% In this file, generators are given for the two groups $\bar\Gamma$ in
% the case $(C_{10},p=2)$.
% We check that these generators are indeed in the division algebra,
% are indeed unitary with respect to the involution iota, and check
% the relations given in the write-up are indeed satisfied.

% REDUCE SYNTAX:
% **************
let h^2=2$      % Square root of 2

let U^2=(1+h)*U-2$
Ubar:=1+h-U$

let W^3=3*W-1$
phiW:=-W^2-W+2$
phi2W:=W^2-2$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The generators for $\bar\Gamma$ in the case $(\cC_{10},p=2,\emptyset)$:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

AA:=(1/9)*mat(
(-2*h*U*W^2-h*U*W+7*h*U+2*h*W^2+h*W-7*h-2*U*W^2-U*W+7*U+3*W^2-12,4*h*U*W^2+5*h*U*W-5*h*U-3*h*W^2-9*h*W+3*U*W^2+6*U*W-11*W^2-10*W+10,-3*h*U+2*h*W^2+h*W+2*h+U*W^2-U*W-5*U+W^2+5*W+1),
(-2*h*U*W^2-h*U*W+h*U-h*W^2-2*h*W+5*h+3*U*W+6,h*U*W^2-h*U*W+h*U-h*W^2+h*W-h+U*W^2-U*W+U+3*W-6,-5*h*U*W^2-h*U*W+13*h*U+9*h*W^2+6*h*W-24*h-6*U*W^2-3*U*W+18*U+10*W^2-W-32),
(3*h*U*W^2-6*h*U-3*h*W^2+3*h*W-2*U*W^2-4*U*W+7*U-2*W^2+8*W-2,h*U*W^2-h*U*W-5*h*U+2*h*W^2+h*W-h-3*U*W^2-3*U*W+6*U+6,h*U*W^2+2*h*U*W+h*U-h*W^2-2*h*W-h+U*W^2+2*U*W+U-3*W^2-3*W))$

BB:=(1/18)*mat(
(2*(-h*U*W^2-2*h*U*W+2*h*U+3*h*W-2*U*W^2-4*U*W+4*U-2*W^2+2*W+4),2*(-h*U*W^2+h*U*W+2*h*U-2*h*W^2-4*h*W+4*h+3*U*W^2-6*U-2*W^2-W-2),2*(2*h*W^2+h*W-h+2*W^2+4*W-4)),
(2*U*(-2*h*W^2-h*W+4*h-W^2+W+5),2*(2*h*U*W^2+h*U*W-4*h*U-3*h*W^2-3*h*W+6*h+4*U*W^2+2*U*W-8*U-2*W^2-4*W+4),2*(-h*U*W^2-2*h*U*W+2*h*U+4*h*W^2+2*h*W-8*h+3*U*W+W^2-W-8)),
(2*h*U*W^2+h*U*W-10*h*U+6*h*W^2+6*h*W-12*h-6*U*W^2+12*U-8*W^2-4*W+16,2*U*(h*W^2-h*W-2*h-W^2-2*W+5),2*(-h*U*W^2+h*U*W+2*h*U+3*h*W^2-6*h-2*U*W^2+2*U*W+4*U+4*W^2+2*W-8)))$

CC:=(1/9)*mat(
(-3*h*U*W^2-3*h*U*W+9*h*U+3*h*W^2+3*h*W-9*h-4*U*W^2-5*U*W+11*U+3*W^2+3*W-9,3*h*U*W^2+6*h*U*W-3*h*U-h*W^2-2*h*W-4*h+4*U*W^2+5*U*W+U-4*W^2-5*W+5,4*h*U*W^2+2*h*U*W-8*h*U-8*h*W^2-4*h*W+13*h+5*U*W^2+4*U*W-13*U-9*W^2-12*W+21),
(2*h*U*W^2+4*h*U*W-4*h*U+4*h*W^2-h*W-5*h-2*U*W^2-U*W-2*U+4*W^2-4*W-8,3*h*U*W^2-3*h*U-3*h*W^2+3*h+5*U*W^2+U*W-7*U-3*W^2+3,-6*h*U*W^2-3*h*U*W+15*h*U+2*h*W^2+h*W-10*h-5*U*W^2-U*W+19*U+5*W^2+W-13),
(3*h*U*W^2-3*h*U*W-h*W^2+4*h*W-7*h+3*U*W^2-6*U*W-6*W^2+6*W+6,-4*h*U*W^2-2*h*U*W+8*h*U+h*W^2+5*h*W+h+U*W^2-U*W-8*U+4*W^2+8*W-8,3*h*U*W+3*h*U-3*h*W-3*h-U*W^2+4*U*W+5*U-3*W-3))$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The generators for $\bar\Gamma$ in the case $(\cC_{10},p=2,\{17-\})$:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

AD:=(1/153)*mat(
(24*h*u*w^2-30*h*u*w-99*h*u-59*h*w^2+44*h*w+169*h+26*u*w^2-41*u*w-103*u-71*w^2+59*w+193,
26*h*u*w^2+58*h*u*w-31*h*u-37*h*w^2-59*h*w+50*h+31*u*w^2+77*u*w-35*u-33*w^2-105*w+57,
-15*h*u*w^2-42*h*u*w+60*h*u+73*h*w^2-37*h*w-122*h-63*u*w^2-3*u*w+99*u+21*w^2+69*w-237),
(9*h*u*w^2-27*h*u*w-99*h*u-3*h*w^2+60*h*w+33*h+82*u*w^2+77*u*w-137*u-84*w^2-54*w+108,
30*h*u*w^2+54*h*u*w-111*h*u-44*h*w^2-103*h*w+139*h+41*u*w^2+67*u*w-133*u-59*w^2-130*w+169,
-58*h*u*w^2-32*h*u*w+137*h*u+59*h*w^2+22*h*w-142*h-77*u*w^2-46*u*w+181*u+105*w^2+72*w-219),
(19*h*u*w^2-25*h*u*w-8*h*u-46*h*w^2+31*h*w+65*h+56*u*w^2-20*u*w-88*u-64*w^2+52*w+86,
27*h*u*w^2+36*h*u*w-135*h*u-60*h*w^2-63*h*w+147*h-77*u*w^2+5*u*w+181*u+54*w^2-30*w-168,
-54*h*u*w^2-24*h*u*w+57*h*u+103*h*w^2+59*h*w-155*h-67*u*w^2-26*u*w+83*u+130*w^2+71*w-209))$

