//Standard generators of L2(23) are a, b where a has order 2,
//b has order 3 and ab has order 23.
//Standard generators of 2.L2(23) = SL2(23) are preimages A, B where
////B has order 3 and AB has order 23. 
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [a^-1, b^-1] ]
             where a is (_LR`F).1 where b is (_LR`F).2;
//two constituents (each twice) all fixed by _LR`AI[1][1]
_LR`G :=
/*
Original group: c9Group("sl223p")
From DB /nb/reps/l2/2l223/d22.2l223.deg4.si2.X9.M
Schur index: 2
Character: ( 22, -22, -2, 0, 2, -zeta(8)_8^3 + zeta(8)_8, zeta(8)_8^3 - 
zeta(8)_8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -zeta(8)_8^3 + zeta(8)_8,
zeta(8)_8^3 - zeta(8)_8, zeta(8)_8^3 - zeta(8)_8, -zeta(8)_8^3 + zeta(8)_8, 1, 1
)
*/
MatrixGroup<22, K | [
Matrix(K,22,22,
[[1/23,-19/69,-11/69,-17/69],[-20/69,26/69,-10/69,-2/23],[
0,0,0,0],[-1/6,-7/138,-1/138,3/46],[-3/23,25/69,-7/69,
-25/69],[35/138,1/6,-25/46,65/138],[59/138,-49/138,3/46,
41/138],[-1/138,21/46,-1/138,-53/138],[1/23,0,-8/23,3/23],
[11/46,-47/138,17/138,29/138],[5/23,-2/3,58/69,-29/69],[
-29/138,-11/138,-1/46,13/138],[-11/138,7/46,-5/138,-25/138],[
17/138,-3/46,-1/138,25/138],[79/138,-11/46,13/138,29/138],[
-16/69,5/69,9/23,-22/69],[6/23,-2/69,-22/69,38/69],[-31/138,
13/46,29/138,-5/138],[-8/23,-5/69,-1/69,2/69],[13/69,-6/23,
-20/69,-7/69],[-31/138,17/138,9/46,-13/138],[-29/69,16/69,
-2/23,-11/69],[-31/138,21/46,-91/138,19/138],[-31/138,1/138,
55/138,-19/46],[0,0,0,0],[2/23,-31/69,10/69,25/69],[
-9/23,8/23,-3/23,-6/23],[5/23,-4/69,-14/69,13/69],[53/138,
-15/46,5/138,31/138],[21/46,-1/46,3/46,1/46],[41/138,1/138,
-125/138,25/46],[9/46,11/138,1/138,-11/138],[35/138,-29/46,
35/138,-59/138],[17/138,-5/138,7/138,-3/46],[-16/69,1/23,
-1/69,-2/69],[43/138,-35/138,3/46,43/138],[-5/69,-2/69,
-1/23,4/69],[-5/69,-1/69,35/69,-3/23],[-29/138,1/46,61/138,
-7/138],[-5/23,5/23,5/23,-3/23],[-29/138,-1/46,-5/138,-1/138
],[14/69,-25/69,-1/23,-4/69],[-7/138,3/46,47/138,-5/138],[
-15/23,2/3,-10/69,-37/69],[-1/138,-11/46,-13/138,-59/138],[
-5/69,-22/69,29/69,-15/23],[25/23,-21/23,0,21/23],[-25/138,
1/6,-7/46,53/138],[-37/138,85/138,-41/138,1/46],[4/23,-2/23,
-3/23,-2/23],[14/69,-11/69,-8/69,14/23],[9/46,41/138,
-17/138,31/138],[0,-2/69,-19/69,-10/69],[-2/69,19/69,-4/23,
16/69],[5/23,-16/23,13/23,-13/23],[-1/69,5/23,-10/69,22/69
],[-6/23,22/69,-13/69,14/69],[-19/138,35/138,-9/46,53/138],
[17/138,37/138,-1/6,13/46],[-11/138,-35/138,19/46,-77/138],[
