Theorems · Definition · field theory
Polynomial.toFinsuppIso
(R : Type u) → [inst : Semiring R] → Polynomial R ≃+* AddMonoidAlgebra R ℕ
Ring 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
- 11 results in Mathlib
- Foundations
- Depth 84 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.
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
- Polynomialstatement · cited by 5,681
- RingEquivstatement · cited by 1,147
- AddMonoidAlgebrastatement · cited by 649
- Polynomial.toFinsuppproof · cited by 64
- Polynomial.toFinsupp_addproof · cited by 5
- Polynomial.toFinsupp_mulproof · cited by 4
Cited by18
Results whose statement or proof uses this declaration.
- Polynomial.toLaurentproof · cited by 29
- Polynomial.opRingEquivproof · cited by 13
- PolynomialModule.equivPolynomialproof · cited by 6
- Polynomial.toFinsuppIso_applystatement and proof · cited by 4
- PolynomialModule.equivPolynomialSelfproof · cited by 4
- LaurentPolynomial.truncproof · cited by 3
- Polynomial.toFinsuppIso_symm_applystatement and proof · cited by 3
- Polynomial.opRingEquiv_op_monomialproof · cited by 3
- Polynomial.toFinsuppIsoAlgproof · cited by 2
- Polynomial.coeff_opRingEquivproof · cited by 2
- Polynomial.toFinsuppIsoLinearproof · cited by 2
- Polynomial.addSubmonoid_closure_setOfPred_eq_monomialproof · cited by 2