Skip to content
This repository has been archived by the owner on Jan 30, 2023. It is now read-only.

Commit

Permalink
Merge branch 'u/jipilab/27071' of trac.sagemath.org:sage into 27071
Browse files Browse the repository at this point in the history
  • Loading branch information
@jplab
jplab committed Mar 14, 2019
2 parents 1040752 + 4a5c06e commit ea744a4
Show file tree
Hide file tree
Showing 3 changed files with 269 additions and 72 deletions.
141 changes: 90 additions & 51 deletions src/sage/geometry/polyhedron/base.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -3682,14 +3682,14 @@ def face_truncation(self, face, linear_coefficients=None, cut_frac=None):
sage: vertex_trunc1 = Cube.face_truncation(Cube.faces(0)[0])
sage: vertex_trunc1.f_vector()
(1, 10, 15, 7, 1)
sage: vertex_trunc1.faces(2)
(<0,1,2,3>,
<2,3,4,5>,
<1,2,5,6>,
<0,1,6,7,8>,
<4,5,6,7,9>,
<7,8,9>,
<0,3,4,8,9>)
sage: tuple(f.ambient_V_indices() for f in vertex_trunc1.faces(2))
((0, 1, 2, 3),
(2, 3, 4, 5),
(1, 2, 5, 6),
(0, 1, 6, 7, 8),
(4, 5, 6, 7, 9),
(7, 8, 9),
(0, 3, 4, 8, 9))
sage: vertex_trunc1.vertices()
(A vertex at (1, -1, -1),
A vertex at (1, 1, -1),
Expand All @@ -3704,14 +3704,14 @@ def face_truncation(self, face, linear_coefficients=None, cut_frac=None):
sage: vertex_trunc2 = Cube.face_truncation(Cube.faces(0)[0],cut_frac=1/2)
sage: vertex_trunc2.f_vector()
(1, 10, 15, 7, 1)
sage: vertex_trunc2.faces(2)
(<0,1,2,3>,
<2,3,4,5>,
<1,2,5,6>,
<0,1,6,7,8>,
<4,5,6,7,9>,
<7,8,9>,
<0,3,4,8,9>)
sage: tuple(f.ambient_V_indices() for f in vertex_trunc2.faces(2))
((0, 1, 2, 3),
(2, 3, 4, 5),
(1, 2, 5, 6),
(0, 1, 6, 7, 8),
(4, 5, 6, 7, 9),
(7, 8, 9),
(0, 3, 4, 8, 9))
sage: vertex_trunc2.vertices()
(A vertex at (1, -1, -1),
A vertex at (1, 1, -1),
Expand All @@ -3738,14 +3738,14 @@ def face_truncation(self, face, linear_coefficients=None, cut_frac=None):
sage: edge_trunc = Cube.face_truncation(Cube.faces(1)[0])
sage: edge_trunc.f_vector()
(1, 10, 15, 7, 1)
sage: edge_trunc.faces(2)
(<0,1,2,3>,
<1,2,4,5>,
<4,5,6,7>,
<0,1,5,6,8>,
<2,3,4,7,9>,
<6,7,8,9>,
<0,3,8,9>)
sage: tuple(f.ambient_V_indices() for f in edge_trunc.faces(2))
((0, 1, 2, 3),
(1, 2, 4, 5),
(4, 5, 6, 7),
(0, 1, 5, 6, 8),
(2, 3, 4, 7, 9),
(6, 7, 8, 9),
(0, 3, 8, 9))
sage: face_trunc = Cube.face_truncation(Cube.faces(2)[0])
sage: face_trunc.vertices()
(A vertex at (1, -1, -1),
Expand Down Expand Up @@ -4063,7 +4063,7 @@ def _make_polyhedron_face(self, Vindices, Hindices):
sage: square = polytopes.hypercube(2)
sage: square._make_polyhedron_face((0,2), (1,))
<0,2>
A 1-dimensional face of a Polyhedron in ZZ^2 defined as the convex hull of 2 vertices
"""
from sage.geometry.polyhedron.face import PolyhedronFace
return PolyhedronFace(self, Vindices, Hindices)
Expand Down Expand Up @@ -4131,16 +4131,16 @@ def face_lattice(self):
EXAMPLES::
sage: square = polytopes.hypercube(2)
sage: square.face_lattice()
sage: fl = square.face_lattice();fl
Finite lattice containing 10 elements with distinguished linear extension
sage: list(_)
[<>, <0>, <1>, <2>, <3>, <0,1>, <0,2>, <2,3>, <1,3>, <0,1,2,3>]
sage: poset_element = _[6]
sage: list(f.ambient_V_indices() for f in fl)
[(), (0,), (1,), (2,), (3,), (0, 1), (0, 2), (2, 3), (1, 3), (0, 1, 2, 3)]
sage: poset_element = fl[6]
sage: a_face = poset_element
sage: a_face
<0,2>
sage: a_face.dim()
1
A 1-dimensional face of a Polyhedron in ZZ^2 defined as the convex hull of 2 vertices
sage: a_face.ambient_V_indices()
(0, 2)
sage: set(a_face.ambient_Vrepresentation()) == \
....: set([square.Vrepresentation(0), square.Vrepresentation(2)])
True
Expand Down Expand Up @@ -4175,33 +4175,67 @@ def face_lattice(self):
Graphics object consisting of 27 graphics primitives
sage: level_sets = polytopes.cross_polytope(2).face_lattice().level_sets()
