from sage.matrix.constructor import matrix
+from sage.rings.all import QQ
from mjo.eja.eja_subalgebra import FiniteDimensionalEuclideanJordanSubalgebra
P = matrix(field, power_vectors)
if orthonormalize_basis == False:
+ # 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 field 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
# 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
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,
# polynomial has the same degree as the space's dimension
# (remember how we constructed the space?), so that must be
# its rank too.
- self.rank.set_cache(W.dimension())
-
-
- def _a_regular_element(self):
- """
- Override the superalgebra method to return the one
- regular element that is sure to exist in this
- subalgebra, namely the element that generated it.
-
- SETUP::
-
- sage: from mjo.eja.eja_algebra import random_eja
-
- TESTS::
-
- sage: set_random_seed()
- sage: J = random_eja().random_element().subalgebra_generated_by()
- sage: J._a_regular_element().is_regular()
- True
-
- """
- if self.dimension() == 0:
- return self.zero()
- else:
- return self.monomial(1)
+ self.rank.set_cache(self.dimension())
def one(self):