Implement broken circuits and NBC sets

[tscrim]

Broken circuits and no broken circuit (NBC) sets are important aspects of matroid theory. In particular, a basis for the Orlik-Solomon algebra can be given by NBC sets. This implements a basic iterator for broken circuits and NBC sets.

[tscrim]

New commits:

​4fa33b6

Add NBC sets for matroids.

[git]

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

​0eb8837	Merge branch 'public/matroids/nbc_sets-17506' of trac in 6.5.b3
​a76ac91	trac #17506 pep8 detail

[chapoton]

ok, looks good to me.

[tscrim]

Thanks Frederic!

[vbraun]

PDF docs don't build

[Stefan]

I'm sorry, I didn't look at this ticket before. You add TWO methods to Matroid that do the same thing:

Matroid.no_broken_circuit_sets

and

Matroid.nbc_sets.

This is needlessly cluttering up the list of methods a user sees through autocomplete. Please keep one of the two (preferably the long one, as it is more descriptive)

[git]

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

​575b68f

Fixed my stupidity with latex commands.

[tscrim]

\union is not a valid latex command *facepalm*

@Stefan, if we are going to keep only one, I would say lets keep nbc_sets since that is how they are more commonly known. However because of this and it is good to have methods with fully spelled out names, I think we should keep both. If you strongly believe there should only be one, then I will remove no_broken_circuit_sets.

[Stefan]

I disagree. People in the field will know what NBC stands for and can find the long name. To others, the long name immediately tells them what the thing does, as opposed to the mysterious abbreviation.

I think clarity should come before brevity.

[tscrim]

I think the short name, being a very common abbreviation, with the documentation is sufficient. Although I still would argue that having both methods gives the option to the user; plus it's not like matroids are current overflowing with methods (as opposed to Graphs with nearly 300). Shall we see what Federic thinks and just go with that?

[Stefan]

Well, we try to keep it from becoming like the Graph class. Maybe Frederic can give a third opinion to settle the matter?

[chapoton]

I would vote for keeping only the long name. The "very common abreviation" NBC is not so universally well-known. But this seems to me to be a very minor point.

[git]

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

​a0abc54

Remove nbc_sets.

[tscrim]

Yea, but it's a point of contention. Anyways, I've removed nbc_sets.