extension(M, L),
extension(M, F),
extension M
This function is provided by the package Matroids.
A matroid N is a (singleelement) extension of a matroid M if M can be obtained from N by deleting a single element e. Every extension N of M is uniquely determined by a modular cut of flats of M whose closure in N contains e.
Given a modular cut K of M, we can construct the corresponding extension.




Every flat F of the matroid M determines a principal modular cut consisting of all flats containing F. The independent sets of the free extension N come in two types: They are either independent sets of M or sets containing e that, after deleting e, become independent sets of M whose closure in M does not contain F. We can construct the extension corresponding to this modular cut as follows.



When no modular cut or flat is specified, the free extension of M is constructed. This is the extension corresponding to the modular cut that contains the ground set of M as its only flat. For a uniform matroid U_{r,n}, the free extension is just U_{r,n+1}.


The object extension is a method function with options.