Adding generic change_ring() method and some other touchups.

src/sage/rings/ideal.py

@@ -48,21 +48,20 @@ def Ideal(*args, **kwds):
     addition to using the :func:`Ideal` function:
 
     -  ``R.ideal(gens, coerce=True)``
-    -  ``gens*R``
-    -  ``R*gens``
+    -  ``gens * R``
+    -  ``R * gens``
 
     INPUT:
 
-    -  ``R`` - A ring (optional; if not given, will try to infer it from
-       ``gens``)
+    -  ``R`` -- (optional) a ring; if not given, will try to infer
+       it from ``gens``
+    -  ``gens`` -- list of elements generating the ideal
+    -  ``coerce`` -- (default: ``True``) boolean;
+       whether ``gens`` need to be coerced into the ring
 
-    -  ``gens`` - list of elements generating the ideal
+    OUTPUT:
 
-    -  ``coerce`` - bool (optional, default: ``True``);
-       whether ``gens`` need to be coerced into the ring.
-
-
-    OUTPUT: The ideal of ring generated by ``gens``.
+    the ideal of ring generated by ``gens``
 
     EXAMPLES::
 
@@ -254,12 +253,10 @@ def __init__(self, ring, gens, coerce=True):
 
         INPUT:
 
-        - ``ring`` -- A ring
-
-        - ``gens`` -- The generators for this ideal
-
-        - ``coerce`` -- (default: ``True``) If ``gens`` needs to be coerced
-          into ``ring``.
+        - ``ring`` -- a ring
+        - ``gens`` -- the generators for this ideal
+        - ``coerce`` -- (default: ``True``) if ``gens`` needs to be
+          coerced into ``ring``
 
         EXAMPLES::
 
@@ -319,7 +316,7 @@ def _repr_short(self):
             return '\n(\n  %s\n)\n' % (',\n\n  '.join(L))
         return '(%s)' % (', '.join(L))
 
-    def __repr__(self):
+    def _repr_(self):
         """
         Return a string representation of ``self``.
 
@@ -689,6 +686,22 @@ def gens_reduced(self):
         """
         return self.gens()
 
+    def change_ring(self, R, *args, **kwds):
+        r"""
+        Convert ``self`` into an ideal of the ring ``R``.
+
+        EXAMPLES::
+
+            sage: Sym = SymmetricFunctions(QQ)
+            sage: s = Sym.s()
+            sage: h = Sym.h()
+            sage: I = s.ideal([s[2], s[1,1]]); I
+            Ideal (s[2], s[1, 1]) of Symmetric Functions over Rational Field in the Schur basis
+            sage: I.change_ring(h)
+            Ideal (h[2], h[1, 1] - h[2]) of Symmetric Functions over Rational Field in the homogeneous basis
+        """
+        return R.ideal([R(g) for g in self.__gens], *args, **kwds)
+
     def is_maximal(self):
         r"""
         Return ``True`` if the ideal is maximal in the ring containing the