Theorems · Theorem · field theory
Polynomial.Monic.leadingCoeff
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R}, p.Monic → p.leadingCoeff = 1- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 101 results in Mathlib
- Foundations
- Depth 62 from the axioms, rests on 961 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.leadingCoeffstatement · cited by 498
- Polynomial.Monicstatement and proof · cited by 461
Cited by101
Results whose statement or proof uses this declaration.
- Polynomial.Monic.natDegree_mul'proof · cited by 9
- Polynomial.leadingCoeff_pow'proof · cited by 8
- minpoly.natDegree_posproof · cited by 8
- IsIntegral.exists_multiple_integral_of_isLocalizationproof · cited by 7
- Polynomial.eq_of_monic_of_dvd_of_natDegree_leproof · cited by 7
- Polynomial.Monic.degree_mulproof · cited by 7
- Polynomial.degree_comp_neg_Xproof · cited by 7
- minpoly.uniqueproof · cited by 7
- Polynomial.leadingCoeff_mul_monicproof · cited by 6
- Polynomial.Monic.natDegree_mulproof · cited by 6
- Polynomial.leadingCoeff_monic_mulproof · cited by 5
- RatFunc.num_zeroproof · cited by 5