Theorems · Theorem · commutative algebra
Polynomial.resultant_succ_left_deg
∀ {R : Type u_1} [inst : CommRing R] (f g : Polynomial R) (m n : ℕ),
f.natDegree ≤ m → f.resultant g (m + 1) n = (-1) ^ n * g.coeff n * f.resultant g m n- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 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.
Cites42
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
- Fintypeproof · cited by 7,736
- Polynomialstatement and proof · cited by 5,681
- Matrixproof · cited by 4,303
- mul_oneproof · cited by 3,885
- Finset.univproof · cited by 3,473
- one_mulproof · cited by 2,841
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- add_commproof · cited by 1,535
- Polynomial.natDegreestatement and proof · cited by 1,105
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.resultant_add_left_degproof · cited by 5