Theorems · Theorem · field theory
Polynomial.ofFn_coeff_eq_zero_of_ge
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : DecidableEq R] {n i : ℕ} (v : Fin n → R),
n ≤ i → ((Polynomial.ofFn n) v).coeff i = 0If n ≤ i the i-th coefficient of ofFn n v is 0.
- Defined in
- Mathlib.Algebra.Polynomial.OfFn
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- Polynomialstatement · cited by 5,681
- Polynomial.coeffstatement · cited by 1,045
- List.toFinsuppproof · cited by 20
- Polynomial.ofFnstatement · cited by 12
- Polynomial.coeff_ofFinsuppproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.ofFn_natDegree_ltproof · cited by 3
- Polynomial.ofFn_comp_toFn_eq_id_of_natDegree_ltproof · cited by 0