X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_element_subalgebra.py;h=dceb3b405a4c5a663c61a966993ce890ed516b49;hb=4c8f9aac69d1cb4097b60b10e5b198b6372ec55e;hp=7edf1df940fb3e16435eb7d232fea0ceb58eff7a;hpb=795ac83cd78143e36d47fa267fe6ddf1ca8da111;p=sage.d.git diff --git a/mjo/eja/eja_element_subalgebra.py b/mjo/eja/eja_element_subalgebra.py index 7edf1df..dceb3b4 100644 --- a/mjo/eja/eja_element_subalgebra.py +++ b/mjo/eja/eja_element_subalgebra.py @@ -2,24 +2,20 @@ from sage.matrix.constructor import matrix from sage.misc.cachefunc import cached_method from sage.rings.all import QQ -from mjo.eja.eja_subalgebra import FiniteDimensionalEuclideanJordanSubalgebra +from mjo.eja.eja_subalgebra import FiniteDimensionalEJASubalgebra -class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclideanJordanSubalgebra): - def __init__(self, elt, orthonormalize_basis): - self._superalgebra = elt.parent() - category = self._superalgebra.category().Associative() - V = self._superalgebra.vector_space() - field = self._superalgebra.base_ring() +class FiniteDimensionalEJAElementSubalgebra(FiniteDimensionalEJASubalgebra): + def __init__(self, elt, orthonormalize=True, **kwargs): + superalgebra = elt.parent() - # 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()) ] - power_vectors = [ p.to_vector() for p in powers ] - P = matrix(field, power_vectors) + 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 == False: + 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 @@ -29,39 +25,26 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide # Beware: QQ supports an entirely different set of "algorithm" # keywords than do AA and RR. algo = None - if field is not QQ: + if superalgebra.base_ring() is not QQ: algo = "scaled_partial_pivoting" - P.echelonize(algorithm=algo) + 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. + # 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() + # Figure out which powers form a linearly-independent set. + ind_rows = P.pivot_rows() - # Pick those out of the list of all powers. - superalgebra_basis = tuple(map(powers.__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. If this - # looks like a roundabout way to orthonormalize, it is. - # But converting everything from algebra elements to vectors - # to matrices and then back again turns out to be about - # as fast as reimplementing our own Gram-Schmidt that - # works in an EJA. - G,_ = P.gram_schmidt(orthonormal=True) - basis_vectors = [ g for g in G.rows() if not g.is_zero() ] - superalgebra_basis = [ self._superalgebra.from_vector(b) - for b in basis_vectors ] - - fdeja = super(FiniteDimensionalEuclideanJordanElementSubalgebra, self) - fdeja.__init__(self._superalgebra, - superalgebra_basis, - category=category, - check_axioms=False) + # Pick those out of the list of all powers. + basis = tuple(map(powers.__getitem__, ind_rows)) + + + super().__init__(superalgebra, + basis, + associative=True, + **kwargs) # The rank is the highest possible degree of a minimal # polynomial, and is bounded above by the dimension. We know