Theorems · Definition · commutative algebra
Polynomial.scaleRoots
{R : Type u_1} → [inst : Semiring R] → Polynomial R → R → Polynomial RscaleRoots p s is a polynomial with root r * s for each root r of p.
- Defined in
- Mathlib.RingTheory.Polynomial.ScaleRoots
- Cited by
- 56 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- Finset.sumproof · cited by 5,195
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- Polynomial.monomialproof · cited by 256
- Polynomial.supportproof · cited by 237
Cited by56
Results whose statement or proof uses this declaration.
- Polynomial.coeff_scaleRootsstatement · cited by 20
- IsIntegral.exists_multiple_integral_of_isLocalizationproof · cited by 7
- Polynomial.zero_scaleRootsstatement · cited by 7
- Polynomial.natDegree_scaleRootsstatement · cited by 7
- Polynomial.coeff_scaleRoots_natDegreestatement and proof · cited by 4
- Polynomial.one_scaleRootsstatement · cited by 4
- Polynomial.scaleRoots_eval₂_eq_zerostatement · cited by 4
- Polynomial.monic_scaleRoots_iffstatement · cited by 4
- Polynomial.mul_scaleRoots'statement and proof · cited by 4
- IsAlgebraic.smulproof · cited by 3
- Polynomial.support_scaleRoots_lestatement · cited by 3
- Polynomial.scaleRoots_aeval_eq_zerostatement and proof · cited by 3