ofComp — Mathlib

English

An alternative formulation of the previous monomial-sumElim identity, expressing the same equality via a different combinatorial decomposition.

Русский

Альтернативная формулировка идентичности мономиалов через разложение сумм.

LaTeX

$$$ (Q.ofComp P).toAlgHom (\\mathrm{monomial}(\\mathrm{Finsupp.sumElim}(v_1,v_2))\\, a) = \\mathrm{monomial}(v_1) (aeval_P(\\mathrm{monomial}(v_2)\\, a)) $$$

Lean4

/-- Given families of generators `X ⊆ T` over `S` and `Y ⊆ S` over `R`,
there is a map of generators `R[X, Y] → S[X]`. -/
@[simps]
noncomputable def ofComp (Q : Generators S T ι') (P : Generators R S ι) : Hom (Q.comp P) Q
    where
  val i := i.elim X (C ∘ P.val)
  aeval_val i := by cases i <;> simp

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