- 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)
-
- # 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)
-
- # 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))
-