purityfiltration.lib. a Singular 3-1-3 Library for Computing the Purity Filtration of Modules over (Non-)commutative Algebras. Purity is a notion with several meanings. In our context it is equidimensionality of a module (that is all M is pure iff any nonzero submodule of N has the same dimension as N). Notably, one should define purity with respect to a given dimension function. In the context of this library the corresponding function is the homological grade number j_A(M) of a module M over an K-algebra A. j_A(M) is the minimal integer k, such that Ext^k_A(M,A) != 0.