Trac #32964: speed up a very slow doctest in functions.orthogonal_polys.

I've got 99 problems, and they're slow. One doctest in this module is
repeating a random test 100 times, taking over four minutes on my
machine. More tests are better, but in this case, coverage will
eventually accrue from the number of testers even if we only repeat
the test once within the file.

Since this particular test is an EXAMPLE, I've also made it a bit more
user-friendly while eliminating the additional runs.

message for your changes. Lines starting # with '#' will be ignored,
and an empty message aborts the commit.  # # On branch
u/mjo/ticket/32964 # Changes to be committed: # modified:
src/sage/functions/orthogonal_polys.py #

Author: orlitzky

src/sage/functions/orthogonal_polys.py

@@ -2081,10 +2081,13 @@ class Func_ultraspherical(GinacFunction):
         sage: gegenbauer(3,2,t)
         32*t^3 - 12*t
         sage: _ = var('x')
-        sage: for N in range(100):
-        ....:     n = ZZ.random_element(5, 5001)
-        ....:     a = QQ.random_element().abs() + 5
-        ....:     assert ((n+1)*ultraspherical(n+1,a,x) - 2*x*(n+a)*ultraspherical(n,a,x) + (n+2*a-1)*ultraspherical(n-1,a,x)).expand().is_zero()
+        sage: n = ZZ.random_element(5, 5001)
+        sage: a = QQ.random_element().abs() + 5
+        sage: s = (  (n+1)*ultraspherical(n+1,a,x)
+        ....:      - 2*x*(n+a)*ultraspherical(n,a,x)
+        ....:      + (n+2*a-1)*ultraspherical(n-1,a,x) )
+        sage: s.expand().is_zero()
+        True
         sage: ultraspherical(5,9/10,3.1416)
         6949.55439044240
         sage: ultraspherical(5,9/10,RealField(100)(pi))