Theorems · Definition · commutative algebra
Polynomial.degreeLTEquiv
(R : Type u) → [inst : Semiring R] → (n : ℕ) → ↥(Polynomial.degreeLT R n) ≃ₗ[R] Fin n → R
The first n coefficients on degreeLT n form a linear equivalence with Fin n → R.
- Defined in
- Mathlib.RingTheory.Polynomial.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 104 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- Submodulestatement · cited by 7,192
- Polynomialstatement and proof · cited by 5,681
- Finset.sumproof · cited by 5,195
- Finset.univproof · cited by 3,473
- LinearEquivstatement · cited by 3,317
- Polynomial.coeffproof · cited by 1,045
- Polynomial.monomialproof · cited by 256
- Polynomial.degreeLTstatement and proof · cited by 47
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.degreeLT.basisproof · cited by 15
- FirstOrder.Field.lift_genericMonicPolystatement · cited by 1
- Polynomial.degreeLTEquiv_eq_zero_iff_eq_zerostatement · cited by 1
- FirstOrder.Field.realize_genericMonicPolyHasRootproof · cited by 1
- Polynomial.eval_eq_sum_degreeLTEquivstatement and proof · cited by 1