let g^2=g+1$  % golden ratio
let z^6=-z^3-1$ % 9-th root of 1

phiz:=z^4$
phi2z:=z^7$

s:=1+2*z^3$ % square root of -3.

ID3:=mat((1,0,0),
         (0,1,0),
         (0,0,1))$

ZMAT:=mat((z,  0,  0),
          (0,z^4,  0),
          (0,  0,z^7))$

gendt:=(g+(2*g-1)*z^3)/2$
gendti:=(g+(2*g-1)*z^6)/2$

SIG:=mat(
(0,1,0),
(0,0,1),
(gendt,0,0))$

SIGI:=mat(
(0,0,gendti),
(1,0,0),
(0,1,0))$

T:=2*((3-2*g)+(-2+g)*Z+(2-g)*Z^2-Z^4+(1-g)*Z^5)$
phiT:=sub(z=z^4,T)$
phi2T:=sub(z=z^7,T)$

FF:=mat(
(T,   0,    0),
(0,phiT,    0),
(0,   0,phi2T))$ 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The generators for $\bar\Gamma$ in the case $(\cC_2,p=2,\emptyset)$:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

AA:=(1/3)*mat(
(g*z^4+g*z^3-g*z^2+z^4+z^3+1,-g*z^5-g*z^3+z^2-1,g*z^5-3*g*z^4-g*z^3-2*g*z+2*z^3-z^2-z+3),
(g*z^5+2*g*z^4+2*g*z^3+2*g*z+z^5+2*z^4+z^2+2,g*z^5-g*z^4+g*z^3+g*z^2-g*z-z^4+z^3-z+1,-(g*z^3+g*z^2+z^5+z^2+1)),
(-g*z^3-g*z^2+z^5+z^3+1,2*g*z^3+g*z^2-2*g*z-z^5-2*z^4-2*z+2,-g*z^5+g*z^3+g*z+z^3+z+1))$

BB:=(1/3)*mat(
(g*z^5+g*z^4-g*z^3-z^5+z^4+z^3-z^2+z+1,-g*z^2-g+z^3+z,-g*z^4+2*g*z^2-g*z+g+z^4+z^3+3),
(-g*z^5+3*g*z^3+g*z+g-z^5+z^4+z^2+1,-g*z^4-g*z^3+g*z^2-g*z+z^5+z^3-z+1,g*z^5+g*z^2-g+z^4+z^3),
((-g*z^4-2*g*z^3+g*z^2+g*z-3*g+z^5-z^3+2*z^2-z)/2,g*z^4+3*g*z^3-g*z^2+g-z^5-z^4-2*z^2-z+1,-g*z^5-g*z^3-g*z^2+g*z-z^4+z^3+z^2+1))$

ZZ:=mat(
(z,  0,  0),
(0,z^4,  0),
(0,  0,z^7))$


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The generators for $\bar\Gamma$ in the case $(\cC_2,p=2,\{3\})$:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

AD:=(1/6)*mat(
(2*(g*z^3-g*z^2-g*z+g-z+1),2*(-2*g*z^5+2*g*z^4-2*g*z^3-3*g*z^2+2*g*z-3*g-3*z^5+2*z^4+z^3-z^2+2*z-1),2*(-2*g*z^5+g*z^4-g*z^3-g*z^2+2*g*z-2*g-z^5+2*z^4-z^2+z-1)),
(2*(-g*z^5-2*g*z^4-2*g*z^3-2*g*z^2-g*z-g-z^5-z^4-z^3-z^2-2*z),2*(g*z^5-g*z^4+g*z^3+g*z^2+g-z^4+1),2*(3*g*z^5-2*g*z^3+g*z^2-2*g*z-3*g+z^5+z^3-2*z^2-2*z-1)),
(2*(3*g*z^5+g*z^4-3*g*z^3+g*z^2+3*g*z-2*g+2*z^5-z^3+3*z^2+z+1),2*(2*g*z^5+g*z^4-2*g*z^3+g*z^2+2*g*z-g+z^5-z^4-z^3+z),2*(-g*z^5+g*z^4+g*z^3+g*z+g+z^4+z+1)))$

BD:=(1/6)*mat(
(2*(-g*z^4-g*z-g+z^3-z),2*(-2*g*z^3+g*z^2-g*z-g-z^5+z^4+z^2+z+1),2*(g*z^5+g*z^3+g*z^2+3*g+z^5-2*z^4+z^3+2*z^2-2*z)),
(2*(2*g*z^4+g*z^3+2*g*z^2+g*z-z^4+3*z^3+1),2*(g*z-g-z^4+z^3),2*(-g*z^5-g*z^4-2*g*z^3-g*z^2-g-z^5-2*z^2-z+1)),
(2*g*z^4+g*z^3-4*g*z^2+2*g*z+2*g-z^3-2*z+3,2*(-2*g*z^5-g*z^4+g*z^3-2*g*z^2-2*g*z+z^4+3*z^3+z+1),2*(g*z^4-g+z^4+z^3+z)))$

ZD:=mat(
(z,  0,  0),
(0,z^4,  0),
(0,  0,z^7))$

a1:=2/3$
a2:=1/3$
a3:=-1/3$
a4:=2/3$
a5:=0/3$
a6:=0/3$
a7:=-1/3$
a8:=0/3$
a9:=1/3$
a10:=0/3$
a11:=1/3$
a12:=0/3$
a13:=0/3$
a14:=1/3$
a15:=0/3$
a16:=0/3$
a17:=0/3$
a18:=0/3$
a19:=0/3$
a20:=0/3$
a21:=0/3$
a22:=0/3$
a23:=0/3$
a24:=0/3$
a25:=-1/3$
a26:=-1/3$
a27:=0/3$
a28:=2/3$
a29:=1/3$
a30:=-1/3$
a31:=-2/3$
a32:=1/3$
a33:=0/3$
a34:=-1/3$
a35:=0/3$
a36:=-1/3$

b1:=1/3$
b2:=1/3$
b3:=0/3$
b4:=1/3$
b5:=1/3$
b6:=1/3$
b7:=1/3$
b8:=-1/3$
b9:=0/3$
b10:=0/3$
b11:=1/3$
b12:=1/3$
b13:=0/3$
b14:=1/3$
b15:=0/3$
b16:=2/3$
b17:=-1/3$
b18:=0/3$
b19:=1/3$
b20:=0/3$
b21:=-1/3$
b22:=-1/3$
b23:=0/3$
b24:=0/3$
b25:=1/3$
b26:=0/3$
b27:=-1/3$
b28:=3/3$
b29:=-1/3$
b30:=0/3$
b31:=-1/3$
b32:=1/3$
b33:=0/3$
b34:=1/3$
b35:=1/3$
b36:=0/3$