BD:=(1/306)*mat((2*(-21*h*u*w^2-12*h*u*w+93*h*u+24*h*w^2+21*h*w-99*h-61*u*w^2-47*u*w+173*u+26*w^2+10*w-154),
2*(41*h*u*w^2+64*h*u*w+8*h*u-59*h*w^2-61*h*w+37*h+60*u*w^2+126*u*w-48*u-3*w^2-144*w-69),
2*(11*h*u*w^2+7*h*u*w+41*h*u+19*h*w^2-25*h*w-59*h+2*u*w^2+43*u*w+26*u-12*w^2-3*w-54)),
(2*(-27*h*u*w^2-21*h*u*w+93*h*u+43*h*w^2+41*h*w-116*h-25*u*w^2+7*u*w+122*u+14*w^2-8*w-154),
2*(12*h*u*w^2-9*h*u*w+27*h*u-21*h*w^2+3*h*w-9*h+47*u*w^2-14*u*w-43*u-10*w^2+16*w-82),
2*(-64*h*u*w^2-23*h*u*w+218*h*u+61*h*w^2+2*h*w-203*h-126*u*w^2-66*u*w+324*u+144*w^2+141*w-363)),
(-29*h*u*w^2-139*h*u*w+235*h*u-132*h*w^2+120*h*w+120*h+174*u*w^2-84*u*w-186*u-92*w^2+164*w-176,
2*(21*h*u*w^2-6*h*u*w-3*h*u-41*h*w^2+2*h*w+52*h-7*u*w^2-32*u*w+86*u+8*w^2+22*w-142),
2*(9*h*u*w^2+21*h*u*w+33*h*u-3*h*w^2-24*h*w-45*h+14*u*w^2+61*u*w+23*u-16*w^2-26*w-70)))$

CD:=(1/153)*mat((5*h*u*w^2-2*h*u*w+41*h*u+21*h*w^2+12*h*w-144*h+4*u*w^2-22*u*w+94*u+44*w^2-38*w-241,
72*h*u*w^2+90*h*u*w-78*h*u-58*h*w^2-98*h*w-25*h+61*u*w^2+89*u*w+43*u-111*w^2-177*w+99,
-h*u*w^2+55*h*u*w+89*h*u+23*h*w^2-41*h*w-211*h+6*u*w^2+78*u*w+129*u+32*w^2-128*w-247),
(-30*h*u*w^2-12*h*u*w+126*h*u+78*h*w^2+72*h*w-297*h-92*u*w^2-64*u*w+247*u+110*w^2+112*w-394,
2*h*u*w^2+7*h*u*w+47*h*u-12*h*w^2+9*h*w-78*h+22*u*w^2+26*u*w+58*u+38*w^2+82*w-229,
-90*h*u*w^2-18*h*u*w+246*h*u+98*h*w^2+40*h*w-337*h-89*u*w^2-28*u*w+343*u+177*w^2+66*w-477),
(-h*u*w^2-47*h*u*w+89*h*u-28*h*w^2+61*h*w-109*h+6*u*w^2-75*u*w+78*u-36*w^2+144*w-60,
12*h*u*w^2-18*h*u*w+42*h*u-72*h*w^2+6*h*w+3*h+64*u*w^2-28*u*w-65*u-112*w^2-2*w+50,
-7*h*u*w^2-5*h*u*w+65*h*u-9*h*w^2-21*h*w-84*h-26*u*w^2-4*u*w+154*u-82*w^2-44*w+11))$

T:=-h+(1-h)*W+W^2$
phiT:=(4-3*h)+h*W+(h-1)*W^2$
phi2T:=(2+h)-W-h*W^2$

TI:=(-(2*h+1)+(2*h+1)*W+(h+2)*W^2)/3$
phiTI:=(4*h+5-(h-1)*W-(2*h+1)*W^2)/3$
phi2TI:=(5-2*h-(h+2)*W+(h-1)*W^2)/3$

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

FFI:=mat(
(TI,   0,    0),
( 0,phiTI,    0),
( 0,   0,phi2TI))$

WMAT:=mat(
(W,   0,    0),
(0,phiW,    0),
(0,   0,phi2W))$

WMATI:=mat(
(WI,   0,    0),
(0,phiWI,    0),
(0,   0,phi2WI))$

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

ZEROMAT:=mat(
(0,0,0),
(0,0,0),
(0,0,0))$

gendt:=U*h/2$
gendti:=(h+2-h*U)/2$  

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

% Here is the inverse of SIG:

