- 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))
+ # 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))