Fixed bug in find_root when full_output=True (size check assumed it w…

…as false)

Also fixed the doctesting in expression.pyx for 1/tan(x)

src/sage/numerical/optimize.py

@@ -141,15 +141,20 @@ def find_root(f, a, b, xtol=10e-13, rtol=2.0**-50, maxiter=100, full_output=Fals
         a = s
 
     import scipy.optimize
-    root = scipy.optimize.brentq(f, a, b,
+    brentqRes = scipy.optimize.brentq(f, a, b,
                                  full_output=full_output, xtol=xtol, rtol=rtol, maxiter=maxiter)
     # A check following ticket 4942, to ensure we actually found a root
     # Maybe should use a different tolerance here?
     # The idea is to take roughly the derivative and multiply by estimated
     # value of the root
+    root = 0
+    if (full_output):
+        root = brentqRes[0]
+    else:
+        root = brentqRes
     if (abs(f(root)) > max(abs(root * rtol * (right - left) / (b - a)), 1e-6)):
         raise RuntimeError("Brent's method failed to find a zero for f on the interval")
-    return root
+    return brentqRes
 
 def find_local_maximum(f, a, b, tol=1.48e-08, maxfun=500):
     """

src/sage/symbolic/expression.pyx

@@ -11733,8 +11733,18 @@ cdef class Expression(CommutativeRingElement):
             -0.588532743981862...
             sage: sin(x).find_root(-1,1)
             0.0
-            sage: (1/tan(x)).find_root(3,3.5)
+
+        This example was ixed along with ticket 4942 - 
+        there was an error in the example
+        pi is a root for tan(x), but an asymptote to 1/tan(x)
+        added an example to show handling of both cases::
+        
+            sage: (tan(x)).find_root(3,3.5)
             3.1415926535...
+            sage: (1/tan(x)).find_root(3, 3.5)
+            Traceback (most recent call last):
+            ...
+            RuntimeError: Brent's method failed to find a zero for f on the interval
 
         An example with a square root::