Changes between Initial Version and Version 3 of Ticket #18703


Ignore:
Timestamp:
12/09/16 10:03:29 (5 years ago)
Author:
moritz
Comment:

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?

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  • Ticket #18703

    • Property Cc stumpc5 Rudi jipilab yomcat Stefan added
    • Property Owner changed from (none) to moritz
  • Ticket #18703 – Description

    initial v3  
    11Currently the Matroid class does not provide oriented matroids.
    2 I propose to implement a base class oriented matroids, that provides:
     2I propose to implement oriented matroids, so that we can handle:
    33
    4 - the usual basic functions, like rank etc.
     4
     5- the properties of the underlying unoriented matroid
     6- the positive and negative elements
    57- a representation of the chirotope functions
     8- checking if the input really is a
    69- checking if it is uniform
    710- giving out the face lattice
    8 - ...
     11- duality
     12- ...
    913
    10 This could then for example be used to add an appropriate function to the Polyhedron class.
     14It should be possible to construct OMs from:
     15
     16- directly formulations as:
     17 - oriented bases of vector configuration
     18 - covectors
     19 - cocircuits
     20 - chirotopes
     21
     22- matrices (point configurations) over ordered fields
     23- directed Graphs
     24- hyperplane arrangements
     25- polytopes
     26