eja: factor out a class for real-embedded matrices.

[sage.d.git] / mjo / eja / eja_algebra.py

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 4d0c802c38c8320a8f10f8faeb50678a85d84e95..5bf597565b2ae292032c3f0a532763d7889cd2a8 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -1725,6 +1725,21 @@ class ConcreteEJA(RationalBasisEJA):
 
 
 class MatrixEJA:
+    @staticmethod
+    def jordan_product(X,Y):
+        return (X*Y + Y*X)/2
+
+    @staticmethod
+    def trace_inner_product(X,Y):
+        r"""
+        A trace inner-product for matrices that aren't embedded in the
+        reals.
+        """
+        # We take the norm (absolute value) because Octonions() isn't
+        # smart enough yet to coerce its one() into the base field.
+        return (X*Y).trace().abs()
+
+class RealEmbeddedMatrixEJA(MatrixEJA):
     @staticmethod
     def dimension_over_reals():
         r"""
@@ -1770,9 +1785,6 @@ class MatrixEJA:
             raise ValueError("the matrix 'M' must be a real embedding")
         return M
 
-    @staticmethod
-    def jordan_product(X,Y):
-        return (X*Y + Y*X)/2
 
     @classmethod
     def trace_inner_product(cls,X,Y):
@@ -1781,29 +1793,11 @@ class MatrixEJA:
 
         SETUP::
 
-            sage: from mjo.eja.eja_algebra import (RealSymmetricEJA,
-            ....:                                  ComplexHermitianEJA,
+            sage: from mjo.eja.eja_algebra import (ComplexHermitianEJA,
             ....:                                  QuaternionHermitianEJA)
 
         EXAMPLES::
 
-        This gives the same answer as it would if we computed the trace
-        from the unembedded (original) matrices::
-
-            sage: set_random_seed()
-            sage: J = RealSymmetricEJA.random_instance()
-            sage: x,y = J.random_elements(2)
-            sage: Xe = x.to_matrix()
-            sage: Ye = y.to_matrix()
-            sage: X = J.real_unembed(Xe)
-            sage: Y = J.real_unembed(Ye)
-            sage: expected = (X*Y).trace()
-            sage: actual = J.trace_inner_product(Xe,Ye)
-            sage: actual == expected
-            True
-
-        ::
-
             sage: set_random_seed()
             sage: J = ComplexHermitianEJA.random_instance()
             sage: x,y = J.random_elements(2)
@@ -1839,14 +1833,7 @@ class MatrixEJA:
         # as a REAL matrix will be 2*a = 2*Re(z_1). And so forth.
         return (X*Y).trace()/cls.dimension_over_reals()
 
-
-class RealMatrixEJA(MatrixEJA):
-    @staticmethod
-    def dimension_over_reals():
-        return 1
-
-
-class RealSymmetricEJA(ConcreteEJA, RealMatrixEJA):
+class RealSymmetricEJA(ConcreteEJA, MatrixEJA):
     """
     The rank-n simple EJA consisting of real symmetric n-by-n
     matrices, the usual symmetric Jordan product, and the trace inner
@@ -1975,12 +1962,12 @@ class RealSymmetricEJA(ConcreteEJA, RealMatrixEJA):
         # because the MatrixEJA is not presently a subclass of the
         # FDEJA class that defines rank() and one().
         self.rank.set_cache(n)
-        idV = matrix.identity(ZZ, self.dimension_over_reals()*n)
+        idV = self.matrix_space().one()
         self.one.set_cache(self(idV))
 
 
 
-class ComplexMatrixEJA(MatrixEJA):
+class ComplexMatrixEJA(RealEmbeddedMatrixEJA):
     # A manual dictionary-cache for the complex_extension() method,
     # since apparently @classmethods can't also be @cached_methods.
     _complex_extension = {}
@@ -2282,7 +2269,7 @@ class ComplexHermitianEJA(ConcreteEJA, ComplexMatrixEJA):
         n = ZZ.random_element(cls._max_random_instance_size() + 1)
         return cls(n, **kwargs)
 
-class QuaternionMatrixEJA(MatrixEJA):
+class QuaternionMatrixEJA(RealEmbeddedMatrixEJA):
 
     # A manual dictionary-cache for the quaternion_extension() method,
     # since apparently @classmethods can't also be @cached_methods.