X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feuclidean_jordan_algebra.py;h=848fc57ae7eea635ba0f014e74b8de64938c6dbe;hb=7929fc4e6fcfaa44e89e37a5233977581cb171a8;hp=2b00302dc73461f089390a715bb1f12dc7aef6c1;hpb=fac7c7f89eb71a0af23af6aeb5e822032ebf8e27;p=sage.d.git

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index 2b00302..848fc57 100644
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -5,13 +5,80 @@ are used in optimization, and have some additional nice methods beyond
 what can be supported in a general Jordan Algebra.
 """
 
-from sage.categories.magmatic_algebras import MagmaticAlgebras
+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):
@@ -38,8 +105,7 @@ 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):
+    def _add_(self, other):
         """
         Add two EJA morphisms in the obvious way.
 
@@ -86,7 +152,7 @@ class FiniteDimensionalEuclideanJordanAlgebraMorphism(FiniteDimensionalAlgebraMo
                                                   check=False)
 
 
-    def __invert__(self):
+    def _invert_(self):
         """
         EXAMPLES::
 
@@ -124,7 +190,7 @@ class FiniteDimensionalEuclideanJordanAlgebraMorphism(FiniteDimensionalAlgebraMo
         return FiniteDimensionalEuclideanJordanAlgebraMorphism(self.parent(),
                                                                 A.inverse())
 
-    def __mul__(self, other):
+    def _lmul_(self, other):
         """
         Compose two EJA morphisms using multiplicative notation.
 
@@ -162,7 +228,7 @@ class FiniteDimensionalEuclideanJordanAlgebraMorphism(FiniteDimensionalAlgebraMo
                   self.matrix()*other.matrix() )
 
 
-    def __neg__(self):
+    def _neg_(self):
         """
         Negate this morphism.
 
@@ -282,7 +348,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                 raise ValueError("input is not a multiplication table")
         mult_table = tuple(mult_table)
 
-        cat = MagmaticAlgebras(field).FiniteDimensional().WithBasis()
+        cat = FiniteDimensionalAlgebrasWithBasis(field)
         cat.or_subcategory(category)
         if assume_associative:
             cat = cat.Associative()
@@ -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,