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Theorems · Theorem · commutative algebra

ascPochhammer_eval_eq_zero_iff

∀ {R : Type u} [inst : Ring R] [IsDomain R] (n : ℕ) (r : R),
  Polynomial.eval r (ascPochhammer R n) = 0 ↔ ∃ k < n, ↑k = -r

Over an integral domain, the Pochhammer polynomial of degree n has roots only at 0, -1, ..., -(n - 1).

Defined in
Mathlib.RingTheory.Polynomial.Pochhammer
Cited by
3 results in Mathlib
Foundations
Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RingIsDomain

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