Linting the changes

Author: jplab

src/sage/geometry/fan.py

@@ -2439,14 +2439,15 @@ def Gale_transform(self):
         m = m.augment(matrix(ZZ, m.nrows(), 1, [1] * m.nrows()))
         return matrix(ZZ, m.integer_kernel().matrix())
 
-    def is_regular(self):
+    def is_polytopal(self):
         r"""
-        Check if ``self`` is regular.
+        Check if ``self`` is the normal fan of a polytope.
 
-        A rational polyhedral fan is *regular* if it is the normal fan of a
-        polytope.
+        A rational polyhedral fan is *polytopal* if it is the normal fan of a
+        polytope. This is also called *regular*, or provide a *coherent*
+        subdivision or leads to a *projective* toric variety.
 
-        OUTPUT: ``True`` if ``self`` is complete and ``False`` otherwise
+        OUTPUT: ``True`` if ``self`` is polytopal and ``False`` otherwise
 
         EXAMPLES:
 
@@ -2459,24 +2460,24 @@ def is_regular(self):
             ....:     S1 = [Cone([rays[i] for i in indices]) for indices in L]
             ....:     return Fan(S1)
 
-        When epsilon=0, it is not regular::
+        When epsilon=0, it is not polytopal::
 
             sage: epsilon = 0
-            sage: mother(epsilon).is_regular()
+            sage: mother(epsilon).is_polytopal()
             False
 
-        Doing a slight perturbation makes the same subdivision regular::
+        Doing a slight perturbation makes the same subdivision polytopal::
 
             sage: epsilon = 1/2
-            sage: mother(epsilon).is_regular()
+            sage: mother(epsilon).is_polytopal()
             True
 
         .. SEEALSO::
 
             :meth:`is_projective`.
         """
         if not self.is_complete():
-            raise ValueError('the fan is not complete')
+            raise ValueError('To be polytopal, the fan should be complete.')
         from sage.geometry.triangulation.point_configuration import PointConfiguration
         from sage.geometry.polyhedron.constructor import Polyhedron
         pc = PointConfiguration(self.rays())
@@ -2492,8 +2493,6 @@ def is_regular(self):
         poly = Polyhedron(ieqs=ieqs)
         return self.is_equivalent(poly.normal_fan())
 
-    is_projective = is_regular
-
     def generating_cone(self, n):
         r"""
         Return the ``n``-th generating cone of ``self``.

src/sage/geometry/polyhedron/base5.py

@@ -711,19 +711,19 @@ def deformation_cone(self):
             2.2 of [ACEP2020].
         """
         from .constructor import Polyhedron
-        A = matrix([_.A() for _ in self.Hrepresentation()])
-        A = A.transpose()
-        A_ker = A.right_kernel_matrix(basis='computed')
-        gale = tuple(A_ker.columns())
+        m = matrix([_.A() for _ in self.Hrepresentation()])
+        m = m.transpose()
+        m_ker = m.right_kernel_matrix(basis='computed')
+        gale = tuple(m_ker.columns())
         collection = [f.ambient_H_indices() for f in self.faces(0)]
         n = len(gale)
-        K = None
+        c = None
         for cone_indices in collection:
             dual_cone = Polyhedron(rays=[gale[i] for i in range(n) if i not in
                                          cone_indices])
-            K = K.intersection(dual_cone) if K is not None else dual_cone
-        preimages = [A_ker.solve_right(r.vector()) for r in K.rays()]
-        return Polyhedron(lines=A.rows(), rays=preimages)
+            c = c.intersection(dual_cone) if c is not None else dual_cone
+        preimages = [A_ker.solve_right(r.vector()) for r in c.rays()]
+        return Polyhedron(lines=m.rows(), rays=preimages)
 
     ###########################################################
     # Binary operations.

src/sage/geometry/triangulation/point_configuration.py

@@ -61,7 +61,7 @@
     (2, 3, 4)
     sage: list(t)
     [(1, 3, 4), (2, 3, 4)]
-    sage: t.plot(axes=False)                                                            # needs sage.plot
+    sage: t.plot(axes=False)                                                       # needs sage.plot
     Graphics object consisting of 12 graphics primitives
 
