Polar of polytopes does not check if polytope is full-dimensional

[kliem]

Currently, the polar of rational polyhedra does not check, whether the polyhedron is full-dimensional:

sage: P = polytopes.simplex(3, base_ring=QQ)
sage: P.polar()
A 4-dimensional polyhedron in QQ^4 defined as the convex hull of 4 vertices and 1 line

We fix this by adding an assertion

sage: P = polytopes.simplex(3, base_ring=QQ)
sage: P.polar()
Traceback (most recent call last):
...
AssertionError: must be full-dimensional

Also we add an extra keyword in_affine_span (default False). By this one can obtain the polar in its affine span (after translation as usual):

sage: P = polytopes.simplex(3, base_ring=QQ)
sage: P.polar(in_affine_span=True)
A 3-dimensional polyhedron in QQ^4 defined as the convex hull of 4 vertices

sage: point = Polyhedron([[0]])
sage: P = polytopes.cube().change_ring(QQ)
sage: (P*point).polar(in_affine_span=True) == P.polar()*point
True

This option seems reasonable and simplifies the current construction of barycentric subdivision.

We change the other message "Not a polytope." according to conventions to "not a polytope".

CC: @jplab @LaisRast

Component: geometry

Keywords: polar, polytopes

Author: Jonathan Kliem

Branch/Commit: 4ee9802

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/28850

[kliem]

Commit: 6b12213

[kliem]

Branch: public/28850

[kliem]

comment:2

I'm not exactly happy with the phrasing and the name in_affine_span.

---

New commits:

6b12213

check whether polytope is full-dimensional before taking the polar; added a polar version in its affine span

[kliem]

comment:3

phrasing in the doctests

[kliem]

Changed keywords from none to polar, polytopes

[tscrim]

comment:5

Check that :trac:`28850` is fixed::

is overindented. Also it is not considered good practice to do an assert to check input but instead raise a ValueError or TypeError. Otherwise LGTM.

[sagetrac-git]

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

4ee9802

alignment in docs; AssertionError -> ValueError

[sagetrac-git]

Changed commit from 6b12213 to 4ee9802

[kliem]

comment:7

Ok, done. I also changed the test for compactness to give a ValueError.

Replying to @tscrim:

Check that :trac:`28850` is fixed::

is overindented. Also it is not considered good practice to do an assert to check input but instead raise a ValueError or TypeError. Otherwise LGTM.

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

comment:8

Thanks.

[vbraun]

Changed branch from public/28850 to 4ee9802