Theorems · Theorem · field theory
Polynomial.map_smul
∀ {R : Type u} {S : Type v} [inst : Semiring R] {p : Polynomial R} [inst_1 : Semiring S] (f : R →+* S) (r : R),
Polynomial.map f (r • p) = f r • Polynomial.map f p- Defined in
- Mathlib.Algebra.Polynomial.Eval.SMul
- Cited by
- 3 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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
- RingHom.compproof · cited by 899
- Polynomial.mapstatement · cited by 806
- Polynomial.eval₂proof · cited by 267
- RingHom.comp_applyproof · cited by 41
- Polynomial.C_mul'proof · cited by 12
- Polynomial.eval₂_smulproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.IsPrimitive.mul_map_mem_lifts_iffproof · cited by 2
- Module.Basis.traceDual_powerBasis_eqproof · cited by 1
- sum_smul_minpolyDiv_eq_X_powproof · cited by 1