Opened 7 years ago
Last modified 5 years ago
#18703 new enhancement
oriented matroids
Reported by: | moritz | Owned by: | moritz |
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Priority: | minor | Milestone: | sage-wishlist |
Component: | matroid theory | Keywords: | |
Cc: | stumpc5, Rudi, jipilab, yomcat, Stefan | Merged in: | |
Authors: | moritz | Reviewers: | |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
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
Change History (5)
comment:1 Changed 7 years ago by
- Cc stumpc5 added
comment:2 Changed 7 years ago by
- Cc Rudi added
comment:3 follow-up: ↓ 5 Changed 5 years ago by
- Cc jipilab yomcat Stefan added
- Description modified (diff)
- Owner changed from (none) to moritz
comment:4 Changed 5 years ago by
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
comment:5 in reply to: ↑ 3 Changed 5 years ago by
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.
As a first idea, I propose to
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?