Theorems · Theorem · commutative algebra
Polynomial.resultant_add_mul_left
∀ {R : Type u_1} [inst : CommRing R] (f g p : Polynomial R) (m n : ℕ),
p.natDegree + n ≤ m → g.natDegree ≤ n → (f + g * p).resultant g m n = f.resultant g m nRes(f + gp, g) = Res(f, g) if deg g + deg p ≤ deg f.
- 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- Nat.cast_oneproof · cited by 2,501
- mul_commproof · cited by 2,262
- mul_assocproof · cited by 1,667
- Polynomial.natDegreestatement and proof · cited by 1,105
- pow_addproof · cited by 315
- two_mulproof · cited by 232
- pow_mulproof · cited by 210
- Polynomial.resultantstatement and proof · cited by 54
- Polynomial.resultant_commproof · cited by 11
- Polynomial.resultant_add_mul_rightproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.resultant_eq_prod_roots_subproof · cited by 1