-from mjo.eja.eja_subalgebra import FiniteDimensionalEuclideanJordanSubalgebra
-
-
-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()
-
- # 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)
-
- if orthonormalize_basis == False:
- # 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.
- superalgebra_basis = tuple(map(powers.__getitem__, ind_rows))
-
- # If our superalgebra is a subalgebra of something else, then
- # these vectors won't have the right coordinates for
- # V.span_of_basis() unless we use V.from_vector() on them.
- basis_vectors = map(power_vectors.__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 ]
-
- W = V.span_of_basis( V.from_vector(v) for v in basis_vectors )
-
- fdeja = super(FiniteDimensionalEuclideanJordanElementSubalgebra, self)
- fdeja.__init__(self._superalgebra,
- superalgebra_basis,
- category=category)
+from mjo.eja.eja_subalgebra import FiniteDimensionalEJASubalgebra
+
+
+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(elt.degree()) )
+
+ super().__init__(superalgebra,
+ powers,
+ associative=True,
+ **kwargs)