X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_element_subalgebra.py;fp=mjo%2Feja%2Feja_element_subalgebra.py;h=846c13b095cb812edff5c3340c1f0cc8337fe149;hb=de451def1161cc9dfefcfc125523029881cb160a;hp=dceb3b405a4c5a663c61a966993ce890ed516b49;hpb=4c8f9aac69d1cb4097b60b10e5b198b6372ec55e;p=sage.d.git diff --git a/mjo/eja/eja_element_subalgebra.py b/mjo/eja/eja_element_subalgebra.py index dceb3b4..846c13b 100644 --- a/mjo/eja/eja_element_subalgebra.py +++ b/mjo/eja/eja_element_subalgebra.py @@ -9,36 +9,33 @@ class FiniteDimensionalEJAElementSubalgebra(FiniteDimensionalEJASubalgebra): def __init__(self, elt, orthonormalize=True, **kwargs): superalgebra = elt.parent() + # 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(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)) + # 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)) super().__init__(superalgebra,