Fix some doctests, work on comparison functions

src/sage/rings/polynomial/padics/omtree/frame.py

@@ -150,6 +150,21 @@ def __init__(self, Phi, prev=None, iteration_count=0):
             self.F = self.prev_frame().F * self.prev.Fplus
             self.depth = self.prev_frame().depth + 1
 
+    def __eq__(self, other):
+        """
+        Check whether self is equal to other
+
+        EXAMPLES::
+
+            sage: from sage.rings.polynomial.padics.omtree.frame import *
+            sage: Phi = ZpFM(2,20,'terse')['x'](x^32+16)
+            sage: f = Frame(Phi)
+            sage: g = Frame(Phi, iteration_count=4)
+            sage: f == g
+            False
+        """
+        return type(self) == type(other) and self.Phi() == other.Phi() and self.phi == other.phi and self.iteration == other.iteration
+
     def seed(self, phi, length=infinity):
         r"""
         Seed all of the intermediate values of the frame based on the new
@@ -273,7 +288,7 @@ def root(self):
             technically be a forest.
 
         .. SEEALSO::
-        
+
             :meth:`omtree.OMTree.roots`
 
         EXAMPLES:

src/sage/rings/polynomial/padics/omtree/frameelt.py

@@ -73,17 +73,17 @@ class FrameElt(SageObject):
         TypeError: not a constant polynomial
 
     Moving to a higher frame, the approximation `\phi` of the previous frame is
-    used. Here `6x^2 + 1` is expressed in its `x`-adic expansion as ``[1,
-    6*x^2]``::
+    used. Here `6x^2 + 1` is expressed in its `x`-adic expansion as ``[1, 6*x^2]``::
 
-        sage: f = f.polygon[0].factors[0].next_frame(); f
+        sage: fr = f.polygon[0].factors[0].next_frame(); fr
         Frame with phi (1 + O(2^20))*x^8 + (0 + O(2^20))*x^7 + (0 + O(2^20))*x^6 + (0 + O(2^20))*x^5 + (0 + O(2^20))*x^4 + (0 + O(2^20))*x^3 + (0 + O(2^20))*x^2 + (0 + O(2^20))*x + (1048574 + O(2^20))
-        sage: FrameElt(f, 6*x^2 + 1)
+        sage: fe = FrameElt(fr, 6*x^2 + 1)
+        sage: fe
         [[1*2^0]phi1^0, [3*2^1]phi1^2]
 
     TESTS::
 
-        sage: isinstance(f, FrameElt)
+        sage: isinstance(fe, FrameElt)
         True
 
     """
@@ -142,7 +142,7 @@ def __eq__(self, other):
 
             sage: from sage.rings.polynomial.padics.omtree.frameelt import FrameElt
             sage: from sage.rings.polynomial.padics.omtree.frame import Frame
-            sage: R.<x> = ZpFM(2, 20, 'terse')
+            sage: R.<x> = ZpFM(2, 20, 'terse')[]
             sage: f = Frame(x^32 + 16); f.seed(x)
             sage: fe = FrameElt(f, 20)
             sage: fe == fe
@@ -159,7 +159,7 @@ def __ne__(self, other):
 
             sage: from sage.rings.polynomial.padics.omtree.frameelt import FrameElt
             sage: from sage.rings.polynomial.padics.omtree.frame import Frame
-            sage: R.<x> = ZpFM(2, 20, 'terse')
+            sage: R.<x> = ZpFM(2, 20, 'terse')[]
             sage: f = Frame(x^32 + 16); f.seed(x)
             sage: fe = FrameElt(f, 20)
             sage: fe != fe

src/sage/rings/polynomial/padics/omtree/omtree.py

@@ -192,7 +192,7 @@ def approximations(self):
 
     def roots(self):
         """
-        The roots of the trees with the leaves the OMTree.
+        The roots of the trees whose leaves are in the OMTree.
 
