Add is_trivial(::NCRing) (#1848)

Also remove some outdated or pointless TODO comments, and
add a docstring for is_perfect

src/Rings.jl

@@ -172,6 +172,21 @@ end
 #
 ###############################################################################
 
+@doc raw"""
+    is_trivial(R::NCRing)
+
+Test whether the ring $R$ is trivial. A ring is trivial if it consists
+of a single element, or equivalently if its characteristic is 1. Such
+rings are also called zero rings.
+"""
+is_trivial(F::NCRing) = characteristic(F) == 1
+is_trivial(F::Field) = false
+
+@doc raw"""
+    is_perfect(F::Field)
+
+Test whether the field $F$ is perfect.
+"""
 is_perfect(F::Field) = characteristic(F) == 0 || F isa FinField ||
                                                  throw(NotImplementedError(:is_perfect, F))
 

src/fundamental_interface.jl

@@ -4,8 +4,6 @@
 #
 ###############################################################################
 
-# TODO: Move more generic functions to this file.
-
 ###############################################################################
 #
 #   Parents, elements and data type methods
@@ -34,7 +32,6 @@ true
 """
 function parent end
 
-# TODO: Give example
 @doc raw"""
     elem_type(parent)
     elem_type(parent_type)