 .. PLOT::
@@ -91,7 +91,7 @@
     sage: p = [[0,-1,-1], [0,0,1], [0,1,0], [1,-1,-1], [1,0,1], [1,1,0]]
     sage: points = PointConfiguration(p)
     sage: triang = points.triangulate()
-    sage: triang.plot(axes=False)                                                       # needs sage.plot
+    sage: triang.plot(axes=False)                                                 # needs sage.plot
     Graphics3d Object
 
 .. PLOT::
@@ -116,7 +116,7 @@
     16
     sage: len(nonregular)
     2
-    sage: nonregular[0].plot(aspect_ratio=1, axes=False)                                # needs sage.plot
+    sage: nonregular[0].plot(aspect_ratio=1, axes=False)                          # needs sage.plot
     Graphics object consisting of 25 graphics primitives
     sage: PointConfiguration.set_engine('internal')   # to make doctests independent of TOPCOM
 
@@ -1131,20 +1131,20 @@ def restricted_automorphism_group(self):
 
             sage: pyramid = PointConfiguration([[1,0,0], [0,1,1], [0,1,-1],
             ....:                               [0,-1,-1], [0,-1,1]])
-            sage: G = pyramid.restricted_automorphism_group()                           # needs sage.graphs sage.groups
-            sage: G == PermutationGroup([[(3,5)], [(2,3),(4,5)], [(2,4)]])              # needs sage.graphs sage.groups
+            sage: G = pyramid.restricted_automorphism_group()                      # needs sage.graphs sage.groups
+            sage: G == PermutationGroup([[(3,5)], [(2,3),(4,5)], [(2,4)]])         # needs sage.graphs sage.groups
             True
-            sage: DihedralGroup(4).is_isomorphic(G)                                     # needs sage.graphs sage.groups
+            sage: DihedralGroup(4).is_isomorphic(G)                                # needs sage.graphs sage.groups
             True
 
         The square with an off-center point in the middle. Note that
         the middle point breaks the restricted automorphism group
         `D_4` of the convex hull::
 
             sage: square = PointConfiguration([(3/4,3/4), (1,1), (1,-1), (-1,-1), (-1,1)])
-            sage: square.restricted_automorphism_group()                                # needs sage.graphs sage.groups
+            sage: square.restricted_automorphism_group()                           # needs sage.graphs sage.groups
             Permutation Group with generators [(3,5)]
-            sage: DihedralGroup(1).is_isomorphic(_)                                     # needs sage.graphs sage.groups
+            sage: DihedralGroup(1).is_isomorphic(_)                                # needs sage.graphs sage.groups
             True
         """
         v_list = [ vector(p.projective()) for p in self ]
@@ -1532,9 +1532,9 @@ def bistellar_flips(self):
             sage: pc.bistellar_flips()
             (((<0,1,3>, <0,2,3>), (<0,1,2>, <1,2,3>)),)
             sage: Tpos, Tneg = pc.bistellar_flips()[0]
-            sage: Tpos.plot(axes=False)                                                 # needs sage.plot
+            sage: Tpos.plot(axes=False)                                            # needs sage.plot
             Graphics object consisting of 11 graphics primitives
-            sage: Tneg.plot(axes=False)                                                 # needs sage.plot
+            sage: Tneg.plot(axes=False)                                            # needs sage.plot
             Graphics object consisting of 11 graphics primitives
 
         The 3d analog::
@@ -1549,7 +1549,7 @@ def bistellar_flips(self):
             sage: pc.bistellar_flips()
             (((<0,1,3>, <0,2,3>), (<0,1,2>, <1,2,3>)),)
             sage: Tpos, Tneg = pc.bistellar_flips()[0]
-            sage: Tpos.plot(axes=False)                                                 # needs sage.plot
+            sage: Tpos.plot(axes=False)                                            # needs sage.plot
             Graphics3d Object
         """
         flips = []
@@ -2080,7 +2080,7 @@ def Gale_transform(self, points=None, homogenize=True):
             [ 1  1  1  0 -3]
             [ 0  2  2 -1 -3]
 
-        It might not affect the dimension of the result:: 
+        It might not affect the dimension of the result::
 
             sage: PC = PointConfiguration([[4,0,0],[0,4,0],[0,0,4],[2,1,1],[1,2,1],[1,1,2]])
             sage: GT = PC.Gale_transform(homogenize=False);GT
@@ -2136,9 +2136,9 @@ def deformation_cone(self, collection):
         - ``collection`` -- a collection of subconfigurations of ``self``.
           Subconfigurations are given as indices
 
-        OUTPUT: a polyhedron. It contains the liftings of the point configuration 
-        making the collection a regular (or coherent, or projective)
-        subdivision.
+        OUTPUT: a polyhedron. It contains the liftings of the point configuration
+        making the collection a regular (or coherent, or projective, or
+        polytopal) subdivision.
 