SIGI:=gendti*SIG^2$

a1:=2/3$
a2:=-4/3$
a3:=10/9$
a4:=0$
a5:=0$
a6:=-10/9$
a7:=0$
a8:=1/3$
a9:=-11/9$
a10:=-2/3$
a11:=7/9$
a12:=0$
a13:=0$
a14:=-1/9$
a15:=2/3$
a16:=1/3$
a17:=-2/9$
a18:=1/3$
a19:=5/9$
a20:=-7/9$
a21:=0$
a22:=1/9$
a23:=1/9$
a24:=-1$
a25:=-1/9$
a26:=2/9$
a27:=-1/3$
a28:=-5/9$
a29:=7/9$
a30:=-5/9$
a31:=2/9$
a32:=-1/9$
a33:=5/9$
a34:=1/9$
a35:=-2/9$
a36:=4/9$
b1:=0$
b2:=4/9$
b3:=-2/9$
b4:=0$
b5:=2/9$
b6:=-1/9$
b7:=0$
b8:=-2/9$
b9:=-2/9$
b10:=-1/9$
b11:=4/9$
b12:=-2/3$
b13:=1/9$
b14:=-4/9$
b15:=0$
b16:=2/9$
b17:=-2/9$
b18:=1/3$
b19:=0$
b20:=0$
b21:=4/9$
b22:=0$
b23:=1/3$
b24:=-4/9$
b25:=0$
b26:=0$
b27:=-2/9$
b28:=-2/9$
b29:=2/9$
b30:=2/9$
b31:=2/9$
b32:=-2/9$
b33:=1/9$
b34:=1/9$
b35:=-1/9$
b36:=-1/9$
c1:=16/9$
c2:=-1$
c3:=5/9$
c4:=-4/9$
c5:=1/3$
c6:=-5/9$
c7:=-8/9$
c8:=1/3$
c9:=-4/9$
c10:=-8/9$
c11:=11/9$
c12:=1/9$
c13:=2/9$
c14:=-5/9$
c15:=5/9$
c16:=1/9$
c17:=-4/9$
c18:=4/9$
c19:=13/9$
c20:=-1$
c21:=-4/9$
c22:=-4/9$
c23:=1/3$
c24:=-2/9$
c25:=-5/9$
c26:=1/3$
c27:=-1/9$
c28:=-4/9$
c29:=1$
c30:=-1/3$
c31:=-2/9$
c32:=-1/3$
c33:=2/3$
c34:=2/9$
c35:=-1/3$
c36:=1/3$
ad1:=-40/51$
ad2:=193/153$
ad3:=19/51$
ad4:=28/51$
ad5:=59/153$
ad6:=-35/51$
ad7:=10/51$
ad8:=-71/153$
ad9:=-11/51$
ad10:=37/153$
ad11:=-103/153$
ad12:=-35/153$
ad13:=-82/153$
ad14:=-41/153$
ad15:=77/153$
ad16:=-5/153$
ad17:=26/153$
ad18:=31/153$
ad19:=-11/17$
ad20:=169/153$
ad21:=50/153$
ad22:=1/51$
ad23:=44/153$
ad24:=-59/153$
ad25:=7/17$
ad26:=-59/153$
ad27:=-37/153$
ad28:=-1/17$
ad29:=-11/17$
ad30:=-31/153$
ad31:=-1/17$
ad32:=-10/51$
ad33:=58/153$
ad34:=-4/17$
ad35:=8/51$
ad36:=26/153$
bd1:=-82/153$
bd2:=-154/153$
bd3:=-23/51$
bd4:=-14/153$
bd5:=10/153$
bd6:=-16/17$
bd7:=-22/153$
bd8:=26/153$
bd9:=-1/51$
bd10:=8/153$
bd11:=173/153$
bd12:=-16/51$
bd13:=25/153$
bd14:=-47/153$
bd15:=14/17$
bd16:=32/153$
bd17:=-61/153$
bd18:=20/51$
bd19:=-26/153$
bd20:=-11/17$
bd21:=37/153$
bd22:=-43/153$
bd23:=7/51$
bd24:=-61/153$
bd25:=-2/153$
bd26:=8/51$
bd27:=-59/153$
bd28:=3/17$
bd29:=31/51$
bd30:=8/153$
bd31:=3/17$
bd32:=-4/51$
bd33:=64/153$
bd34:=2/51$
bd35:=-7/51$
bd36:=41/153$
cd1:=-178/153$
cd2:=-241/153$
cd3:=11/17$
cd4:=-110/153$
cd5:=-38/153$
cd6:=-59/51$
cd7:=2/153$
cd8:=44/153$
cd9:=-37/51$
cd10:=7/153$
cd11:=94/153$
cd12:=43/153$
cd13:=92/153$
cd14:=-22/153$
cd15:=89/153$
cd16:=28/153$
cd17:=4/153$
cd18:=61/153$
cd19:=-43/51$
cd20:=-16/17$
cd21:=-25/153$
cd22:=-26/51$
cd23:=4/51$
cd24:=-98/153$
cd25:=-2/51$
cd26:=7/51$
cd27:=-58/153$
cd28:=10/51$
cd29:=41/153$
cd30:=-26/51$
cd31:=10/51$
cd32:=-2/153$
cd33:=10/17$
cd34:=2/17$
cd35:=5/153$
cd36:=8/17$


AA - (
 a1*h^0*U^0*WMAT^0*SIGI+a2*h^0*U^0*WMAT^0*SIG^0+a3*h^0*U^0*WMAT^0*SIG^1
+a4*h^0*U^0*WMAT^1*SIGI+a5*h^0*U^0*WMAT^1*SIG^0+a6*h^0*U^0*WMAT^1*SIG^1
+a7*h^0*U^0*WMAT^2*SIGI+a8*h^0*U^0*WMAT^2*SIG^0+a9*h^0*U^0*WMAT^2*SIG^1

+a10*h^0*U^1*WMAT^0*SIGI+a11*h^0*U^1*WMAT^0*SIG^0+a12*h^0*U^1*WMAT^0*SIG^1
+a13*h^0*U^1*WMAT^1*SIGI+a14*h^0*U^1*WMAT^1*SIG^0+a15*h^0*U^1*WMAT^1*SIG^1
+a16*h^0*U^1*WMAT^2*SIGI+a17*h^0*U^1*WMAT^2*SIG^0+a18*h^0*U^1*WMAT^2*SIG^1
 
+a19*h^1*U^0*WMAT^0*SIGI+a20*h^1*U^0*WMAT^0*SIG^0+a21*h^1*U^0*WMAT^0*SIG^1
+a22*h^1*U^0*WMAT^1*SIGI+a23*h^1*U^0*WMAT^1*SIG^0+a24*h^1*U^0*WMAT^1*SIG^1
+a25*h^1*U^0*WMAT^2*SIGI+a26*h^1*U^0*WMAT^2*SIG^0+a27*h^1*U^0*WMAT^2*SIG^1

+a28*h^1*U^1*WMAT^0*SIGI+a29*h^1*U^1*WMAT^0*SIG^0+a30*h^1*U^1*WMAT^0*SIG^1
+a31*h^1*U^1*WMAT^1*SIGI+a32*h^1*U^1*WMAT^1*SIG^0+a33*h^1*U^1*WMAT^1*SIG^1
+a34*h^1*U^1*WMAT^2*SIGI+a35*h^1*U^1*WMAT^2*SIG^0+a36*h^1*U^1*WMAT^2*SIG^1);

BB - (
 b1*h^0*U^0*WMAT^0*SIGI+b2*h^0*U^0*WMAT^0*SIG^0+b3*h^0*U^0*WMAT^0*SIG^1
+b4*h^0*U^0*WMAT^1*SIGI+b5*h^0*U^0*WMAT^1*SIG^0+b6*h^0*U^0*WMAT^1*SIG^1
+b7*h^0*U^0*WMAT^2*SIGI+b8*h^0*U^0*WMAT^2*SIG^0+b9*h^0*U^0*WMAT^2*SIG^1

+b10*h^0*U^1*WMAT^0*SIGI+b11*h^0*U^1*WMAT^0*SIG^0+b12*h^0*U^1*WMAT^0*SIG^1
+b13*h^0*U^1*WMAT^1*SIGI+b14*h^0*U^1*WMAT^1*SIG^0+b15*h^0*U^1*WMAT^1*SIG^1
+b16*h^0*U^1*WMAT^2*SIGI+b17*h^0*U^1*WMAT^2*SIG^0+b18*h^0*U^1*WMAT^2*SIG^1
 
