## H-representation of a polytope

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Emiliano

### H-representation of a polytope

Hi! I a trying to compute the H-representation of a polytope. After adding al the extreme points the command

print_constraints

Facets:
[..]
14: -x1 - x4 - x7 >= -1
[..]

Affine hull:
0: x1 + x4 + x7 + x10 = 1
[..]

Why is facet (14) displayed? isn't it dominated by (0)? What am I missing?

assarf
Developer
Posts: 74
Joined: 12 Oct 2011, 15:52

### Re: H-representation of a polytope

I don't see why.

In (14) the indices which play a role are: 1, 4, and 7. In (0) the indices are 1,4,7, and 10.

When (0) is true, why should (14) be true?

Consider the following example:
$$x_1 = x_4 = x_7 = 1 \qquad \text{and} \qquad x_{10} = -2$$

Then we've got:
$$x_1 + x_4 + x_7 + x_{10} = 1 + 1 + 1 - 2 = 1$$
So (0) is true. BUT:
$$-x_1 - x_4 - x_7 = -1 -1 -1 = -3 \not\ge -1$$
so (14) is not true.

And for
$$x_1 = x_4 = x_7 = x_{10} = -1$$
you get that (14) is true and (0) is not.

But since I do not know your complete input, I cannot say if the configuration I gave you, is indeed feasible. But from the information you gave (14) and (0) are independent.
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