Add test output

Author: user202729

src/sage/modules/free_module_element.pyx

@@ -4285,11 +4285,16 @@ cdef class FreeModuleElement(Vector):   # abstract base class
 
             sage: f(x, y, z) = (y, z, x)
             sage: f.compositional_inverse()
+            (x, y, z) |--> (z, x, y)
 
         TESTS::
 
             sage: f.change_ring(SR)
+            (y, z, x)
             sage: f.change_ring(SR).compositional_inverse()
+            Traceback (most recent call last):
+            ...
+            ValueError: base ring must be a symbolic expression ring
         """
         from sage.rings.abc import CallableSymbolicExpressionRing
         if not isinstance(self.base_ring(), CallableSymbolicExpressionRing):

src/sage/symbolic/expression.pyx

@@ -13529,38 +13529,62 @@ cdef class Expression(Expression_abc):
 
             sage: f(x) = x+1
             sage: f.compositional_inverse()
+            x |--> x - 1
             sage: var("y")
+            y
             sage: f(x) = x+y
             sage: f.compositional_inverse()
+            x |--> x - y
             sage: f(x) = x^2
             sage: f.compositional_inverse()
+            x |--> -sqrt(x)
 
         When ``allow_inverse_multivalued=False``, there is some additional checking::
 
             sage: f(x) = x^2
             sage: f.compositional_inverse(allow_inverse_multivalued=False)
+            Traceback (most recent call last):
+            ...
+            ValueError: inverse is multivalued, pass allow_inverse_multivalued=True to bypass
 
         Nonetheless, the checking is not always foolproof (``x |--> log(x) + 2*pi*I`` is another possibility)::
 
             sage: f(x) = exp(x)
             sage: f.compositional_inverse(allow_inverse_multivalued=False)
+            x |--> log(x)
 
         Sometimes passing ``kwargs`` is useful, for example ``algorithm`` can be used
         when the default solver fails::
 
             sage: f(x) = (2/3)^x
             sage: f.compositional_inverse()
-            sage: f.compositional_inverse(algorithm="giac")  # needs sage.libs.giac
+            Traceback (most recent call last):
+            ...
+            KeyError: x
+            sage: f.compositional_inverse(algorithm="giac")                             # needs sage.libs.giac
+            x |--> -log(x)/(log(3) - log(2))
 
         TESTS::
 
             sage: f(x) = x+exp(x)
             sage: f.compositional_inverse()
+            Traceback (most recent call last):
+            ...
+            ValueError: cannot find an inverse
             sage: f(x) = 0
             sage: f.compositional_inverse()
+            Traceback (most recent call last):
+            ...
+            ValueError: cannot find an inverse
             sage: f(x, y) = (x, x)
             sage: f.compositional_inverse()
+            Traceback (most recent call last):
+            ...
+            ValueError: cannot find an inverse
             sage: (x+1).compositional_inverse()
+            Traceback (most recent call last):
+            ...
+            ValueError: base ring must be a symbolic expression ring
         """
         from sage.modules.free_module_element import vector
         return vector([self]).compositional_inverse(allow_inverse_multivalued=allow_inverse_multivalued, **kwargs)[0]