-5/138,-3/46,43/138,-19/138],[-41/138,-5/138,29/46,-95/138],[
-31/138,9/46,-25/138,43/138],[7/46,-15/46,1/46,-11/46],[
-7/138,5/138,3/46,-25/138],[-31/69,35/69,-6/23,5/69],[
-11/138,-17/138,-13/46,-11/138],[33/46,-71/138,53/138,-13/138
],[4/23,35/69,-1/3,34/69],[-1/23,8/69,-26/69,19/69],[
-3/23,5/69,28/69,-26/69],[-2/69,4/69,-8/23,22/69],[7/23,
-17/69,-1/69,35/69],[35/138,5/138,-9/46,-25/138],[-2/23,
11/69,-29/69,10/69],[-1/138,43/138,25/138,3/46],[73/138,
-145/138,59/138,7/46],[3/46,7/138,-7/138,17/138],[-43/69,
3/23,17/69,-47/69],[-4/23,-4/23,5/23,-5/23],[5/46,-11/138,
35/138,-31/138],[-14/69,-8/69,6/23,-14/69],[11/46,-3/46,
11/46,13/46],[-37/138,9/46,65/138,-59/138],[-13/46,29/138,
-53/138,19/138],[26/69,-6/23,-10/69,10/69],[-5/69,1/3,
-10/69,0],[-77/138,67/138,-13/46,-47/138],[7/23,-41/69,
-16/69,20/69],[7/46,-35/138,35/138,-37/138],[4/23,35/69,
-1/3,34/69],[-1/23,-26/69,38/69,-1/69],[-13/46,37/138,
17/138,-67/138],[1/138,-13/138,-43/138,17/46],[47/138,
-29/138,-47/138,1/2],[-1/6,5/46,43/138,-91/138],[2/69,14/69,
-10/23,8/69],[-2/23,20/69,-26/69,4/69],[34/69,-16/23,34/69,
-10/69],[-7/138,-29/138,37/138,-13/46],[-11/46,49/138,1/6,
5/138],[-17/69,16/69,-5/23,-2/69],[25/138,1/138,-11/46,
-17/138],[-7/46,-19/138,31/138,-29/138],[-11/46,11/138,
13/138,37/138],[-29/69,7/69,11/23,-1/3],[-10/69,2/69,-2/23,
8/69],[3/23,-2/69,-13/69,-4/69],[-19/138,31/138,-11/138,5/46
],[-8/23,29/69,-11/69,-2/69],[5/69,1/69,-35/69,3/23],[
-2/69,-20/69,8/23,-26/69],[0,0,0,0],[-53/138,15/46,-5/138,
-31/138],[-2/23,31/69,-10/69,-25/69],[29/138,-1/46,-61/138,
7/138],[15/23,-2/3,10/69,37/69],[5/69,2/69,1/23,-4/69],[
7/138,-3/46,-47/138,5/138],[16/69,-1/23,1/69,2/69],[31/138,
-21/46,91/138,-19/138],[29/138,1/46,5/138,1/138],[-21/46,
1/46,-3/46,-1/46],[-17/138,5/138,-7/138,3/46],[9/23,-8/23,
3/23,6/23],[5/23,-5/23,-5/23,3/23],[-35/138,29/46,-35/138,
59/138],[-41/138,-1/138,125/138,-25/46],[-9/46,-11/138,
-1/138,11/138],[31/138,-1/138,-55/138,19/46],[-14/69,25/69,
1/23,4/69],[-43/138,35/138,-3/46,-43/138],[-3/23,-7/69,
-17/69,-5/69],[-11/46,-15/46,11/46,-9/46],[4/23,35/69,-1/3,
34/69],[-11/138,11/138,-7/138,13/46],[-3/23,13/23,-12/23,
-2/23],[31/69,-2/23,-14/69,1/3],[13/138,-25/138,-19/138,9/46
],[25/138,-7/138,41/138,-13/46],[-1/46,37/138,-67/138,5/138
],[-9/23,2/23,6/23,-15/23],[10/69,-40/69,26/69,-5/23],[
-5/69,16/69,-8/23,10/69],[-14/69,4/69,-6/23,-14/69],[-4/69,
2/23,-7/69,13/69],[6/23,-19/69,37/69,-8/69],[-7/138,-1/46,
35/138,-41/138],[19/69,-29/69,4/23,40/69],[-53/138,7/46,
