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sumiya11
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One issue here is that the number of variables in the MQS ideal will now depend on input polynomials (that is, if we factor the saturating polynomial and introduce $t_1$,..., $t_k$).

This causes inconsistencies with rings in the surrounding code; as a result, this PR does not work.

We can try to hide details about saturation inside the MQS ideal.

It is also possible that this is not worth the candle, and the real work on saturation must be done on the Groebner.jl side

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