Theorems · Theorem · commutative algebra
ascPochhammer_eval_neg_coe_nat_of_lt
∀ {R : Type u} [inst : Ring R] {n k : ℕ}, k < n → Polynomial.eval (-↑k) (ascPochhammer R n) = 0The Pochhammer polynomial of degree n has roots at 0, -1, ..., -(n - 1).
- Defined in
- Mathlib.RingTheory.Polynomial.Pochhammer
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- Polynomial.evalstatement and proof · cited by 796
- neg_add_cancelproof · cited by 256
- lt_trichotomyproof · cited by 178
- ascPochhammerstatement and proof · cited by 80
- ascPochhammer_succ_evalproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- ascPochhammer_eval_eq_zero_iffproof · cited by 3
- descPochhammer_eval_coe_nat_of_ltproof · cited by 0