A function checking if a tropical polytope is ordinarily convex (ie a polytrope)

[Sami-Halaseh]

No description provided.

[Sami-Halaseh]

@ooinaruhugh @lenweis

[Sami-Halaseh]

@danteluber

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 84.56%. Comparing base (184dd4a) to head (f34d439).
Report is 23 commits behind head on master.

Additional details and impacted files

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##           master    #3989      +/-   ##
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+ Coverage   84.44%   84.56%   +0.11%     
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  Files         596      596              
  Lines       81888    82074     +186     
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+ Hits        69150    69404     +254     
+ Misses      12738    12670      -68     

Files	Coverage Δ
src/TropicalGeometry/matrix.jl	97.29% <100.00%> (+2.29%)	⬆️

... and 19 files with indirect coverage changes

[YueRen]

Dear @Sami-Halaseh,

Thanks for the pull-request! Overall it looks great, I just have a few super-minor changes.

One general question: Wouldn't it be more sensible to make the input a polytope?

Best regards, Yue.

[Sami-Halaseh]

Dear @Sami-Halaseh,

Thanks for the pull-request! Overall it looks great, I just have a few super-minor changes.

One general question: Wouldn't it be more sensible to make the input a polytope?

Best regards, Yue.

@YueRen thank you for the feedback. I have made the changes you suggested over a few commits (sorry about that). One thing I have not addressed is this comment you made. This is actually a confusion of mine. Are tropical polytopes a type in OSCAR? I thought the way do tropical convex hull computations was to somehow go through polymake. For example

tropical > $H = new Polytope<Min>(POINTS=>[[0,1,0],[0,0,1],[1,0,0]]);
julia> H = Polymake.Shell.H
name: H
type: Polytope<Min, Rational>
...
julia> typeof(H)
Polymake.LibPolymake.BigObjectAllocated

Here it seems like I get two different types. The one when I pull $P into julia out of Polymake says something about type Polytope<Min, Rational>. But then the typeof gives something else. Excuse my ignorance here. At MEGA you suggested I speak with Michael Joswig about tropical convexity in OSCAR. I have reached out about a meeting so hopefully that will help soon.

[YueRen]

Dear @Sami-Halaseh,

The pull request looks great, maybe just two little changes to the docstring to make it clearer and it's good to be merged. If the changes works for you, you can just ask github to apply my suggestions (no need to manually change them yourself).

Best regards, Yue.

[Sami-Halaseh]

Dear @Sami-Halaseh,

The pull request looks great, maybe just two little changes to the docstring to make it clearer and it's good to be merged. If the changes works for you, you can just ask github to apply my suggestions (no need to manually change them yourself).

Best regards, Yue.

Hey Yue, thanks for the feedback. I think those suggestions are good and I have committed them. We are talking about a tropical polytope/polyhedron type but it looks like it will take some time to flesh out what it should look like and how to put it into OSCAR. For now I think its good for this function to work on matrices.
Sami

[thofma]

It is kind of opposite the design of Oscar to have something like

function is_polytrope(A::QQMatrix)

For the same reason we don't have is_bijective(A::QQMatrix), although one could interpret A in some (arbitrary) way as a linear map between vector spaces.

[YueRen]

It is kind of opposite the design of Oscar to have something like

function is_polytrope(A::QQMatrix)

For the same reason we don't have is_bijective(A::QQMatrix), although one could interpret A in some (arbitrary) way as a linear map between vector spaces.

Then how about renaming the function to do_rows_form_polytrope?

[benlorenz]

Maybe we can keep this function internal (non-exported) for now, until we have the tropical polytope type? Then we don't need to commit to a public interface function but it is still possible to be used for development.

[YueRen]

@benlorenz That's also a good solution (removing the export part of the changes). @Sami-Halaseh What do you say?

1. Rename the function to do_rows_form_polytrope (or something similar; optional)
2. Remove the export of the function so that it remains private

and wait for the tropical polytope type before having a public is_polytrope function?

[benlorenz]

Suggested change

	pPMCV = P.POLYTOPE_MAXIMAL_COVECTORS
	Polymake.Shell.CV = pPMCV
	Polymake.shell_execute(raw"""$tmp = $CV->size;""")
	l = Polymake.Shell.tmp
	return l == 1
	return length(P.POLYTOPE_MAXIMAL_COVECTORS) == 1

as above

[Sami-Halaseh]

Thank you for the feedback everyone. @YueRen I made those two changes. @benlorenz Thank you for the fix, the perl shell code was definitely not a good way to get the length. The wrapped type is much better, we just couldn't figure out how to do that properly.
We are working on a tropical polytope type in OSCAR. There are some bigger things to figure out since it would be nice for them to be able to exist in tropical projective space, not just the tropical torus. Hopefully there will be something to show in the coming months.

[benlorenz]

This now needs the Oscar. prefix until exported again.

[YueRen]

Thanks for incorporating all suggestions! Looking forward to having polytropes in OSCAR, in the meantime this function is an excellent bandaid.

[micjoswig]

This is the wrong algorithm; must be replaced. Will be dealt with in #4001 .

@ooinaruhugh