2*L1^2g0^3g2\
x0x1 + -L1*L2g0^3g2^2y2x2 + L1*L2-L2^2g0^3g2^2y2x1 + L2^2g0^3g2^2y2x0 + 2*L1^2\
g0^3g1x1x2 + -2*L1*L2g0^3g1x0x2 + 2*L1^2g0^3g1x0x1 + -L1*L2+L2^2g0^3g1^2y1x2 +\
 L1*L2-L2^2g0^3g1^2y1x0 + -6*L1^2*L2+3*L1*L2^2g0^3g1^3 + L2g2y1y2y3x2 + L2g2y1\
y0y2x2 + -L2g2y0y2y3x2 + L2g2y0y1y3x2 + -L2g2y0y1y0x2 + 2*L1^2g2^2y2y3 + -2*L1\
^2g2^2y1y3 + 2*L1^2g2^2y0y2 + -2*L1^2g2^2y0y1 + -L2g1y2y1y3x1 + -L2g1y1y2y3x1 \
+ L2g1y0y2y1x1 + L2g1y0y1y2x1 + 2*L1*L2g1g3x2x1 + 2*L1^2g1^2y2y1 + 2*L1^2g1^2y\
1y3 + 2*L1^2g1^2y1y2 + -2*L1^2g1^2y0y3 + 2*L1^2g1^2y0y1 + L2g0y2y1y0x0 + -L2g0\
y1y2y1x0 + -L2g0y1y0y3x0 + -L2g0y0y1y3x0 + 2*L1*L2-L2^2g0g3x1x0 + 2*L1^2g0g3^2\
y3x2 + -L1^2g0g3^2y1x2 + -L1^2g0g3^2y1x0 + 2*L1*L2-L2^2g0g2x0x2 + 2*L1^2g0g2^2\
y3x0 + -2*L1^2g0g2^2y2x1 + L1*L2g0g2^2y0x1 + -L1*L2g0g2^2y0x0 + -L2^2g0g1y2y3 \
+ L2^2g0g1y1y3 + -L2^2g0g1y1y0 + -L2^2g0g1y0y2 + L2^2g0g1g3y2x1 + -L2^2g0g1g3y\
2x0 + -L2^2g0g1g3y1x2 + L2^2g0g1g3y1x0 + L2^2g0g1g3y0x2 + -L2^2g0g1g3y0x1 + -L\
2^2g0g1^2y3x1 + 2*L1*L2g0g1^2y3x0 + 2*L1*L2g0g1^2y2x2 + -2*L1*L2g0g1^2y2x1 + -\
2*L1*L2g0g1^2y1x2 + 2*L1*L2g0g1^2y1x1 + L2^2g0g1^2y0x1 + -L1*L2g0g1^2y0x0 + -2\
*L1^2g0^2y2y3 + -2*L1^2g0^2y1y2 + 2*L1^2g0^2y1y0 + 2*L1^2g0^2y0y3 + 2*L1*L2g0^\
2g3y3x2 + -L2^2g0^2g3y3x1 + -L2^2g0^2g3y3x0 + -L1*L2g0^2g3y2x2 + L2^2g0^2g3y2x\
1 + L2^2g0^2g3y2x0 + 2*L1*L2g0^2g3y1x1 + -2*L1*L2g0^2g3y1x0 + -2*L1*L2g0^2g3y0\
x1 + 2*L1*L2g0^2g3y0x0 + -L1*L2^2-L2^3g0^2g3^2 + 2*L1^2g0^2g2y3x1 + L1*L2g0^2g\
2y1x2 + -L1*L2g0^2g2y1x1 + -2*L1^2g0^2g2y0x2 + -L1^2*L2g0^2g2^2 + -L2^2g0^2g1y\
3x2 + L1*L2g0^2g1y3x1 + -L2^2g0^2g1y3x0 + 2*L1*L2g0^2g1y2x2 + -2*L1*L2g0^2g1y2\
x0 + L2^2g0^2g1y1x2 + -L1*L2g0^2g1y1x1 + -2*L1*L2g0^2g1y0x2 + 2*L1*L2g0^2g1y0x\
0 + -L1*L2^2g0^2g1g3 + -L1*L2^2+L2^3g0^2g1^2 + 6*L1^2*L2-L1*L2^2g0^3g3 + 2*L1^\
2*L2g0^3g2 + -2*L1^2*L2g0^3g1 + -2*L1*L2g2y3x2 + -L1*L2g2y2x2 + 2*L1*L2-L2^2g2\
y1x2 + L2^2g2y0x2 + L1^2*L2g2^2 + -2*L1*L2+L2^2g1y3x1 + 2*L1*L2-L2^2g1y0x1 + -\
L1^2*L2g1^2 + -2*L1*L2+L2^2g0y3x0 + 2*L1*L2-L2^2g0y2x0 + L2^2g0y1x0 + -L1*L2g0\
y0x0 + L1*L2^2g0g1 + L1^2*L2g0^2 
Recall that gamma(z)=z - L2 z' - L2(L1-L2)z''
We compute lambda(z')- z' otimes 1 - g otimes z' and take U=1: 
 - g0^3g1^3x2x1x0x2 - g0^3g1^3x1x0x2x1 - g0^3g1^3x0x2x1x0 + g0^2g3^2x1x0x2x1 +\
 g0^2g1g3x0x2x1x0 + g0^2g1^2x2x1x0x2 + g0g1g3y2x2x1x0 - g0g1g3y2x1x0x2 + g0g1g\
