Theorems · Definition · commutative algebra
Polynomial.adjSylvester
{m n : ℕ} →
{R : Type u_1} →
[inst : CommRing R] →
Polynomial R →
Polynomial R → ↥(Polynomial.degreeLT R (m + n)) →ₗ[R] ↥(Polynomial.degreeLT R m) × ↥(Polynomial.degreeLT R n)The adjugate map of the sylvester map. It takes P to (p, q) such that
f * q + g * p = Res(f, g) * P.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 106 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.
Cites14
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 · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Submodulestatement · cited by 7,192
- Polynomialstatement and proof · cited by 5,681
- Matrix.toLinproof · cited by 77
- Matrix.adjugateproof · cited by 64
- Module.Basis.reindexproof · cited by 57
- Polynomial.degreeLTstatement · cited by 47
- finSumFinEquivproof · cited by 33
- Module.Basis.prodproof · cited by 26
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.sylveserMap_comp_adjSylvesterstatement · cited by 1
- Polynomial.exists_mul_add_mul_eq_C_resultantproof · cited by 1
- Polynomial.adjSylvester_comp_sylveserMapstatement · cited by 0