Theorems · Theorem · field theory
Polynomial.natDegree_eq_zero
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R}, p.natDegree = 0 ↔ ∃ x, Polynomial.C x = p- Cited by
- 14 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.coeffproof · cited by 1,045
- Polynomial.natDegree_Cproof · cited by 59
- Polynomial.eq_C_of_natDegree_eq_zeroproof · cited by 22
Cited by14
Results whose statement or proof uses this declaration.
- Irreducible.natDegree_posproof · cited by 8
- Polynomial.Splits.of_natDegree_eq_zeroproof · cited by 4
- Polynomial.resultant_X_sub_C_leftproof · cited by 3
- RatFunc.eq_C_iffproof · cited by 2
- Polynomial.natDegree_eraseLead_le_of_nextCoeff_eq_zeroproof · cited by 1
- Polynomial.resultant_scaleRootsproof · cited by 1
- IsPrimitiveRoot.sum_eq_zero_iff_forall_eqproof · cited by 1
- Polynomial.resultant_selfproof · cited by 1
- Polynomial.isOpenQuotientMap_evalproof · cited by 1
- Polynomial.natSepDegree_mul_eq_iffproof · cited by 1
- Polynomial.C_eq_or_isOpenQuotientMap_evalproof · cited by 1
- Valuation.Integers.isIntegral_iff_v_le_oneproof · cited by 1