67/138,-55/138],[-14/69,16/69,4/23,10/69],[65/69,-12/23,
-1/69,22/69],[4/23,7/69,-7/69,14/69],[-67/138,11/138,7/46,
-73/138],[-29/138,-13/138,-43/138,-1/46],[-11/69,-3/23,19/69,
-25/69],[4/23,35/69,-1/3,34/69],[-17/138,-13/138,-31/138,
-1/46],[-29/46,59/138,19/138,-119/138],[55/138,-1/46,-41/138,
41/138],[13/69,-35/69,7/23,7/69],[19/138,43/138,-15/46,7/138
],[-5/69,2/23,-32/69,14/69],[-3/46,-7/46,11/46,-17/46],[
7/138,-97/138,53/138,-5/46],[2/23,3/23,-1/23,5/23],[-25/138,
7/46,-13/138,1/138],[0,14/69,-29/69,19/69],[10/69,7/23,
13/69,8/69],[9/46,-35/138,47/138,-19/138],[52/69,-6/23,
19/69,29/69],[1/69,-9/23,34/69,2/69],[-1/3,4/23,-14/69,
-7/69],[25/138,-13/138,-19/138,1/46],[-4/23,4/23,-2/23,4/23
],[-43/138,-5/138,61/138,-15/46],[5/138,-29/138,-1/6,-7/46],
[31/138,-13/46,-29/138,5/138],[0,0,0,0],[11/138,-7/46,
5/138,25/138],[-11/46,47/138,-17/138,-29/138],[31/138,
-17/138,-9/46,13/138],[1/138,-21/46,1/138,53/138],[29/138,
11/138,1/46,-13/138],[-5/23,2/3,-58/69,29/69],[29/69,-16/69,
2/23,11/69],[20/69,-26/69,10/69,2/23],[1/6,7/138,1/138,
-3/46],[-17/138,3/46,1/138,-25/138],[3/23,-25/69,7/69,25/69
],[8/23,5/69,1/69,-2/69],[-35/138,-1/6,25/46,-65/138],[
-13/69,6/23,20/69,7/69],[-6/23,2/69,22/69,-38/69],[-59/138,
49/138,-3/46,-41/138],[16/69,-5/69,-9/23,22/69],[-1/23,
19/69,11/69,17/69],[-79/138,11/46,-13/138,-29/138],[18/23,
-10/23,-3/23,3/23],[-9/46,-25/138,37/138,-41/138],[4/23,
35/69,-1/3,34/69],[-11/69,14/69,14/69,5/23],[-15/46,29/46,
-1/2,-7/46],[2/23,7/69,-19/69,14/69],[-11/69,-8/23,22/69,
-19/69],[11/69,-3/23,20/69,-26/69],[19/69,-2/69,-8/23,19/69
],[5/69,13/69,-5/69,3/23],[61/138,-29/46,55/138,-25/138],[
17/138,-15/46,77/138,-11/138],[-17/46,41/138,-29/138,-29/138],
[-7/46,-13/138,31/138,-17/138],[14/69,7/69,-5/69,2/23],[
-17/69,-6/23,16/69,-7/69],[-4/69,16/69,7/69,1/23],[-1/2,
5/46,19/46,-13/46],[-2/23,10/69,-28/69,14/69],[11/138,
-29/138,-1/6,5/46],[6/23,-22/69,-5/69,37/69],[-9/23,17/69,
-1/3,-1/3],[-1/138,-29/138,25/138,-13/46],[-5/138,-35/138,
5/46,-71/138],[0,0,0,0],[-1/23,-2/23,1/23,0],[25/138,
5/46,-5/138,-7/138],[25/138,7/46,-5/138,47/138],[5/23,
-26/69,2/69,20/69],[26/69,3/23,2/69,-11/69],[5/69,20/69,
-16/23,35/69],[-7/46,1/138,-1/138,-7/138],[71/138,-91/138,
-3/46,17/138],[17/69,-7/69,1/23,8/69],[1/138,-41/138,5/46,
25/138],[-5/46,-1/46,-1/46,7/46],[-11/138,59/138,-7/138,
-15/46],[-2/69,-20/69,8/23,-26/69],[1/23,13/69,-7/69,29/69
],[-31/69,20/69,14/23,-31/69],[-29/69,-7/69,-4/69,2/23],[
