# appeal to the "long vectors" isometry.
oper_vecs = [ _mat2vec(g.operator().matrix()) for g in self.gens() ]
- # Now we use basis linear algebra to find the coefficients,
+ # Now we use basic linear algebra to find the coefficients,
# of the matrices-as-vectors-linear-combination, which should
# work for the original algebra basis too.
- A = matrix.column(self.base_ring(), oper_vecs)
+ A = matrix(self.base_ring(), oper_vecs)
# We used the isometry on the left-hand side already, but we
# still need to do it for the right-hand side. Recall that we
# wanted something that summed to the identity matrix.
b = _mat2vec( matrix.identity(self.base_ring(), self.dimension()) )
- # Now if there's an identity element in the algebra, this should work.
- coeffs = A.solve_right(b)
- return self.linear_combination(zip(self.gens(), coeffs))
+ # Now if there's an identity element in the algebra, this
+ # should work. We solve on the left to avoid having to
+ # transpose the matrix "A".
+ return self.from_vector(A.solve_left(b))
def peirce_decomposition(self, c):
Beware, this will crash for "most instances" because the
constructor below looks wrong.
"""
- if cls is TrivialEJA:
- # The TrivialEJA class doesn't take an "n" argument because
- # there's only one.
- return cls(field)
-
n = ZZ.random_element(cls._max_random_instance_size() + 1)
return cls(n, field, **kwargs)
# largest subalgebra generated by any element.
self.rank.set_cache(0)
+ @classmethod
+ def random_instance(cls, field=AA, **kwargs):
+ # We don't take a "size" argument so the superclass method is
+ # inappropriate for us.
+ return cls(field, **kwargs)
class DirectSumEJA(FiniteDimensionalEuclideanJordanAlgebra):
r"""