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Hello !

It seems that you are looking for that:

http://doc.sagemath.org/html/en/reference/geometry/sage/geometry/polyhedron/base.html#sage.geometry.polyhedron.base.Polyhedron_base.integral_points

Note that it is a bit slow currently, but it should be improved in a couple of months if I get to do what I plan to.

Also, in case you want to solve such a system of equations and would be looking for one solution (not all of them), know that you can use Mixed Integer Linear Programming in Sage quite easily:

http://doc.sagemath.org/html/en/thematic_tutorials/linear_programming.html#linear-programming

Good luck,

Nathann