         EXAMPLES::
 
@@ -2170,58 +2170,56 @@ def deformation_cone(self, collection):
         Let's verify the mother of all examples explained in Section 7.1.1 of
         [DLRS2010]_::
 
+            sage: def mother(epsilon=0):
+            ....:     return PointConfiguration([(4-epsilon,epsilon,0),(0,4-epsilon,epsilon),(epsilon,0,4-epsilon),(2,1,1),(1,2,1),(1,1,2)])
+
             sage: epsilon = 0
-            sage: mother = PointConfiguration([(4-epsilon,epsilon,0),(0,4-epsilon,epsilon),(epsilon,0,4-epsilon),(2,1,1),(1,2,1),(1,1,2)])
+            sage: m = mother(0)
             sage: mother.points()
             (P(4, 0, 0), P(0, 4, 0), P(0, 0, 4), P(2, 1, 1), P(1, 2, 1), P(1, 1, 2))
             sage: S1 = [(0,1,4),(0,3,4),(1,2,5),(1,4,5),(0,2,3),(2,3,5)]
             sage: S2 = [(0,1,3),(1,3,4),(1,2,4),(2,4,5),(0,2,5),(0,3,5)]
 
         Both subdivisions `S1` and `S2` are not regular::
 
-            sage: mother_dc1 = mother.deformation_cone(S1)
+            sage: mother_dc1 = m.deformation_cone(S1)
             sage: mother_dc1
             A 4-dimensional polyhedron in QQ^6 defined as the convex hull of 1 vertex, 1 ray, 3 lines
-            sage: mother_dc2 = mother.deformation_cone(S2)
+            sage: mother_dc2 = m.deformation_cone(S2)
             sage: mother_dc2
             A 4-dimensional polyhedron in QQ^6 defined as the convex hull of 1 vertex, 1 ray, 3 lines
 
         Notice that they have a ray which provides a degenerate lifting which
         only provides a coarsening of the subdivision from the lower hull (it
         has 5 facets, and should have 8)::
 
-            sage: result = Polyhedron([vector(list(mother.points()[_])+[mother_dc1.rays()[0][_]]) for _ in range(len(mother.points()))])
+            sage: result = Polyhedron([vector(list(m.points()[_])+[mother_dc1.rays()[0][_]]) for _ in range(len(m.points()))])
             sage: result.f_vector()
             (1, 6, 9, 5, 1)
 
         But if we use epsilon to perturb the configuration, suddenly
         `S1` becomes regular::
 
             sage: epsilon = 1/2
-            sage: mother = PointConfiguration([(4-epsilon,epsilon,0), 
-                                               (0,4-epsilon,epsilon),
-                                               (epsilon,0,4-epsilon),
-                                               (2,1,1),
-                                               (1,2,1),
-                                               (1,1,2)])
-            sage: mother.points()
+            sage: mp = mother(epsilon)
+            sage: mp.points()
             (P(7/2, 1/2, 0),
              P(0, 7/2, 1/2),
              P(1/2, 0, 7/2),
              P(2, 1, 1),
              P(1, 2, 1),
              P(1, 1, 2))
-            sage: mother_dc1 = mother.deformation_cone(S1);mother_dc1
+            sage: mother_dc1 = mp.deformation_cone(S1);mother_dc1
             A 6-dimensional polyhedron in QQ^6 defined as the convex hull of 1 vertex, 3 rays, 3 lines
-            sage: mother_dc2 = mother.deformation_cone(S2);mother_dc2
+            sage: mother_dc2 = mp.deformation_cone(S2);mother_dc2
             A 3-dimensional polyhedron in QQ^6 defined as the convex hull of 1 vertex and 3 lines
 
-        .. SEEALSO::                                                                                                                                                                                        
-                   
+        .. SEEALSO::
+
             :meth:`~sage.schemes.toric.variety.Kaehler_cone`
-                   
+
         REFERENCES:
-                   
+
             For more information, see Section 5.4 of [DLRS2010]_ and Section
             2.2 of [ACEP2020].
         """