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[Merged by Bors] - golf(data/polynomial): factorization into linear factors when #roots=degree #14862
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…degree (#14862) + Golf the proofs of `prod_multiset_X_sub_C_of_monic_of_roots_card_eq` and `C_leading_coeff_mul_prod_multiset_X_sub_C` and move them from *splitting_field.lean* to *ring_division.lean*; instead of using the former to deduce the latter as is currently done in mathlib, we prove the latter first and deduce the former easily. Remove the less general auxiliary, `private` `_of_field` versions. + Move `pairwise_coprime_X_sub` from *field_division.lean* to *ring_division.lean*. Rename it to `pairwise_coprime_X_sub_C` to conform with existing convention. Golf its proof using the more general new lemma `is_coprime_X_sub_C_of_is_unit_sub`. + Golf `monic.irreducible_of_irreducible_map`, but it's essentially the same proof.
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Golf the proofs of
prod_multiset_X_sub_C_of_monic_of_roots_card_eq
andC_leading_coeff_mul_prod_multiset_X_sub_C
and move them from splitting_field.lean to ring_division.lean; instead of using the former to deduce the latter as is currently done in mathlib, we prove the latter first and deduce the former easily. Remove the less general auxiliary,private
_of_field
versions.Move
pairwise_coprime_X_sub
from field_division.lean to ring_division.lean. Rename it topairwise_coprime_X_sub_C
to conform with existing convention. Golf its proof using the more general new lemmais_coprime_X_sub_C_of_is_unit_sub
.Golf
monic.irreducible_of_irreducible_map
, but it's essentially the same proof.