Theorems · Theorem · commutative algebra
Polynomial.resultant_C_mul_left
∀ {R : Type u_1} [inst : CommRing R] (f g : Polynomial R) (m n : ℕ) (r : R),
(Polynomial.C r * f).resultant g m n = r ^ n * f.resultant g m nRes(a • f, g) = a ^ {deg g} * Res(f, g).
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 103 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- one_mulproof · cited by 2,841
- mul_commproof · cited by 2,262
- mul_assocproof · cited by 1,667
- Polynomial.Cstatement and proof · cited by 1,598
- neg_negproof · cited by 960
- one_powproof · cited by 521
- mul_powproof · cited by 220
- mul_left_commproof · cited by 184
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.resultant_eq_prod_evalproof · cited by 3
- Polynomial.resultant_eq_zero_iffproof · cited by 0