SETUP::
sage: from mjo.eja.eja_algebra import (ComplexHermitianEJA,
- ....: JordanSpinEJA)
+ ....: JordanSpinEJA,
+ ....: RealSymmetricEJA)
+ sage: from mjo.eja.eja_subalgebra import FiniteDimensionalEuclideanJordanSubalgebra
+
+ EXAMPLES:
+
+ The following Peirce subalgebras of the 2-by-2 real symmetric
+ matrices do not contain the superalgebra's identity element::
+
+ sage: J = RealSymmetricEJA(2)
+ sage: E11 = matrix(AA, [ [1,0],
+ ....: [0,0] ])
+ sage: E22 = matrix(AA, [ [0,0],
+ ....: [0,1] ])
+ sage: K1 = FiniteDimensionalEuclideanJordanSubalgebra(J, (J(E11),))
+ sage: K1.one().natural_representation()
+ [1 0]
+ [0 0]
+ sage: K2 = FiniteDimensionalEuclideanJordanSubalgebra(J, (J(E22),))
+ sage: K2.one().natural_representation()
+ [0 0]
+ [0 1]
TESTS:
EXAMPLES::
sage: J = RealSymmetricEJA(3)
- sage: X = matrix(QQ, [ [0,0,1],
+ sage: X = matrix(AA, [ [0,0,1],
....: [0,1,0],
....: [1,0,0] ])
sage: x = J(X)
EXAMPLES::
sage: J = RealSymmetricEJA(3)
- sage: E11 = matrix(QQ, [ [1,0,0],
+ sage: E11 = matrix(ZZ, [ [1,0,0],
....: [0,0,0],
....: [0,0,0] ])
- sage: E22 = matrix(QQ, [ [0,0,0],
+ sage: E22 = matrix(ZZ, [ [0,0,0],
....: [0,1,0],
....: [0,0,0] ])
sage: b1 = J(E11)