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a7b393c)
Orthonormalizing a high-degree element over AA takes roughly forever.
Better that we test *something* than the nothing that gets tested if
I Ctrl-C the process.
sage: x = J.random_element()
sage: J.one()*x == x and x*J.one() == x
True
sage: x = J.random_element()
sage: J.one()*x == x and x*J.one() == x
True
- sage: A = x.subalgebra_generated_by()
+ sage: A = x.subalgebra_generated_by(orthonormalize=False)
sage: y = A.random_element()
sage: A.one()*y == y and y*A.one() == y
True
sage: y = A.random_element()
sage: A.one()*y == y and y*A.one() == y
True
sage: actual == expected
True
sage: x = J.random_element()
sage: actual == expected
True
sage: x = J.random_element()
- sage: A = x.subalgebra_generated_by()
+ sage: A = x.subalgebra_generated_by(orthonormalize=False)
sage: actual = A.one().operator().matrix()
sage: expected = matrix.identity(A.base_ring(), A.dimension())
sage: actual == expected
sage: actual = A.one().operator().matrix()
sage: expected = matrix.identity(A.base_ring(), A.dimension())
sage: actual == expected
Ensure that the determinant is multiplicative on an associative
subalgebra as in Faraut and Korányi's Proposition II.2.2::
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
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()
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
sage: x,y,z = A.random_elements(3)
sage: (x*y)*z == x*(y*z)
True
the superalgebra::
sage: x = random_eja().random_element()
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
sage: A(x^2) == A(x)*A(x)
True