Theorems · Theorem · field theory
Polynomial.natDegree_mul_leadingCoeff_inv
∀ {K : Type u_1} [inst : DivisionRing K] (p : Polynomial K) {q : Polynomial K},
q ≠ 0 → (p * Polynomial.C q.leadingCoeff⁻¹).natDegree = p.natDegree- Defined in
- Mathlib.Algebra.Polynomial.Degree.Lemmas
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRing
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 · cited by 62,936
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Cstatement · cited by 1,598
- Polynomial.natDegreestatement · cited by 1,105
- DivisionRingstatement and proof · cited by 1,062
- Polynomial.leadingCoeffstatement · cited by 498
- Polynomial.natDegree_eq_of_degree_eqproof · cited by 19
- Polynomial.degree_mul_leadingCoeff_invproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.irreducible_iff_roots_eq_zero_of_degree_le_threeproof · cited by 1
- Polynomial.irreducible_iff_degree_ltproof · cited by 0
- Polynomial.irreducible_iff_lt_natDegree_ltproof · cited by 0