From: Michael Orlitzky <michael@orlitzky.com>
Date: Mon, 22 Feb 2021 17:02:04 +0000 (-0500)
Subject: eja: cache one() for Cartesian product algebras.
X-Git-Url: http://gitweb.michael.orlitzky.com/?p=sage.d.git;a=commitdiff_plain;h=9c771ecf5712b700f294f1ff2f18f785008f0f63

eja: cache one() for Cartesian product algebras.
---

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index fe18d56..03bf404 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,9 +1,9 @@
-1. Finish CartesianProductEJA: add to_matrix(), random_instance(),
-   one()... methods. This will require rethinking what a "matrix
-   representation" and "matrix space" means for a cartesian product
-   algebra. Do we want our matrix basis to consist of ordered pairs
-   (or triples, or...)? Should the matrix_space() of the algebra be
-   the cartesian product of the factors' matrix spaces? Can we just
+1. Finish CartesianProductEJA: add to_matrix(),
+   random_instance(),... methods. This will require rethinking what a
+   "matrix representation" and "matrix space" means for a cartesian
+   product algebra. Do we want our matrix basis to consist of ordered
+   pairs (or triples, or...)? Should the matrix_space() of the algebra
+   be the cartesian product of the factors' matrix spaces? Can we just
    fix the matrix basis/space after we call the FDEJA initializer?
 
 2. Add references and start citing them.
diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 3390df7..850447b 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -2780,6 +2780,19 @@ class CartesianProductEJA(CombinatorialFreeModule_CartesianProduct,
         True
         sage: x.inner_product(y) == J.cartesian_inner_product(x,y)
         True
+
+    The cached unit element is the same one that would be computed::
+
+        sage: set_random_seed()              # long time
+        sage: J1 = random_eja()              # long time
+        sage: J2 = random_eja()              # long time
+        sage: J = cartesian_product([J1,J2]) # long time
+        sage: actual = J.one()               # long time
+        sage: J.one.clear_cache()            # long time
+        sage: expected = J.one()             # long time
+        sage: actual == expected             # long time
+        True
+
     """
     def __init__(self, modules, **kwargs):
         CombinatorialFreeModule_CartesianProduct.__init__(self,
@@ -2819,6 +2832,8 @@ class CartesianProductEJA(CombinatorialFreeModule_CartesianProduct,
                                       check_axioms=False,
                                       category=self.category())
 
+        ones = tuple(J.one() for J in modules)
+        self.one.set_cache(self._cartesian_product_of_elements(ones))
         self.rank.set_cache(sum(J.rank() for J in modules))
 
     @cached_method