Theorems · Definition · field theory
Polynomial.toFinsuppIsoLinear
(R : Type u) → [inst : Semiring R] → Polynomial R ≃ₗ[R] AddMonoidAlgebra R ℕ
Linear isomorphism between R[X] and R[ℕ]. This is just an
implementation detail, but it can be useful to transfer results from Finsupp to polynomials.
- Defined in
- Mathlib.Algebra.Polynomial.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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.
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- LinearEquivstatement · cited by 3,317
- RingEquivproof · cited by 1,147
- AddMonoidAlgebrastatement and proof · cited by 649
- Equiv.toFunproof · cited by 279
- Equiv.invFunproof · cited by 163
- RingEquiv.toEquivproof · cited by 101
- Polynomial.toFinsuppIsoproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.basisMonomialsproof · cited by 2
- Polynomial.toFinsuppIsoLinear_applystatement and proof · cited by 0
- Polynomial.toFinsuppIsoLinear_symm_apply_toFinsuppstatement and proof · cited by 0