with PPL providing MIP solver thanks to #20354 and #20351, it becomes important to have an option to ask for integer solutions only. A silly bug is fixed along the way.

Depends on #20351
Depends on #20354
Depends on #20361

CC: @mkoeppe

Component: coding theory

Author: Dima Pasechnik

Branch/Commit: eb15d11

Reviewer: Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/20367