Let M = (E, B) be a matroid with bases B. If there is a subset S of E that is both a circuit and a hyperplane of M, then the set $B \cup \{S\}$ is the set of bases of a matroid on E, called the relaxation of M by S.
Many interesting matroids arise as relaxations of other matroids: e.g. the non-Fano matroid is a relaxation of the Fano matroid, and the non-Pappus matroid is a relaxation of the Pappus matroid.
i1 : P = specificMatroid "pappus" o1 = a matroid of rank 3 on 9 elements o1 : Matroid |
i2 : NP = specificMatroid "nonpappus" o2 = a matroid of rank 3 on 9 elements o2 : Matroid |
i3 : NP == relaxation(P, set{6,7,8}) o3 = true |
Note that relaxation does not change the ground set. Thus e.g. representationOf will return the same for both the Fano and non-Fano matroids.
The object relaxation is a method function.