Coercion/conversion from Cone and other objects to Polyhedron

[nthiery]

Mixed intersections between Cones and Polyhedron returning a Polyhedron:

   sage: cone = Cone([(1,0), (-1,0), (0,1)])
   sage: p = polytopes.hypercube(2)
   sage: p & cone
   A 2-dimensional polyhedron in ZZ^2 defined as the convex hull of 3 vertices

In a similar direction, we extend the Polyhedron constructor so it can take various types as objects as input, for example:

        sage: H.<x,y> = HyperplaneArrangements(QQ)
        sage: h = x + y - 1; h
        Hyperplane x + y - 1
        sage: Polyhedron(h, base_ring=ZZ)
        A 1-dimensional polyhedron in ZZ^2 defined as the convex hull of 1 vertex and 1 line
        sage: Polyhedron(h)

CC: @vbraun @mo271 @jplab @yuan-zhou @kliem

Component: geometry

Keywords: cone, polyhedron

Author: Matthias Koeppe

Branch/Commit: 576076a

Reviewer: Jonathan Kliem

Issue created by migration from https://trac.sagemath.org/ticket/14222

[mo271]

comment:5

the dimension alias is working..;
I remove it from the list.

[jplab]

Changed keywords from none to cone, polyhedron

[mkoeppe]

Branch: u/mkoeppe/coercion_from_cone_to_polyhedron

[sagetrac-git]

Commit: d0ef08f

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

8a2b4c6	RationalPolyhedralCone.intersection: Delegate to Polyhedron if other is not a RationalPolyhedralCone
36bc14d	PolyhedronFace.as_polyhedron, {ConvexRationalPolyhedralCone,LatticePolytopeClass,Hyperplane}.polyhedron: Accept and pass on kwds
d0ef08f	Polyhedron: If first arg is an object with an 'as_polyhedron' or 'polyhedron' method, call it

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

859779f

Polyhedron: Add examples for conversions

[sagetrac-git]

Changed commit from d0ef08f to 859779f

[mkoeppe]

Author: Matthias Koeppe

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

46b5cb7

Polyhedron: Allow converting from a given polyhedron

[sagetrac-git]

Changed commit from 859779f to 46b5cb7

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

16270cb

src/sage/geometry/cone.py: Fix doctest

[sagetrac-git]

Changed commit from 46b5cb7 to 16270cb

[sagetrac-git]

Changed commit from 16270cb to 576076a

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

88e7190	ConvexRationalPolyhedralCone: Make `__and__` an alias for intersection
40d4965	RationalPolyhedralCone.intersection: Delegate to Polyhedron if other is not a RationalPolyhedralCone
fccf307	PolyhedronFace.as_polyhedron, {ConvexRationalPolyhedralCone,LatticePolytopeClass,Hyperplane}.polyhedron: Accept and pass on kwds
3624fce	Polyhedron: If first arg is an object with an 'as_polyhedron' or 'polyhedron' method, call it
8b3cd6a	Polyhedron: Add examples for conversions
0f83724	Polyhedron: Allow converting from a given polyhedron
576076a	src/sage/geometry/cone.py: Fix doctest

[kliem]

Reviewer: Jonathan Kliem

[kliem]

comment:23

Nice. LGTM.

[mkoeppe]

comment:25

Thanks!

[vbraun]

Changed branch from u/mkoeppe/coercion_from_cone_to_polyhedron to 576076a