z1:=0$
z2:=0$
z3:=0$
z4:=0$
z5:=1$
z6:=0$
z7:=0$
z8:=0$
z9:=0$
z10:=0$
z11:=0$
z12:=0$
z13:=0$
z14:=0$
z15:=0$
z16:=0$
z17:=0$
z18:=0$
z19:=0$
z20:=0$
z21:=0$
z22:=0$
z23:=0$
z24:=0$
z25:=0$
z26:=0$
z27:=0$
z28:=0$
z29:=0$
z30:=0$
z31:=0$
z32:=0$
z33:=0$
z34:=0$
z35:=0$
z36:=0$

ad1:=0/3$
ad2:=1/3$
ad3:=-1/3$
ad4:=1/3$
ad5:=-1/3$
ad6:=2/3$
ad7:=1/3$
ad8:=0/3$
ad9:=-1/3$
ad10:=-1/3$
ad11:=0/3$
ad12:=1/3$
ad13:=2/3$
ad14:=0/3$
ad15:=2/3$
ad16:=0/3$
ad17:=0/3$
ad18:=-3/3$
ad19:=-1/3$
ad20:=1/3$
ad21:=-3/3$
ad22:=-1/3$
ad23:=-1/3$
ad24:=2/3$
ad25:=1/3$
ad26:=-1/3$
ad27:=-3/3$
ad28:=-2/3$
ad29:=1/3$
ad30:=-2/3$
ad31:=1/3$
ad32:=0/3$
ad33:=2/3$
ad34:=-1/3$
ad35:=0/3$
ad36:=-2/3$

bd1:=1/3$
bd2:=0/3$
bd3:=1/3$
bd4:=-1/3$
bd5:=-1/3$
bd6:=1/3$
bd7:=0/3$
bd8:=0/3$
bd9:=1/3$
bd10:=3/3$
bd11:=1/3$
bd12:=0/3$
bd13:=0/3$
bd14:=0/3$
bd15:=1/3$
bd16:=0/3$
bd17:=0/3$
bd18:=-1/3$
bd19:=0/3$
bd20:=-1/3$
bd21:=-1/3$
bd22:=1/3$
bd23:=-1/3$
bd24:=-1/3$
bd25:=0/3$
bd26:=0/3$
bd27:=1/3$
bd28:=1/3$
bd29:=0/3$
bd30:=-2/3$
bd31:=-1/3$
bd32:=-1/3$
bd33:=0/3$
bd34:=2/3$
bd35:=0/3$
bd36:=0/3$

zd1:=0$
zd2:=0$
zd3:=0$
zd4:=0$
zd5:=1$
zd6:=0$
zd7:=0$
zd8:=0$
zd9:=0$
zd10:=0$
zd11:=0$
zd12:=0$
zd13:=0$
zd14:=0$
zd15:=0$
zd16:=0$
zd17:=0$
zd18:=0$
zd19:=0$
zd20:=0$
zd21:=0$
zd22:=0$
zd23:=0$
zd24:=0$
zd25:=0$
zd26:=0$
zd27:=0$
zd28:=0$
zd29:=0$
zd30:=0$
zd31:=0$
zd32:=0$
zd33:=0$
zd34:=0$
zd35:=0$
zd36:=0$



AA-( 
  a1*g^0*ZMAT^0*SIGI+ a2*g^0*ZMAT^0*SIG^0+ a3*g^0*ZMAT^0*SIG^1
+ a4*g^0*ZMAT^1*SIGI+ a5*g^0*ZMAT^1*SIG^0+ a6*g^0*ZMAT^1*SIG^1
+ a7*g^0*ZMAT^2*SIGI+ a8*g^0*ZMAT^2*SIG^0+ a9*g^0*ZMAT^2*SIG^1
+a10*g^0*ZMAT^3*SIGI+a11*g^0*ZMAT^3*SIG^0+a12*g^0*ZMAT^3*SIG^1
+a13*g^0*ZMAT^4*SIGI+a14*g^0*ZMAT^4*SIG^0+a15*g^0*ZMAT^4*SIG^1
+a16*g^0*ZMAT^5*SIGI+a17*g^0*ZMAT^5*SIG^0+a18*g^0*ZMAT^5*SIG^1
+a19*g^1*ZMAT^0*SIGI+a20*g^1*ZMAT^0*SIG^0+a21*g^1*ZMAT^0*SIG^1
+a22*g^1*ZMAT^1*SIGI+a23*g^1*ZMAT^1*SIG^0+a24*g^1*ZMAT^1*SIG^1
+a25*g^1*ZMAT^2*SIGI+a26*g^1*ZMAT^2*SIG^0+a27*g^1*ZMAT^2*SIG^1
+a28*g^1*ZMAT^3*SIGI+a29*g^1*ZMAT^3*SIG^0+a30*g^1*ZMAT^3*SIG^1
+a31*g^1*ZMAT^4*SIGI+a32*g^1*ZMAT^4*SIG^0+a33*g^1*ZMAT^4*SIG^1
+a34*g^1*ZMAT^5*SIGI+a35*g^1*ZMAT^5*SIG^0+a36*g^1*ZMAT^5*SIG^1);


BB-( 
  b1*g^0*ZMAT^0*SIGI+ b2*g^0*ZMAT^0*SIG^0+ b3*g^0*ZMAT^0*SIG^1
+ b4*g^0*ZMAT^1*SIGI+ b5*g^0*ZMAT^1*SIG^0+ b6*g^0*ZMAT^1*SIG^1
+ b7*g^0*ZMAT^2*SIGI+ b8*g^0*ZMAT^2*SIG^0+ b9*g^0*ZMAT^2*SIG^1
+b10*g^0*ZMAT^3*SIGI+b11*g^0*ZMAT^3*SIG^0+b12*g^0*ZMAT^3*SIG^1
+b13*g^0*ZMAT^4*SIGI+b14*g^0*ZMAT^4*SIG^0+b15*g^0*ZMAT^4*SIG^1
+b16*g^0*ZMAT^5*SIGI+b17*g^0*ZMAT^5*SIG^0+b18*g^0*ZMAT^5*SIG^1
+b19*g^1*ZMAT^0*SIGI+b20*g^1*ZMAT^0*SIG^0+b21*g^1*ZMAT^0*SIG^1
+b22*g^1*ZMAT^1*SIGI+b23*g^1*ZMAT^1*SIG^0+b24*g^1*ZMAT^1*SIG^1
+b25*g^1*ZMAT^2*SIGI+b26*g^1*ZMAT^2*SIG^0+b27*g^1*ZMAT^2*SIG^1
+b28*g^1*ZMAT^3*SIGI+b29*g^1*ZMAT^3*SIG^0+b30*g^1*ZMAT^3*SIG^1
+b31*g^1*ZMAT^4*SIGI+b32*g^1*ZMAT^4*SIG^0+b33*g^1*ZMAT^4*SIG^1
+b34*g^1*ZMAT^5*SIGI+b35*g^1*ZMAT^5*SIG^0+b36*g^1*ZMAT^5*SIG^1);

