Ditto for the quaternions::
- sage: J = QuaternionHermitianEJA(3)
+ sage: J = QuaternionHermitianEJA(2)
sage: J.one().inner_product(J.one())
- 3
+ 2
TESTS:
::
sage: set_random_seed()
- sage: J1 = ComplexHermitianEJA(3)
- sage: J2 = ComplexHermitianEJA(3,field=QQ,orthonormalize=False)
- sage: X = matrix.random(GaussianIntegers(),3)
+ sage: J1 = ComplexHermitianEJA(2)
+ sage: J2 = ComplexHermitianEJA(2,field=QQ,orthonormalize=False)
+ sage: X = matrix.random(GaussianIntegers(), 2)
sage: X = X + X.H
sage: expected = AA(X.det())
sage: actual1 = J1(J1.real_embed(X)).det()
::
- sage: J = QuaternionHermitianEJA(3)
+ sage: J = QuaternionHermitianEJA(2)
sage: J.one()
- e0 + e5 + e14
+ e0 + e5
sage: J.one().to_matrix()
- [1 0 0 0 0 0 0 0 0 0 0 0]
- [0 1 0 0 0 0 0 0 0 0 0 0]
- [0 0 1 0 0 0 0 0 0 0 0 0]
- [0 0 0 1 0 0 0 0 0 0 0 0]
- [0 0 0 0 1 0 0 0 0 0 0 0]
- [0 0 0 0 0 1 0 0 0 0 0 0]
- [0 0 0 0 0 0 1 0 0 0 0 0]
- [0 0 0 0 0 0 0 1 0 0 0 0]
- [0 0 0 0 0 0 0 0 1 0 0 0]
- [0 0 0 0 0 0 0 0 0 1 0 0]
- [0 0 0 0 0 0 0 0 0 0 1 0]
- [0 0 0 0 0 0 0 0 0 0 0 1]
+ [1 0 0 0 0 0 0 0]
+ [0 1 0 0 0 0 0 0]
+ [0 0 1 0 0 0 0 0]
+ [0 0 0 1 0 0 0 0]
+ [0 0 0 0 1 0 0 0]
+ [0 0 0 0 0 1 0 0]
+ [0 0 0 0 0 0 1 0]
+ [0 0 0 0 0 0 0 1]
+
"""
B = self.parent().matrix_basis()
W = self.parent().matrix_space()