eja: cache one() for Cartesian product algebras.

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index fe18d5634835c97dcc1ee635c4fadecab25787ea..03bf40459e26805a2b2d6e3bae114779f0de57d3 100644 (file)
--- 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 3390df7545bb41257ee58c68f04154ce7a18d462..850447b38f55b09b707f745959e85dfdfa7d62c1 100644 (file)
--- 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