Theorems · Theorem · field theory
Polynomial.map_multiset_prod
∀ {R : Type u} {S : Type v} [inst : CommSemiring R] [inst_1 : CommSemiring S] (f : R →+* S)
(m : Multiset (Polynomial R)), Polynomial.map f m.prod = (Multiset.map (Polynomial.map f) m).prod- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringCommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Multisetstatement and proof · cited by 2,627
- Multiset.mapstatement · cited by 876
- Polynomial.mapstatement · cited by 806
- Multiset.prodstatement · cited by 528
- RingHom.toMonoidHomproof · cited by 132
- Polynomial.mapRingHomproof · cited by 98
- Multiset.prod_homproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.count_map_rootsproof · cited by 2
- Polynomial.Splits.of_splits_map_of_injectiveproof · cited by 1