We can convert back and forth faithfully::
sage: set_random_seed()
- sage: J = random_eja()
+ sage: J = random_eja(field=QQ, orthonormalize=False)
sage: x = J.random_element()
- sage: A = x.subalgebra_generated_by()
+ sage: A = x.subalgebra_generated_by(orthonormalize=False)
sage: A(x).superalgebra_element() == x
True
sage: y = A.random_element()
sage: A(y.superalgebra_element()) == y
True
- sage: B = y.subalgebra_generated_by()
+ sage: B = y.subalgebra_generated_by(orthonormalize=False)
sage: B(y).superalgebra_element() == y
True
....: [0,0] ])
sage: E22 = matrix(AA, [ [0,0],
....: [0,1] ])
- sage: K1 = FiniteDimensionalEJASubalgebra(J, (J(E11),))
+ sage: K1 = FiniteDimensionalEJASubalgebra(J, (J(E11),), associative=True)
sage: K1.one().to_matrix()
[1 0]
[0 0]
- sage: K2 = FiniteDimensionalEJASubalgebra(J, (J(E22),))
+ sage: K2 = FiniteDimensionalEJASubalgebra(J, (J(E22),), associative=True)
sage: K2.one().to_matrix()
[0 0]
[0 1]
super().__init__(matrix_basis,
jordan_product,
inner_product,
+ field=field,
prefix=prefix,
**kwargs)
....: [1,0,0] ])
sage: x = J(X)
sage: basis = ( x, x^2 ) # x^2 is the identity matrix
- sage: K = FiniteDimensionalEJASubalgebra(J, basis, orthonormalize=False)
+ sage: K = FiniteDimensionalEJASubalgebra(J,
+ ....: basis,
+ ....: associative=True,
+ ....: orthonormalize=False)
sage: K(J.one())
f1
sage: K(J.one() + x)