matrices do not contain the superalgebra's identity element::
sage: J = RealSymmetricEJA(2)
- sage: E11 = matrix(QQ, [ [1,0],
+ sage: E11 = matrix(AA, [ [1,0],
....: [0,0] ])
- sage: E22 = matrix(QQ, [ [0,0],
+ sage: E22 = matrix(AA, [ [0,0],
....: [0,1] ])
sage: K1 = FiniteDimensionalEuclideanJordanSubalgebra(J, (J(E11),))
sage: K1.one().natural_representation()
1
"""
- def __init__(self, superalgebra, basis, rank=None, category=None):
+ def __init__(self, superalgebra, basis, category=None):
self._superalgebra = superalgebra
V = self._superalgebra.vector_space()
field = self._superalgebra.base_ring()
fdeja = super(FiniteDimensionalEuclideanJordanSubalgebra, self)
- return fdeja.__init__(field,
- mult_table,
- rank,
- prefix=prefix,
- category=category,
- natural_basis=natural_basis)
+ fdeja.__init__(field,
+ mult_table,
+ prefix=prefix,
+ category=category,
+ natural_basis=natural_basis)
EXAMPLES::
sage: J = RealSymmetricEJA(3)
- sage: X = matrix(QQ, [ [0,0,1],
+ sage: X = matrix(AA, [ [0,0,1],
....: [0,1,0],
....: [1,0,0] ])
sage: x = J(X)
if elt not in self.superalgebra():
raise ValueError("not an element of this subalgebra")
- coords = self.vector_space().coordinate_vector(elt.to_vector())
- return self.from_vector(coords)
+ # The extra hackery is because foo.to_vector() might not
+ # live in foo.parent().vector_space()!
+ coords = sum( a*b for (a,b)
+ in zip(elt.to_vector(),
+ self.superalgebra().vector_space().basis()) )
+ return self.from_vector(self.vector_space().coordinate_vector(coords))
EXAMPLES::
sage: J = RealSymmetricEJA(3)
- sage: E11 = matrix(QQ, [ [1,0,0],
+ sage: E11 = matrix(ZZ, [ [1,0,0],
....: [0,0,0],
....: [0,0,0] ])
- sage: E22 = matrix(QQ, [ [0,0,0],
+ sage: E22 = matrix(ZZ, [ [0,0,0],
....: [0,1,0],
....: [0,0,0] ])
sage: b1 = J(E11)