From: Michael Orlitzky <michael@orlitzky.com>
Date: Sat, 7 Nov 2020 18:00:38 +0000 (-0500)
Subject: eja: let random_eja() return zero-dimensional algebras of all types.
X-Git-Url: http://gitweb.michael.orlitzky.com/?p=sage.d.git;a=commitdiff_plain;h=309fc28265693c9abd51780ea76f8beec39ce27f

eja: let random_eja() return zero-dimensional algebras of all types.
---

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index a915812..e02257f 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -10,9 +10,3 @@
 
 5. Factor out the unit-norm basis (and operator symmetry) tests once
    all of the algebras pass.
-
-6. Can we make the minimal and characteristic polynomial tests work
-   for trivial algebras, too? Then we wouldn't need the "nontrivial"
-   argument to random_eja(). This would also allow us to potentially
-   pass a "size" of zero to the other constructors in random_eja() --
-   a code path that is basically untested right now.
diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 055bbbd..4e66b2d 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -438,8 +438,15 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
         """
         Return the matrix space in which this algebra's natural basis
         elements live.
+
+        Generally this will be an `n`-by-`1` column-vector space,
+        except when the algebra is trivial. There it's `n`-by-`n`
+        (where `n` is zero), to ensure that two elements of the
+        natural basis space (empty matrices) can be multiplied.
         """
-        if self._natural_basis is None or len(self._natural_basis) == 0:
+        if self.is_trivial():
+            return MatrixSpace(self.base_ring(), 0)
+        elif self._natural_basis is None or len(self._natural_basis) == 0:
             return MatrixSpace(self.base_ring(), self.dimension(), 1)
         else:
             return self._natural_basis[0].matrix_space()
@@ -666,7 +673,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
             # there's only one.
             return cls(field)
 
-        n = ZZ.random_element(cls._max_test_case_size()) + 1
+        n = ZZ.random_element(cls._max_test_case_size() + 1)
         return cls(n, field, **kwargs)
 
     @cached_method