Theorems · Theorem · field theory
Polynomial.Monic.coeff_natDegree
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R}, p.Monic → p.coeff p.natDegree = 1- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 62 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.
Cites5
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.natDegreestatement · cited by 1,105
- Polynomial.coeffstatement · cited by 1,045
- Polynomial.Monicstatement and proof · cited by 461
Cited by12
Results whose statement or proof uses this declaration.
- Polynomial.Monic.natDegree_mapproof · cited by 21
- Polynomial.isMonicOfDegree_iffproof · cited by 5
- Polynomial.Monic.mem_nonZeroDivisorsproof · cited by 3
- norm_root_le_spectralValueproof · cited by 3
- Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_root_of_monic_memproof · cited by 2
- Polynomial.Monic.eq_X_add_Cproof · cited by 2
- Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegreeproof · cited by 1
- Polynomial.Monic.C_dvd_iff_isUnitproof · cited by 1
- Valuation.Integers.isIntegral_iff_v_le_oneproof · cited by 1
- Lagrange.leadingCoeff_basisproof · cited by 1
- Polynomial.Monic.not_irreducible_iff_exists_add_mul_eq_coeffproof · cited by 1
- spectralValue_le_one_iffproof · cited by 0