src/sage/symbolic/integration: help libgiac handle infinite endpoints

When integrating to/from plus/minus infinity, Giac can get stuck:

  sage: integral(1/max_symbolic(x, 1)**2, x, 0, oo, algorithm='giac')
  ...
  RuntimeError: Unable to check sign: 1>Infinity

This is apparently due to the type of infinity that is used for
integration. There are (at least?) two kinds:

  sage: from sage.libs.giac import libgiac
  sage: libgiac(Infinity)
  Infinity
  sage: libgiac(Infinity._giac_())
  +infinity

And, for integration, I guess we want the second kind, because it
allows the integration to proceed with a warning. This commit calls
_giac_() on the endpoints of a definite integral before passing them
to libgiac.integrate(). It fixes the example above, and we update the
corresponding doctest.

src/sage/symbolic/integration/external.py

@@ -256,6 +256,16 @@ def libgiac_integrator(expression, v, a=None, b=None):
     if a is None:
         result = libgiac.integrate(Pygen(expression), v)
     else:
+        # We use _giac_() in the endpoints if they are infinite because
+        # for some reason, passing them straight to libgiac() gives us
+        # a different kind of infinity back that doesn't work as well,
+        # at least for integration.
+        from sage.rings.infinity import PlusInfinity, MinusInfinity
+        if isinstance(a, PlusInfinity) or isinstance(a, MinusInfinity):
+            a = a._giac_()
+        if isinstance(b, PlusInfinity) or isinstance(b, MinusInfinity):
+            b = b._giac_()
+
         result = libgiac.integrate(Pygen(expression), v, a, b)
     if 'integrate' in format(result) or 'integration' in format(result):
         return expression.integrate(v, a, b, hold=True)

src/sage/symbolic/integration/integral.py

@@ -206,7 +206,9 @@ def __init__(self):
             sage: ex = 1/max_symbolic(x, 1)**2
             sage: integral(ex, x, 0, 2, algorithm='giac')
             3/2
-            sage: integral(1/max_symbolic(x, 1)**2, x, 0, oo, algorithm='giac')
+            sage: result = integral(ex, x, 0, oo, algorithm='giac')
+            ...
+            sage: result
             2
         """
         # The automatic evaluation routine will try these integrators