Theorems · Theorem · field theory
Polynomial.map_mul
∀ {R : Type u} {S : Type v} [inst : Semiring R] {p q : Polynomial R} [inst_1 : Semiring S] (f : R →+* S),
Polynomial.map f (p * q) = Polynomial.map f p * Polynomial.map f q- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 90 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Polynomial.coeffproof · cited by 1,045
- RingHom.compproof · cited by 899
- Polynomial.mapstatement · cited by 806
- Polynomial.eval₂proof · cited by 267
- Commute.symmproof · cited by 79
- Polynomial.commute_Xproof · cited by 13
Cited by91
Results whose statement or proof uses this declaration.
- Polynomial.mapRingHomproof · cited by 98
- Polynomial.Splits.mapproof · cited by 19
- Polynomial.derivative_mapproof · cited by 17
- descPochhammer_succ_rightproof · cited by 14
- Polynomial.map_compproof · cited by 14
- Polynomial.map_dvd_map'proof · cited by 14
- Polynomial.Separable.mapproof · cited by 14
- ascPochhammer_succ_rightproof · cited by 11
- hasDerivAt_bernoulliFunproof · cited by 5
- WeierstrassCurve.map_Ψ₂Sqproof · cited by 5
- ascPochhammer_mapproof · cited by 5
- Polynomial.IsPrimitive.irreducible_iff_irreducible_map_fraction_mapproof · cited by 4