3y1x1x0x2 - g0g1g3y1x0x2x1 - g0g1g3y0x2x1x0 + g0g1g3y0x0x2x1 - g0g1^2y3x1x2x1 \
+ g0g1^2y0x1x2x1 - g0^2g3y3x0x1x0 + g0^2g3y2x0x1x0 + g0^2g1y3x0x1x2 - g0^2g1y1\
x0x1x2 - g1g3y1y2x2x1 + g1g3y0y2x2x1 - g1g3y0y1x2x1 + g0g3y2y1x1x0 + g0g3y1y2x\
1x0 + g0g2y1y0x0x2 + g0g2y0y1x0x2 + g0g1y2y3x1x2 + 2g0g1y2y3x0x1 - g0g1y2y1x1x\
2 - g0g1y2y1x0x1 - 2g0g1y1y3x1x2 - g0g1y1y3x0x1 + g0g1y1y0x1x2 + g0g1y0y3x1x2 \
- g0g1y0y3x0x1 + g0g1y0y2x0x1 + -L2g0^2g3^2x2x1 + L2g0^2g3^2x1x2 + -L1g0^2g3^2\
x0x2 + -L1g0^2g1g3x2x1 + L2g0^2g1g3x0x1 + -L2g0^2g1^2x1x2 + -L1g0^2g1^2x1x0 + \
-L2g0^2g1^2x0x1 + g2y1y2y3x2 + g2y1y0y2x2 - g2y0y2y3x2 + g2y0y1y3x2 - g2y0y1y0\
x2 - g1y2y1y3x1 - g1y1y2y3x1 + g1y0y2y1x1 + g1y0y1y2x1 + g0y2y1y0x0 - g0y1y2y1\
x0 - g0y1y0y3x0 - g0y0y1y3x0 + L2g0g1g3y2x1 + -L2g0g1g3y2x0 + -L2g0g1g3y1x2 + \
L2g0g1g3y1x0 + L2g0g1g3y0x2 + -L2g0g1g3y0x1 + L1g0g1^2y3x0 + L1g0^2g3y3x2 + -L\
2g0^2g3y3x1 + L2g0^2g3y2x1 + -L2g0^2g1y3x2 + L1g0^2g1y3x1 + -L2g0^2g1y3x0 + L2\
g0^2g1y1x2 + -L1g0^2g1y1x1 + L1g2^2y0y3 + L1+L2g1g3x2x1 + L1g1^2y2y3 + L1g0g3x\
1x0 + L1g0g2x0x2 + -L2g0g1y2y3 + L2g0g1y2y1 + L2g0g1y1y3 + L1g0^2y1y3 + L2^2g0\
^2g1^2 + -L1-L2g2y3x2 + -L1g2y2x2 + L1g2y1x2 + L2g2y0x2 + -L1g1y3x1 + L1g1y0x1\
 + -L1g0y3x0 + L1g0y2x0 + L2g0y1x0 + -L1g0y0x0 + -L2^2g0g1 
We compute lambda(z'')- z'' otimes 1 - g otimes z'' and take U=1: 
 - g0^3g1^3x2x1 - g0^3g1^3x1x0 - g0^3g1^3x0x2 + g1g3x2x1 + g0g3x1x0 + g0g2x0x2\
 - g2y3x2 + g2y1x2 - g1y3x1 + g1y0x1 - g0y3x0 + g0y2x0 
Finally, lambda ( gamma(z) ) -  gamma(z) otimes 1 - g otimes gamma(z) is: 
 -L1^2g0^2g3^2y2y3 + -L1^2g0^2g3^2y0y2 + -L1^2g0^2g1g3y2y1 + -L1^2g0^2g1g3y1y3\
 + -L1^2g0^2g1^2y1y0 + -L1^2g0^2g1^2y0y3 + -2*L1^2*L2+2*L1*L2^2-L2^3g0^3g1^3 +\
 2*L1^2g2^2y2y3 + -2*L1^2g2^2y1y3 + -L1*L2g2^2y0y3 + 2*L1^2g2^2y0y2 + -2*L1^2g\
2^2y0y1 + -L1*L2g1^2y2y3 + 2*L1^2g1^2y2y1 + 2*L1^2g1^2y1y3 + 2*L1^2g1^2y1y2 + \
-2*L1^2g1^2y0y3 + 2*L1^2g1^2y0y1 + -L2^2g0g1y2y1 + -L2^2g0g1y1y0 + -L2^2g0g1y0\
y2 + -2*L1^2*L2g0g1^3 + -2*L1^2g0^2y2y3 + -L1*L2g0^2y1y3 + -2*L1^2g0^2y1y2 + 2\
*L1^2g0^2y1y0 + 2*L1^2g0^2y0y3 + L1^2*L2-L1*L2^2g0^2g3^2 + -L1^2*L2g0^2g2^2 + \
L1^2*L2-L1*L2^2g0^2g1g3 + L1^2*L2-L1*L2^2g0^2g1^2 + 3*L1^2*L2g0^3g3 + -2*L1^2*\
L2g0^3g1 + L1^2*L2g2^2 + -L1^2*L2g1^2 + L1*L2^2+L2^3g0g1 + L1^2*L2g0^2 
gap> quit;