+b19*h^1*U^0*WMAT^0*SIGI+b20*h^1*U^0*WMAT^0*SIG^0+b21*h^1*U^0*WMAT^0*SIG^1
+b22*h^1*U^0*WMAT^1*SIGI+b23*h^1*U^0*WMAT^1*SIG^0+b24*h^1*U^0*WMAT^1*SIG^1
+b25*h^1*U^0*WMAT^2*SIGI+b26*h^1*U^0*WMAT^2*SIG^0+b27*h^1*U^0*WMAT^2*SIG^1

+b28*h^1*U^1*WMAT^0*SIGI+b29*h^1*U^1*WMAT^0*SIG^0+b30*h^1*U^1*WMAT^0*SIG^1
+b31*h^1*U^1*WMAT^1*SIGI+b32*h^1*U^1*WMAT^1*SIG^0+b33*h^1*U^1*WMAT^1*SIG^1
+b34*h^1*U^1*WMAT^2*SIGI+b35*h^1*U^1*WMAT^2*SIG^0+b36*h^1*U^1*WMAT^2*SIG^1);

CC - (
 c1*h^0*U^0*WMAT^0*SIGI+c2*h^0*U^0*WMAT^0*SIG^0+c3*h^0*U^0*WMAT^0*SIG^1
+c4*h^0*U^0*WMAT^1*SIGI+c5*h^0*U^0*WMAT^1*SIG^0+c6*h^0*U^0*WMAT^1*SIG^1
+c7*h^0*U^0*WMAT^2*SIGI+c8*h^0*U^0*WMAT^2*SIG^0+c9*h^0*U^0*WMAT^2*SIG^1

+c10*h^0*U^1*WMAT^0*SIGI+c11*h^0*U^1*WMAT^0*SIG^0+c12*h^0*U^1*WMAT^0*SIG^1
+c13*h^0*U^1*WMAT^1*SIGI+c14*h^0*U^1*WMAT^1*SIG^0+c15*h^0*U^1*WMAT^1*SIG^1
+c16*h^0*U^1*WMAT^2*SIGI+c17*h^0*U^1*WMAT^2*SIG^0+c18*h^0*U^1*WMAT^2*SIG^1
 
+c19*h^1*U^0*WMAT^0*SIGI+c20*h^1*U^0*WMAT^0*SIG^0+c21*h^1*U^0*WMAT^0*SIG^1
+c22*h^1*U^0*WMAT^1*SIGI+c23*h^1*U^0*WMAT^1*SIG^0+c24*h^1*U^0*WMAT^1*SIG^1
+c25*h^1*U^0*WMAT^2*SIGI+c26*h^1*U^0*WMAT^2*SIG^0+c27*h^1*U^0*WMAT^2*SIG^1

+c28*h^1*U^1*WMAT^0*SIGI+c29*h^1*U^1*WMAT^0*SIG^0+c30*h^1*U^1*WMAT^0*SIG^1
+c31*h^1*U^1*WMAT^1*SIGI+c32*h^1*U^1*WMAT^1*SIG^0+c33*h^1*U^1*WMAT^1*SIG^1
+c34*h^1*U^1*WMAT^2*SIGI+c35*h^1*U^1*WMAT^2*SIG^0+c36*h^1*U^1*WMAT^2*SIG^1);

AD - (
 ad1*h^0*U^0*WMAT^0*SIGI+ad2*h^0*U^0*WMAT^0*SIG^0+ad3*h^0*U^0*WMAT^0*SIG^1
+ad4*h^0*U^0*WMAT^1*SIGI+ad5*h^0*U^0*WMAT^1*SIG^0+ad6*h^0*U^0*WMAT^1*SIG^1
+ad7*h^0*U^0*WMAT^2*SIGI+ad8*h^0*U^0*WMAT^2*SIG^0+ad9*h^0*U^0*WMAT^2*SIG^1

+ad10*h^0*U^1*WMAT^0*SIGI+ad11*h^0*U^1*WMAT^0*SIG^0+ad12*h^0*U^1*WMAT^0*SIG^1
+ad13*h^0*U^1*WMAT^1*SIGI+ad14*h^0*U^1*WMAT^1*SIG^0+ad15*h^0*U^1*WMAT^1*SIG^1
+ad16*h^0*U^1*WMAT^2*SIGI+ad17*h^0*U^1*WMAT^2*SIG^0+ad18*h^0*U^1*WMAT^2*SIG^1
 
+ad19*h^1*U^0*WMAT^0*SIGI+ad20*h^1*U^0*WMAT^0*SIG^0+ad21*h^1*U^0*WMAT^0*SIG^1
+ad22*h^1*U^0*WMAT^1*SIGI+ad23*h^1*U^0*WMAT^1*SIG^0+ad24*h^1*U^0*WMAT^1*SIG^1
+ad25*h^1*U^0*WMAT^2*SIGI+ad26*h^1*U^0*WMAT^2*SIG^0+ad27*h^1*U^0*WMAT^2*SIG^1

+ad28*h^1*U^1*WMAT^0*SIGI+ad29*h^1*U^1*WMAT^0*SIG^0+ad30*h^1*U^1*WMAT^0*SIG^1
+ad31*h^1*U^1*WMAT^1*SIGI+ad32*h^1*U^1*WMAT^1*SIG^0+ad33*h^1*U^1*WMAT^1*SIG^1
+ad34*h^1*U^1*WMAT^2*SIGI+ad35*h^1*U^1*WMAT^2*SIG^0+ad36*h^1*U^1*WMAT^2*SIG^1);

BD - (
 bd1*h^0*U^0*WMAT^0*SIGI+bd2*h^0*U^0*WMAT^0*SIG^0+bd3*h^0*U^0*WMAT^0*SIG^1
+bd4*h^0*U^0*WMAT^1*SIGI+bd5*h^0*U^0*WMAT^1*SIG^0+bd6*h^0*U^0*WMAT^1*SIG^1
+bd7*h^0*U^0*WMAT^2*SIGI+bd8*h^0*U^0*WMAT^2*SIG^0+bd9*h^0*U^0*WMAT^2*SIG^1

+bd10*h^0*U^1*WMAT^0*SIGI+bd11*h^0*U^1*WMAT^0*SIG^0+bd12*h^0*U^1*WMAT^0*SIG^1
+bd13*h^0*U^1*WMAT^1*SIGI+bd14*h^0*U^1*WMAT^1*SIG^0+bd15*h^0*U^1*WMAT^1*SIG^1
+bd16*h^0*U^1*WMAT^2*SIGI+bd17*h^0*U^1*WMAT^2*SIG^0+bd18*h^0*U^1*WMAT^2*SIG^1
 
