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Using polyhedrons (here a simplified example) :

sage: P = Polyhedron(ieqs=[[0,1,0],[0,0,1]],eqns=[[-15,1,1]]) ; P
A 1-dimensional polyhedron in QQ^2 defined as the convex hull of 2 vertices
sage: P.integral_points()
((0, 15),
 (1, 14),
 (2, 13),
 (3, 12),
 (4, 11),
 (5, 10),
 (6, 9),
 (7, 8),
 (8, 7),
 (9, 6),
 (10, 5),
 (11, 4),
 (12, 3),
 (13, 2),
 (14, 1),
 (15, 0))