- powers = tuple( elt**k for k in range(superalgebra.dimension()) )
- power_vectors = ( p.to_vector() for p in powers )
- P = matrix(superalgebra.base_ring(), power_vectors)
-
- if orthonormalize:
- basis = powers # let god sort 'em out
- else:
- # Echelonize the matrix ourselves, because otherwise the
- # call to P.pivot_rows() below can choose a non-optimal
- # row-reduction algorithm. In particular, scaling can
- # help over AA because it avoids the RecursionError that
- # gets thrown when we have to look too hard for a root.
- #
- # Beware: QQ supports an entirely different set of "algorithm"
- # keywords than do AA and RR.
- algo = None
- if superalgebra.base_ring() is not QQ:
- algo = "scaled_partial_pivoting"
- P.echelonize(algorithm=algo)
-
- # 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.
-
- # Figure out which powers form a linearly-independent set.
- ind_rows = P.pivot_rows()
-
- # Pick those out of the list of all powers.
- basis = tuple(map(powers.__getitem__, ind_rows))
-
+ # TODO: going up to the superalgebra dimension here is
+ # overkill. We should append p vectors as rows to a matrix
+ # and continually rref() it until the rank stops going
+ # up. When n=10 but the dimension of the algebra is 1, that
+ # can save a shitload of time (especially over AA).
+ powers = tuple( elt**k for k in range(elt.degree()) )