Theorems · Definition · linear algebra
Lagrange.basisDivisor
{F : Type u_1} → [inst : Field F] → F → F → Polynomial FbasisDivisor x y is the unique linear or constant polynomial such that
when evaluated at x it gives 1 and y it gives 0 (where when x = y it is identically 0).
Such polynomials are the building blocks for the Lagrange interpolants.
- Defined in
- Mathlib.LinearAlgebra.Lagrange
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
Cited by20
Results whose statement or proof uses this declaration.
- Lagrange.basisproof · cited by 26
- Lagrange.basisDivisor_eq_zero_iffstatement · cited by 3
- Lagrange.basisDivisor_selfstatement · cited by 3
- Lagrange.basis_pair_leftstatement and proof · cited by 3
- Lagrange.eval_basis_of_neproof · cited by 3
- Lagrange.eval_basis_selfproof · cited by 3
- Lagrange.natDegree_basisproof · cited by 3
- Lagrange.basis_pair_rightstatement and proof · cited by 2
- Lagrange.basisDivisor_injstatement and proof · cited by 1
- Lagrange.basis_ne_zeroproof · cited by 1
- Lagrange.basis_singletonproof · cited by 1
- Lagrange.degree_basisDivisor_of_nestatement · cited by 1