Bennett Residue Taylor homogenize
ProvedD1Bound5.bennettResidueTaylor_homogenizediophantine-tuplesnumber-theory
Clearing the common N denominator recovers the polynomial G used in the node-removal determinant induction.
Preamble
import Lean.Elab.Tactic.Omega import Mathlib.Algebra.Polynomial.BigOperators import Mathlib.Algebra.Polynomial.Degree.Operations import Mathlib.RingTheory.PowerSeries.Binomial import Mathlib.Tactic.Ring import Definitions.Def_D1Bound5_BennettClearedResidues_Definitions import Definitions.Def_D1Bound5_BennettResiduePolynomials_Definitions
Formal statement
section
open Finset
namespace D1Bound5
variable {F : Type*} [Field F] [CharZero F]
theorem _root_.D1Bound5.bennettResidueTaylor_homogenize (k r : ℕ) (hr : r ≤ k)
(ν a N : F) (B : PowerSeries F) (hN : N ≠ 0) :
N ^ k * (bennettResidueTaylor k r ν a B).eval N⁻¹ =
(bennettClearedTaylor k r ν a B).eval N := by sorry
section Nodes
variable {I : Type*} [DecidableEq I]
end Nodes
end D1Bound5
end
Source
D1Bound5/BennettResiduePolynomials.lean, lines 57-74, SHA-256 5264fd8f08d4a6fb748bab8f101f05ca183c3e4658b02954972b81e086f0144d. Project: https://github.com/tomislav-math/d1-bound5-lean