ZZ-( 
  z1*g^0*ZMAT^0*SIGI+ z2*g^0*ZMAT^0*SIG^0+ z3*g^0*ZMAT^0*SIG^1
+ z4*g^0*ZMAT^1*SIGI+ z5*g^0*ZMAT^1*SIG^0+ z6*g^0*ZMAT^1*SIG^1
+ z7*g^0*ZMAT^2*SIGI+ z8*g^0*ZMAT^2*SIG^0+ z9*g^0*ZMAT^2*SIG^1
+z10*g^0*ZMAT^3*SIGI+z11*g^0*ZMAT^3*SIG^0+z12*g^0*ZMAT^3*SIG^1
+z13*g^0*ZMAT^4*SIGI+z14*g^0*ZMAT^4*SIG^0+z15*g^0*ZMAT^4*SIG^1
+z16*g^0*ZMAT^5*SIGI+z17*g^0*ZMAT^5*SIG^0+z18*g^0*ZMAT^5*SIG^1
+z19*g^1*ZMAT^0*SIGI+z20*g^1*ZMAT^0*SIG^0+z21*g^1*ZMAT^0*SIG^1
+z22*g^1*ZMAT^1*SIGI+z23*g^1*ZMAT^1*SIG^0+z24*g^1*ZMAT^1*SIG^1
+z25*g^1*ZMAT^2*SIGI+z26*g^1*ZMAT^2*SIG^0+z27*g^1*ZMAT^2*SIG^1
+z28*g^1*ZMAT^3*SIGI+z29*g^1*ZMAT^3*SIG^0+z30*g^1*ZMAT^3*SIG^1
+z31*g^1*ZMAT^4*SIGI+z32*g^1*ZMAT^4*SIG^0+z33*g^1*ZMAT^4*SIG^1
+z34*g^1*ZMAT^5*SIGI+z35*g^1*ZMAT^5*SIG^0+z36*g^1*ZMAT^5*SIG^1);

AD-( 
  ad1*g^0*ZMAT^0*SIGI+ ad2*g^0*ZMAT^0*SIG^0+ ad3*g^0*ZMAT^0*SIG^1
+ ad4*g^0*ZMAT^1*SIGI+ ad5*g^0*ZMAT^1*SIG^0+ ad6*g^0*ZMAT^1*SIG^1
+ ad7*g^0*ZMAT^2*SIGI+ ad8*g^0*ZMAT^2*SIG^0+ ad9*g^0*ZMAT^2*SIG^1
+ad10*g^0*ZMAT^3*SIGI+ad11*g^0*ZMAT^3*SIG^0+ad12*g^0*ZMAT^3*SIG^1
+ad13*g^0*ZMAT^4*SIGI+ad14*g^0*ZMAT^4*SIG^0+ad15*g^0*ZMAT^4*SIG^1
+ad16*g^0*ZMAT^5*SIGI+ad17*g^0*ZMAT^5*SIG^0+ad18*g^0*ZMAT^5*SIG^1
+ad19*g^1*ZMAT^0*SIGI+ad20*g^1*ZMAT^0*SIG^0+ad21*g^1*ZMAT^0*SIG^1
+ad22*g^1*ZMAT^1*SIGI+ad23*g^1*ZMAT^1*SIG^0+ad24*g^1*ZMAT^1*SIG^1
+ad25*g^1*ZMAT^2*SIGI+ad26*g^1*ZMAT^2*SIG^0+ad27*g^1*ZMAT^2*SIG^1
+ad28*g^1*ZMAT^3*SIGI+ad29*g^1*ZMAT^3*SIG^0+ad30*g^1*ZMAT^3*SIG^1
+ad31*g^1*ZMAT^4*SIGI+ad32*g^1*ZMAT^4*SIG^0+ad33*g^1*ZMAT^4*SIG^1
+ad34*g^1*ZMAT^5*SIGI+ad35*g^1*ZMAT^5*SIG^0+ad36*g^1*ZMAT^5*SIG^1);

BD-( 
  bd1*g^0*ZMAT^0*SIGI+ bd2*g^0*ZMAT^0*SIG^0+ bd3*g^0*ZMAT^0*SIG^1
+ bd4*g^0*ZMAT^1*SIGI+ bd5*g^0*ZMAT^1*SIG^0+ bd6*g^0*ZMAT^1*SIG^1
+ bd7*g^0*ZMAT^2*SIGI+ bd8*g^0*ZMAT^2*SIG^0+ bd9*g^0*ZMAT^2*SIG^1
+bd10*g^0*ZMAT^3*SIGI+bd11*g^0*ZMAT^3*SIG^0+bd12*g^0*ZMAT^3*SIG^1
+bd13*g^0*ZMAT^4*SIGI+bd14*g^0*ZMAT^4*SIG^0+bd15*g^0*ZMAT^4*SIG^1
+bd16*g^0*ZMAT^5*SIGI+bd17*g^0*ZMAT^5*SIG^0+bd18*g^0*ZMAT^5*SIG^1
+bd19*g^1*ZMAT^0*SIGI+bd20*g^1*ZMAT^0*SIG^0+bd21*g^1*ZMAT^0*SIG^1
+bd22*g^1*ZMAT^1*SIGI+bd23*g^1*ZMAT^1*SIG^0+bd24*g^1*ZMAT^1*SIG^1
+bd25*g^1*ZMAT^2*SIGI+bd26*g^1*ZMAT^2*SIG^0+bd27*g^1*ZMAT^2*SIG^1
+bd28*g^1*ZMAT^3*SIGI+bd29*g^1*ZMAT^3*SIG^0+bd30*g^1*ZMAT^3*SIG^1
+bd31*g^1*ZMAT^4*SIGI+bd32*g^1*ZMAT^4*SIG^0+bd33*g^1*ZMAT^4*SIG^1
+bd34*g^1*ZMAT^5*SIGI+bd35*g^1*ZMAT^5*SIG^0+bd36*g^1*ZMAT^5*SIG^1);

