Add function is_quotient for matroids

[danteluber]

Checks if two matroids of successive rank form a quotient.

[fingolfin]

The matroids code is by @bschroter and @LukasKuehne so it would be good if they reviewed this PR. But of course if @antonydellavecchia or @benlorenz or anyone else has further thoughts, have a go as well.

But this has now been sitting for almost full month and it is unclear to me what the status is. Should we merge it? Should something be changed?

[bschroter]

It is of course nice to have a function like this, but maybe call it `elementary quotient' or implement one of the general tests for arbitrary ranks.

More importantly there is an issue with the groundset. I don't like the unnecessary restriction to $[n]$, which is also never tested, as you are calling a polymake function. It would be better to ask for the same groundset.

[danteluber]

I have simplified the function and implemented @bschroter 's suggestions to make it more general. I just used the definition of a quotient on page 2 here

[codecov[bot]]

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 81.30%. Comparing base (4d5956d) to head (1f7483f). Report is 205 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #3627      +/-   ##
==========================================
- Coverage   82.78%   81.30%   -1.49%     
==========================================
  Files         577      579       +2     
  Lines       77743    79295    +1552     
==========================================
+ Hits        64358    64467     +109     
- Misses      13385    14828    +1443     

Files	Coverage Δ
src/Combinatorics/Matroids/matroids.jl	98.80% <100.00%> (+0.01%)	:arrow_up:

... and 235 files with indirect coverage changes

[fingolfin]

Is this good to go now? @bschroter your thoughts?

[fingolfin]

@bschroter @antonydellavecchia any further remarks? or can we merge this?

[antonydellavecchia]

@bschroter @antonydellavecchia any further remarks? or can we merge this?

Ok for me

[bschroter]

Please go ahead. I think this can be merged.