Theorems · Theorem · field theory
Polynomial.leadingCoeff_C
∀ {R : Type u} [inst : Semiring R] (a : R), (Polynomial.C a).leadingCoeff = a- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 107 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Polynomialstatement · cited by 5,681
- Polynomial.Cstatement · cited by 1,598
- Polynomial.leadingCoeffstatement · cited by 498
- Polynomial.leadingCoeff_monomialproof · cited by 6
Cited by39
Results whose statement or proof uses this declaration.
- Polynomial.monic_mul_leadingCoeff_invproof · cited by 19
- minpoly.eq_of_irreducibleproof · cited by 8
- Polynomial.monic_oneproof · cited by 5
- Polynomial.coeffList_eraseLeadproof · cited by 4
- Polynomial.splits_iff_exists_multiset'proof · cited by 4
- Polynomial.monic_mul_C_of_leadingCoeff_mul_eq_oneproof · cited by 4
- Polynomial.irreducible_of_monicproof · cited by 3
- Polynomial.div_wf_lemmaproof · cited by 3
- Polynomial.eq_mul_leadingCoeff_of_monic_of_dvd_of_natDegree_leproof · cited by 2
- Cubic.leadingCoeff_of_c_eq_zeroproof · cited by 2
- IsLocalization.exists_isIntegral_smul_of_isIntegral_mapproof · cited by 2
- Polynomial.tendsto_abv_eval₂_atTopproof · cited by 2