sage: level_sets[0], level_sets[-1]
([<>], [<0,1,2,3>])
([A -1-dimensional face of a Polyhedron in ZZ^2],
[A 2-dimensional face of a Polyhedron in ZZ^2 defined as the convex hull of 4 vertices])
Various degenerate polyhedra::
sage: Polyhedron(vertices=[[0,0,0],[1,0,0],[0,1,0]]).face_lattice().level_sets()
[[<>], [<0>, <1>, <2>], [<0,1>, <0,2>, <1,2>], [<0,1,2>]]
[[A -1-dimensional face of a Polyhedron in ZZ^3],
[A 0-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 1 vertex,
A 0-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 1 vertex,
A 0-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 1 vertex],
[A 1-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 2 vertices,
A 1-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 2 vertices,
A 1-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 2 vertices],
[A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices]]
sage: Polyhedron(vertices=[(1,0,0),(0,1,0)], rays=[(0,0,1)]).face_lattice().level_sets()
[[<>], [<1>, <2>], [<0,1>, <0,2>, <1,2>], [<0,1,2>]]
[[A -1-dimensional face of a Polyhedron in ZZ^3],
[A 0-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 1 vertex,
A 0-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 1 vertex],
[A 1-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 1 vertex and 1 ray,
A 1-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 1 vertex and 1 ray,
A 1-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 2 vertices],
[A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 2 vertices and 1 ray]]
sage: Polyhedron(rays=[(1,0,0),(0,1,0)], vertices=[(0,0,1)]).face_lattice().level_sets()
[[<>], [<0>], [<0,1>, <0,2>], [<0,1,2>]]
[[A -1-dimensional face of a Polyhedron in ZZ^3],
[A 0-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 1 vertex],
[A 1-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 1 vertex and 1 ray,
A 1-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 1 vertex and 1 ray],
[A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 1 vertex and 2 rays]]
sage: Polyhedron(rays=[(1,0),(0,1)], vertices=[(0,0)]).face_lattice().level_sets()
[[<>], [<0>], [<0,1>, <0,2>], [<0,1,2>]]
[[A -1-dimensional face of a Polyhedron in ZZ^2],
[A 0-dimensional face of a Polyhedron in ZZ^2 defined as the convex hull of 1 vertex],
[A 1-dimensional face of a Polyhedron in ZZ^2 defined as the convex hull of 1 vertex and 1 ray,
A 1-dimensional face of a Polyhedron in ZZ^2 defined as the convex hull of 1 vertex and 1 ray],
[A 2-dimensional face of a Polyhedron in ZZ^2 defined as the convex hull of 1 vertex and 2 rays]]
sage: Polyhedron(vertices=[(1,),(0,)]).face_lattice().level_sets()
[[<>], [<0>, <1>], [<0,1>]]
[[A -1-dimensional face of a Polyhedron in ZZ^1],
[A 0-dimensional face of a Polyhedron in ZZ^1 defined as the convex hull of 1 vertex,
A 0-dimensional face of a Polyhedron in ZZ^1 defined as the convex hull of 1 vertex],
[A 1-dimensional face of a Polyhedron in ZZ^1 defined as the convex hull of 2 vertices]]
sage: Polyhedron(vertices=[(1,0,0),(0,1,0)], lines=[(0,0,1)]).face_lattice().level_sets()
[[<>], [<0,1>, <0,2>], [<0,1,2>]]
[[A -1-dimensional face of a Polyhedron in ZZ^3],
[A 1-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 1 vertex and 1 line,
A 1-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 1 vertex and 1 line],
[A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 2 vertices and 1 line]]
sage: Polyhedron(lines=[(1,0,0)], vertices=[(0,0,1)]).face_lattice().level_sets()
[[<>], [<0,1>]]
[[A -1-dimensional face of a Polyhedron in ZZ^3],
[A 1-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 1 vertex and 1 line]]
sage: Polyhedron(lines=[(1,0),(0,1)], vertices=[(0,0)]).face_lattice().level_sets()
[[<>], [<0,1,2>]]
