Theorems · Theorem · field theory
Polynomial.eq_C_coeff_zero_iff_natDegree_eq_zero
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R}, p = Polynomial.C (p.coeff 0) ↔ p.natDegree = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 105 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Cstatement and proof · cited by 1,598
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffstatement and proof · cited by 1,045
- Polynomial.natDegree_Cproof · cited by 59
- Polynomial.eq_C_of_natDegree_eq_zeroproof · cited by 22
Cited by1
Results whose statement or proof uses this declaration.
- IsAlgClosed.roots_eq_zero_iff_natDegree_eq_zeroproof · cited by 2