LatticePolytopeClass, NefPartition, PointCollection, ToricLattice_amb…

…ient: Add _sage_input_ methods

src/sage/geometry/lattice_polytope.py

@@ -548,6 +548,28 @@ def __init__(self, points=None, compute_vertices=None,
             self._ambient_facet_indices = tuple(ambient_facet_indices)
             self._vertices = ambient.vertices(self._ambient_vertex_indices)
 
+    def _sage_input_(self, sib, coerced):
+        """
+        Return Sage command to reconstruct ``self``.
+
+        See :mod:`sage.misc.sage_input` for details.
+
+        EXAMPLES::
+
+            sage: p = lattice_polytope.cross_polytope(2)
+            sage: sage_input(p, verify=True)
+            # Verified
+            LatticePolytope(sage.geometry.point_collection.PointCollection((vector(ZZ, [1, 0]),
+                                                                            vector(ZZ, [0, 1]),
+                                                                            vector(ZZ, [-1, 0]),
+                                                                            vector(ZZ, [0, -1]))),
+                            compute_vertices=False)
+        """
+        if self._ambient is not self:
+            raise NotImplementedError
+        data = self._vertices
+        return sib.name('LatticePolytope')(sib(self._vertices), compute_vertices=False)
+
     def __contains__(self, point):
         r"""
         Check if ``point`` is contained in ``self``.
@@ -4495,6 +4517,31 @@ def _repr_(self):
             pass
         return result
 
+    def _sage_input_(self, sib, coerced):
+        """
+        Return Sage command to reconstruct ``self``.
+
+        See :mod:`sage.misc.sage_input` for details.
+
+        EXAMPLES::
+
+            sage: o = lattice_polytope.cross_polytope(3)
+            sage: np = o.nef_partitions()[0]; np
+            Nef-partition {0, 1, 3} U {2, 4, 5}
+            sage: sage_input(np, verify=True)
+            # Verified
+            NefPartition([0, 0, 1, 0, 1, 1],
+                         LatticePolytope(sage.geometry.point_collection.PointCollection((vector(ZZ, [1, 0, 0]),
+                                                                                         vector(ZZ, [0, 1, 0]),
+                                                                                         vector(ZZ, [0, 0, 1]),
+                                                                                         vector(ZZ, [-1, 0, 0]),
+                                                                                         vector(ZZ, [0, -1, 0]),
+                                                                                         vector(ZZ, [0, 0, -1]))),
+                                         compute_vertices=False))
+        """
+        vertex_to_part = [ZZ(i) for i in self._vertex_to_part]
+         return sib.name('NefPartition')(vertex_to_part, sib(self.Delta_polar()))
+
     def Delta(self, i=None):
         r"""
         Return the polytope $\Delta$ or $\Delta_i$ corresponding to ``self``.

src/sage/geometry/point_collection.pyx

@@ -129,12 +129,10 @@ cdef class PointCollection(SageObject):
       if ``points`` are already accessible to you as a :class:`tuple`, it is
       preferable to use it for speed and memory consumption reasons;
 
-    - ``module`` -- an ambient module for ``points``. If ``None``, it will be
-      determined as :func:`parent` of the first point. Of course, this cannot
-      be done if there are no points, so in this case you must give an
-      appropriate ``module`` directly. Note that ``None`` is *not* the default
-      value - you always *must* give this argument explicitly, even if it is
-      ``None``.
+    - ``module`` -- an ambient module for ``points``. If ``None`` (the default),
+      it will be determined as :func:`parent` of the first point. Of course, this
+      cannot be done if there are no points, so in this case you must give an
+      appropriate ``module`` directly.
 
     OUTPUT:
 
@@ -172,6 +170,29 @@ cdef class PointCollection(SageObject):
         self._points = tuple(points)
         self._module = self._points[0].parent() if module is None else module
 
+    def _sage_input_(self, sib, coerced):
+        r"""
+        Return Sage command to reconstruct ``self``.
+
+        See :mod:`sage.misc.sage_input` for details.
+
+        EXAMPLES::
+
+            sage: c = Cone([(0,0,1), (1,0,1), (0,1,1), (1,1,1)]).rays()
+            sage: sage_input(c, verify=True)
+            # Verified
+            sage.geometry.point_collection.PointCollection((vector(ZZ, [0, 0, 1]), vector(ZZ, [1, 0, 1]), vector(ZZ, [0, 1, 1]), vector(ZZ, [1, 1, 1])))
+
+            sage: c = sage.geometry.point_collection.PointCollection([], ToricLattice(2, 'U'))
+            sage: sage_input(c, verify=True)
+            # Verified
+            sage.geometry.point_collection.PointCollection((), ToricLattice(2, 'U', 'U*', 'U', 'U^*'))
+        """
+        args = [sib(self._points)]
+        if not self._points or self._module is not self._points[0].parent():
+            args.append(sib(self._module))
+        return sib.name('sage.geometry.point_collection.PointCollection')(*args)
+
     def __add__(left, right):
         r"""
         Return the joint point collection.

src/sage/geometry/toric_lattice.py

@@ -901,6 +901,29 @@ def __init__(self, rank, name, dual_name, latex_name, latex_dual_name):
         self._latex_name = latex_name
         self._latex_dual_name = latex_dual_name
 
+    def _sage_input_(self, sib, coerced):
+        r"""
+        Return Sage command to reconstruct ``self``.
+
+        See :mod:`sage.misc.sage_input` for details.
+
+        EXAMPLES::
+
+            sage: N = ToricLattice(3, "N", "M", "N", "M")
+            sage: sage_input(N, verify=True)
+            # Verified
+            ToricLattice(3, 'N', 'M')
+
+            sage: N = ToricLattice(3, "N")
+            sage: sage_input(N, verify=True)
+            # Verified
+            ToricLattice(3, 'N', 'N*', 'N', 'N^*')
+        """
+        args = [self.rank(), self._name, self._dual_name]
+        if self._latex_name != self._name or self._latex_dual_name != self._dual_name:
+            args.extend([self._latex_name, self._latex_dual_name])
+        return sib.name('ToricLattice')(*args)
+
     def __richcmp__(self, right, op):
         r"""
         Compare ``self`` and ``right``.