SETUP::
sage: from mjo.eja.eja_algebra import (ComplexHermitianEJA,
- ....: QuaternionHermitianEJA)
+ ....: HadamardEJA,
+ ....: QuaternionHermitianEJA,
+ ....: RealSymmetricEJA)
EXAMPLES::
[0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 1]
+ This also works in Cartesian product algebras::
+
+ sage: J1 = HadamardEJA(1)
+ sage: J2 = RealSymmetricEJA(2)
+ sage: J = cartesian_product([J1,J2])
+ sage: x = sum(J.gens())
+ sage: x.to_matrix()[0]
+ [1]
+ sage: x.to_matrix()[1]
+ [ 1 0.7071067811865475?]
+ [0.7071067811865475? 1]
+
"""
B = self.parent().matrix_basis()
W = self.parent().matrix_space()
- # This is just a manual "from_vector()", but of course
- # matrix spaces aren't vector spaces in sage, so they
- # don't have a from_vector() method.
- return W.linear_combination( zip(B, self.to_vector()) )
+ if self.parent()._matrix_basis_is_cartesian:
+ # Aaaaand linear combinations don't work in Cartesian
+ # product spaces, even though they provide a method
+ # with that name.
+ pairs = zip(B, self.to_vector())
+ return sum( ( W(tuple(alpha*b_i for b_i in b))
+ for (b,alpha) in pairs ),
+ W.zero())
+ else:
+ # This is just a manual "from_vector()", but of course
+ # matrix spaces aren't vector spaces in sage, so they
+ # don't have a from_vector() method.
+ return W.linear_combination( zip(B, self.to_vector()) )
SETUP::
- sage: from mjo.eja.eja_algebra import random_eja
+ sage: from mjo.eja.eja_algebra import (random_eja,
+ ....: HadamardEJA,
+ ....: RealSymmetricEJA)
+
+ EXAMPLES:
+
+ We can create subalgebras of Cartesian product EJAs that are not
+ themselves Cartesian product EJAs (they're just "regular" EJAs)::
+
+ sage: J1 = HadamardEJA(3)
+ sage: J2 = RealSymmetricEJA(2)
+ sage: J = cartesian_product([J1,J2])
+ sage: J.one().subalgebra_generated_by()
+ Euclidean Jordan algebra of dimension 1 over Algebraic Real Field
TESTS:
True
"""
- from mjo.eja.eja_subalgebra import FiniteDimensionalEJASubalgebra
powers = tuple( self**k for k in range(self.degree()) )
- A = FiniteDimensionalEJASubalgebra(self.parent(),
- powers,
- associative=True,
- **kwargs)
+ A = self.parent().subalgebra(powers, associative=True, **kwargs)
A.one.set_cache(A(self.parent().one()))
return A
"""
return self.trace_inner_product(self).sqrt()
-
-
-
-class CartesianProductEJAElement(FiniteDimensionalEJAElement):
-
- def to_matrix(self):
- r"""
- SETUP::
-
- sage: from mjo.eja.eja_algebra import (HadamardEJA,
- ....: RealSymmetricEJA)
-
- EXAMPLES::
-
- sage: J1 = HadamardEJA(1)
- sage: J2 = RealSymmetricEJA(2)
- sage: J = cartesian_product([J1,J2])
- sage: x = sum(J.gens())
- sage: x.to_matrix()[0]
- [1]
- sage: x.to_matrix()[1]
- [ 1 0.7071067811865475?]
- [0.7071067811865475? 1]
-
- """
- B = self.parent().matrix_basis()
- W = self.parent().matrix_space()
-
- # Aaaaand linear combinations don't work in Cartesian
- # product spaces, even though they provide a method
- # with that name.
- pairs = zip(B, self.to_vector())
- sigma = W.zero()
- for (b,alpha) in pairs:
- # sum(...) ALSO doesn't work on Cartesian products.
- sigma += W(tuple(alpha*b_i for b_i in b))
- return sigma