RelativeInterior: Add documentation, tests, comparison methods, metho…

…d relative_interior

src/sage/geometry/cone.py

@@ -181,9 +181,18 @@
 """
 
 # ****************************************************************************
-#       Copyright (C) 2010 Volker Braun <vbraun.name@gmail.com>
-#       Copyright (C) 2012 Andrey Novoseltsev <novoselt@gmail.com>
-#       Copyright (C) 2010 William Stein <wstein@gmail.com>
+#       Copyright (C) 2010-2014 Volker Braun <vbraun.name@gmail.com>
+#       Copyright (C) 2010-2018 Andrey Novoseltsev <novoselt@gmail.com>
+#       Copyright (C) 2010      William Stein <wstein@gmail.com>
+#       Copyright (C) 2012      Christian Stump
+#       Copyright (C) 2014-2018 Frédéric Chapoton
+#       Copyright (C) 2014      Peter Bruin
+#       Copyright (C) 2015-2017 Jori Mäntysalo
+#       Copyright (C) 2015-2020 Michael Orlitzky
+#       Copyright (C) 2016-2020 John H. Palmieri
+#       Copyright (C) 2018      David Coudert
+#       Copyright (C) 2019-2020 Jonathan Kliem
+#       Copyright (C) 2020-2021 Matthias Koeppe
 #
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU General Public License as published by

src/sage/geometry/relative_interior.py

@@ -16,21 +16,96 @@
 
 class RelativeInterior(SageObject):
 
-    """
+    r"""
     The relative interior of a polyhedron or cone
+
+    This class should not be used directly. Use methods
+    :meth:`~sage.geometry.polyhedron.Polyhedron_base.relative_interior`,
+    :meth:`~sage.geometry.polyhedron.Polyhedron_base.interior`,
+    :meth:`~sage.geometry.cone.ConvexRationalPolyhedralCone.relative_interior`,
+    :meth:`~sage.geometry.cone.ConvexRationalPolyhedralCone.interior` instead.
+
+    EXAMPLES::
+
+        sage: segment = Polyhedron([[1, 2], [3, 4]])
+        sage: segment.relative_interior()
+        Relative interior of
+         a 1-dimensional polyhedron in ZZ^2 defined as the convex hull of 2 vertices
+        sage: octant = Cone([(1,0,0), (0,1,0), (0,0,1)])
+        sage: octant.relative_interior()
+        Relative interior of 3-d cone in 3-d lattice N
+
     """
 
     def __init__(self, polyhedron):
+        r"""
+        Initialize ``self``.
+
+        INPUT:
+
+        - ``polyhedron`` - an instance of :class:`Polyhedron_base` or
+          :class:`ConvexRationalPolyhedralCone`.
+
+        TESTS::
+
+            sage: P = Polyhedron()
+            sage: from sage.geometry.relative_interior import RelativeInterior
+            sage: TestSuite(RelativeInterior(P)).run()
+
+        """
         self._polyhedron = polyhedron
 
     def __contains__(self, point):
+        r"""
+        Return whether ``self`` contains ``point``.
+
+        EXAMPLES::
+
+            sage: octant = Cone([(1,0,0), (0,1,0), (0,0,1)])
+            sage: ri_octant = octant.relative_interior(); ri_octant
+            Relative interior of 3-d cone in 3-d lattice N
+            sage: (1, 1, 1) in ri_octant
+            True
+            sage: (1, 0, 0) in ri_octant
+            False
+        """
         return self._polyhedron.relative_interior_contains(point)
 
+    def relative_interior(self):
+        r"""
+        Return the relative interior of ``self``.
+
+        As ``self`` is already relatively open, this method just returns ``self``.
+
+        EXAMPLES::
+
+            sage: segment = Polyhedron([[1, 2], [3, 4]])
+            sage: ri_segment = segment.relative_interior(); ri_segment
+            Relative interior of
+             a 1-dimensional polyhedron in ZZ^2 defined as the convex hull of 2 vertices
+            sage: ri_segment.relative_interior() is ri_segment
+            True
+        """
+        return self
+
     def closure(self):
+        r"""
+        Return the topological closure of ``self``.
+
+        EXAMPLES::
+
+            sage: segment = Polyhedron([[1, 2], [3, 4]])
+            sage: ri_segment = segment.relative_interior(); ri_segment
+            Relative interior of
+             a 1-dimensional polyhedron in ZZ^2 defined as the convex hull of 2 vertices
+            sage: ri_segment.closure() is segment
+            True
+
+        """
         return self._polyhedron
 
     def _repr_(self):
-        """
+        r"""
         Return a description of ``self``.
 
         EXAMPLES::
@@ -46,3 +121,51 @@ def _repr_(self):
         if repr_P.startswith('A '):
             repr_P = 'a ' + repr_P[2:]
         return 'Relative interior of ' + repr_P
+
+    def __eq__(self, other):
+        r"""
+        Compare ``self`` and ``other``.
+
+        INPUT:
+
+        - ``other`` -- a polyhedron
+
+        EXAMPLES::
+
+            sage: segment = Polyhedron([[1, 2], [3, 4]])
+            sage: ri_segment = segment.relative_interior(); ri_segment
+            Relative interior of
+             a 1-dimensional polyhedron in ZZ^2 defined as the convex hull of 2 vertices
+            sage: segment2 = Polyhedron([[1, 2], [3, 4]], base_ring=AA)
+            sage: ri_segment2 = segment2.relative_interior(); ri_segment2
+            Relative interior of
+             a 1-dimensional polyhedron in AA^2 defined as the convex hull of 2 vertices
+            sage: ri_segment == ri_segment2
+            True
+
+        """
+        return self._polyhedron == other._polyhedron
+
+    def __ne__(self, other):
+        r"""
+        Compare ``self`` and ``other``.
+
+        INPUT:
+
+        - ``other`` -- a polyhedron
+
+        TESTS::
+
+            sage: segment = Polyhedron([[1, 2], [3, 4]])
+            sage: ri_segment = segment.relative_interior(); ri_segment
+            Relative interior of
+             a 1-dimensional polyhedron in ZZ^2 defined as the convex hull of 2 vertices
+            sage: segment2 = Polyhedron([[1, 2], [3, 4]], base_ring=AA)
+            sage: ri_segment2 = segment2.relative_interior(); ri_segment2
+            Relative interior of
+             a 1-dimensional polyhedron in AA^2 defined as the convex hull of 2 vertices
+            sage: ri_segment != ri_segment2
+            False
+
+        """
+        return self._polyhedron != other._polyhedron