Improvements for `is_reflexive` for polyhedra over the integers

[gh-kliem]

Currently, this method has almost no documentation.

Also it relies on polar to work differently for Polyhedron_ZZ than for Polyhedron_base. However, this is not being tested at all. We fix this by checking being reflexive just from the inequalities.

This also improves the error messages. We raise a ValueError if the polyhedron is unbounded. If the polytope does not have the origin in the interior, we return False, as this is clearly not reflexive.

[gh-kliem]

New commits:

​1d71889

some improvements for `is_reflexive`

[jipilab]

Some remarks:

-        A lattice polytope is reflexive if it is polar to a lattice polytope.
+        A lattice polytope is reflexive if its polar is a lattice polytope.

Even though the raised error is not wrong as written (that it is not a polytope), I would still say "the polyhedron is not compact" or "the polyhedron should be compact". Simply because this avoids an eventual confusion in nomenclature polytope vs polyhedron.

[gh-kliem]

Replying to jipilab:

Some remarks:

-        A lattice polytope is reflexive if it is polar to a lattice polytope.
+        A lattice polytope is reflexive if its polar is a lattice polytope.

Those two statements are not equivalent. I would say that a polytope without origin in interior is not reflexive and that the return value shall be False (and no error message). However, in this case the polar is not defined. This is why I chose this specific formulation.

Even though the raised error is not wrong as written (that it is not a polytope), I would still say "the polyhedron is not compact" or "the polyhedron should be compact". Simply because this avoids an eventual confusion in nomenclature polytope vs polyhedron.

[jipilab]

Replying to gh-kliem:

Replying to jipilab:

Some remarks:

-        A lattice polytope is reflexive if it is polar to a lattice polytope.
+        A lattice polytope is reflexive if its polar is a lattice polytope.

Those two statements are not equivalent. I would say that a polytope without origin in interior is not reflexive and that the return value shall be False (and no error message). However, in this case the polar is not defined. This is why I chose this specific formulation.

Then, one should be transparent. Why not something like:

+       A lattice polytope is reflexive if it contains the origin and its polar with respect to the origin is a lattice polytope.

[gh-kliem]

New commits:

​1930179	some improvements for `is_reflexive`
​0718db8	small improvments

[git]

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

​c2abdd6

typo in doc

[jipilab]

One last things:

- "the polyhedron should be compact"
+ "the polyhedron is not compact"

sounds better to me. A "should" gives it too many ways to be interpreted, whereas a "is not" is only reporting a fact, which I prefer. Not a big thing...

Patchbots look okay to me. So you can put this on positive review once you make this change on my behalf.

[git]

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

​27fa75c

improved error message