prodXSubSMul — Mathlib

English

The action by g commutes with taking coefficients of the product: g • (prodXSubSMul G R x).coeff n = (prodXSubSMul G R x).coeff n.

Русский

Действие g commutes со взятием коэффициента: g•(prodXSubSMul G R x).coeff n = (prodXSubSMul G R x).coeff n.

LaTeX

$$$g \cdot \bigl((prodXSubSMul\ G\ R\ x).coeff\ n\bigr) = (prodXSubSMul\ G\ R\ x).coeff\ n$.$$

Lean4

/-- the product of `(X - g • x)` over distinct `g • x`. -/
noncomputable def prodXSubSMul (x : R) : R[X] :=
  letI := Classical.decEq R
  (Finset.univ : Finset (G ⧸ MulAction.stabilizer G x)).prod fun g ↦
    Polynomial.X - Polynomial.C (ofQuotientStabilizer G x g)

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