- sage: from mjo.eja.eja_algebra import (RealCartesianProductEJA,
- ....: random_eja)
-
- EXAMPLES::
-
- sage: J = RealCartesianProductEJA(5)
- sage: J.one()
- e0 + e1 + e2 + e3 + e4
- sage: x = sum(J.gens())
- sage: A = x.subalgebra_generated_by()
- sage: A.one()
- f0
- sage: A.one().superalgebra_element()
- e0 + e1 + e2 + e3 + e4
-
- TESTS:
-
- The identity element acts like the identity::
-
- sage: set_random_seed()
- sage: J = random_eja().random_element().subalgebra_generated_by()
- sage: x = J.random_element()
- sage: J.one()*x == x and x*J.one() == x
- True
-
- The matrix of the unit element's operator is the identity::
-
- sage: set_random_seed()
- sage: J = random_eja().random_element().subalgebra_generated_by()
- sage: actual = J.one().operator().matrix()
- sage: expected = matrix.identity(J.base_ring(), J.dimension())
- sage: actual == expected
- True
- """
- if self.dimension() == 0:
- return self.zero()
- else:
- return self.monomial(self.one_basis())