+bd19*h^1*U^0*WMAT^0*SIGI+bd20*h^1*U^0*WMAT^0*SIG^0+bd21*h^1*U^0*WMAT^0*SIG^1
+bd22*h^1*U^0*WMAT^1*SIGI+bd23*h^1*U^0*WMAT^1*SIG^0+bd24*h^1*U^0*WMAT^1*SIG^1
+bd25*h^1*U^0*WMAT^2*SIGI+bd26*h^1*U^0*WMAT^2*SIG^0+bd27*h^1*U^0*WMAT^2*SIG^1

+bd28*h^1*U^1*WMAT^0*SIGI+bd29*h^1*U^1*WMAT^0*SIG^0+bd30*h^1*U^1*WMAT^0*SIG^1
+bd31*h^1*U^1*WMAT^1*SIGI+bd32*h^1*U^1*WMAT^1*SIG^0+bd33*h^1*U^1*WMAT^1*SIG^1
+bd34*h^1*U^1*WMAT^2*SIGI+bd35*h^1*U^1*WMAT^2*SIG^0+bd36*h^1*U^1*WMAT^2*SIG^1);

CD - (
 cd1*h^0*U^0*WMAT^0*SIGI+cd2*h^0*U^0*WMAT^0*SIG^0+cd3*h^0*U^0*WMAT^0*SIG^1
+cd4*h^0*U^0*WMAT^1*SIGI+cd5*h^0*U^0*WMAT^1*SIG^0+cd6*h^0*U^0*WMAT^1*SIG^1
+cd7*h^0*U^0*WMAT^2*SIGI+cd8*h^0*U^0*WMAT^2*SIG^0+cd9*h^0*U^0*WMAT^2*SIG^1

+cd10*h^0*U^1*WMAT^0*SIGI+cd11*h^0*U^1*WMAT^0*SIG^0+cd12*h^0*U^1*WMAT^0*SIG^1
+cd13*h^0*U^1*WMAT^1*SIGI+cd14*h^0*U^1*WMAT^1*SIG^0+cd15*h^0*U^1*WMAT^1*SIG^1
+cd16*h^0*U^1*WMAT^2*SIGI+cd17*h^0*U^1*WMAT^2*SIG^0+cd18*h^0*U^1*WMAT^2*SIG^1
 
+cd19*h^1*U^0*WMAT^0*SIGI+cd20*h^1*U^0*WMAT^0*SIG^0+cd21*h^1*U^0*WMAT^0*SIG^1
+cd22*h^1*U^0*WMAT^1*SIGI+cd23*h^1*U^0*WMAT^1*SIG^0+cd24*h^1*U^0*WMAT^1*SIG^1
+cd25*h^1*U^0*WMAT^2*SIGI+cd26*h^1*U^0*WMAT^2*SIG^0+cd27*h^1*U^0*WMAT^2*SIG^1

+cd28*h^1*U^1*WMAT^0*SIGI+cd29*h^1*U^1*WMAT^0*SIG^0+cd30*h^1*U^1*WMAT^0*SIG^1
+cd31*h^1*U^1*WMAT^1*SIGI+cd32*h^1*U^1*WMAT^1*SIG^0+cd33*h^1*U^1*WMAT^1*SIG^1
+cd34*h^1*U^1*WMAT^2*SIGI+cd35*h^1*U^1*WMAT^2*SIG^0+cd36*h^1*U^1*WMAT^2*SIG^1);



AASTAR:=sub(U=Ubar,tp(AA))$
BBSTAR:=sub(U=Ubar,tp(BB))$
CCSTAR:=sub(U=Ubar,tp(CC))$

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

ADSTAR:=sub(U=Ubar,tp(AD))$
BDSTAR:=sub(U=Ubar,tp(BD))$
CDSTAR:=sub(U=Ubar,tp(CD))$

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

cvec:=mat((c1),(c2),(c3),(c4),(c5),(c6),(c7),(c8),(c9),(c10),(c11),(c12),(c13),(c14),(c15),(c16),(c17),(c18),
          (c19),(c20),(c21),(c22),(c23),(c24),(c25),(c26),(c27),(c28),(c29),(c30),(c31),(c32),(c33),(c34),(c35),(c36))$


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))$

cdvec:=mat((cd1),(cd2),(cd3),(cd4),(cd5),(cd6),(cd7),(cd8),(cd9),(cd10),(cd11),(cd12),(cd13),(cd14),(cd15),(cd16),(cd17),(cd18),
          (cd19),(cd20),(cd21),(cd22),(cd23),(cd24),(cd25),(cd26),(cd27),(cd28),(cd29),(cd30),(cd31),(cd32),(cd33),(cd34),(cd35),(cd36))$


