1 | initial version |

If the inequalities are linear (as in your example), you can define a polyhedron `P`

from them. Then given a new inequality, it also defines a polyhedron `Q`

(a half space), and ask wether this new polyhedron `Q`

contains the initial one `P`

.

You can define polytopes fro inequalities using the `Polyhedron(ieqs=...)`

syntax, see, for example:

- https://doc.sagemath.org/html/en/thematic_tutorials/geometry/polyhedra_quicktutorial.html
- https://doc.sagemath.org/html/en/reference/discrete_geometry/sage/geometry/polyhedron/constructor.html

To test that `Q`

contains `P`

, you can do:

```
sage: P.intersection(Q) == P
```

Note that inequalities have to be large (`<=`

), not strict (`<`

). If you absolutely want to test strict inequalities, you can use vertices and test inclusion in the interior, using `P.interior_contains`

method.

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