Parametrize the cube/hypercube functions in the library of polytopes

[selia]

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.

[vdelecroix]

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]

[jipilab]

Replying to vdelecroix:

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]

Ticket retargeted after milestone closed

[selia]

New commits:

​301b3a1

first version

[git]

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

​c6ac53d

fixing doctests

[git]

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

​f6bcc4e

pyflakes

[git]

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

​17d8398

edits

[gh-kliem]

Please make the zero-one string consistent.

[gh-kliem]

Looks mostly good. Some comments:

• In the docstring of cube remove empty line and unindent the output of cc.vertices_list().
• three intervals of length 2: Do not specify the length of interval.
• Instead of vectors in \RR^{{\text{dim}} one could specify the length or dimension of the vectors, to account for the polyhedron to be constructed in ZZ or QQ`.}
• I would maybe move the test of the error the dimension of the hypercube must match the number of intervals to tests. I don't think it is very interesting for the user.

• -        elif isinstance(intervals,str):
  +        elif isinstance(intervals, str):
  

• Missing parenthesis

  -            cp = list(itertools.product(*intervals)
  +            cp = list(itertools.product(*intervals))
  

[git]

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

​8967a0f

adding edits

[git]

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

​a9d7a71

fixing variable name

[gh-kliem]

Some minor commens:

• Please update the description to include arbitrary intervals.
• The INPUT block should also mention the behavior for the input None.
• Instead of list/tuple/iterable of length I would just say list, especially as an iterable does not even work in general (len does not work).
• A string should be written as code:

  -          - 'zero_one' -- (string). Return the `0/1`-cube.
  +          - ``'zero_one'`` -- Return the `0/1`-cube.
  

• Usually INPUT blocks do not have periods, but I don't know if you should change this for this method now.

[git]

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

​696dbe0

fixing comments

[selia]

@gh-kliem -

Please update the description to include arbitrary intervals.

Can you elaborate on what you mean by including arbitrary intervals?

[gh-kliem]

The code is more general than the description of the ticket. E.g. you also add the 0/2-cube.

It would be nice if the description reflects that one can now get the [a_1,b_1],…,[a_n,b_n] Cube.

[gh-kliem]

See the very first comment of the ticket. That should somehow go up in the description.

[gh-kliem]

I think you accidentially commited this:

 .. csv-table::
-    :class: contentstable
+ )   :class: contentstable
     :widths: 30
     :delim: |

[git]

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

​ce4627f

removing parenthesis

[gh-kliem]

There is a double colon after EXAMPLES cube, followed by another comment. This makes building the documentation fail. Please remove it:

-         EXAMPLES::
+         EXAMPLES:
 
          Return the `\pm 1`-cube::

[git]

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

​6da26d9

removing colon

[gh-kliem]

LGTM.

@JP: I put you as reviewer, I hope that is ok.