CondMtxDM3Type1:=mat(
(23,1,8,13,26,22,5,1,14,4,0,23,2,0,10,4,0,11,26,0,3,16,0,0,14,0,0,8,0,19,4,0,20,8,0,22),
(13,0,15,8,0,0,7,0,0,4,0,23,2,0,10,4,0,11,23,1,8,13,26,22,5,1,14,4,0,23,2,0,10,4,0,11),
(25,0,2,26,0,22,25,0,8,17,1,14,10,26,7,26,1,11,23,0,4,25,0,17,23,0,16,18,0,11,12,0,7,6,0,5),
(25,0,2,26,0,22,25,0,8,9,0,19,6,0,17,3,0,16,25,0,2,26,0,22,25,0,8,17,1,14,10,26,7,26,1,11),
(22,0,22,4,1,4,18,25,0,7,0,14,18,0,15,11,0,4,16,0,20,16,0,10,15,0,20,23,0,19,0,0,12,4,0,26),
(8,0,10,8,0,5,21,0,10,25,0,23,0,0,6,2,0,13,22,0,22,4,1,4,18,25,0,7,0,14,18,0,15,11,0,4),
(10,0,20,18,0,6,8,0,25,7,0,19,22,1,4,24,25,12,2,0,4,0,0,21,25,0,14,11,0,10,25,0,16,2,0,3),
(1,0,2,0,0,24,26,0,7,19,0,5,26,0,8,1,0,15,10,0,20,18,0,6,8,0,25,7,0,19,22,1,4,24,25,12),
(6,0,13,17,0,2,19,1,3,0,0,20,9,0,23,7,0,17,13,0,24,25,0,17,14,0,17,0,0,4,0,0,19,23,0,16),
(20,0,12,26,0,22,7,0,22,0,0,2,0,0,23,25,0,8,6,0,13,17,0,2,19,1,3,0,0,20,9,0,23,7,0,17),
(0,0,17,9,0,2,10,0,5,6,0,1,26,0,8,4,1,0,0,0,25,0,0,4,2,0,19,13,0,2,16,0,25,9,0,19),
(0,0,26,0,0,2,1,0,23,20,0,1,8,0,26,18,0,23,0,0,17,9,0,2,10,0,5,6,0,1,26,0,8,4,1,0),
(9,0,3,18,0,9,21,24,18,6,0,6,6,0,21,6,0,18,15,0,3,3,0,0,9,0,24,12,0,12,12,0,15,12,0,9),
(21,0,15,15,0,0,18,0,12,6,0,6,6,0,21,6,0,18,9,0,3,18,0,9,21,24,18,6,0,6,6,0,21,6,0,18),
(24,0,24,24,0,3,24,0,18,0,0,21,9,0,18,12,24,18,21,0,21,21,0,6,21,0,9,3,0,18,18,0,12,24,0,15),
(24,0,24,24,0,3,24,0,18,15,0,9,9,0,6,12,0,21,24,0,24,24,0,3,24,0,18,0,0,21,9,0,18,12,24,18),
(26,1,26,22,26,4,8,1,17,25,0,2,2,0,19,4,0,8,5,0,3,4,0,3,20,0,3,23,0,4,4,0,11,8,0,16),
(16,0,15,2,0,15,10,0,15,25,0,2,2,0,19,4,0,8,26,1,26,22,26,4,8,1,17,25,0,2,2,0,19,4,0,8),
(1,0,26,26,0,4,25,0,23,2,1,23,19,26,16,2,1,5,2,0,25,25,0,8,23,0,19,9,0,26,0,0,19,12,0,14),
(1,0,26,26,0,4,25,0,23,18,0,13,0,0,23,6,0,7,1,0,26,26,0,4,25,0,23,2,1,23,19,26,16,2,1,5),
(23,0,15,9,1,5,10,1,23,9,0,16,16,0,13,7,0,12,11,0,14,12,0,7,22,0,17,0,0,23,23,0,8,23,0,15),
(19,0,7,6,0,17,11,0,22,0,0,25,25,0,4,25,0,21,23,0,15,9,1,5,10,1,23,9,0,16,16,0,13,7,0,12),
(9,0,19,19,0,7,10,0,21,5,0,9,3,1,8,22,1,23,0,0,2,2,0,23,2,0,6,2,0,0,25,0,17,17,0,11),
(0,0,1,1,0,25,1,0,3,1,0,0,26,0,22,22,0,19,9,0,19,19,0,7,10,0,21,5,0,9,3,1,8,22,1,23),
(0,0,12,12,24,0,12,24,15,12,0,0,12,0,12,18,0,21,18,0,3,12,0,24,3,0,21,24,0,0,24,0,24,9,0,15),
(9,0,15,6,0,12,15,0,24,12,0,0,12,0,12,18,0,21,0,0,12,12,24,0,12,24,15,12,0,0,12,0,12,18,0,21),
(21,0,0,21,0,21,18,0,3,9,0,12,21,24,9,12,24,24,15,0,0,15,0,15,9,0,6,21,0,3,15,0,0,21,0,6),
(21,0,0,21,0,21,18,0,3,24,0,15,21,0,0,24,0,3,21,0,0,21,0,21,18,0,3,9,0,12,21,24,9,12,24,24),
(21,0,3,3,0,21,21,24,3,0,0,21,6,0,0,12,0,9,9,0,6,24,0,6,0,0,9,0,0,15,12,0,0,24,0,18),
(18,0,3,12,0,3,0,0,18,0,0,21,6,0,0,12,0,9,21,0,3,3,0,21,21,24,3,0,0,21,6,0,0,12,0,9),
(0,0,3,24,0,0,21,0,9,21,0,12,21,0,21,3,24,3,0,0,6,21,0,0,15,0,18,9,0,18,12,0,6,3,0,18),
(0,0,3,24,0,0,21,0,9,18,0,9,6,0,3,15,0,9,0,0,3,24,0,0,21,0,9,21,0,12,21,0,21,3,24,3),
(5,1,20,19,2,1,14,4,23,25,0,2,23,0,25,19,0,8,23,0,21,7,0,24,20,0,24,23,0,4,19,0,23,11,0,16),
(25,0,24,17,0,12,10,0,12,25,0,2,23,0,25,19,0,8,5,1,20,19,2,1,14,4,23,25,0,2,23,0,25,19,0,8),
(1,0,26,2,0,1,4,0,23,8,1,17,25,2,4,26,4,11,2,0,25,4,0,2,8,0,19,0,0,17,15,0,1,9,0,8),
(1,0,26,2,0,1,4,0,23,0,0,22,21,0,14,18,0,4,1,0,26,2,0,1,4,0,23,8,1,17,25,2,4,26,4,11))$

