Theorems · Theorem · commutative algebra
Polynomial.resultant_mul_right
∀ {R : Type u_1} [inst : CommRing R] (f g₁ g₂ : Polynomial R) (m : ℕ),
f.natDegree ≤ m → f.resultant (g₁ * g₂) m (g₁.natDegree + g₂.natDegree) = f.resultant g₁ m * f.resultant g₂ mRes(f, g₁ * g₂) = Res(f, g₁) * Res(f, g₂).
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomproof · cited by 10,189
- Fieldproof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- map_mulproof · cited by 1,137
- Polynomial.natDegreestatement and proof · cited by 1,105
- pow_oneproof · cited by 894
- Multiset.mapproof · cited by 876
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.resultant_mul_leftproof · cited by 2
- Polynomial.isUnit_resultant_iff_isCoprimeproof · cited by 2
- Polynomial.resultant_dvd_leadingCoeff_powproof · cited by 1