[[A -1-dimensional face of a Polyhedron in ZZ^2],
[A 2-dimensional face of a Polyhedron in ZZ^2 defined as the convex hull of 1 vertex and 2 lines]]
sage: Polyhedron(lines=[(1,0)], rays=[(0,1)], vertices=[(0,0)])\
....: .face_lattice().level_sets()
[[<>], [<0,1>], [<0,1,2>]]
[[A -1-dimensional face of a Polyhedron in ZZ^2],
[A 1-dimensional face of a Polyhedron in ZZ^2 defined as the convex hull of 1 vertex and 1 line],
[A 2-dimensional face of a Polyhedron in ZZ^2 defined as the convex hull of 1 vertex, 1 ray, 1 line]]
sage: Polyhedron(vertices=[(0,)], lines=[(1,)]).face_lattice().level_sets()
[[<>], [<0,1>]]
[[A -1-dimensional face of a Polyhedron in ZZ^1],
[A 1-dimensional face of a Polyhedron in ZZ^1 defined as the convex hull of 1 vertex and 1 line]]
sage: Polyhedron(lines=[(1,0)], vertices=[(0,0)]).face_lattice().level_sets()
[[<>], [<0,1>]]
[[A -1-dimensional face of a Polyhedron in ZZ^2],
[A 1-dimensional face of a Polyhedron in ZZ^2 defined as the convex hull of 1 vertex and 1 line]]
"""
coatom_to_Hindex = [ h.index() for h in self.inequality_generator() ]
Hindex_to_coatom = [None] * self.n_Hrepresentation()
Expand Down Expand Up @@ -4259,10 +4293,15 @@ def faces(self, face_dimension):
facets of the four-dimensional hypercube::
sage: p = polytopes.hypercube(4)
sage: p.faces(3)
(<0,1,2,3,4,5,6,7>, <0,1,2,3,8,9,10,11>, <0,1,4,5,8,9,12,13>,
<0,2,4,6,8,10,12,14>, <2,3,6,7,10,11,14,15>, <8,9,10,11,12,13,14,15>,
<4,5,6,7,12,13,14,15>, <1,3,5,7,9,11,13,15>)
sage: list(f.ambient_V_indices() for f in p.faces(3))
[(0, 1, 2, 3, 4, 5, 6, 7),
(0, 1, 2, 3, 8, 9, 10, 11),
(0, 1, 4, 5, 8, 9, 12, 13),
(0, 2, 4, 6, 8, 10, 12, 14),
(2, 3, 6, 7, 10, 11, 14, 15),
(8, 9, 10, 11, 12, 13, 14, 15),
(4, 5, 6, 7, 12, 13, 14, 15),
(1, 3, 5, 7, 9, 11, 13, 15)]
sage: face = p.faces(3)[0]
sage: face.ambient_Hrepresentation()
Expand Down Expand Up @@ -4301,9 +4340,9 @@ def faces(self, face_dimension):
sage: pr.faces(4)
()
sage: pr.faces(3)
(<0,1,2,3>,)
(A 3-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 1 vertex, 1 ray, 2 lines,)
sage: pr.faces(2)
(<0,1,2>,)
(A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 1 vertex and 2 lines,)
sage: pr.faces(1)
()
sage: pr.faces(0)
Expand Down Expand Up @@ -4616,7 +4655,7 @@ def one_point_suspension(self, vertex):
sage: cube.one_point_suspension(e)
Traceback (most recent call last):
...
TypeError: The vertex <0,1> should be a Vertex or PolyhedronFace of dimension 0
TypeError: The vertex A 1-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 2 vertices should be a Vertex or PolyhedronFace of dimension 0
"""
from sage.geometry.polyhedron.representation import Vertex
from sage.geometry.polyhedron.face import PolyhedronFace
Expand Down
13 changes: 9 additions & 4 deletions src/sage/geometry/polyhedron/constructor.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -100,11 +100,16 @@
sage: strip.lines()
(A line in the direction (0, 1),)
sage: strip.faces(1)
(<0,1>, <0,2>)
(A 1-dimensional face of a Polyhedron in ZZ^2 defined as the convex hull of 1 vertex and 1 line,
A 1-dimensional face of a Polyhedron in ZZ^2 defined as the convex hull of 1 vertex and 1 line)
sage: for face in strip.faces(1):
....: print("{} = {}".format(face, face.as_polyhedron().Vrepresentation()))
<0,1> = (A line in the direction (0, 1), A vertex at (-1, 0))
<0,2> = (A line in the direction (0, 1), A vertex at (1, 0))
....: print(face.ambient_V_indices())
(0, 1)
(0, 2)
sage: for face in strip.faces(1):
....: print("{} = {}".format(face.ambient_V_indices(), face.as_polyhedron().Vrepresentation()))
(0, 1) = (A line in the direction (0, 1), A vertex at (-1, 0))
(0, 2) = (A line in the direction (0, 1), A vertex at (1, 0))
EXAMPLES::
Expand Down
Loading

0 comments on commit ea744a4

Please sign in to comment.