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Simplify empty permutations #2171

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Simplify empty permutations #2171

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leonardoalt
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Permutations of the form 0 $ [...] is S $ [...] can be simplified to S = 0. If this were a lookup, it would be a tautology and the constraint could be removed entirely. But as a permutation we're saying the LHS (empty set) is a permutation of the RHS, therefore RHS must also be the empty set. This is enforced by the simplified constraint.

expression: right.selector.clone(),
source: source.clone(),
};
*identity = Identity::Polynomial(pol);
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Can we just remove the phantom? Shouldn't we keep it so that the multiplicity can be set to zero?

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Ah, there is no multiplicity. Hm.

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I'm not too aware of that stuff, but if changing the multiplicity only makes more sense can do that too

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What I'm saying is: If we remove the phantom, we should also remove the columns and constraints generated from the phantom. We had a similar problem before, but not sure how we resolved it.

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Do you have a simple example of the other constraints that are generated?
I think it could be the case that they are still sound regardless, because we're not removing the phantom permutation, rather making them unsatisfiable.

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I don't know how this is passing CI

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