eja: factor a few things out of the FDEJA constructor.

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 9edb3790ca89f859627c43e59db540b716fe5f16..6223bff9331ba3144cbfdd8fbdd8fe616139a230 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -13,5 +13,3 @@
 5. In CartesianProductEJA we already know the multiplication table and
    inner product matrix. Refactor things until it's no longer
    necessary to duplicate that work.
 5. In CartesianProductEJA we already know the multiplication table and
    inner product matrix. Refactor things until it's no longer
    necessary to duplicate that work.

-
-6. Figure out how to remove Unital() from subalgebras.

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index e26146ec81b5a0f922c27cca487aed9277ceb7e1..79187594472d82e24a0b700305b7ddfc7b192536 100644 (file)
--- 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
 
 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.
 class FiniteDimensionalEJA(CombinatorialFreeModule):
     r"""
     A finite-dimensional Euclidean Jordan algebra.


@@ -228,6 +239,26 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
     """
     Element = FiniteDimensionalEJAElement
 
     """
     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,
     def __init__(self,
                  basis,
                  jordan_product,


@@ -244,30 +275,14 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         n = len(basis)
 
         if check_field:
         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 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
 
         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)
 
                                for bj in basis
                                for bk in basis)
 

+        category = EuclideanJordanAlgebras(field)
+

         if associative:
             # Element subalgebras can take advantage of this.
             category = category.Associative()
         if associative:
             # Element subalgebras can take advantage of this.
             category = category.Associative()