ZD-( 
  zd1*g^0*ZMAT^0*SIGI+ zd2*g^0*ZMAT^0*SIG^0+ zd3*g^0*ZMAT^0*SIG^1
+ zd4*g^0*ZMAT^1*SIGI+ zd5*g^0*ZMAT^1*SIG^0+ zd6*g^0*ZMAT^1*SIG^1
+ zd7*g^0*ZMAT^2*SIGI+ zd8*g^0*ZMAT^2*SIG^0+ zd9*g^0*ZMAT^2*SIG^1
+zd10*g^0*ZMAT^3*SIGI+zd11*g^0*ZMAT^3*SIG^0+zd12*g^0*ZMAT^3*SIG^1
+zd13*g^0*ZMAT^4*SIGI+zd14*g^0*ZMAT^4*SIG^0+zd15*g^0*ZMAT^4*SIG^1
+zd16*g^0*ZMAT^5*SIGI+zd17*g^0*ZMAT^5*SIG^0+zd18*g^0*ZMAT^5*SIG^1
+zd19*g^1*ZMAT^0*SIGI+zd20*g^1*ZMAT^0*SIG^0+zd21*g^1*ZMAT^0*SIG^1
+zd22*g^1*ZMAT^1*SIGI+zd23*g^1*ZMAT^1*SIG^0+zd24*g^1*ZMAT^1*SIG^1
+zd25*g^1*ZMAT^2*SIGI+zd26*g^1*ZMAT^2*SIG^0+zd27*g^1*ZMAT^2*SIG^1
+zd28*g^1*ZMAT^3*SIGI+zd29*g^1*ZMAT^3*SIG^0+zd30*g^1*ZMAT^3*SIG^1
+zd31*g^1*ZMAT^4*SIGI+zd32*g^1*ZMAT^4*SIG^0+zd33*g^1*ZMAT^4*SIG^1
+zd34*g^1*ZMAT^5*SIGI+zd35*g^1*ZMAT^5*SIG^0+zd36*g^1*ZMAT^5*SIG^1);


AASTAR:=sub(z=z^8,tp(AA))$
BBSTAR:=sub(z=z^8,tp(BB))$
ZZSTAR:=sub(z=z^8,tp(ZZ))$

% Checking that the elements $\xi$ satisfy $\iota(\xi)\xi=1$:
% The following are zero:
AASTAR*FF*AA-FF;
BBSTAR*FF*BB-FF;
ZZSTAR*FF*ZZ-FF;

ADSTAR:=sub(z=z^8,tp(AD))$
BDSTAR:=sub(z=z^8,tp(BD))$
ZDSTAR:=sub(z=z^8,tp(ZD))$

% Checking that the elements $\xi$ satisfy $\iota(\xi)\xi=1$:
% The following are zero:
ADSTAR*FF*AD-FF;
BDSTAR*FF*BD-FF;
ZDSTAR*FF*ZD-FF;

avec:=mat((a1),(a2),(a3),(a4),(a5),(a6),(a7),(a8),(a9),(a10),(a11),(a12),(a13),(a14),(a15),(a16),(a17),(a18),
          (a19),(a20),(a21),(a22),(a23),(a24),(a25),(a26),(a27),(a28),(a29),(a30),(a31),(a32),(a33),(a34),(a35),(a36))$

bvec:=mat((b1),(b2),(b3),(b4),(b5),(b6),(b7),(b8),(b9),(b10),(b11),(b12),(b13),(b14),(b15),(b16),(b17),(b18),
          (b19),(b20),(b21),(b22),(b23),(b24),(b25),(b26),(b27),(b28),(b29),(b30),(b31),(b32),(b33),(b34),(b35),(b36))$

zvec:=mat((z1),(z2),(z3),(z4),(z5),(z6),(z7),(z8),(z9),(z10),(z11),(z12),(z13),(z14),(z15),(z16),(z17),(z18),
          (z19),(z20),(z21),(z22),(z23),(z24),(z25),(z26),(z27),(z28),(z29),(z30),(z31),(z32),(z33),(z34),(z35),(z36))$


advec:=mat((ad1),(ad2),(ad3),(ad4),(ad5),(ad6),(ad7),(ad8),(ad9),(ad10),(ad11),(ad12),(ad13),(ad14),(ad15),(ad16),(ad17),(ad18),
          (ad19),(ad20),(ad21),(ad22),(ad23),(ad24),(ad25),(ad26),(ad27),(ad28),(ad29),(ad30),(ad31),(ad32),(ad33),(ad34),(ad35),(ad36))$

bdvec:=mat((bd1),(bd2),(bd3),(bd4),(bd5),(bd6),(bd7),(bd8),(bd9),(bd10),(bd11),(bd12),(bd13),(bd14),(bd15),(bd16),(bd17),(bd18),
          (bd19),(bd20),(bd21),(bd22),(bd23),(bd24),(bd25),(bd26),(bd27),(bd28),(bd29),(bd30),(bd31),(bd32),(bd33),(bd34),(bd35),(bd36))$

zdvec:=mat((zd1),(zd2),(zd3),(zd4),(zd5),(zd6),(zd7),(zd8),(zd9),(zd10),(zd11),(zd12),(zd13),(zd14),(zd15),(zd16),(zd17),(zd18),
          (zd19),(zd20),(zd21),(zd22),(zd23),(zd24),(zd25),(zd26),(zd27),(zd28),(zd29),(zd30),(zd31),(zd32),(zd33),(zd34),(zd35),(zd36))$


