From 8059516ad9df112ac18c740af7d6f856639d4b8d Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Fri, 26 Feb 2021 13:30:28 -0500
Subject: [PATCH] eja: more tests/examples.

---
 mjo/eja/eja_algebra.py | 40 +++++++++++++++++++++++++++++++++++-----
 mjo/eja/eja_utils.py   | 27 +++++++++++++++++++++++++++
 2 files changed, 62 insertions(+), 5 deletions(-)

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index ad619f6..5d96a53 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -3115,6 +3115,33 @@ class CartesianProductEJA(CombinatorialFreeModule_CartesianProduct,
         sage: CP2.is_associative()
         False
 
+    Cartesian products of Cartesian products work::
+
+        sage: J1 = JordanSpinEJA(1)
+        sage: J2 = JordanSpinEJA(1)
+        sage: J3 = JordanSpinEJA(1)
+        sage: J = cartesian_product([J1,cartesian_product([J2,J3])])
+        sage: J.multiplication_table()
+        +--------------++---------+--------------+--------------+
+        | *            || e(0, 0) | e(1, (0, 0)) | e(1, (1, 0)) |
+        +==============++=========+==============+==============+
+        | e(0, 0)      || e(0, 0) | 0            | 0            |
+        +--------------++---------+--------------+--------------+
+        | e(1, (0, 0)) || 0       | e(1, (0, 0)) | 0            |
+        +--------------++---------+--------------+--------------+
+        | e(1, (1, 0)) || 0       | 0            | e(1, (1, 0)) |
+        +--------------++---------+--------------+--------------+
+        sage: HadamardEJA(3).multiplication_table()
+        +----++----+----+----+
+        | *  || e0 | e1 | e2 |
+        +====++====+====+====+
+        | e0 || e0 | 0  | 0  |
+        +----++----+----+----+
+        | e1 || 0  | e1 | 0  |
+        +----++----+----+----+
+        | e2 || 0  | 0  | e2 |
+        +----++----+----+----+
+
     TESTS:
 
     All factors must share the same base field::
@@ -3200,6 +3227,9 @@ class CartesianProductEJA(CombinatorialFreeModule_CartesianProduct,
         r"""
         Convert a monomial index into a generator index.
 
+        This is needed in product algebras because the multiplication
+        table is in terms of the generator indices.
+
         SETUP::
 
             sage: from mjo.eja.eja_algebra import random_eja
@@ -3216,15 +3246,15 @@ class CartesianProductEJA(CombinatorialFreeModule_CartesianProduct,
             True
 
         """
-        # The superclass method indexes into a matrix, so we have to
-        # turn the tuples i and j into integers. This is easy enough
-        # given that the first coordinate of i and j corresponds to
-        # the factor, and the second coordinate corresponds to the
-        # index of the generator within that factor.
+        # This works recursively so that we can handle Cartesian
+        # products of Cartesian products.
         try:
+            # monomial is an ordered pair
             factor = mon[0]
         except TypeError: # 'int' object is not subscriptable
+            # base case where the monomials are integers
             return mon
+
         idx_in_factor = self._monomial_to_generator(mon[1])
 
         offset = sum( f.dimension()
diff --git a/mjo/eja/eja_utils.py b/mjo/eja/eja_utils.py
index c25b819..832dcef 100644
--- a/mjo/eja/eja_utils.py
+++ b/mjo/eja/eja_utils.py
@@ -6,6 +6,32 @@ def _scale(x, alpha):
     r"""
     Scale the vector, matrix, or cartesian-product-of-those-things
     ``x`` by ``alpha``.
+
+    This works around the inability to scale certain elements of
+    Cartesian product spaces, as reported in
+
+      https://trac.sagemath.org/ticket/31435
+
+    ..WARNING:
+
+        This will do the wrong thing if you feed it a tuple or list.
+
+    SETUP::
+
+        sage: from mjo.eja.eja_utils import _scale
+
+    EXAMPLES::
+
+        sage: v = vector(QQ, (1,2,3))
+        sage: _scale(v,2)
+        (2, 4, 6)
+        sage: m = matrix(QQ, [[1,2],[3,4]])
+        sage: M = cartesian_product([m.parent(), m.parent()])
+        sage: _scale(M((m,m)), 2)
+        ([2 4]
+        [6 8], [2 4]
+        [6 8])
+
     """
     if hasattr(x, 'cartesian_factors'):
         P = x.parent()
@@ -14,6 +40,7 @@ def _scale(x, alpha):
     else:
         return x*alpha
 
+
 def _all2list(x):
     r"""
     Flatten a vector, matrix, or cartesian product of those things
-- 
2.44.2