eja: normalize the real symmetric matrix basis.

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

diff --git a/mjo/eja/eja_subalgebra.py b/mjo/eja/eja_subalgebra.py
index c82bd1a485c5eb6b82e92134fc30658be4d6d669..646da2fb8b649c11baa226833085c26564d75d46 100644 (file)
--- a/mjo/eja/eja_subalgebra.py
+++ b/mjo/eja/eja_subalgebra.py
@@ -197,6 +197,30 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
                               natural_basis=natural_basis)
 
 
+    def _a_regular_element(self):
+        """
+        Override the superalgebra method to return the one
+        regular element that is sure to exist in this
+        subalgebra, namely the element that generated it.
+
+        SETUP::
+
+            sage: from mjo.eja.eja_algebra import random_eja
+
+        TESTS::
+
+            sage: set_random_seed()
+            sage: J = random_eja().random_element().subalgebra_generated_by()
+            sage: J._a_regular_element().is_regular()
+            True
+
+        """
+        if self.dimension() == 0:
+            return self.zero()
+        else:
+            return self.monomial(1)
+
+
     def _element_constructor_(self, elt):
         """
         Construct an element of this subalgebra from the given one.
@@ -289,6 +313,18 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
             return self.monomial(self.one_basis())
 
 
+    def natural_basis_space(self):
+        """
+        Return the natural basis space of this algebra, which is identical
+        to that of its superalgebra.
+
+        This is correct "by definition," and avoids a mismatch when the
+        subalgebra is trivial (with no natural basis to infer anything
+        from) and the parent is not.
+        """
+        return self.superalgebra().natural_basis_space()
+
+
     def superalgebra(self):
         """
         Return the superalgebra that this algebra was generated from.
@@ -306,20 +342,20 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
         EXAMPLES::
 
             sage: J = RealSymmetricEJA(3)
-            sage: x = sum( i*J.gens()[i] for i in range(6) )
+            sage: x = J.monomial(0) + 2*J.monomial(2) + 5*J.monomial(5)
             sage: K = FiniteDimensionalEuclideanJordanElementSubalgebra(x)
             sage: K.vector_space()
-            Vector space of degree 6 and dimension 3 over Rational Field
+            Vector space of degree 6 and dimension 3 over...
             User basis matrix:
             [ 1  0  1  0  0  1]
-            [ 0  1  2  3  4  5]
-            [10 14 21 19 31 50]
+            [ 1  0  2  0  0  5]
+            [ 1  0  4  0  0 25]
             sage: (x^0).to_vector()
             (1, 0, 1, 0, 0, 1)
             sage: (x^1).to_vector()
-            (0, 1, 2, 3, 4, 5)
+            (1, 0, 2, 0, 0, 5)
             sage: (x^2).to_vector()
-            (10, 14, 21, 19, 31, 50)
+            (1, 0, 4, 0, 0, 25)
 
         """
         return self._vector_space