CondMtxDM3Type1:=mat(
(1,1,5,4,1,3,6,1,8,6,0,1,6,0,2,2,0,1,6,0,5,8,0,6,0,0,8,6,0,8,8,0,6,0,0,8),
(3,0,8,3,0,7,7,0,8,7,1,6,1,1,5,8,1,0,3,0,1,1,0,3,0,0,1,3,0,4,7,0,3,0,0,7),
(6,0,5,8,0,6,0,0,8,6,0,8,8,0,6,0,0,8,7,1,1,3,1,0,6,1,7,3,0,0,5,0,8,2,0,0),
(3,0,1,1,0,3,0,0,1,3,0,4,7,0,3,0,0,7,6,0,0,4,0,1,7,0,0,1,1,1,8,1,8,8,1,7),
(7,0,8,5,1,3,3,2,4,1,0,2,8,7,6,3,5,4,4,0,2,1,0,2,4,0,5,4,0,5,7,0,8,4,0,8),
(8,0,7,1,2,3,6,4,5,8,0,1,4,8,0,6,7,8,5,0,4,2,0,1,5,0,1,8,0,7,8,0,1,8,0,4),
(4,0,2,1,0,2,4,0,5,4,0,5,7,0,8,4,0,8,2,0,1,6,1,5,7,2,0,5,0,7,6,7,5,7,5,3),
(5,0,4,2,0,1,5,0,1,8,0,7,8,0,1,8,0,4,4,0,2,3,2,4,2,4,6,7,0,8,3,8,1,5,7,3),
(2,0,6,0,0,2,5,1,5,5,0,0,6,0,5,8,7,8,7,0,2,8,0,4,3,0,3,7,0,8,2,0,7,3,0,3),
(4,0,0,3,0,4,1,2,1,7,0,6,6,0,7,4,8,4,2,0,1,7,0,2,6,0,6,5,0,1,1,0,2,6,0,6),
(7,0,2,8,0,4,3,0,3,7,0,8,2,0,7,3,0,3,0,0,8,8,0,6,8,1,8,3,0,8,8,0,3,2,7,2),
(2,0,1,7,0,2,6,0,6,5,0,1,1,0,2,6,0,6,6,0,1,1,0,6,7,2,7,3,0,7,7,0,0,1,8,1),
(8,0,3,8,0,8,0,1,4,2,0,2,6,0,3,0,8,8,7,0,4,2,0,7,3,0,2,2,0,3,4,0,2,6,0,8),
(7,0,7,3,0,6,0,1,1,1,0,5,5,0,2,0,0,3,7,0,6,5,0,7,3,0,1,0,0,7,6,0,0,0,0,1),
(7,0,4,2,0,7,3,0,2,2,0,3,4,0,2,6,0,8,6,0,7,1,0,6,3,1,6,4,0,5,1,0,5,6,8,7),
(7,0,6,5,0,7,3,0,1,0,0,7,6,0,0,0,0,1,5,0,4,8,0,4,3,1,2,1,0,3,2,0,2,0,0,4),
(5,1,2,4,1,7,8,7,1,1,0,1,6,0,6,4,0,3,2,0,4,7,0,2,8,0,1,2,0,7,7,0,5,5,0,4),
(8,0,8,3,0,3,5,0,6,6,1,3,1,1,4,3,7,4,7,0,2,2,0,4,4,0,5,4,0,2,5,0,7,4,0,5),
(2,0,4,7,0,2,8,0,1,2,0,7,7,0,5,5,0,4,7,1,6,2,1,0,7,7,2,3,0,8,4,0,2,0,0,7),
(7,0,2,2,0,4,4,0,5,4,0,2,5,0,7,4,0,5,6,0,1,5,0,7,0,0,2,1,1,5,6,1,2,7,7,0),
(3,0,4,6,1,6,7,8,5,2,0,5,4,0,3,1,0,4,0,0,3,1,0,3,4,0,4,5,0,4,6,0,7,0,0,5),
(7,0,4,5,0,6,8,0,5,5,0,0,1,1,0,8,8,0,4,0,5,3,0,2,0,0,4,5,0,7,7,0,1,4,0,0),
(0,0,3,1,0,3,4,0,4,5,0,4,6,0,7,0,0,5,3,0,7,7,1,0,2,8,0,7,0,0,1,0,1,1,0,0),
(4,0,5,3,0,2,0,0,4,5,0,7,7,0,1,4,0,0,2,0,0,8,0,8,8,0,0,1,0,7,8,1,1,3,8,0),
(0,0,5,1,1,5,2,8,7,4,0,1,3,8,5,8,1,5,4,0,3,1,0,4,8,0,1,2,0,8,2,0,6,3,0,3),
(5,0,8,6,1,4,1,8,4,4,0,6,4,0,1,1,0,3,7,0,1,7,0,3,6,0,6,6,0,2,3,0,1,2,0,4),
(4,0,3,1,0,4,8,0,1,2,0,8,2,0,6,3,0,3,4,0,8,2,1,0,1,8,8,6,0,0,5,8,2,2,1,8),
(7,0,1,7,0,3,6,0,6,6,0,2,3,0,1,2,0,4,3,0,0,4,1,7,7,8,1,1,0,8,7,0,2,3,0,7),
(8,0,5,4,6,3,2,2,0,5,0,5,7,0,6,8,8,3,5,0,7,1,0,8,3,0,6,5,0,7,7,0,8,0,0,3),
(4,0,4,2,0,3,1,1,6,4,0,1,2,6,0,1,1,3,4,0,2,2,0,1,0,0,6,1,0,5,8,0,7,3,0,0),
(5,0,7,1,0,8,3,0,6,5,0,7,7,0,8,0,0,3,4,0,3,5,6,2,5,2,6,1,0,3,5,0,5,8,8,6),
(4,0,2,2,0,1,0,0,6,1,0,5,8,0,7,3,0,0,8,0,6,4,0,4,1,1,3,5,0,6,1,6,7,4,1,3),
(3,1,2,1,7,8,4,1,0,2,0,7,6,0,1,3,0,5,1,0,0,3,0,1,1,0,0,1,0,3,3,0,7,4,0,6),
(7,0,2,3,0,8,6,0,4,5,1,0,7,7,0,7,1,5,8,0,6,6,0,2,5,0,3,2,0,3,6,0,8,5,0,6),
(1,0,0,3,0,1,1,0,0,1,0,3,3,0,7,4,0,6,4,1,2,4,7,0,5,1,0,3,0,1,0,0,8,7,0,2),
(8,0,6,6,0,2,5,0,3,2,0,3,6,0,8,5,0,6,6,0,8,0,0,1,2,0,7,7,1,3,4,7,8,3,1,2))$

