- # This list is guaranteed to contain all independent powers,
- # because it's the maximal set of powers that could possibly
- # be independent (by a dimension argument).
- powers = [ elt**k for k in range(V.dimension()) ]
-
- if orthonormalize_basis == False:
- # In this case, we just need to figure out which elements
- # of the "powers" list are redundant... First compute the
- # vector subspace spanned by the powers of the given
- # element.
- power_vectors = [ p.to_vector() for p in powers ]
-
- # Figure out which powers form a linearly-independent set.
- ind_rows = matrix(field, power_vectors).pivot_rows()
-
- # Pick those out of the list of all powers.
- superalgebra_basis = tuple(map(powers.__getitem__, ind_rows))
-
- # If our superalgebra is a subalgebra of something else, then
- # these vectors won't have the right coordinates for
- # V.span_of_basis() unless we use V.from_vector() on them.
- basis_vectors = map(power_vectors.__getitem__, ind_rows)
- else:
- # If we're going to orthonormalize the basis anyway, we
- # might as well just do Gram-Schmidt on the whole list of
- # powers. The redundant ones will get zero'd out.
- superalgebra_basis = gram_schmidt(powers)
- basis_vectors = [ b.to_vector() for b in superalgebra_basis ]
-
- W = V.span_of_basis( V.from_vector(v) for v in basis_vectors )
- n = len(superalgebra_basis)
+ # If our superalgebra is a subalgebra of something else, then
+ # these vectors won't have the right coordinates for
+ # V.span_of_basis() unless we use V.from_vector() on them.
+ W = V.span_of_basis( V.from_vector(b.to_vector()) for b in basis )
+
+ n = len(basis)