Theorems · Theorem · commutative algebra
Polynomial.resultant_map_map
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] (f g : Polynomial R) (m n : ℕ) (φ : R →+* S),
(Polynomial.map φ f).resultant (Polynomial.map φ g) m n = φ (f.resultant g m n)- Cited by
- 10 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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 and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.mapstatement and proof · cited by 806
- Matrix.detproof · cited by 665
- Matrix.mapproof · cited by 247
- Matrix.det.congr_simpproof · cited by 91
- RingHom.mapMatrix_applyproof · cited by 73
- RingHom.mapMatrixproof · cited by 55
- Polynomial.resultantstatement · cited by 54
- RingHom.map_detproof · cited by 41
Cited by10
Results whose statement or proof uses this declaration.
- Polynomial.resultant_mul_rightproof · cited by 3
- Polynomial.resultant_eq_prod_evalproof · cited by 3
- Polynomial.UniversalCoprimeFactorizationRing.isCoprime_factor₁_factor₂proof · cited by 1
- Polynomial.UniversalFactorizationRing.jacobian_resentationproof · cited by 1
- Polynomial.resultant_scaleRootsproof · cited by 1
- Polynomial.resultant_selfproof · cited by 1
- MvPolynomial.universalFactorizationMapPresentation_jacobianproof · cited by 1
- Polynomial.resultant_eq_prod_roots_subproof · cited by 1
- Polynomial.resultant_integralNormalizationproof · cited by 0
- Polynomial.resultant_taylorproof · cited by 0