X-Git-Url: http://gitweb.michael.orlitzky.com/?p=sage.d.git;a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=2bad32c2f500193e4126b7c5e209c0acb3116ede;hp=af4080b0807d6ac6848849f23edd237657896413;hb=f0cabe7c6e37781e4f92c9ba0e0c7413a5f6b939;hpb=6d6af7c2560b2886cd47a2c8f3c0b9d1b843f649

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index af4080b..2bad32c 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -166,9 +166,10 @@ from sage.modules.free_module import FreeModule, VectorSpace
 from sage.rings.all import (ZZ, QQ, AA, QQbar, RR, RLF, CLF,
                             PolynomialRing,
                             QuadraticField)
-from mjo.eja.eja_element import FiniteDimensionalEJAElement
+from mjo.eja.eja_element import (CartesianProductEJAElement,
+                                 FiniteDimensionalEJAElement)
 from mjo.eja.eja_operator import FiniteDimensionalEJAOperator
-from mjo.eja.eja_utils import _all2list, _mat2vec
+from mjo.eja.eja_utils import _all2list
 
 def EuclideanJordanAlgebras(field):
     r"""
@@ -1281,7 +1282,9 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         #
         # Of course, matrices aren't vectors in sage, so we have to
         # appeal to the "long vectors" isometry.
-        oper_vecs = [ _mat2vec(g.operator().matrix()) for g in self.gens() ]
+
+        V = VectorSpace(self.base_ring(), self.dimension()**2)
+        oper_vecs = [ V(g.operator().matrix().list()) for g in self.gens() ]
 
         # Now we use basic linear algebra to find the coefficients,
         # of the matrices-as-vectors-linear-combination, which should
@@ -1291,7 +1294,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         # We used the isometry on the left-hand side already, but we
         # still need to do it for the right-hand side. Recall that we
         # wanted something that summed to the identity matrix.
-        b = _mat2vec( matrix.identity(self.base_ring(), self.dimension()) )
+        b = V( matrix.identity(self.base_ring(), self.dimension()).list() )
 
         # Now if there's an identity element in the algebra, this
         # should work. We solve on the left to avoid having to
@@ -2045,7 +2048,6 @@ class MatrixEJA(FiniteDimensionalEJA):
         # if the user passes check_axioms=True.
         if "check_axioms" not in kwargs: kwargs["check_axioms"] = False
 
-
         super().__init__(self._denormalized_basis(matrix_space),
                          self.jordan_product,
                          self.trace_inner_product,
@@ -2140,10 +2142,6 @@ class RealSymmetricEJA(MatrixEJA, RationalBasisEJA, ConcreteEJA):
         return cls(n, **kwargs)
 
     def __init__(self, n, field=AA, **kwargs):
-        # We know this is a valid EJA, but will double-check
-        # if the user passes check_axioms=True.
-        if "check_axioms" not in kwargs: kwargs["check_axioms"] = False
-
         A = MatrixSpace(field, n)
         super().__init__(A, **kwargs)
 
@@ -2227,10 +2225,6 @@ class ComplexHermitianEJA(MatrixEJA, RationalBasisEJA, ConcreteEJA):
 
     """
     def __init__(self, n, field=AA, **kwargs):
-        # We know this is a valid EJA, but will double-check
-        # if the user passes check_axioms=True.
-        if "check_axioms" not in kwargs: kwargs["check_axioms"] = False
-
         from mjo.hurwitz import ComplexMatrixAlgebra
         A = ComplexMatrixAlgebra(n, scalars=field)
         super().__init__(A, **kwargs)
@@ -2317,10 +2311,6 @@ class QuaternionHermitianEJA(MatrixEJA, RationalBasisEJA, ConcreteEJA):
 
     """
     def __init__(self, n, field=AA, **kwargs):
-        # We know this is a valid EJA, but will double-check
-        # if the user passes check_axioms=True.
-        if "check_axioms" not in kwargs: kwargs["check_axioms"] = False
-
         from mjo.hurwitz import QuaternionMatrixAlgebra
         A = QuaternionMatrixAlgebra(n, scalars=field)
         super().__init__(A, **kwargs)
@@ -3100,6 +3090,7 @@ class CartesianProductEJA(FiniteDimensionalEJA):
         sage: actual == expected             # long time
         True
     """
+    Element = CartesianProductEJAElement
     def __init__(self, factors, **kwargs):
         m = len(factors)
         if m == 0:
@@ -3203,6 +3194,34 @@ class CartesianProductEJA(FiniteDimensionalEJA):
         ones = tuple(J.one().to_matrix() for J in factors)
         self.one.set_cache(self(ones))
 
+    def _sets_keys(self):
+        r"""
+
+        SETUP::
+
+            sage: from mjo.eja.eja_algebra import (ComplexHermitianEJA,
+            ....:                                  RealSymmetricEJA)
+
+        TESTS:
+
+        The superclass uses ``_sets_keys()`` to implement its
+        ``cartesian_factors()`` method::
+
+            sage: J1 = RealSymmetricEJA(2,
+            ....:                       field=QQ,
+            ....:                       orthonormalize=False,
+            ....:                       prefix="a")
+            sage: J2 = ComplexHermitianEJA(2,field=QQ,orthonormalize=False)
+            sage: J = cartesian_product([J1,J2])
+            sage: x = sum(i*J.gens()[i] for i in range(len(J.gens())))
+            sage: x.cartesian_factors()
+            (a1 + 2*a2, 3*b0 + 4*b1 + 5*b2 + 6*b3)
+
+        """
+        # Copy/pasted from CombinatorialFreeModule_CartesianProduct,
+        # but returning a tuple instead of a list.
+        return tuple(range(len(self.cartesian_factors())))
+
     def cartesian_factors(self):
         # Copy/pasted from CombinatorialFreeModule_CartesianProduct.
         return self._sets