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 = -rOver 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
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringproof · cited by 13,802
- Ringstatement and proof · cited by 7,463
- Polynomialproof · cited by 5,681
- IsDomainstatement and proof · cited by 2,196
- neg_negproof · cited by 960
- Polynomial.evalstatement and proof · cited by 796
- lt_add_oneproof · cited by 105
- mul_eq_zeroproof · cited by 94
- Polynomial.eval_oneproof · cited by 86
- ascPochhammerstatement and proof · cited by 80
- eq_neg_of_add_eq_zero_rightproof · cited by 8
- ascPochhammer_succ_evalproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- ordinaryHypergeometricSeries_eq_zero_of_neg_natproof · cited by 3
- ordinaryHypergeometricSeries_norm_div_succ_normproof · cited by 1
- ordinaryHypergeometricSeries_eq_zero_iffproof · cited by 0