Theorems · Theorem · linear algebra
Lagrange.eq_interpolate
∀ {F : Type u_1} [inst : Field F] {ι : Type u_2} [inst_1 : DecidableEq ι] {s : Finset ι} {v : ι → F} {f : Polynomial F},
Set.InjOn v ↑s → f.degree < ↑s.card → f = (Lagrange.interpolate s v) fun i => Polynomial.eval (v i) f- Defined in
- Mathlib.LinearAlgebra.Lagrange
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Finsetstatement and proof · cited by 13,712
- LinearMapstatement · cited by 10,215
- SetLike.coestatement and proof · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Finset.cardstatement and proof · cited by 2,327
- WithBotstatement · cited by 1,498
- Polynomial.evalstatement and proof · cited by 796
- Polynomial.degreestatement and proof · cited by 643
- Set.InjOnstatement and proof · cited by 543
Cited by4
Results whose statement or proof uses this declaration.
- Lagrange.eq_interpolate_of_eval_eqproof · cited by 2
- Lagrange.coeff_eq_sumproof · cited by 1
- Lagrange.interpolate_poly_eq_selfproof · cited by 0
- Lagrange.eval_iterate_derivative_eq_sumproof · cited by 0