From 08aba469c5f8d8947a543f8882fa676ed165e7ee Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Mon, 14 Oct 2019 09:43:17 -0400
Subject: [PATCH] eja: define subalgebra_generated_by() to contain the
 identity.

---
 mjo/eja/eja_algebra.py    |  3 ---
 mjo/eja/eja_element.py    | 16 +++++++++++-----
 mjo/eja/eja_subalgebra.py | 18 ------------------
 3 files changed, 11 insertions(+), 26 deletions(-)

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index df6a048..6589575 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -449,9 +449,6 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
             sage: J = ComplexHermitianEJA(3)
             sage: J.is_trivial()
             False
-            sage: A = J.zero().subalgebra_generated_by()
-            sage: A.is_trivial()
-            True
 
         """
         return self.dimension() == 0
diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index e7dff75..ee33e4b 100644
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -1046,6 +1046,13 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         Return the associative subalgebra of the parent EJA generated
         by this element.
 
+        Since our parent algebra is unital, we want "subalgebra" to mean
+        "unital subalgebra" as well; thus the subalgebra that an element
+        generates will itself be a Euclidean Jordan algebra after
+        restricting the algebra operations appropriately. This is the
+        subalgebra that Faraut and Korányi work with in section II.2, for
+        example.
+
         SETUP::
 
             sage: from mjo.eja.eja_algebra import random_eja
@@ -1070,14 +1077,13 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: A(x^2) == A(x)*A(x)
             True
 
-        The subalgebra generated by the zero element is trivial::
+        By definition, the subalgebra generated by the zero element is the
+        one-dimensional algebra generated by the identity element::
 
             sage: set_random_seed()
             sage: A = random_eja().zero().subalgebra_generated_by()
-            sage: A
-            Euclidean Jordan algebra of dimension 0 over...
-            sage: A.one()
-            0
+            sage: A.dimension()
+            1
 
         """
         return FiniteDimensionalEuclideanJordanElementSubalgebra(self, orthonormalize_basis)
diff --git a/mjo/eja/eja_subalgebra.py b/mjo/eja/eja_subalgebra.py
index 2c877f3..0f64141 100644
--- a/mjo/eja/eja_subalgebra.py
+++ b/mjo/eja/eja_subalgebra.py
@@ -128,24 +128,6 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
         except ValueError:
             prefix = prefixen[0]
 
-        if elt.is_zero():
-            # Short circuit because 0^0 == 1 is going to make us
-            # think we have a one-dimensional algebra otherwise.
-            natural_basis = tuple()
-            mult_table = tuple()
-            rank = 0
-            self._vector_space = V.zero_subspace()
-            self._superalgebra_basis = []
-            fdeja = super(FiniteDimensionalEuclideanJordanElementSubalgebra,
-                          self)
-            return fdeja.__init__(field,
-                                  mult_table,
-                                  rank,
-                                  prefix=prefix,
-                                  category=category,
-                                  natural_basis=natural_basis)
-
-
         # This list is guaranteed to contain all independent powers,
         # because it's the maximal set of powers that could possibly
         # be independent (by a dimension argument).
-- 
2.44.2