Implement Integer.radical() to fix ArithmeticError on 0.radical()

src/sage/arith/misc.py

@@ -2775,9 +2775,7 @@ def radical(n, *args, **kwds):
         sage: radical(2 * 3^2 * 5^5)
         30
         sage: radical(0)
-        Traceback (most recent call last):
-        ...
-        ArithmeticError: radical of 0 is not defined
+        0
         sage: K.<i> = QuadraticField(-1)                                                # needs sage.rings.number_field
         sage: radical(K(2))                                                             # needs sage.rings.number_field
         i - 1

src/sage/categories/unique_factorization_domains.py

@@ -262,9 +262,7 @@ def radical(self, *args, **kwds):
                 sage: Integer(-100).radical()
                 10
                 sage: Integer(0).radical()
-                Traceback (most recent call last):
-                ...
-                ArithmeticError: radical of 0 is not defined
+                0
 
             The next example shows how to compute the radical of a number,
             assuming no prime > 100000 has exponent > 1 in the factorization::

src/sage/rings/integer.pyx

@@ -5911,6 +5911,25 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
         flag = self < 0 and proof
         return objtogen(self).qfbclassno(flag).sage()
 
+    def radical(self, *args, **kwds):
+        """
+        Return the radical of this integer, i.e., the product of its
+        prime divisors.
+
+        EXAMPLES::
+
+            sage: 0.radical()
+            0
+            sage: 10.radical()
+            10
+            sage: (-12).radical()
+            6
+        """
+        if self.is_zero():
+            return self
+
+        return self.factor(*args, **kwds).radical_value()
+
     def squarefree_part(self, long bound=-1):
         r"""
         Return the square free part of `x` (=``self``), i.e., the unique integer