eja: create our own Homset class for EJAs (ugh).

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index 9414d2cf27fd2728ef205650b128ab37d1b83949..848fc57ae7eea635ba0f014e74b8de64938c6dbe 100644 (file)
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -6,12 +6,79 @@ what can be supported in a general Jordan Algebra.
 """
 
 from sage.categories.finite_dimensional_algebras_with_basis import FiniteDimensionalAlgebrasWithBasis
+from sage.categories.morphism import SetMorphism
 from sage.structure.element import is_Matrix
 from sage.structure.category_object import normalize_names
 
 from sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra import FiniteDimensionalAlgebra
 from sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra_element import FiniteDimensionalAlgebraElement
-from sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra_morphism import FiniteDimensionalAlgebraMorphism
+from sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra_morphism import FiniteDimensionalAlgebraMorphism, FiniteDimensionalAlgebraHomset
+
+
+class FiniteDimensionalEuclideanJordanAlgebraHomset(FiniteDimensionalAlgebraHomset):
+
+    def has_coerce_map_from(self, S):
+        """
+        EXAMPLES::
+
+            sage: J = RealSymmetricEJA(2)
+            sage: H = J.Hom(J)
+            sage: H.has_coerce_map_from(QQ)
+            True
+
+        """
+        try:
+            # The Homset classes override has_coerce_map_from() with
+            # something that crashes when it's given e.g. QQ.
+            if S.is_subring(self.codomain().base_ring()):
+                return True
+        except:
+            pclass = super(FiniteDimensionalEuclideanJordanAlgebraHomset, self)
+            return pclass.has_coerce_map_from(S)
+
+
+    def _coerce_map_from_(self, S):
+        """
+        EXAMPLES::
+
+            sage: J = RealSymmetricEJA(2)
+            sage: H = J.Hom(J)
+            sage: H.coerce(2)
+            Morphism from Euclidean Jordan algebra of degree 3 over Rational
+            Field to Euclidean Jordan algebra of degree 3 over Rational Field
+            given by matrix
+            [2 0 0]
+            [0 2 0]
+            [0 0 2]
+
+        """
+        C = self.codomain()
+        R = C.base_ring()
+        if S.is_subring(R):
+            h = S.hom(self.codomain())
+            return SetMorphism(Hom(S,C), lambda x: h(x).operator())
+
+
+    def __call__(self, x):
+        """
+        EXAMPLES::
+
+            sage: J = RealSymmetricEJA(2)
+            sage: H = J.Hom(J)
+            sage: H(2)
+            Morphism from Euclidean Jordan algebra of degree 3 over Rational
+            Field to Euclidean Jordan algebra of degree 3 over Rational Field
+            given by matrix
+            [2 0 0]
+            [0 2 0]
+            [0 0 2]
+
+        """
+        if x in self.base_ring():
+            cols = self.domain().dimension()
+            rows = self.codomain().dimension()
+            x = x*identity_matrix(self.codomain().base_ring(), rows, cols)
+        return FiniteDimensionalEuclideanJordanAlgebraMorphism(self, x)
 
 
 class FiniteDimensionalEuclideanJordanAlgebraMorphism(FiniteDimensionalAlgebraMorphism):
@@ -38,7 +105,6 @@ class FiniteDimensionalEuclideanJordanAlgebraMorphism(FiniteDimensionalAlgebraMo
     algebra morphism, but they don't seem to be callable on elements of
     our EJA, and you can't add/multiply/etc. them.
     """
-
     def _add_(self, other):
         """
         Add two EJA morphisms in the obvious way.
@@ -300,6 +366,15 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                                  natural_basis=natural_basis)
 
 
+    def _Hom_(self, B, cat):
+        """
+        Construct a homset of ``self`` and ``B``.
+        """
+        return FiniteDimensionalEuclideanJordanAlgebraHomset(self,
+                                                             B,
+                                                             category=cat)
+
+
     def __init__(self,
                  field,
                  mult_table,