quadric_space.ipynb

Kernel: SageMath 10.3

%run '/home/user/Equivariant_Vector_Bundles_On_Homogeneous_Varieties__0-0-1/src/Initialize.ipynb'

from IPython.display import clear_output , display , HTML

X = Quadric_Space(7)
print( 'X:' , X )
print()

for Counter , ( WeylElement , ReducedDescription ) in enumerate( X.Weyl_Group_Coset_Representatives_Of_Minimal_Length() , start=1 ) :
    print( 'Counter='+str(Counter) )
    print( 'Weyl group element ...' )
    print( 3*' ' , '... as matrix:' )
    for Line in str(WeylElement).split('\n') :
        print( 6*' ' , Line )
    print( 3*' ' , '... as reduced word:' )
    print( 6*' ' , ReducedDescription )
    print()

X: Quadric space of dimension 7.

Counter=1
Weyl group element ...
    ... as matrix:
       [1 0 0 0]
       [0 1 0 0]
       [0 0 1 0]
       [0 0 0 1]
    ... as reduced word:
       []

Counter=2
Weyl group element ...
    ... as matrix:
       [0 1 0 0]
       [1 0 0 0]
       [0 0 1 0]
       [0 0 0 1]
    ... as reduced word:
       [1]

Counter=3
Weyl group element ...
    ... as matrix:
       [0 0 1 0]
       [1 0 0 0]
       [0 1 0 0]
       [0 0 0 1]
    ... as reduced word:
       [1, 2]

Counter=4
Weyl group element ...
    ... as matrix:
       [0 0 0 1]
       [1 0 0 0]
       [0 1 0 0]
       [0 0 1 0]
    ... as reduced word:
       [1, 2, 3]

Counter=5
Weyl group element ...
    ... as matrix:
       [ 0  0  0 -1]
       [ 1  0  0  0]
       [ 0  1  0  0]
       [ 0  0  1  0]
    ... as reduced word:
       [1, 2, 3, 4]

Counter=6
Weyl group element ...
    ... as matrix:
       [ 0  0 -1  0]
       [ 1  0  0  0]
       [ 0  1  0  0]
       [ 0  0  0  1]
    ... as reduced word:
       [1, 2, 3, 4, 3]

Counter=7
Weyl group element ...
    ... as matrix:
       [ 0 -1  0  0]
       [ 1  0  0  0]
       [ 0  0  1  0]
       [ 0  0  0  1]
    ... as reduced word:
       [1, 2, 3, 4, 3, 2]

Counter=8
Weyl group element ...
    ... as matrix:
       [-1  0  0  0]
       [ 0  1  0  0]
       [ 0  0  1  0]
       [ 0  0  0  1]
    ... as reduced word:
       [1, 2, 3, 4, 3, 2, 1]