[Merged by Bors] - feat(FieldTheory/Separable): add some results regarding separable and no repeated roots #9263
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… no repeated roots (#9263) - `nodup_[a]roots_iff_of_splits`: a polynomial has no repeated roots if and only if it is separable. - `card_rootSet_eq_natDegree_iff_of_splits`: a polynomial has number of roots equal to its degree if and only if it is separable. A converse to `card_rootSet_eq_natDegree`. Also add some convenience lemmas: - `Separable.ne_zero`: a separable polynomial is not zero. - `Separable.map_minpoly`: if an element is separable over a small field, then it's also separable over a large field.
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nodup_[a]roots_iff_of_splits: a polynomial has no repeated roots if and only if it is separable.card_rootSet_eq_natDegree_iff_of_splits: a polynomial has number of roots equal to its degree if and only if it is separable. A converse tocard_rootSet_eq_natDegree.Also add some convenience lemmas:
Separable.ne_zero: a separable polynomial is not zero.Separable.map_minpoly: if an element is separable over a small field, then it's also separable over a large field.