Theorems · Theorem · commutative algebra
Polynomial.resultant_C_mul_right
∀ {R : Type u_1} [inst : CommRing R] (f g : Polynomial R) (m n : ℕ) (r : R),
f.resultant (Polynomial.C r * g) m n = r ^ m * f.resultant g m nRes(f, a • g) = a ^ {deg f} * Res(f, g).
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 102 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.
Cites28
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
- Fintypeproof · cited by 7,736
- Polynomialstatement and proof · cited by 5,681
- Matrixproof · cited by 4,303
- one_mulproof · cited by 2,841
- MulZeroClass.mul_zeroproof · cited by 2,091
- mul_assocproof · cited by 1,667
- Polynomial.Cstatement and proof · cited by 1,598
- le_rflproof · cited by 1,558
- eq_or_neproof · cited by 1,117
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.resultant_eq_prod_evalproof · cited by 3
- Polynomial.resultant_C_mul_leftproof · cited by 2
- Polynomial.resultant_scaleRootsproof · cited by 1
- Polynomial.resultant_eq_prod_roots_subproof · cited by 1
- Polynomial.resultant_integralNormalizationproof · cited by 0