- # 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)