CondMtxDM3Type2:=mat(
(1,1,5,4,1,3,6,1,8,6,0,1,6,0,2,2,0,1,6,0,5,8,0,6,0,0,8,6,0,8,8,0,6,0,0,8),
(3,0,8,3,0,7,7,0,8,7,1,6,1,1,5,8,1,0,3,0,1,1,0,3,0,0,1,3,0,4,7,0,3,0,0,7),
(6,0,5,8,0,6,0,0,8,6,0,8,8,0,6,0,0,8,7,1,1,3,1,0,6,1,7,3,0,0,5,0,8,2,0,0),
(3,0,1,1,0,3,0,0,1,3,0,4,7,0,3,0,0,7,6,0,0,4,0,1,7,0,0,1,1,1,8,1,8,8,1,7),
(6,0,5,2,1,7,6,2,5,5,0,6,6,0,7,3,0,4,8,0,5,1,0,0,8,0,2,7,0,3,0,0,1,7,0,6),
(4,0,3,3,0,2,6,0,5,2,0,2,8,1,5,0,2,0,2,0,6,0,0,8,2,0,3,6,0,8,1,0,1,6,0,8),
(8,0,5,1,0,0,8,0,2,7,0,3,0,0,1,7,0,6,5,0,1,3,1,7,5,2,7,3,0,0,6,0,8,1,0,1),
(2,0,6,0,0,8,2,0,3,6,0,8,1,0,1,6,0,8,6,0,0,3,0,1,8,0,8,8,0,1,0,1,6,6,2,8),
(8,0,1,2,0,5,8,1,2,6,0,7,8,0,3,3,0,6,5,0,3,5,0,6,6,0,0,1,0,4,6,0,8,3,0,6),
(3,0,2,1,0,6,6,0,3,5,0,8,1,0,8,2,1,8,8,0,5,3,0,1,6,0,3,6,0,7,2,0,5,0,0,6),
(5,0,3,5,0,6,6,0,0,1,0,4,6,0,8,3,0,6,4,0,4,7,0,2,5,1,2,7,0,2,5,0,2,6,0,3),
(8,0,5,3,0,1,6,0,3,6,0,7,2,0,5,0,0,6,2,0,7,4,0,7,3,0,6,2,0,6,3,0,4,2,1,5),
(3,0,7,2,0,5,0,8,2,0,0,1,5,0,8,0,8,2,2,0,1,1,0,2,6,0,0,2,0,7,1,0,2,6,0,6),
(0,0,8,4,0,1,0,1,7,3,0,8,7,0,4,0,7,4,7,0,2,8,0,7,3,0,3,4,0,8,2,0,4,3,0,6),
(2,0,1,1,0,2,6,0,0,2,0,7,1,0,2,6,0,6,5,0,8,3,0,7,6,8,2,2,0,8,6,0,1,6,8,8),
(7,0,2,8,0,7,3,0,3,4,0,8,2,0,4,3,0,6,7,0,1,3,0,8,3,1,1,7,0,7,0,0,8,3,7,1),
(5,1,2,4,1,7,8,7,1,1,0,1,6,0,6,4,0,3,2,0,4,7,0,2,8,0,1,2,0,7,7,0,5,5,0,4),
(8,0,8,3,0,3,5,0,6,6,1,3,1,1,4,3,7,4,7,0,2,2,0,4,4,0,5,4,0,2,5,0,7,4,0,5),
(2,0,4,7,0,2,8,0,1,2,0,7,7,0,5,5,0,4,7,1,6,2,1,0,7,7,2,3,0,8,4,0,2,0,0,7),
(7,0,2,2,0,4,4,0,5,4,0,2,5,0,7,4,0,5,6,0,1,5,0,7,0,0,2,1,1,5,6,1,2,7,7,0),
(3,0,4,6,1,6,7,8,5,2,0,5,4,0,3,1,0,4,0,0,3,1,0,3,4,0,4,5,0,4,6,0,7,0,0,5),
(7,0,4,5,0,6,8,0,5,5,0,0,1,1,0,8,8,0,4,0,5,3,0,2,0,0,4,5,0,7,7,0,1,4,0,0),
(0,0,3,1,0,3,4,0,4,5,0,4,6,0,7,0,0,5,3,0,7,7,1,0,2,8,0,7,0,0,1,0,1,1,0,0),
(4,0,5,3,0,2,0,0,4,5,0,7,7,0,1,4,0,0,2,0,0,8,0,8,8,0,0,1,0,7,8,1,1,3,8,0),
(8,0,7,7,8,6,0,1,8,5,0,7,4,8,3,6,1,8,8,0,1,5,0,7,5,0,7,8,0,4,5,0,4,8,0,4),
(4,0,2,5,1,6,3,8,1,4,0,5,2,7,0,6,2,7,1,0,5,4,0,5,1,0,5,7,0,5,1,0,2,4,0,2),
(8,0,1,5,0,7,5,0,7,8,0,4,5,0,4,8,0,4,7,0,8,3,8,4,5,1,6,4,0,2,0,8,7,5,1,3),
(1,0,5,4,0,5,1,0,5,7,0,5,1,0,2,4,0,2,5,0,7,0,1,2,4,8,6,2,0,1,3,7,2,1,2,0),
(8,0,5,4,6,3,2,2,0,5,0,5,7,0,6,8,8,3,5,0,7,1,0,8,3,0,6,5,0,7,7,0,8,0,0,3),
(4,0,4,2,0,3,1,1,6,4,0,1,2,6,0,1,1,3,4,0,2,2,0,1,0,0,6,1,0,5,8,0,7,3,0,0),
(5,0,7,1,0,8,3,0,6,5,0,7,7,0,8,0,0,3,4,0,3,5,6,2,5,2,6,1,0,3,5,0,5,8,8,6),
(4,0,2,2,0,1,0,0,6,1,0,5,8,0,7,3,0,0,8,0,6,4,0,4,1,1,3,5,0,6,1,6,7,4,1,3),
(3,1,2,1,7,8,4,1,0,2,0,7,6,0,1,3,0,5,1,0,0,3,0,1,1,0,0,1,0,3,3,0,7,4,0,6),
(7,0,2,3,0,8,6,0,4,5,1,0,7,7,0,7,1,5,8,0,6,6,0,2,5,0,3,2,0,3,6,0,8,5,0,6),
(1,0,0,3,0,1,1,0,0,1,0,3,3,0,7,4,0,6,4,1,2,4,7,0,5,1,0,3,0,1,0,0,8,7,0,2),
(8,0,6,6,0,2,5,0,3,2,0,3,6,0,8,5,0,6,6,0,8,0,0,1,2,0,7,7,1,3,4,7,8,3,1,2))$

