Parametrize the cube/hypercube functions in the library of polytopes

[sophiasage]

Currently, the polytopes.cube and polytopes.hypercubes use vertex coordinates +/-1. It would be nice to have the 0/1 cube and the 0/1 hypercube. This ticket adds them to the library of polytopes.

CC: @jplab @sagetrac-nailuj @kliem

Component: geometry

Keywords: polytopes, cube, days100

Author: Sophia Elia

Branch/Commit: 6da26d9

Reviewer: Jean-Philippe Labbé, Jonathan Kliem

Issue created by migration from https://trac.sagemath.org/ticket/28247

[videlec]

comment:2

Don't you want to parametrize the already existing cube/hypercube functions? Given x and y and more generally x1,y1, ..., xd,yd you can create the polytope

[x1,y1] x [x2,y2] x ... x [xd,yd]

[jplab]

comment:3

Replying to @videlec:

Don't you want to parametrize the already existing cube/hypercube functions? Given x and y and more generally x1,y1, ..., xd,yd you can create the polytope

[x1,y1] x [x2,y2] x ... x [xd,yd]

Yes, yes, that's the idea; making it inside cube and hypercube was the intended plan.

I am not sure whether to also include:

[x1,y1] x [x2,y2] x ... x [xd,yd]

as well in there. One could try.

There are many ways to interpret x above. There is polytopes.zonotope which does:

sage: corner = vector([1,2,3,4])
sage: directions = diagonal_matrix([10,9,8,7]).columns()
sage: z = polytopes.zonotope(directions).translation(corner)
sage: z.vertices_list()
[[1, 2, 3, 4],
 [1, 2, 3, 11],
 [1, 2, 11, 4],
 [1, 2, 11, 11],
 [1, 11, 3, 4],
 [1, 11, 3, 11],
 [1, 11, 11, 4],
 [1, 11, 11, 11],
 [11, 2, 3, 4],
 [11, 2, 3, 11],
 [11, 2, 11, 4],
 [11, 2, 11, 11],
 [11, 11, 3, 4],
 [11, 11, 3, 11],
 [11, 11, 11, 4],
 [11, 11, 11, 11]]
sage: hc = polytopes.hypercube(4)
sage: z.is_combinatorially_isomorphic(hc)
True

That said, I see that it might be nice to have this directly possible inside of cube and hypercube...

[embray]

comment:4

Ticket retargeted after milestone closed

[sophiasage]

Branch: public/28247

[sophiasage]

Commit: 301b3a1

[sophiasage]

New commits:

301b3a1

first version

[sagetrac-git]

Changed commit from 301b3a1 to c6ac53d

[sagetrac-git]

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

c6ac53d

fixing doctests

[sagetrac-git]

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

f6bcc4e

pyflakes