-1/46,-11/46,7/46,-7/46],[-1/138,3/46,-1/138,13/138],[
-31/138,43/138,-11/138,-11/46],[-2/69,4/69,-7/23,-17/69],[
11/46,-31/46,13/46,3/46],[4/23,35/69,-1/3,34/69],[-7/69,0,
-4/69,13/69],[-7/23,13/69,8/69,-40/69],[7/138,7/138,-13/46,
37/138],[10/69,-10/69,-22/69,10/23],[41/138,29/138,-1/46,
17/138],[-1/6,-5/138,-21/46,43/138],[5/46,-37/138,73/138,
-1/6],[3/23,-35/69,29/69,-19/69],[1/23,-1/23,-5/23,-2/23],
[-17/138,37/138,-19/46,13/138],[-1/2,3/46,11/46,-1/2],[
1/69,17/69,-13/69,-3/23],[10/69,-13/69,17/69,-4/23],[-1/138,
1/6,7/46,17/138],[34/69,-16/69,41/69,-3/23],[-11/46,-7/46,
11/46,-9/46],[59/138,-15/46,-7/138,25/138],[-35/138,25/138,
-7/46,31/138],[-59/138,25/46,13/138,-13/138],[-4/23,-17/69,
-19/69,2/69],[-1/23,-2/23,6/23,-9/23],[4/23,35/69,-1/3,
34/69],[-25/46,-1/46,13/46,-1/2],[-17/69,15/23,4/69,-10/69
],[7/46,29/138,-47/138,13/138],[6/23,-29/69,-13/69,14/69],[
19/69,3/23,-2/69,2/69],[43/138,-53/138,-19/46,79/138],[
-19/138,35/138,-9/46,-25/138],[139/138,-41/46,73/138,-1/138],
[17/138,1/6,-17/46,29/138],[-41/138,-5/46,31/138,-55/138],[
0,-20/69,35/69,-1/69],[3/46,13/46,-17/46,5/46],[-13/46,
-5/46,9/46,-7/46],[13/69,0,10/69,17/69],[-1/46,-5/138,
77/138,-37/138],[-17/138,5/46,-11/138,29/138],[2/69,-13/69,
-3/23,8/69],[-17/138,7/46,-17/138,1/6],[-32/69,11/69,11/69,
-10/23],[-13/138,-7/138,-11/46,-19/138],[14/69,-22/69,8/23,
-16/69],[4/23,35/69,-1/3,34/69],[-5/23,-6/23,6/23,-5/23],[
-26/69,41/69,-22/69,-9/23],[7/69,2/69,-22/69,6/23],[13/46,
-15/46,-1/46,19/46],[1/3,17/69,-8/23,8/69],[109/138,-31/138,
-43/138,19/46],[-1/23,-5/69,17/69,-19/69],[17/69,-32/69,
28/69,-7/23],[-26/69,2/69,20/69,-13/23],[-17/138,-31/138,
71/138,-9/46],[-8/69,20/69,11/69,5/23],[31/138,25/138,-3/46,
25/138],[-7/69,1/23,14/69,-26/69],[-11/69,5/69,11/69,5/23],
[-5/69,2/69,32/69,-7/23],[-1/6,-3/46,-35/138,-13/138],[
-7/138,-25/138,-9/46,1/6],[-5/23,2/69,-8/69,19/69],[-35/69,
12/23,-32/69,-7/69],[37/138,-11/46,-1/6,-1/138],[-13/138,
-1/46,29/138,-65/138],[4/23,35/69,-1/3,34/69],[-9/46,
-25/138,37/138,-17/138],[-29/138,49/138,-17/46,-53/138],[
133/138,-13/46,-1/6,65/138],[47/138,-97/138,27/46,29/138],[
5/23,1/3,16/69,4/69],[-17/138,5/46,-59/138,29/138],[7/138,
5/46,-11/138,5/138],[1/69,-38/69,8/23,-11/69],[-17/138,9/46,
-1/6,-13/138],[-22/69,1/3,-9/23,2/69],[-5/138,1/6,-13/138,
13/46],[-11/46,11/138,37/138,-83/138],[16/69,-14/23,19/69,
11/69],[-14/69,-5/69,3/23,22/69],[-17/46,11/138,61/138,
-47/138],[-6/23,-16/69,16/69,-20/69],[3/46,-19/138,-17/138,