% The following are zero, checking that CondMtxDM3Type1*avec, CondMtxDM3Type1*bvec, CondMtxDM3Type1*zvec have entries in $\Z_3$:

CondMtxDM3Type1*avec - mat((-4),(-4),(6),(-9),(-1),(-2),(-4),(0),(-3),(1),(-1),(-3),(3),(-3),(-1),(1),(-8),(0),(-8),(-1),(-1),(1),(0),(-6),(-4),(3),(-3),(-6),(0),(-1),(-8),(5),(-5),(-1),(-1),(8));
CondMtxDM3Type1*bvec - mat((5),(15),(12),(8),(12),(19),(18),(23),(12),(10),(10),(15),(9),(4),(18),(8),(10),(12),(15),(12),(9),(13),(8),(11),(13),(11),(14),(11),(12),(3),(11),(13),(13),(16),(12),(18));
CondMtxDM3Type1*zvec - mat((1),(0),(0),(0),(1),(2),(0),(0),(0),(0),(0),(0),(0),(0),(0),(0),(1),(0),(0),(0),(1),(0),(0),(0),(1),(1),(0),(0),(6),(0),(0),(0),(7),(0),(0),(0));

% The following are zero, checking that CondMtxDM3Type2*advec, CondMtxDM3Type2*bdvec, CondMtxDM3Type2*zdvec have entries in $\Z_3$:

CondMtxDM3Type2*advec - mat((-18),(0),(-1),(1),(-11),(-9),(-7),(-20),(6),(-14),(-3),(-15),(-1),(-12),(-19),(1),(4),(-10),(-10),(0),(0),(-12),(-12),(7),(-19),(-17),(-13),(-14),(-5),(-10),(-6),(-6),(3),(-8),(-3),(-12));
CondMtxDM3Type2*bdvec - mat((6),(12),(14),(7),(17),(4),(10),(19),(6),(6),(9),(6),(6),(5),(-4),(5),(3),(15),(-4),(9),(2),(8),(11),(4),(13),(5),(11),(7),(0),(6),(17),(4),(3),(10),(4),(5));
CondMtxDM3Type2*zdvec - mat((1),(0),(0),(0),(1),(0),(0),(0),(0),(0),(0),(0),(0),(0),(0),(0),(1),(0),(0),(0),(1),(0),(0),(0),(8),(1),(0),(0),(6),(0),(0),(0),(7),(0),(0),(0));

% The following are zero, checking the statements about determinants:
det(AA)-1;
det(BB)-gendt;
det(ZZ)-z^3;

% The following are zero, checking the statements about determinants:
det(AD)-1;
det(BD)-gendt;
det(ZD)-z^3;


% Here is the inverse of FF:
FFI:=mat(((2*g*z^5-2*g*z^4+4*g*z^2-4*g*z+3*g+z^5-z^4+2*z^2-2*z+3)/6,                                                       0,                                                      0),
         (                                                        0,(-4*g*z^5-2*g*z^4-2*g*z^2+2*g*z+3*g-2*z^5-z^4-z^2+z+3)/6,                                                      0),
         (                                                        0,                                                       0,(2*g*z^5+4*g*z^4-2*g*z^2+2*g*z+3*g+z^5+2*z^4-z^2+z+3)/6))$

AAI:=FFI*AASTAR*FF;
BBI:=FFI*BBSTAR*FF;
ZZI:=FFI*ZZSTAR*FF;

ADI:=FFI*ADSTAR*FF;
BDI:=FFI*BDSTAR*FF;
ZDI:=FFI*ZDSTAR*FF;


AAI:=mat(
((g*z^5+g*z^4-g*z^3+g*z-g+z^5-z^3)/3,(2*g*z^5-3*g*z^4+g*z^3+g*z^2-3*g*z+z^5-z^4+2*z^3+z^2+3)/3,(-2*g*z^5+g*z^4-2*g*z^3-g*z-g+z^4-3*z^3-1)/3),
((-g*z^5-g*z^4-g*z^2+g*z+3*g-2*z^5-z^3-z^2+z)/3,(-g*z^3+g*z^2-g*z-g-z^3+z^2)/3,(-g*z^5+g*z^3+g*z^2+3*g*z-z^5+z^4+2*z^3+z+3)/3),
((-2*g*z^5-g*z^4+2*g*z^3-g*z^2-2*g*z-g-z^5-z^4-z^3-3*z)/3,(g*z^5+2*g*z^4+g*z+3*g+z^5+z^4-z^3-z^2)/3,(-(g*z^5+g*z^4+g*z^3+g*z^2+g+z^5+z^3+z^2))/3));

BBI:=mat(
((g*z^5+g*z^4+g*z^3+g-z^3-z^2+z)/3,(2*g*z^5-2*g*z^4+g*z^3+g*z^2-3*g*z+2*g+z^5-z^4+2*z^3+z^2-z+3)/3,(g*z^5-5*g*z^4+5*g*z^3-2*g*z^2-g*z+g+4*z^5-z^4+z^3-z^2+2*z+2)/6),
((3*g*z^5+g*z^4+g*z^3+g*z^2-g*z-g+2*z^4-z^3-2)/3,(-g*z^4+g*z^3+g*z^2-g*z+g+z^5+z^4-z^3+z^2)/3,(-g*z^5-g*z^4+g*z^3+g*z^2+2*g*z+2*g-z^5+2*z^3+z+3)/3),
((-2*g*z^5+3*g*z^3-g*z^2-2*g*z-z^5+z^3-2*z+1)/3,(-g*z^5-2*g*z^4+g*z^3+2*g*z^2-g*z-g-2*z^4-z^3-2*z-2)/3,(-g*z^5+g*z^3-g*z^2+g*z+g-z^5-z^4-z^3-z)/3));

ZZI:=mat(
(-z^2*(z^3+1),0,0),
(0,z^5,0),
(0,0,z^2));

ADI:=mat(
((g*z^5+g*z^4-g*z^3+g*z^2+g*z+z^5+z^2+1)/3,(-g*z^5+g*z^4-g*z^3+g*z^2-g*z+g+z^5+z^4-z^3+2*z^2)/3,(g*z^5+2*g*z^3+g*z+2*g-3*z^4+z^2-z)/3),
((2*g*z^4+g*z^3+g*z^2-g*z+z^5-z^4+z^3-1)/3,(-g*z^5-g*z^3-g*z-z^5+1)/3,(-g*z^5-2*g*z^4-g*z^3-2*g*z^2-g*z+g-2*z^5-z^4-z^3-z^2-z)/3),
((-g*z^5+2*g*z^4+g*z^3-2*g*z^2+g*z+2*g+z^5+z^4+z^3-z^2+1)/3,(-g*z^5-3*g*z^4+g*z^3-g*z^2-2*g*z+z^4+z^3+z^2+z-1)/3,(-g*z^4-g*z^3-g*z^2-z^2+1)/3));

