Theorems · Theorem · commutative algebra
Polynomial.resultant_scaleRoots
∀ {R : Type u_1} [inst : CommRing R] (f g : Polynomial R) (r : R),
(f.scaleRoots r).resultant (g.scaleRoots r) = r ^ (f.natDegree * g.natDegree) * f.resultant g- Cited by
- 1 results in Mathlib
- Foundations
- Depth 163 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.
Cites70
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
- RingHomproof · cited by 10,189
- Fieldproof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- one_mulproof · cited by 2,841
- Multisetproof · cited by 2,627
- zero_addproof · cited by 2,366
- MulZeroClass.mul_zeroproof · cited by 2,091
- Polynomial.Xproof · cited by 1,639
- MulZeroClass.zero_mulproof · cited by 1,625
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.resultant_integralNormalizationproof · cited by 0