Ensure that the determinant is multiplicative on an associative
subalgebra as in Faraut and Korányi's Proposition II.2.2::
- sage: J = random_eja().random_element().subalgebra_generated_by()
+ sage: x0 = random_eja().random_element()
+ sage: J = x0.subalgebra_generated_by(orthonormalize=False)
sage: x,y = J.random_elements(2)
sage: (x*y).det() == x.det()*y.det()
True
This subalgebra, being composed of only powers, is associative::
sage: x0 = random_eja().random_element()
- sage: A = x0.subalgebra_generated_by()
+ sage: A = x0.subalgebra_generated_by(orthonormalize=False)
sage: x,y,z = A.random_elements(3)
sage: (x*y)*z == x*(y*z)
True
the superalgebra::
sage: x = random_eja().random_element()
- sage: A = x.subalgebra_generated_by()
+ sage: A = x.subalgebra_generated_by(orthonormalize=False)
sage: A(x^2) == A(x)*A(x)
True