Theorems · Theorem · commutative algebra
Polynomial.isCoprime_scaleRoots
∀ {R : Type u_1} [inst : CommSemiring R] (p q : Polynomial R) (r : R),
IsUnit r → IsCoprime p q → IsCoprime (p.scaleRoots r) (q.scaleRoots r)- Defined in
- Mathlib.RingTheory.Polynomial.ScaleRoots
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- mul_oneproof · cited by 3,885
- Units.valproof · cited by 1,966
- mul_assocproof · cited by 1,667
- IsUnitstatement and proof · cited by 1,602
- one_smulproof · cited by 1,374
- Polynomial.natDegreeproof · cited by 1,105
- one_powproof · cited by 521
- smul_smulproof · cited by 360
- IsCoprimestatement and proof · cited by 321
- IsUnit.unitproof · cited by 252
Cited by1
Results whose statement or proof uses this declaration.
- IsCoprime.scaleRootsproof · cited by 0