From 07f5168dc8e9434171ab89d7089330c561da4380 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Sun, 8 Nov 2020 08:43:37 -0500
Subject: [PATCH] eja: make random_element() more random.

---
 mjo/eja/TODO           |  2 --
 mjo/eja/eja_algebra.py | 52 ++++++++++++++++++++++++++++++++++++++++--
 2 files changed, 50 insertions(+), 4 deletions(-)

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 32e78d4..985e50a 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -8,5 +8,3 @@
 
 5. Factor out the unit-norm basis (and operator symmetry) tests once
    all of the algebras pass.
-
-6. The EJA random element method only returns two summands by default.
\ No newline at end of file
diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index ed2e258..91088a2 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -672,10 +672,57 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
         return (J0, J5, J1)
 
 
-    def random_elements(self, count):
+    def random_element(self, thorough=False):
+        r"""
+        Return a random element of this algebra.
+
+        Our algebra superclass method only returns a linear
+        combination of at most two basis elements. We instead
+        want the vector space "random element" method that
+        returns a more diverse selection.
+
+        INPUT:
+
+        - ``thorough`` -- (boolean; default False) whether or not we
+          should generate irrational coefficients for the random
+          element when our base ring is irrational; this slows the
+          algebra operations to a crawl, but any truly random method
+          should include them
+
+        """
+        # For a general base ring... maybe we can trust this to do the
+        # right thing? Unlikely, but.
+        V = self.vector_space()
+        v = V.random_element()
+
+        if self.base_ring() is AA:
+            # The "random element" method of the algebraic reals is
+            # stupid at the moment, and only returns integers between
+            # -2 and 2, inclusive. Instead, we implement our own
+            # "random vector" method, and then coerce that into the
+            # algebra. We use the vector space degree here instead of
+            # the dimension because a subalgebra could (for example) be
+            # spanned by only two vectors, each with five coordinates.
+            # We need to generate all five coordinates.
+            if thorough:
+                v *= QQbar.random_element().real()
+            else:
+                v *= QQ.random_element()
+
+        return self.from_vector(V.coordinate_vector(v))
+
+    def random_elements(self, count, thorough=False):
         """
         Return ``count`` random elements as a tuple.
 
+        INPUT:
+
+        - ``thorough`` -- (boolean; default False) whether or not we
+          should generate irrational coefficients for the random
+          elements when our base ring is irrational; this slows the
+          algebra operations to a crawl, but any truly random method
+          should include them
+
         SETUP::
 
             sage: from mjo.eja.eja_algebra import JordanSpinEJA
@@ -690,7 +737,8 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
             True
 
         """
-        return tuple( self.random_element() for idx in range(count) )
+        return tuple( self.random_element(thorough)
+                      for idx in range(count) )
 
     @classmethod
     def random_instance(cls, field=AA, **kwargs):
-- 
2.44.2