- n = len(superalgebra_basis)
- mult_table = [[W.zero() for i in range(n)] for j in range(n)]
- for i in range(n):
- for j in range(n):
- product = superalgebra_basis[i]*superalgebra_basis[j]
- # product.to_vector() might live in a vector subspace
- # if our parent algebra is already a subalgebra. We
- # use V.from_vector() to make it "the right size" in
- # that case.
- product_vector = V.from_vector(product.to_vector())
- mult_table[i][j] = W.coordinate_vector(product_vector)
-
- natural_basis = tuple( b.natural_representation()
- for b in superalgebra_basis )
-
-
- self._vector_space = W
-
- fdeja = super(FiniteDimensionalEuclideanJordanSubalgebra, self)
- fdeja.__init__(field,
- mult_table,
- prefix=prefix,
- category=category,
- natural_basis=natural_basis,
- check_field=False,
- check_axioms=check_axioms)