CondMtxDM17Type2:=(1/17)*mat(
(0,17,0,0,1275,0,0,2278,0,0,0,0,0,0,0,0,0,0,0,4148,0,0,1581,0,0,663,0,0,0,0,0,0,0,0,0,0),
(0,0,0,0,0,0,0,0,0,0,17,0,0,1275,0,0,2278,0,0,0,0,0,0,0,0,0,0,0,4148,0,0,1581,0,0,663,0),
(0,0,17,0,0,1275,0,0,2278,0,0,0,0,0,0,0,0,0,0,0,4148,0,0,1581,0,0,663,0,0,0,0,0,0,0,0,0),
(0,0,0,0,0,0,0,0,0,0,0,17,0,0,1275,0,0,2278,0,0,0,0,0,0,0,0,0,0,0,4148,0,0,1581,0,0,663),
(2091,0,0,4522,0,0,153,0,0,4148,0,0,1581,0,0,663,0,0,4165,0,0,2856,0,0,2941,0,0,34,0,0,2550,0,0,4556,0,0),
(2839,0,0,1666,0,0,2125,0,0,0,0,0,0,0,0,0,0,0,4896,0,0,3638,0,0,2635,0,0,0,0,0,0,0,0,0,0,0),
(17,0,0,1394,0,0,1309,0,0,0,0,0,0,0,0,0,0,0,4148,0,0,1139,0,0,51,0,0,0,0,0,0,0,0,0,0,0),
(0,0,0,0,0,0,0,0,0,17,0,0,1394,0,0,1309,0,0,0,0,0,0,0,0,0,0,0,4148,0,0,1139,0,0,51,0,0),
(0,17,0,0,1394,0,0,1309,0,0,0,0,0,0,0,0,0,0,0,4148,0,0,1139,0,0,51,0,0,0,0,0,0,0,0,0,0),
(0,0,0,0,0,0,0,0,0,0,17,0,0,1394,0,0,1309,0,0,0,0,0,0,0,0,0,0,0,4148,0,0,1139,0,0,51,0),
(0,0,17,0,0,1394,0,0,1309,0,0,0,0,0,0,0,0,0,0,0,4148,0,0,1139,0,0,51,0,0,0,0,0,0,0,0,0),
(0,0,0,0,0,0,0,0,0,0,0,17,0,0,1394,0,0,1309,0,0,0,0,0,0,0,0,0,0,0,4148,0,0,1139,0,0,51),
(0,0,0,0,0,0,0,0,0,0,0,765,0,0,2720,0,0,391,0,0,0,0,0,0,0,0,0,0,0,4879,0,0,425,0,0,2057),
(0,0,2074,0,0,3553,0,0,2261,0,0,2091,0,0,884,0,0,3689,0,0,17,0,0,2244,0,0,1428,0,0,4165,0,0,4437,0,0,1037),
(17,0,0,2244,0,0,1428,0,0,0,0,0,0,0,0,0,0,0,4148,0,0,2193,0,0,4522,0,0,0,0,0,0,0,0,0,0,0),
(0,0,0,0,0,0,0,0,0,17,0,0,2244,0,0,1428,0,0,0,0,0,0,0,0,0,0,0,4148,0,0,2193,0,0,4522,0,0),
(0,17,0,0,2244,0,0,1428,0,0,0,0,0,0,0,0,0,0,0,4148,0,0,2193,0,0,4522,0,0,0,0,0,0,0,0,0,0),
(0,0,0,0,0,0,0,0,0,0,17,0,0,2244,0,0,1428,0,0,0,0,0,0,0,0,0,0,0,4148,0,0,2193,0,0,4522,0),
(0,17,0,0,1275,0,0,2278,0,0,0,0,0,0,0,0,0,0,0,765,0,0,3332,0,0,4250,0,0,0,0,0,0,0,0,0,0),
(0,0,0,0,0,0,0,0,0,0,17,0,0,1275,0,0,2278,0,0,0,0,0,0,0,0,0,0,0,765,0,0,3332,0,0,4250,0),
(935,0,3536,1343,0,4811,2465,0,2176,3009,0,3298,4590,0,1700,340,0,4675,2771,0,1904,1479,0,323,2839,0,4573,2754,0,1020,204,0,2805,561,0,4029),
(952,0,3264,2618,0,4063,4743,0,119,510,0,1377,3859,0,102,4471,0,2737,3536,0,4403,4811,0,1054,2176,0,442,3298,0,3009,1700,0,4590,4675,0,340),
(3961,0,3298,2295,0,1700,170,0,4675,4658,0,0,527,0,0,221,0,0,1377,0,1020,102,0,2805,2737,0,4029,3264,0,0,4063,0,0,119,0,0),
(2584,0,0,2193,0,0,2346,0,0,0,0,3298,0,0,1700,0,0,4675,3281,0,0,425,0,0,2397,0,0,0,0,1020,0,0,2805,0,0,4029),
(4370,0,387,269,0,3399,672,0,718,91,0,2832,1104,0,4193,1516,0,2931,708,0,364,545,0,74,1051,0,231,2650,0,569,4885,0,3436,1172,0,3290),
(2411,0,3497,4361,0,360,4155,0,991,543,0,1143,4644,0,2041,4241,0,64,3588,0,2172,14,0,3195,4327,0,3268,4205,0,4617,4368,0,3989,3862,0,568),
(1615,17,3281,1921,4165,3740,3009,4743,2074,0,0,0,0,0,0,0,0,0,3893,765,255,2924,731,1258,2754,2176,4896,0,0,0,0,0,0,0,0,0),
(0,0,0,0,0,0,0,0,0,1615,17,3281,1921,4165,3740,3009,4743,2074,0,0,0,0,0,0,0,0,0,3893,765,255,2924,731,1258,2754,2176,4896),
(2017,0,181,653,4699,1548,3831,3623,4689,2123,0,3245,3374,3085,4545,308,3582,2770,3776,0,4677,3953,4242,1456,3908,2062,2925,
1032,0,2392,4151,972,1647,277,1084,1247),
(1395,0,834,3226,914,184,4759,3122,3528,2896,0,4732,4260,214,3365,1082,1290,224,4397,0,3717,381,4427,1633,2318,4371,1833,1137,0,236,
960,671,3457,1005,2851,1988),
(17,0,0,1394,0,0,1309,0,0,0,0,4148,0,0,2193,0,0,4522,765,0,0,3774,0,0,4862,0,0,0,0,4879,0,0,425,0,0,2057),
(0,0,2839,0,0,1360,0,0,2652,17,0,2856,1394,0,3604,1309,0,4080,0,0,17,0,0,2244,0,0,1428,765,0,782,3774,0,51,4862,0,1819),
(3536,0,1377,17,68,4828,2244,4726,2856,3298,0,1615,2992,2142,4692,1904,1479,1530,1904,0,3009,765,3060,1088,2720,1411,782,1020,0,3893,
1989,3043,4794,2159,2686,68),
(3264,0,1649,3417,3842,2567,3961,1717,4148,1377,0,3536,4896,4845,85,2669,187,2057,4403,0,510,1462,935,2516,1377,3570,4879,3009,0,1904,
4148,1853,3825,2193,3502,4131),
(3298,17,1632,2992,4386,1173,1904,2907,2839,0,0,0,0,0,0,0,0,0,1020,765,4658,1989,850,3655,2159,3077,17,0,0,0,0,0,0,0,0,0),
(0,0,0,0,0,0,0,0,0,3298,17,1632,2992,4386,1173,1904,2907,2839,0,0,0,0,0,0,0,0,0,1020,765,4658,1989,850,3655,2159,3077,17))$

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

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

CondMtxDM3Type1*avec- mat((13),(20),(-28),(-20),(41),(7),(-27),(-47),(40),(14),(21),(19),(6),(44),(45),(31),(17),(1),
                          (-8),(-7),(6),(-4),(6),(-1),(9),(10),(-22),(-28),(9),(-15),(-17),(-18),(-5),(29),(1),(10));

