TESTS::
- The natural representation of an element in the subalgebra is
- the same as its natural representation in the superalgebra::
+ The matrix representation of an element in the subalgebra is
+ the same as its matrix representation in the superalgebra::
sage: set_random_seed()
sage: A = random_eja().random_element().subalgebra_generated_by()
sage: y = A.random_element()
- sage: actual = y.natural_representation()
- sage: expected = y.superalgebra_element().natural_representation()
+ sage: actual = y.to_matrix()
+ sage: expected = y.superalgebra_element().to_matrix()
sage: actual == expected
True
sage: E22 = matrix(AA, [ [0,0],
....: [0,1] ])
sage: K1 = FiniteDimensionalEuclideanJordanSubalgebra(J, (J(E11),))
- sage: K1.one().natural_representation()
+ sage: K1.one().to_matrix()
[1 0]
[0 0]
sage: K2 = FiniteDimensionalEuclideanJordanSubalgebra(J, (J(E22),))
- sage: K2.one().natural_representation()
+ sage: K2.one().to_matrix()
[0 0]
[0 1]
mult_table[i][j] = W.coordinate_vector(product_vector)
self._inner_product_matrix = matrix(field, ip_table)
- natural_basis = tuple( b.natural_representation() for b in basis )
+ matrix_basis = tuple( b.to_matrix() for b in basis )
self._vector_space = W
mult_table,
prefix=prefix,
category=category,
- natural_basis=natural_basis,
+ matrix_basis=matrix_basis,
check_field=False,
check_axioms=check_axioms)
- def natural_basis_space(self):
+ def matrix_space(self):
"""
- Return the natural basis space of this algebra, which is identical
- to that of its superalgebra.
+ Return the matrix space of this algebra, which is identical to
+ that of its superalgebra.
- This is correct "by definition," and avoids a mismatch when the
- subalgebra is trivial (with no natural basis to infer anything
- from) and the parent is not.
+ This is correct "by definition," and avoids a mismatch when
+ the subalgebra is trivial (with no matrix basis elements to
+ infer anything from) and the parent is not.
"""
- return self.superalgebra().natural_basis_space()
+ return self.superalgebra().matrix_space()
def superalgebra(self):