sage: from mjo.eja.eja_operator import FiniteDimensionalEuclideanJordanAlgebraOperator
sage: from mjo.eja.eja_algebra import (
....: JordanSpinEJA,
- ....: RealCartesianProductEJA,
+ ....: HadamardEJA,
....: RealSymmetricEJA)
EXAMPLES::
sage: J1 = JordanSpinEJA(3)
- sage: J2 = RealCartesianProductEJA(2)
+ sage: J2 = HadamardEJA(2)
sage: J3 = RealSymmetricEJA(1)
- sage: mat1 = matrix(QQ, [[1,2,3],
+ sage: mat1 = matrix(AA, [[1,2,3],
....: [4,5,6]])
- sage: mat2 = matrix(QQ, [[7,8]])
+ sage: mat2 = matrix(AA, [[7,8]])
sage: g = FiniteDimensionalEuclideanJordanAlgebraOperator(J1,
....: J2,
....: mat1)
algebras represented by the matrix:
[39 54 69]
Domain: Euclidean Jordan algebra of dimension 3 over
- Rational Field
+ Algebraic Real Field
Codomain: Euclidean Jordan algebra of dimension 1 over
- Rational Field
+ Algebraic Real Field
"""
return FiniteDimensionalEuclideanJordanAlgebraOperator(
[1 0]
[0 1]
Domain: Euclidean Jordan algebra of dimension 2 over
- Rational Field
+ Algebraic Real Field
Codomain: Euclidean Jordan algebra of dimension 2 over
- Rational Field
+ Algebraic Real Field
"""
msg = ("Linear operator between finite-dimensional Euclidean Jordan "
EXAMPLES::
- sage: J = RealSymmetricEJA(4,AA)
+ sage: J = RealSymmetricEJA(4)
sage: x = sum(J.gens())
sage: A = x.subalgebra_generated_by(orthonormalize_basis=True)
sage: L0x = A(x).operator()