"""
Return the matrix space in which this algebra's natural basis
elements live.
+
+ Generally this will be an `n`-by-`1` column-vector space,
+ except when the algebra is trivial. There it's `n`-by-`n`
+ (where `n` is zero), to ensure that two elements of the
+ natural basis space (empty matrices) can be multiplied.
"""
- if self._natural_basis is None or len(self._natural_basis) == 0:
+ if self.is_trivial():
+ return MatrixSpace(self.base_ring(), 0)
+ elif self._natural_basis is None or len(self._natural_basis) == 0:
return MatrixSpace(self.base_ring(), self.dimension(), 1)
else:
return self._natural_basis[0].matrix_space()
# there's only one.
return cls(field)
- n = ZZ.random_element(cls._max_test_case_size()) + 1
+ n = ZZ.random_element(cls._max_test_case_size() + 1)
return cls(n, field, **kwargs)
@cached_method
return x.to_vector().inner_product(y.to_vector())
-def random_eja(field=AA, nontrivial=False):
+def random_eja(field=AA):
"""
Return a "random" finite-dimensional Euclidean Jordan Algebra.
Euclidean Jordan algebra of dimension...
"""
- eja_classes = [HadamardEJA,
- JordanSpinEJA,
- RealSymmetricEJA,
- ComplexHermitianEJA,
- QuaternionHermitianEJA]
- if not nontrivial:
- eja_classes.append(TrivialEJA)
- classname = choice(eja_classes)
+ classname = choice([TrivialEJA,
+ HadamardEJA,
+ JordanSpinEJA,
+ RealSymmetricEJA,
+ ComplexHermitianEJA,
+ QuaternionHermitianEJA])
return classname.random_instance(field=field)
-
-
class MatrixEuclideanJordanAlgebra(FiniteDimensionalEuclideanJordanAlgebra):
@staticmethod
def _max_test_case_size():