Theorems · Theorem · linear algebra
Lagrange.eval_interpolate_at_node
∀ {F : Type u_1} [inst : Field F] {ι : Type u_2} [inst_1 : DecidableEq ι] {s : Finset ι} {i : ι} {v : ι → F}
(r : ι → F), Set.InjOn v ↑s → i ∈ s → Polynomial.eval (v i) ((Lagrange.interpolate s v) r) = r i- Defined in
- Mathlib.LinearAlgebra.Lagrange
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 109 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.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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.sumproof · cited by 5,195
- mul_oneproof · cited by 3,885
- Finset.sum_congrproof · cited by 2,323
- MulZeroClass.mul_zeroproof · cited by 2,091
- Polynomial.Cproof · cited by 1,598
Cited by5
Results whose statement or proof uses this declaration.
- Lagrange.eq_interpolateproof · cited by 4
- Lagrange.values_eq_on_of_interpolate_eqproof · cited by 1
- Lagrange.interpolate_eq_sum_interpolate_insert_sdiffproof · cited by 1
- Polynomial.exists_eval_eq_iffproof · cited by 0
- Lagrange.eq_interpolate_iffproof · cited by 0