Theorems · Theorem · field theory
Polynomial.degree_mul_leadingCoeff_inv
∀ {K : Type u_1} [inst : DivisionRing K] (p : Polynomial K) {q : Polynomial K},
q ≠ 0 → (p * Polynomial.C q.leadingCoeff⁻¹).degree = p.degree- Defined in
- Mathlib.Algebra.Polynomial.Degree.Lemmas
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 104 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.
Cites11
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
- WithBotstatement and proof · cited by 1,498
- DivisionRingstatement and proof · cited by 1,062
- Polynomial.degreestatement and proof · cited by 643
- Polynomial.leadingCoeffstatement and proof · cited by 498
- inv_ne_zeroproof · cited by 99
- Polynomial.leadingCoeff_eq_zeroproof · cited by 55
- Polynomial.degree_mul_Cproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- minpoly.degree_le_of_ne_zeroproof · cited by 3
- Polynomial.natDegree_mul_leadingCoeff_invproof · cited by 3
- Polynomial.degree_mul_leadingCoeff_self_invproof · cited by 2
- Polynomial.div_eq_zero_iffproof · cited by 1
- Polynomial.mod_eq_self_iffproof · cited by 1
- Polynomial.degree_div_leproof · cited by 0
- Polynomial.degree_div_ltproof · cited by 0
- Polynomial.leadingCoeff_divproof · cited by 0