Magma V2.13-10    Mon Mar 17 2008 20:09:17 on Macintosh [Seed = 1405813307]
Type ? for help.  Type <Ctrl>-D to quit.
> load "G2.mag";
Loading "G2.mag"


c =  
[ 0  0  0  0  t  0  0]
[-t  0  0  0  0  0  0]
[ 0  0  0  0  0  0  0]
[ 0  0  0  0  0  0  0]
[ 0  0  0  0  0  0  0]
[ 0  0  0 -1  0  0  0]
[ 0  0  1  0  0  0  0]


d =  
[ 0  0  0  t  0  0  0]
[ 0  0  0  0  0 -1  0]
[ 0  0  0  0  1  0  0]
[ 0  0  0  0  0  0  0]
[ 0  0  0  0  0  0  0]
[ 0  0  0  0  0  0  0]
[-t  0  0  0  0  0  0]


ab-ba = -c true
ac-ca = -2d true
ad-da = -3e true
ae-ea = 0 true
af-fa = 0 true 

bc-cb = 0 true
bd-db = 0 true
be-eb = f true
bf-fb = 0 true 

cd-dc = -3f true
ce-ec = 0 true
cf-fc = 0 true 

de-ed = 0 true
df-fd = 0 true 

ef-fe = 0 true 

fa is not 0 true
fb = 0 true 

h1 a - a h1 = -a true
h1 b - b h1 = 2b true

h2 a - a h2 = a true
h2 b - b h2 = -b true

h3 a - a h3 = 0 true
h3 b - b h3 = -b true

dim V [N,N] = 5
basis of V [N,N] [
    (1 0 0 0 0 0 0),
    (0 0 1 0 0 0 0),
    (0 0 0 1 0 0 0),
    (0 0 0 0 1 0 0),
    (0 0 0 0 0 1 0)
]


dim V N_a =  6
dim W N_a=  4
dim (W N_a + W h1) =  6
dim (W N_a + W h2) =  5
dim (W N_a + W h3) =  5 

dim V N_b =  5
basis of V N_b [
    (1 0 0 0 0 0 0),
    (0 0 1 0 0 0 0),
    (0 0 0 1 0 0 0),
    (0 0 0 0 1 0 0),
    (0 0 0 0 0 1 0)
]


basis of W1 [
    (1 0 0 0 0 0 0),
    (0 1 0 0 0 0 0),
    (0 0 1 0 0 0 0),
    (0 0 0 1 0 0 0),
    (0 0 0 0 1 0 0),
    (0 0 0 0 0 1 0)
]
dim W1 N_b =  5 

basis of W2 [
    (1 0 0 0 0 0 0),
    (0 0 1 0 0 0 0),
    (0 0 0 1 0 0 0),
    (0 0 0 0 1 0 0),
    (0 0 0 0 0 1 0),
    (0 0 0 0 0 0 1)
]
dim W2 N_b =  5 

dim V N_b N_b =  2
basis of V N_b N_b [
    (0 0 0 1 0 0 0),
    (0 0 0 0 1 0 0)
]
>