# matrix for the successive basis elements b0, b1,... of
# that subspace.
field = superalgebra.base_ring()
- mult_table = []
- for b_right in superalgebra_basis:
- b_right_cols = []
- # The first column of the left-multiplication matrix by
- # b1 is what we get if we apply that matrix to b1. The
- # second column of the left-multiplication matrix by b1
- # is what we get when we apply that matrix to b2...
- for b_left in superalgebra_basis:
- # Multiply in the original EJA, but then get the
- # coordinates from the subalgebra in terms of its
- # basis.
- this_col = W.coordinates((b_left*b_right).to_vector())
- b_right_cols.append(this_col)
- b_right_matrix = matrix.column(field, b_right_cols)
- mult_table.append(b_right_matrix)
-
- for m in mult_table:
- m.set_immutable()
- mult_table = tuple(mult_table)
+ n = len(superalgebra_basis)
+ mult_table = [[W.zero() for i in range(n)] for j in range(n)]
+ for i in range(n):
+ for j in range(n):
+ product = superalgebra_basis[i]*superalgebra_basis[j]
+ mult_table[i][j] = W.coordinate_vector(product.to_vector())
# TODO: We'll have to redo this and make it unique again...
prefix = 'f'