English
The contraction M / C is the matroid on E \\ C in which an independent subset I ⊆ E \\ C is independent if and only if I ∪ J is independent for some J that is a basis of C; equivalently, M / C = (M^*) \setminus C)^*.
Русский
У матроида M / C — это матроид на E \\ C, где независимый набор I ⊆ E \\ C де-روز независим, если существует базис J для C, такой что I ∪ J независим; эквивалентно M / C = (M^*) \\setminus C)^*.
LaTeX
$$$ M / C = (M^{*} \\setminus C)^{*} $$$
Lean4
/-- The contraction `M ／ C` is the matroid on `M.E \ C` in which a set `I ⊆ M.E \ C` is independent
if and only if `I ∪ J` is independent, where `J` is an arbitrarily chosen basis for `C`.
It is also equal by definition to `(M✶ ＼ C)✶`; see `Matroid.IsBasis.contract_indep_iff` for
a proof that its independent sets are the claimed ones. -/
def contract (M : Matroid α) (C : Set α) : Matroid α :=
(M✶ ＼ C)✶