7/138],[-1/46,37/138,-13/138,11/138],[-43/138,21/46,-67/138,
-5/138],[-11/69,2/23,-8/69,-13/69],[-3/46,-11/138,71/138,
-31/138],[0,0,0,0],[1/23,-2/69,2/69,5/69],[-35/138,
55/138,-7/46,-41/138],[65/138,-7/138,-35/46,83/138],[16/69,
-10/23,4/69,26/69],[89/138,-29/138,19/138,7/46],[-4/23,4/69,
-10/69,-4/69],[7/46,5/46,-1/46,-7/46],[37/138,-101/138,1/2,
-53/138],[-19/138,-7/138,1/46,5/138],[-32/69,11/23,-5/69,
-28/69],[-1/3,-1/23,-5/69,11/69],[6/23,1/69,2/69,-7/69],[
-1/138,3/46,-1/138,13/138],[-5/138,-5/138,27/46,1/138],[
-35/138,-1/138,77/138,-19/46],[1/23,-29/69,8/69,20/69],[
-3/46,17/46,-25/46,15/46],[-1/69,7/69,-17/69,-1/23],[-13/69,
13/69,-5/69,-3/23],[20/69,-14/69,-50/69,6/23],[-17/69,
-16/69,38/69,-13/23],[0,0,0,0],[37/138,-47/138,5/46,43/138
],[-65/138,107/138,-25/138,-27/46],[-1/23,14/23,-16/23,11/23
],[47/138,-19/46,11/138,31/138],[32/69,-22/69,4/23,14/69],[
-7/46,41/138,-41/138,13/138],[-31/138,-1/46,-7/138,1/138],[
41/138,-61/138,7/46,-1/138],[1/69,-4/69,2/69,2/23],[-53/138,
7/138,-1/46,-11/138],[2/23,4/69,-1/69,5/69],[7/23,7/69,
-1/69,-7/69],[-11/138,-31/138,95/138,-19/46],[-2/69,4/23,
28/69,20/69],[-17/69,-5/69,13/23,-35/69],[5/138,-17/138,
1/138,5/46],[9/46,-41/138,-7/138,5/138],[1/46,49/138,
-49/138,65/138],[-10/23,20/69,-8/69,-17/69],[3/46,11/138,
-71/138,31/138],[1/138,-3/46,1/138,-13/138],[0,0,0,0],[
-7/46,-5/46,1/46,7/46],[-1/23,29/69,-8/69,-20/69],[4/23,
-4/69,10/69,4/69],[32/69,-11/23,5/69,28/69],[1/3,1/23,5/69,
-11/69],[5/138,5/138,-27/46,-1/138],[-16/69,10/23,-4/69,
-26/69],[3/46,-17/46,25/46,-15/46],[35/138,-55/138,7/46,
41/138],[13/69,-13/69,5/69,3/23],[-6/23,-1/69,-2/69,7/69],
[19/138,7/138,-1/46,-5/138],[-5/138,-31/138,47/138,-13/46],[
1/69,-7/69,17/69,1/23],[-65/138,7/138,35/46,-83/138],[-1/23,
2/69,-2/69,-5/69],[11/69,-2/23,8/69,13/69],[-37/138,101/138,
-1/2,53/138],[-89/138,29/138,-19/138,-7/46],[5/23,-4/23,
-6/23,-1/23],[-10/69,-14/69,16/69,-7/23],[4/23,35/69,-1/3,
34/69],[-11/46,25/138,-49/138,29/138],[-13/69,31/69,-14/69,
-4/23],[14/69,10/69,-20/69,4/23],[31/138,-17/138,11/46,
61/138],[2/23,19/69,-10/69,-13/69],[-14/69,8/69,-34/69,6/23
],[5/46,31/138,-55/138,17/138],[9/46,-55/138,49/138,-53/138
],[-2/69,-3/23,19/69,-13/69],[-11/69,16/69,-2/23,7/69],[
-11/138,-1/138,-37/138,-1/46],[2/23,-11/69,17/69,-22/69],[
49/69,-31/69,26/69,0],[-17/138,17/138,1/6,7/46],[-32/69,
-1/23,31/69,-16/69],[-2/23,-8/23,12/23,-2/23],[32/69,-47/69,
-8/69,11/23],[31/138,5/138,-1/138,11/46],[-56/69,22/69,4/23,
