field = superalgebra.base_ring()
mult_table = []
for b_right in superalgebra_basis:
- b_right_rows = []
- # The first row of the right-multiplication matrix by
+ 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 row of the right multiplication matrix by b1
+ # second column of the left-multiplication matrix by b1
# is what we get when we apply that matrix to b2...
- #
- # IMPORTANT: this assumes that all vectors are COLUMN
- # vectors, unlike our superclass (which uses row vectors).
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_row = W.coordinates((b_left*b_right).to_vector())
- b_right_rows.append(this_row)
- b_right_matrix = matrix(field, b_right_rows)
+ 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: