Theorems · Definition · field theory
Polynomial.map
{R : Type u} → {S : Type v} → [inst : Semiring R] → [inst_1 : Semiring S] → (R →+* S) → Polynomial R → Polynomial Smap f p maps a polynomial p across a ring hom f
- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 806 results in Mathlib
- Foundations
- Depth 101 from the axioms, rests on 1,825 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement · cited by 5,681
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- RingHom.compproof · cited by 899
- Polynomial.eval₂proof · cited by 267
Cited by861
Results whose statement or proof uses this declaration.
- Polynomial.cyclotomicproof · cited by 130
- Polynomial.map_Xstatement · cited by 122
- Polynomial.coeff_mapstatement · cited by 114
- Polynomial.map_Cstatement · cited by 107
- Polynomial.mapRingHomproof · cited by 98
- Polynomial.map_mulstatement · cited by 90
- Polynomial.arootsproof · cited by 89
- Polynomial.map_mapstatement · cited by 75
- Polynomial.map_powstatement · cited by 59
- Polynomial.Monic.mapstatement and proof · cited by 52
- Polynomial.map_addstatement · cited by 50
- Polynomial.eval_map_algebraMapstatement and proof · cited by 49
Showing the 200 most cited of 861.