-56/69],[2/69,-4/23,-28/69,-20/69],[-1/46,-49/138,49/138,
-65/138],[0,0,0,0],[-7/23,-7/69,1/69,7/69],[-32/69,
22/69,-4/23,-14/69],[17/69,16/69,-38/69,13/23],[65/138,
-107/138,25/138,27/46],[31/138,1/46,7/138,-1/138],[11/138,
31/138,-95/138,19/46],[-1/69,4/69,-2/69,-2/23],[1/23,-14/23,
16/23,-11/23],[10/23,-20/69,8/69,17/69],[-5/138,17/138,
-1/138,-5/46],[-47/138,19/46,-11/138,-31/138],[53/138,-7/138,
1/46,11/138],[-41/138,61/138,-7/46,1/138],[1/138,-5/138,
11/46,19/138],[-20/69,14/69,50/69,-6/23],[-2/23,-4/69,1/69,
-5/69],[7/46,-41/138,41/138,-13/138],[17/69,5/69,-13/23,
35/69],[-37/138,47/138,-5/46,-43/138],[-25/138,-7/46,5/138,
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11/138,61/138,-47/138],[-6/23,-16/69,16/69,-20/69],[-14/69,
-5/69,3/23,22/69],[1/69,-38/69,8/23,-11/69],[-11/46,11/138,
37/138,-83/138],[-9/46,-25/138,37/138,-17/138],[-43/138,
21/46,-67/138,-5/138],[133/138,-13/46,-1/6,65/138],[-29/138,
49/138,-17/46,-53/138],[25/138,5/138,-13/138,5/46],[-1/46,
37/138,-13/138,11/138],[3/46,-19/138,-17/138,7/138],[-17/138,
9/46,-1/6,-13/138],[37/138,-11/46,-1/6,-1/138],[5/23,1/3,
16/69,4/69],[-7/138,-1/46,35/138,-41/138],[-4/69,2/23,-7/69,
13/69],[-9/23,2/23,6/23,-15/23],[-11/46,-15/46,11/46,-9/46
],[-14/69,4/69,-6/23,-14/69],[4/23,35/69,-1/3,34/69],[
-1/46,37/138,-67/138,5/138],[-53/138,7/46,67/138,-55/138],[
-14/69,16/69,4/23,10/69],[19/69,-29/69,4/23,40/69],[10/69,
-40/69,26/69,-5/23],[6/23,-19/69,37/69,-8/69],[-11/138,
11/138,-7/138,13/46],[-67/138,11/138,7/46,-73/138],[31/69,
-2/23,-14/69,1/3],[-3/23,13/23,-12/23,-2/23],[-17/69,8/69,
-10/69,3/23],[4/23,7/69,-7/69,14/69],[65/69,-12/23,-1/69,
22/69],[-5/69,16/69,-8/23,10/69],[-3/23,-7/69,-17/69,-5/69
],[25/138,-7/138,41/138,-13/46],[-11/138,-35/138,19/46,
-77/138],[-19/138,35/138,-9/46,53/138],[-2/69,19/69,-4/23,
16/69],[-5/69,-22/69,29/69,-15/23],[-6/23,22/69,-13/69,14/69
],[25/23,-21/23,0,21/23],[0,-2/69,-19/69,-10/69],[-41/138,
-5/138,29/46,-95/138],[-31/138,9/46,-25/138,43/138],[-5/138,
-3/46,43/138,-19/138],[5/23,-16/23,13/23,-13/23],[17/138,
37/138,-1/6,13/46],[-25/138,1/6,-7/46,53/138],[-31/69,35/69,
-6/23,5/69],[4/23,-2/23,-3/23,-2/23],[-37/138,85/138,
-41/138,1/46],[-1/23,-2/69,5/69,-19/69],[-7/138,5/138,3/46,
-25/138],[7/46,-15/46,1/46,-11/46],[-1/69,5/23,-10/69,22/69
],[-1/138,-11/46,-13/138,-59/138],[9/46,41/138,-17/138,31/138
]])
]> where w := K.1 where K := ext<K|Polynomial(K, [1, 0, 0, 0, 1])> where K is 
RationalField();

return _LR;