BDI:=mat(
((g*z^2-g+z^5-z^3+z^2-1)/3,(g*z^5+g*z^3-g*z^2-g*z-z^5-z^4+z+1)/3,(-g*z^5+3*g*z^4-4*g*z^3-g*z^2-g*z-2*g-z^5-z^4-2*z^3+2*z^2-2*z-2)/6),
((-g*z^5-g*z^3+g*z+g-z^4-z^2+z+1)/3,(-(g*z^5+g*z^2+g+z^5+z^3+1))/3,(g*z^5-g*z^4+g*z^3+2*g*z^2+2*z^4-z^2+z+1)/3),
((-g*z^4+g*z^3+z^4-z^3+2*z^2-z-1)/3,(g*z^4-g*z^3-g*z^2+g+z^5+2*z^4+z^2+z+1)/3,(g*z^5-g-z^3-z^2-1)/3));

ZDI:=mat(
(-z^2*(z^3+1),0,0),
(0,z^5,0),
(0,0,z^2));

% The following are zero, checking that the relations in the stated presentation 
% of group $\bar\Gamma_{(\cC_2,p=2,\emptyset)}$ do indeed hold:

ZZ^3 - z^3*ID3;
(ZZI*BB*AAI)^3 - z^6*gendt*ID3;
BB*AAI^2*ZZI*BB^2*ZZ*AA - z^3*gendt*ID3;
AAI*BBI*ZZ*AA*BBI^2*AAI*ZZI - z^3*gendti*ID3;
AAI*ZZI*BB*AAI^2*ZZ*BBI*ZZI*BBI*ZZ*AA*ZZI*BB*ZZ - z^6*ID3;
AAI*ZZI*AAI*ZZI*BBI*ZZI*AA*ZZI*BBI*ZZI*BBI*ZZI - z^3*gendti*ID3;
BBI*ZZ*AA*ZZ*AA*ZZ*AA*ZZI*BBI*ZZI*AA*ZZ*AA*ZZI*BBI*ZZI - z^6*gendti*ID3;
BBI*ZZ*BBI*ZZ*AAI*ZZI*BB*ZZI*AA*ZZI*BB*ZZ*AA*ZZ*AA*ZZI - ID3;
ZZI*BB*ZZI*BB*ZZ*BBI*ZZ*AA*ZZI*BB*ZZI*BB*AA*ZZI*BBI*ZZ*AA*ZZI*BB - z^3*gendt*ID3;


% The following are zero, checking that the relations in the stated presentation 
% of group $\bar\Gamma_{(\cC_2,p=2,\{3\})}$ do indeed hold:

ZD^3-z^3*ID3;
(BD*ZD)^3 - z^3*gendt*ID3;
AD*ZD*BD*ZDI*ADI*ZDI*ADI*ZD*BDI - ID3;
ADI*BDI*ZDI*ADI*ZD*BDI*ZD*ADI*BDI*ZDI - z^3*gendti*ID3;
BDI*ZD*ADI*BDI*ZD*BD*ZDI*AD*BDI*ZDI*BDI - gendti*ID3;
BD*ZDI*AD*ZDI*BDI*AD*BDI*ZD*AD*ZD*BD - z^6*ID3;
ADI^2*ZDI*ADI*ZDI*BDI*ZD*ADI^2*BD*ZD - z^3*ID3;
(ADI*ZDI*ADI*BD)^3 - z^6*gendt*ID3;
BDI*ZD*BDI*AD*ZDI*ADI^2*BD*ZDI*ADI*BD*ZD*ADI - z^6*ID3;
ZD*ADI*BD*ZD*BDI*ZD*ADI*ZD*BD^2*AD*ZDI*BD - z^3*gendt*ID3;
ZDI*ADI*ZD*ADI*ZDI*ADI*BD*AD*ZDI*BDI*AD*ZDI*ADI^2 - z^3*ID3;
ADI*BDI*ZDI*ADI*ZDI*AD*ZD*AD^2*ZD*AD*ZD*AD*ZDI*BD - ID3;
ADI*BD*ZDI*BD*AD*BDI*ZD*ADI*BDI^2*ZD*ADI^2*BD*ZDI - z^6*ID3;
BDI*AD*BDI*ZD*BDI*AD*ZDI*BDI*ZDI^2*ADI*BDI^2*ZD*ADI*ZD - gendti^2*ID3;
AD*ZDI*BD^2*ZDI*ADI^2*BD*ZD*ADI*ZD*BD*AD*ZD*BDI*ZDI - gendt*ID3;
BDI^2*AD^2*ZDI*BD^2*AD*ZD*BDI*ZDI*AD*BDI*ZD*ADI*BDI - z^3*gendti*ID3;
ADI*BD*ZDI*BD*AD*ZD*ADI*BD*ZD*ADI*BDI*ZDI*ADI*ZD*BD*AD*ZDI*BD*ADI*BDI - z^3*gendt*ID3;
ZD*ADI*BD*ZDI*AD*BD*ZD*BD*ADI*BD*ZD*BD*AD*ZD*BDI*ZDI*AD*BD*ZD*BD*ADI - gendt^2*ID3;


% The following three elements generate in $\bar\Gamma_{(\cC_2,p=2,\emptyset)}$
% the intersection in $\bar\Gamma_{(\cC_2,p=2,\emptyset)}$ and
% $\bar\Gamma_{(\cC_2,p=2,\{3\})}$, a subgroup of index 10. 

int1:=ZZ$
int2:=AA^2*BBI$
int3:=BB*ZZI*AA$

% The following are zero:
int1 - ZD;
int2 - z^6*ZDI*BDI*BDI*ZDI*ADI*BD*ZDI*BD*ZD*BDI*ZDI;
int3 - z^3*gendt*BDI*ZD*BD*ZDI*AD*BDI*ZDI*BDI*ZDI*AD*ZD;


% T3:=BB*ZZ*BB*ZZ*AAI*ZZI*AAI*ZZI;

;end;