Always use PPL for facet normals of lattice polytopes

[novoselt]

A follow up to #22310. As promised there, this switch makes even full-dimensional polytopes faster, on the same example we now get

sage: timeit("LatticePolytope(lattice_polytope.cross_polytope(3).vertices()).facet_normals()")
625 loops, best of 3: 976 µs per loop

The reason is that dimension computation used to be quite complicated.

Next in the chain of lattice polytope improvements is #22524

[novoselt]

Last 10 new commits:

​db3b54e	Fix doctests - mostly due to different order of vertices
​5281cf4	Use PPL for facet normals of full-dimensional polytopes
​d244793	Update a lot of toric doctests for the new facet order
​e70f34d	Merge tag '7.6.beta3' into PPL_for_normals
​b27e343	Always use PPL for LatticePolytope.facet_normals()
​8e77861	Update docstrings for facet normals and constants
​ba7656a	Use PPL for LatticePolytope.dim()
​38bbdb2	Don't use embedding in LatticePolytope.distances()
​f4a696b	Implement point containment test for LatticePolytope
​b4410f1	Do not rely on distances for containment check

[ursula]

I successfully installed this patch and tried some variants on the example. Speed seems to work as advertised:

sage: sim = ReflexivePolytope(3,0)
sage: timeit("sim.facet_normals()")
625 loops, best of 3: 576 ns per loop

[vdelecroix]

Have you tried using normaliz? In dimension >= 10 it is likely to be faster. For that reason, it is good to have an optional keyword method= or algorithm= that simplifies speed comparisons.

[novoselt]

Replying to vdelecroix:

Have you tried using normaliz? In dimension >= 10 it is likely to be faster. For that reason, it is good to have an optional keyword method= or algorithm= that simplifies speed comparisons.

The interest here is mostly in polytopes of dimensions 3-4-5, when the bottleneck is often the interface between programs. Also, the old code was quite convoluted for many reasons and adding different algorithms would be tricky. One of the goals of this and related tickets was to clean up the mess to indeed allow using different backends for certain operations.

[ursula]

I tried building again, and now this patch fails, with errors involving sage-ursula/src/build/cythonized/sage/. My guess is that the transition from Sage 7.6 to the current development branch is too great. Do you mind updating the patch?

[novoselt]

Can you please be more specific in how it fails? The branch merges cleanly and passes tests according to the patchbot.

[tscrim]

It also works for me. I am guessing what happened is @ursula just used the branch, effectively downgrading her version of Sage to that of the branch, and ran sage -b, which does not rebuild the necessary parts of Sage. In general, I always make sure to merge it ontop of (my version of) develop to avoid regressing Sage (which will include long compilation time). If that is not what [@ursula] did, then try running make build and then sage -t.

[tscrim]

I made some small formatting changes to more match our style guide. If my changes look good, then positive review.

---

New commits:

​49be993	Merge branch 'u/novoselt/PPL_for_normals' of git://trac.sagemath.org/sage into u/novoselt/PPL_for_normals
​baf0a4a	A little bit of reviewer cleanup.

[novoselt]

Thank you!!!

Of course your changes look good - anything to get it in ;-) A small question however:

         TypeError: the point M(1, 1) and
-        2-d cone in 2-d lattice N have incompatible lattices!
+         2-d cone in 2-d lattice N have incompatible lattices

Your new line apart from dropping the exclamation point due to exception formatting change also adds a space in front of the second part of the broken line. Is this also the style recommended somewhere? I can't recall ever reading it.

[tscrim]

Not really, but I feel its gives better grouping that it is part of the error message and not some new line of output, similar to indenting function blocks.

[tscrim]

Also, Python does not use sentence ending punctuation for any exceptions (or initial uppercase letters).