X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=79187594472d82e24a0b700305b7ddfc7b192536;hb=b259821a73cb75a6d5a81d13256802be023b0fa9;hp=8e522527413b89c0e704687583dc9c4636303170;hpb=da6160ad4c8156d51290fd056aa7d5b3d609c8e9;p=sage.d.git

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 8e52252..7918759 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -170,6 +170,17 @@ from mjo.eja.eja_element import FiniteDimensionalEJAElement
 from mjo.eja.eja_operator import FiniteDimensionalEJAOperator
 from mjo.eja.eja_utils import _all2list, _mat2vec
 
+def EuclideanJordanAlgebras(field):
+    r"""
+    The category of Euclidean Jordan algebras over ``field``, which
+    must be a subfield of the real numbers. For now this is just a
+    convenient wrapper around all of the other category axioms that
+    apply to all EJAs.
+    """
+    category = MagmaticAlgebras(field).FiniteDimensional()
+    category = category.WithBasis().Unital().Commutative()
+    return category
+
 class FiniteDimensionalEJA(CombinatorialFreeModule):
     r"""
     A finite-dimensional Euclidean Jordan algebra.
@@ -228,6 +239,26 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
     """
     Element = FiniteDimensionalEJAElement
 
+    @staticmethod
+    def _check_input_field(field):
+        if not field.is_subring(RR):
+            # Note: this does return true for the real algebraic
+            # field, the rationals, and any quadratic field where
+            # we've specified a real embedding.
+            raise ValueError("scalar field is not real")
+
+    @staticmethod
+    def _check_input_axioms(basis, jordan_product, inner_product):
+        if not all( jordan_product(bi,bj) == jordan_product(bj,bi)
+                    for bi in basis
+                    for bj in basis ):
+            raise ValueError("Jordan product is not commutative")
+
+        if not all( inner_product(bi,bj) == inner_product(bj,bi)
+                    for bi in basis
+                    for bj in basis ):
+            raise ValueError("inner-product is not commutative")
+
     def __init__(self,
                  basis,
                  jordan_product,
@@ -244,30 +275,14 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         n = len(basis)
 
         if check_field:
-            if not field.is_subring(RR):
-                # Note: this does return true for the real algebraic
-                # field, the rationals, and any quadratic field where
-                # we've specified a real embedding.
-                raise ValueError("scalar field is not real")
+            self._check_input_field(field)
 
         if check_axioms:
             # Check commutativity of the Jordan and inner-products.
             # This has to be done before we build the multiplication
             # and inner-product tables/matrices, because we take
             # advantage of symmetry in the process.
-            if not all( jordan_product(bi,bj) == jordan_product(bj,bi)
-                        for bi in basis
-                        for bj in basis ):
-                raise ValueError("Jordan product is not commutative")
-
-            if not all( inner_product(bi,bj) == inner_product(bj,bi)
-                        for bi in basis
-                        for bj in basis ):
-                raise ValueError("inner-product is not commutative")
-
-
-        category = MagmaticAlgebras(field).FiniteDimensional()
-        category = category.WithBasis().Unital().Commutative()
+            self._check_input_axioms(basis, jordan_product, inner_product)
 
         if n <= 1:
             # All zero- and one-dimensional algebras are just the real
@@ -286,6 +301,8 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
                                for bj in basis
                                for bk in basis)
 
+        category = EuclideanJordanAlgebras(field)
+
         if associative:
             # Element subalgebras can take advantage of this.
             category = category.Associative()
@@ -779,13 +796,11 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
             if elt.parent().superalgebra() == self:
                 return elt.superalgebra_element()
 
-        try:
-            # Try to convert a vector into a column-matrix...
+        if hasattr(elt, 'sparse_vector'):
+            # Convert a vector into a column-matrix. We check for
+            # "sparse_vector" and not "column" because matrices also
+            # have a "column" method.
             elt = elt.column()
-        except (AttributeError, TypeError):
-            # and ignore failure, because we weren't really expecting
-            # a vector as an argument anyway.
-            pass
 
         if elt not in self.matrix_space():
             raise ValueError(msg)
@@ -1411,7 +1426,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         # corresponding to trivial spaces (e.g. it returns only the
         # eigenspace corresponding to lambda=1 if you take the
         # decomposition relative to the identity element).
-        trivial = self.subalgebra(())
+        trivial = self.subalgebra((), check_axioms=False)
         J0 = trivial                          # eigenvalue zero
         J5 = VectorSpace(self.base_ring(), 0) # eigenvalue one-half
         J1 = trivial                          # eigenvalue one