Implement join of polytopes

[jipilab]

From ​​https://www.csun.edu/~ctoth/Handbook/chap15.pdf:

The join of two polytopes P (of dimension d) and Q (of dimension d') is the (d+d'+1)-polytope obtained as the convex hull of P\cup Q after embedding P and Q in a space where their affine hulls are skew.

[jipilab]

New commits:

​c807893	first version of the join
​a14d2c7	pep8

[vdelecroix]

According to the developer guide:

• the docstring should start with a one line sentence. Then a line break, then a longer description.

• better than - ``other`` -- a :class:`Polyhedron_base`., I would just use - ``other`` -- a polyhedron.

• there is no need to fill an OUTPUT section as it is already described before.

And I would like to see the definition of a "skew subspace".

This is not the proper thing to do

        try:
            new_ring = self.parent()._coerce_base_ring(other)
        except TypeError:
            raise TypeError("no common canonical parent for objects with parents: " + str(self.parent())
                     + " and " + str(other.parent()))

You should try to coerce the objects to a common parent as in

sage: C = polytopes.cube()
sage: I = polytopes.icosahedron()
sage: cm = get_coercion_model()
sage: cm.common_parent(C, I)
Polyhedra in (Number Field in sqrt5 with defining polynomial x^2 - 5)^3

And even simpler, you could use the decorator @coerce_binop from sage.structure.element.

Moreover, when you construct the resulting polytope you should just use directly the common parent.

[git]

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

​347f99f

Made docstring corrections

[jipilab]

According to the developer guide:

Yes, you are right. I should read it again every season... I made the changes you suggested.

And I would like to see the definition of a "skew subspace".

I added a short definition.

And even simpler, you could use the decorator @coerce_binop from sage.structure.element.

Unfortunately, doing the join changes the dimension, and hence the parents.

Merci!

[jipilab]

I'll put you as a review if you don't mind... ;)

[git]

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

​ec6ad8a

Merge branch 'sage8.2.b7' into 24848

[moritz]

This looks like a nice new feature! A few remarks:

• In the description: ... of the two polyhedron plus ... --> ... of the two polyhedra plus ...

• I would be nice to have some more test, for example:

  C = polytopes.hypercube(5)
  S = Polyhedron([[1]])
  C.join(S).is_combinatorially_isomorphic(C.pyramid())
  

• You wrote the method such that it works also for unbounded polyhedra: this should be doctested for at least one unbounded polyhedron!

Also: see the remarks by Vincent above, they are only partially integrated. You didn't address the coercion question, or am I missing something?

[jipilab]

Replying to moritz:

This looks like a nice new feature! A few remarks:

• In the description: ... of the two polyhedron plus ... --> ... of the two polyhedra plus ...

• I would be nice to have some more test, for example:

  C = polytopes.hypercube(5)
  S = Polyhedron([[1]])
  C.join(S).is_combinatorially_isomorphic(C.pyramid())
  

• You wrote the method such that it works also for unbounded polyhedra: this should be doctested for at least one unbounded polyhedron!

Indeed, I added a test and an unbounded example.

Also: see the remarks by Vincent above, they are only partially integrated. You didn't address the coercion question, or am I missing something?

Coercion can not be used since the dimension is included in the parent of Polyhedron objects and they can be different and the output also has a different dimension:

sage: C = polytopes.cube()
sage: S = polytopes.hypercube(2)
sage: C.parent()
Polyhedra in ZZ^3
sage: S.parent()
Polyhedra in ZZ^2
sage: cm = get_coercion_model()
sage: cm.common_parent(C,S)
Traceback (most recent call last):
...
TypeError: no common canonical parent for objects with parents: 'Polyhedra in ZZ^3' and 'Polyhedra in ZZ^2'

That's the explanation of the short sentence I gave above...

[git]

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

​3b9a7ea	Merge branch sage8.2.rc1 with 24848
​f887745	Added tests and examples

[jipilab]

It still needs to be added to the quick tips of the tutorial.

[git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

​7f5e125	fixed typos in polyhedra_quickref.rst
​bd6c356	LateX -> LaTeX in polytope_tikz.rst
​b1ce45b	Several other corrections
​d526f70	renamed tutorial files
​d7896f8	Merge branch 'develop' into 22572
​597b802	Merge branch sage8.2.rc1 into 22572
​eee533a	Corrections from review
​b74ae85	Made tests pass
​7a8e91b	Merge branch thematic tutorial into 24848
​0c9793f	Added join to quickref