oriented matroids

[Moritz Firsching]

Currently the Matroid class does not provide oriented matroids. I propose to implement oriented matroids, so that we can handle:

• the properties of the underlying unoriented matroid
• the positive and negative elements
• a representation of the chirotope functions
• checking if the input really is a
• checking if it is uniform
• giving out the face lattice
• duality
• ...

It should be possible to construct OMs from:

• directly formulations as:
  • oriented bases of vector configuration
  • covectors
  • cocircuits
  • chirotopes

• matrices (point configurations) over ordered fields
• directed Graphs
• hyperplane arrangements
• polytopes

[Moritz Firsching]

As a first idea, I propose to

1. add a abstract OrientedMatroid? class as a child of the abstract Matroid class
2. add a class OrientedBasisMatroid? as a subclass of the new OrientedMatroid? class
3. (possibly add other OrientedMatroid? subclasses)
4. add a constructor function OrientedMatroid? similar to the Matroid Conctructor, that can handle the various inputs

Perhaps its best to make this ticket a meta ticket and open new tickets for the points mentioned above. What do you think of the plan?

[Rudi Pendavingh]

Hi Moritz,

I really like the plan.

1) The OrientedBasisMatroid? class perhaps should be a subclass of BasisMatroid? (or BasisExchangeMatroid?) as well as OrientedMatroid?; otherwise you have to do a extra work for each method already supported by BasisMatroid?. For example, there is code for enumerating (unoriented) circuits in BasisExchangeMatroid?. You don't want to repeat that code, I guess.

2) we use plain python sets in the Matroid interface to communicate subsets of the ground set. What will you use for the oriented sets, dictionaries or pairs of sets? I can imagine that the former is a lot faster as making pairs is a bit expensive, but I haven't tested it.

Cheers, Rudi

[Vincent Delecroix]

Replying to moritz:

Perhaps its best to make this ticket a meta ticket and open new tickets for the points mentioned above.

+1 would be easier to follow activity and reviews.