         As a note, the leaves for a polynomial's OM Tree may have different roots.
         Becuase optimal OM Trees remove 'improvement frames' (those for which

src/sage/rings/polynomial/padics/omtree/residual_factor.py

@@ -165,7 +165,7 @@ def __eq__(self, other):
             sage: R.<x> = ZpFM(2, 20, 'terse')[]
             sage: T = OMTree(x^4 + 20*x^3 + 44*x^2 + 80*x + 1040)
             sage: T.leaves()[0].prev == T.leaves()[0].prev
-            False
+            True
 
         """
         return type(self) == type(other) and self.segment == other.segment and self.rho == other.rho and self.multiplicity == other.multiplicity
@@ -180,7 +180,7 @@ def __ne__(self, other):
             sage: R.<x> = ZpFM(2, 20, 'terse')[]
             sage: T = OMTree(x^4 + 20*x^3 + 44*x^2 + 80*x + 1040)
             sage: T.leaves()[0].prev != T.leaves()[0].prev
-            True
+            False
 
         """
         return not (self == other)

src/sage/rings/polynomial/padics/omtree/segment.py

@@ -6,6 +6,7 @@
 - Brian Sinclair (2012-02-22): initial version
 
 """
+
 from sage.rings.polynomial.padics.omtree.residual_factor import ResidualFactor
 from sage.rings.infinity import infinity
 from sage.structure.sage_object import SageObject
@@ -126,24 +127,6 @@ def __init__(self, frame, slope, verts):
         self.factors = [ResidualFactor(self, afact[0], afact[1])
                         for afact in list(self.residual_polynomial().factor())]
 
-    def __cmp__(self, other):
-        """
-        Comparison.
-
-        EXAMPLES::
-
-            sage: from sage.rings.polynomial.padics.omtree.frame import Frame
-            sage: k = ZpFM(2, 20, 'terse'); kx.<x> = k[]
-            sage: Phi = x^4 + 20*x^3 + 44*x^2 + 80*x + 1040
-            sage: f = Frame(Phi); f.seed(Phi.parent().gen()); P = f.polygon
-            sage: f = f.polygon[0].factors[0].next_frame(); Q = f.polygon
-            sage: P == Q
-            False
-        """
-        c = cmp(type(self), type(other))
-        if c: return c
-        return cmp((self.length, self.verts, self.slope), (other.length, other.verts, other.slope))
-
     @cached_method
     def residual_polynomial(self):
         """
@@ -215,7 +198,37 @@ def __hash__(self):
         return hash((self.length, self.slope))
 
     def __eq__(self, other):
-        raise NotImplementedError
+        r"""
+        Return whether this is equal to the segment ``other``.
+
+        EXAMPLES::
+
+            sage: from sage.rings.polynomial.padics.omtree.frame import Frame
+            sage: k = ZpFM(2, 20, 'terse'); kx.<x> = k[]
+            sage: Phi = x^4 + 20*x^3 + 44*x^2 + 80*x + 1040
+            sage: f1 = Frame(Phi); f1.seed(Phi.parent().gen())
+            sage: s1 = f1.polygon[0] # first segment of the polygon of frame f1
+            sage: f2 = f1.polygon[0].factors[0].next_frame()
+            sage: s2 = f2.polygon[0] # first segment of the polygon of frame f2
+            sage: s1 == s2
+            False
+        """
+        return type(self) is type(other) and self.length == other.length and self.verts == other.verts and self.slope == other.slope
 
     def __ne__(self, other):
-        raise NotImplementedError
+        r"""
+        Return whether this is not equal to the segment ``other``.
+
+        EXAMPLES::
+
+            sage: from sage.rings.polynomial.padics.omtree.frame import Frame
+            sage: k = ZpFM(2, 20, 'terse'); kx.<x> = k[]
+            sage: Phi = x^4 + 20*x^3 + 44*x^2 + 80*x + 1040
+            sage: f1 = Frame(Phi); f1.seed(Phi.parent().gen())
+            sage: s1 = f1.polygon[0] # first segment of the polygon of frame f1
+            sage: f2 = f1.polygon[0].factors[0].next_frame()
+            sage: s2 = f2.polygon[0] # first segment of the polygon of frame f2
+            sage: s1 != s2
+            True
+        """
+        return not (self == other)