Theorems · Theorem · commutative algebra
Polynomial.sylveserMap_comp_adjSylvester
∀ {m n : ℕ} {R : Type u_1} [inst : CommRing R] (f g : Polynomial R) (hf : f.natDegree ≤ m) (hg : g.natDegree ≤ n),
f.sylvesterMap g hf hg ∘ₗ f.adjSylvester g = f.resultant g m n • LinearMap.id- Cited by
- 1 results in Mathlib
- Foundations
- Depth 110 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.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement and proof · cited by 10,215
- Submodulestatement · cited by 7,192
- Polynomialstatement and proof · cited by 5,681
- Matrixproof · cited by 4,303
- LinearMap.compstatement and proof · cited by 1,642
- Module.Basisproof · cited by 1,477
- Polynomial.natDegreestatement and proof · cited by 1,105
- Matrix.detproof · cited by 665
- LinearMap.idstatement and proof · cited by 625
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.exists_mul_add_mul_eq_C_resultantproof · cited by 1