PPL's solver is a rational MIP solver.
Its support for integer variables should be exposed in Sage.

Reference: http://bugseng.com/products/ppl/documentation/user/ppl-user-1.2-html/classParma__Polyhedra__Library_1_1MIP__Problem.html

For sage.libs.ppl.MIP_Problem, I think one just needs to add a wrapper for this method:

void Parma_Polyhedra_Library::MIP_Problem::add_to_integer_space_dimensions(const Variables_Set &i_vars)	

and then a wrapper class for Variables_Set.

On another ticket (#20354), PPLBackend will be updated accordingly.

CC: @dimpase @videlec @jdemeyer

Component: numerical

Author: Matthias Koeppe

Branch/Commit: 9f35b65

Reviewer: Dima Pasechnik

Issue created by migration from https://trac.sagemath.org/ticket/20351