Theorems · Theorem · commutative algebra
Polynomial.resultant_prod_left
∀ {R : Type u_1} [inst : CommRing R] {ι : Type u_3} (s : Finset ι) (f : ι → Polynomial R) (g : Polynomial R) (n : ℕ),
∏ i ∈ s, (f i).leadingCoeff ≠ 0 →
g.natDegree ≤ n →
(∏ i ∈ s, f i).resultant g (∏ i ∈ s, f i).natDegree n = ∏ i ∈ s, (f i).resultant g (f i).natDegree n- Cited by
- 2 results in Mathlib
- Foundations
- Depth 158 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.
Cites17
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
- Finsetstatement and proof · cited by 13,712
- Polynomialstatement and proof · cited by 5,681
- Finset.prodstatement and proof · cited by 2,356
- MulZeroClass.mul_zeroproof · cited by 2,091
- Polynomial.natDegreestatement and proof · cited by 1,105
- one_powproof · cited by 521
- Polynomial.leadingCoeffstatement and proof · cited by 498
- Finset.prod_insertproof · cited by 109
- Finset.inductionproof · cited by 108
- Polynomial.resultantstatement and proof · cited by 54
- Polynomial.natDegree_oneproof · cited by 43
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.resultant_pow_leftproof · cited by 1
- Polynomial.resultant_prod_rightproof · cited by 1