# in the "normal" case without us having to think about it.
return self.operator().minimal_polynomial()
- A = self.subalgebra_generated_by(orthonormalize_basis=False)
+ A = self.subalgebra_generated_by(orthonormalize=False)
return A(self).operator().minimal_polynomial()
[(0, f2), (1, f0)]
"""
- A = self.subalgebra_generated_by(orthonormalize_basis=True)
+ A = self.subalgebra_generated_by(orthonormalize=True)
result = []
for (evalue, proj) in A(self).operator().spectral_decomposition():
result.append( (evalue, proj(A.one()).superalgebra_element()) )
class FiniteDimensionalEJAElementSubalgebra(FiniteDimensionalEJASubalgebra):
- def __init__(self, elt, orthonormalize=True, **kwargs):
+ def __init__(self, elt, **kwargs):
superalgebra = elt.parent()
# TODO: going up to the superalgebra dimension here is
sage: J.one()
e0 + e1 + e2 + e3 + e4
sage: x = sum(J.gens())
- sage: A = x.subalgebra_generated_by()
+ sage: A = x.subalgebra_generated_by(orthonormalize=False)
sage: A.one()
f0
sage: A.one().superalgebra_element()
sage: set_random_seed()
sage: x = random_eja().random_element()
- sage: A = x.subalgebra_generated_by(orthonormalize_basis=True)
+ sage: A = x.subalgebra_generated_by()
sage: x = A.random_element()
sage: A.one()*x == x and x*A.one() == x
True
sage: set_random_seed()
sage: x = random_eja(field=QQ,orthonormalize=False).random_element()
- sage: A = x.subalgebra_generated_by()
+ sage: A = x.subalgebra_generated_by(orthonormalize=False)
sage: actual = A.one().operator().matrix()
sage: expected = matrix.identity(A.base_ring(), A.dimension())
sage: actual == expected
sage: set_random_seed()
sage: x = random_eja().random_element()
- sage: A = x.subalgebra_generated_by(orthonormalize_basis=True)
+ sage: A = x.subalgebra_generated_by()
sage: actual = A.one().operator().matrix()
sage: expected = matrix.identity(A.base_ring(), A.dimension())
sage: actual == expected
the same as its matrix representation in the superalgebra::
sage: set_random_seed()
- sage: x = random_eja(field=QQ).random_element()
+ sage: x = random_eja(field=QQ,orthonormalize=False).random_element()
sage: A = x.subalgebra_generated_by(orthonormalize=False)
sage: y = A.random_element()
sage: actual = y.to_matrix()