Theorems · Theorem · commutative algebra

wittStructureRat_rec

∀ (p : ℕ) {idx : Type u_2} [hp : Fact (Nat.Prime p)] (Φ : MvPolynomial idx ℚ) (n : ℕ),
  wittStructureRat p Φ n =
    MvPolynomial.C (1 / ↑p ^ n) *
      ((MvPolynomial.bind₁ fun b => (MvPolynomial.rename fun i => (b, i)) (wittPolynomial p ℚ n)) Φ -
        ∑ i ∈ Finset.range n, MvPolynomial.C (↑p ^ i) * wittStructureRat p Φ i ^ p ^ (n - i))

Write wittStructureRat p φ n in terms of wittStructureRat p φ i for i < n.

Defined in

Mathlib.RingTheory.WittVector.StructurePolynomial

Cited by

1 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Fact