From ccc84213906ff6bf34d2e5c6b50d146a2901ec9c Mon Sep 17 00:00:00 2001
From: Matthias Koeppe <mkoeppe@math.ucdavis.edu>
Date: Sun, 6 Jun 2021 22:54:52 -0700
Subject: [PATCH] ConvexSet_base.is_compact, ConvexSet_compact: New

---
 src/sage/geometry/convex_set.py       | 43 +++++++++++++++++++++++++++
 src/sage/geometry/lattice_polytope.py |  4 +--
 2 files changed, 45 insertions(+), 2 deletions(-)

diff --git a/src/sage/geometry/convex_set.py b/src/sage/geometry/convex_set.py
index 56189f2518c..37ef89ae39e 100644
--- a/src/sage/geometry/convex_set.py
+++ b/src/sage/geometry/convex_set.py
@@ -101,6 +101,21 @@ def is_closed(self):
 
         """
 
+    def is_compact(self):
+        r"""
+        Return whether ``self`` is compact.
+
+        OUTPUT:
+
+        Boolean.
+
+        """
+        if not self.is_closed():
+            return False
+        if self.dimension() < 1:
+            return True
+        raise NotImplementedError
+
     def closure(self):
         r"""
         Return the topological closure of ``self``.
@@ -152,6 +167,34 @@ def is_open(self):
         return self.is_empty() or self.is_universe()
 
 
+class ConvexSet_compact(ConvexSet_closed):
+
+    r"""
+    Abstract base class for compact convex sets.
+    """
+
+    def is_universe(self):
+        r"""
+        Return whether ``self`` is the whole ambient space
+
+        OUTPUT:
+
+        Boolean.
+        """
+        return self.ambient_dim() == 0 and not self.is_empty()
+
+    def is_compact(self):
+        r"""
+        Return whether ``self`` is compact.
+
+        OUTPUT:
+
+        Boolean.
+
+        """
+        return True
+
+
 class ConvexSet_relatively_open(ConvexSet_base):
 
     r"""
diff --git a/src/sage/geometry/lattice_polytope.py b/src/sage/geometry/lattice_polytope.py
index 10866bc8c31..a063657e30a 100644
--- a/src/sage/geometry/lattice_polytope.py
+++ b/src/sage/geometry/lattice_polytope.py
@@ -135,7 +135,7 @@
 from sage.structure.all import Sequence
 from sage.structure.sage_object import SageObject
 from sage.structure.richcmp import richcmp_method, richcmp
-from sage.geometry.convex_set import ConvexSet_closed
+from sage.geometry.convex_set import ConvexSet_compact
 
 from copy import copy
 from collections.abc import Hashable
@@ -465,7 +465,7 @@ def is_LatticePolytope(x):
     return isinstance(x, LatticePolytopeClass)
 
 @richcmp_method
-class LatticePolytopeClass(ConvexSet_closed, Hashable):
+class LatticePolytopeClass(ConvexSet_compact, Hashable):
     r"""
     Create a lattice polytope.