spanCoeffs — Mathlib

English

spanCoeffs is the ideal generated by all coefficients of subProdXSubC(f) for all monic f and all natural indices.

Русский

spanCoeffs — порожденная идеалами всеми коэффициентами subProdXSubC(f) при всех монических f и всех индексов по Naturals.

LaTeX

$$$\\operatorname{spanCoeffs}(k) = \\operatorname{Ideal}.span\\{ (\\mathrm{subProdXSubC}(f)).coeff(n) : f \\in \\mathrm{Monics}(k), n \\in \\mathbb{N} \\}$$$

Lean4

/-- The span of all coefficients of `subProdXSubC f` as `f` ranges all polynomials in `k[X]`. -/
def spanCoeffs : Ideal (MvPolynomial (Vars k) k) :=
  Ideal.span <| Set.range fun fn : Monics k × ℕ ↦ (subProdXSubC fn.1).coeff fn.2

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