From ee9ac102b8b392793466c13039a6e50b1e3c4c01 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Wed, 24 Feb 2021 21:17:21 -0500
Subject: [PATCH] eja: remove a completed TODO, and doctest it.

---
 mjo/eja/TODO           |  5 +----
 mjo/eja/eja_algebra.py | 26 +++++++++++++++++++-------
 2 files changed, 20 insertions(+), 11 deletions(-)

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 93aa9fb..1407ebd 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -14,9 +14,6 @@ RealSymmetricEJA(4):
 sage: F = J.base_ring()
 sage: a0 = (1/4)*X[4]**2*X[6]**2 - (1/2)*X[2]*X[5]*X[6]**2 - (1/2)*X[3]*X[4]*X[6]*X[7] + (F(2).sqrt()/2)*X[1]*X[5]*X[6]*X[7] + (1/4)*X[3]**2*X[7]**2 - (1/2)*X[0]*X[5]*X[7]**2 + (F(2).sqrt()/2)*X[2]*X[3]*X[6]*X[8] - (1/2)*X[1]*X[4]*X[6*X[8] - (1/2)*X[1]*X[3]*X[7]*X[8] + (F(2).sqrt()/2)*X[0]*X[4]*X[7]*X[8] + (1/4)*X[1]**2*X[8]**2 - (1/2)*X[0]*X[2]*X[8]**2 - (1/2)*X[2]*X[3]**2*X[9] + (F(2).sqrt()/2)*X[1]*X[3]*X[4]*X[9] - (1/2)*X[0]*X[4]**2*X[9] - (1/2)*X[1]**2*X[5]*X[9] + X[0]*X[2]*X[5]*X[9]
 
-5. The main EJA element constructor is happy to convert between
-   e.g. HadamardEJA(3) and JordanSpinEJA(3).
-
-6. Profile the construction of "large" matrix algebras (like the
+5. Profile the construction of "large" matrix algebras (like the
    15-dimensional QuaternionHermitianAlgebra(3)) to find out why
    they're so slow.
diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 618e09c..3a832c1 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -447,13 +447,23 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
             sage: J(x.to_vector().column()) == x
             True
 
+        We cannot coerce elements between algebras just because their
+        matrix representations are compatible::
+
+            sage: J1 = HadamardEJA(3)
+            sage: J2 = JordanSpinEJA(3)
+            sage: J2(J1.one())
+            Traceback (most recent call last):
+            ...
+            ValueError: not an element of this algebra
+            sage: J1(J2.zero())
+            Traceback (most recent call last):
+            ...
+            ValueError: not an element of this algebra
+
         """
         msg = "not an element of this algebra"
-        if elt == 0:
-            # The superclass implementation of random_element()
-            # needs to be able to coerce "0" into the algebra.
-            return self.zero()
-        elif elt in self.base_ring():
+        if elt in self.base_ring():
             # Ensure that no base ring -> algebra coercion is performed
             # by this method. There's some stupidity in sage that would
             # otherwise propagate to this method; for example, sage thinks
@@ -461,9 +471,11 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
             raise ValueError(msg)
 
         try:
+            # Try to convert a vector into a column-matrix...
             elt = elt.column()
         except (AttributeError, TypeError):
-            # Try to convert a vector into a column-matrix
+            # and ignore failure, because we weren't really expecting
+            # a vector as an argument anyway.
             pass
 
         if elt not in self.matrix_space():
@@ -477,7 +489,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         # could be QQ instead of QQbar.
         #
         # And, we also have to handle Cartesian product bases (when
-        # the matric basis consists of tuples) here. The "good news"
+        # the matrix basis consists of tuples) here. The "good news"
         # is that we're already converting everything to long vectors,
         # and that strategy works for tuples as well.
         #
-- 
2.43.2