Theorems · Theorem · field theory
Polynomial.coeffList_eq_nil
∀ {R : Type u_1} [inst : Semiring R] {P : Polynomial R}, P.coeffList = [] ↔ P = 0Only the zero polynomial has no coefficients.
- Defined in
- Mathlib.Algebra.Polynomial.CoeffList
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- Polynomial.coeffListstatement · cited by 22
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.signVariations_eq_eraseLead_add_iteproof · cited by 1
- Polynomial.head_coeffListproof · cited by 0