CondMtxDM3Type1*bvec - mat((-7),(-10),(-24),(-24),(-17),(-2),(-22),(5),(-6),(9),(5),(10),(-7),(-7),(-5),(4),
(-8),(3),(-25),(-9),(-2),(-4),(-7),(13),(-7),(12),(-22),(-20),(-12),(-15),(-12),(-2),(-9),(4),(1),(-3));

CondMtxDM3Type1*cvec - mat((68),(56),(-22),(4),(46),(0),(-22),(-58),(22),(20),(-2),(-8),(18),(46),(32),(19),
(29),(26),(-56),(-75),(26),(44),(13),(10),(27),(9),(-11),(-18),(24),(44),(-66),(-73),(1),(19),(-11),(0));

CondMtxDM3Type1*advec - (1/17)*mat((-295),(-187),(-671),(-628),(-402),(-72),(-76),(-424),(252),(145),(229),(494),(-212),(67),(55),
(151),(505),(29),(290),(698),(-361),(-843),(41),(-334),(-40),(53),(-701),(-690),(-962),(-796),(453),(560),(152),(58),(-122),(-150));

CondMtxDM3Type1*bdvec - (1/17)*mat((-373),(-272),(-809),(-632),(-103),(46),(-367),(-292),(60),(-27),(299),(507),(194),(105),(-318),
(-317),(-19),(-87),(-258),(-54),(-158),(-310),(-38),(152),(358),(249),(-668),(-633),(-599),(-332),(69),(105),(292),(81),(-8),(127));

CondMtxDM3Type1*cdvec - (1/17)*mat((-1204),(-629),(-1696),(-1590),(-156),(-321),(-251),(-519),(-143),(-999),(608),(535),(-387),(-246),
(-716),(-968),(-482),(-788),(-366),(-485),(-678),(-811),(-148),(-156),(37),(84),(-967),(-1151),(-862),(-1098),(-31),(-110),(-195),(-165),(197),(364));

CondMtxDM17Type2*advec - (1/9)*mat((2243),(-1512),(-410),(514),(-871),(-1539),(-864),(-587),(2563),(-1621),(-174),(298),(421),(-863),(381),(-1420),
(1955),(-1469),(-201),(-237),(-1392),(-1247),(-2047),(582),(-1592),(-1138),(-2480),(214),(-993),(-773),(1685),(-896),(-3178),(-5076),(-390),(-629));

CondMtxDM17Type2*bdvec - (1/9)*mat((-1011),(543),(-601),(1585),(-983),(-2048),(-715),(761),(-1177),(791),(-432),(1251),(1661),(-1003),(-953),(1039),
(-689),(259),(573),(-879),(-1838),(-1422),(-3487),(992),(938),(-82),(-4952),(2124),(72),(1069),(891),(880),(-301),(-2867),(-2351),(1328));

CondMtxDM17Type2*cdvec - (1/9)*mat((-1788),(529),(-2678),(414),(-4479),(-5590),(-2692),(1123),(-2014),(499),(-2106),(-44),(362),(-1505),(-3392),(1793),
(-1739),(506),(231),(99),(-1016),(-2715),(-6496),(-436),(-179),(-2159),(-7716),(5337),(-4028),(-583),(-418),(2071),(-2696),(-4990),(-7360),(2620));

% Here are the inverses of AA,...,CD:
AAI:=FFI*AASTAR*FF$
BBI:=FFI*BBSTAR*FF$
CCI:=FFI*CCSTAR*FF$

ADI:=FFI*ADSTAR*FF$
BDI:=FFI*BDSTAR*FF$
CDI:=FFI*CDSTAR*FF$

% The following are zero, confirming the relations given in the write up 
% for the group (C_{10},p=2,\emptyset) are indeed satisfied:

BB^3 - gendt*ID3;
(BB*AAI)^3 - gendt*ID3;
CCI*AA*BB*CCI^2*AA^3*CC*AAI*BBI - ID3;
AA*CC*BBI*CC*AAI*BBI*AAI*CCI*BB*AA*CCI*BB - ID3;
CCI*BB*AAI*BBI*CCI*AA*BBI*AA*CCI*AAI^2*BB*CCI - ID3;
CCI*BB*AAI*BBI*AA*BB*AA*CCI*AAI*CC^2*BBI*AAI - ID3;
AAI*BB*AA*BBI*CC*AAI*BBI*CC*AA*CC*AAI*BBI*CC*BBI - gendti*ID3;
CC^2*BBI*AAI*CCI*AA^3*CC*BBI*CC^2*BBI*AAI - gendti*ID3;
CC*BBI*CC*AAI*BBI*CCI*AA*CC*AAI*BBI*CCI*AAI^2*CC - gendti*ID3;
CC*BBI*AAI*CC*BBI*AAI*BB*AA^2*CC*AAI*BBI*CC*BBI*AAI - gendti*ID3;
CC*BBI*AAI*CCI*BB*AA*CC*BBI*AA^3*BB*CCI^2*AA*CC - ID3;
AA^2*CC*BB*AA*CCI*AA*CC*AAI*BBI*CCI^2*BB*AA*CC*BBI - ID3;

% The following are zero, confirming the relations given in the write up 
% for the group (C_{10},p=2,\{17-\}) are indeed satisfied:

(BD*ADI)^3 - gendt*ID3;
(BD*CDI)^3 - gendt*ID3;
CDI*BD*ADI^2*BD*CD*BDI*AD^2*BDI - ID3;
BD*AD*BDI*CD*BDI*ADI^2*BD^2*CDI*BD^2*CDI - gendt*ID3;
ADI*BD*ADI^2*BD*ADI^2*CD*AD^3*BDI*CD*BDI - ID3;
AD*BD^2*AD^3*BDI*CD^2*BDI*CDI*BD*CDI*BDI*CD - ID3;
BDI*AD^2*BDI^2*AD^2*BDI*CD*BDI*AD^2*BDI*CD^4 - gendti^2*ID3;
BD*AD*CDI*BD*CDI*BDI*CD*AD*BD*ADI*BD*CD*BDI*CD*ADI^3*BD*CDI - gendt*ID3;
AD*BD*AD*BDI*CD*BDI^2*AD*BD*AD*CDI*BD*CDI*BDI*AD*BD*AD*CDI*BD*CDI*BDI - ID3;
AD*BDI*CD*AD^2*BDI^2*ADI*BD*ADI^2*CD*AD*BD^3*ADI^2*CD*BDI*AD - ID3;

;end;