Theorems · Theorem · commutative algebra
Polynomial.natDegree_scaleRoots
∀ {R : Type u_1} [inst : Semiring R] (p : Polynomial R) (s : R), (p.scaleRoots s).natDegree = p.natDegree- Defined in
- Mathlib.RingTheory.Polynomial.ScaleRoots
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 102 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- Polynomial.natDegreestatement · cited by 1,105
- Polynomial.degreeproof · cited by 643
- Polynomial.scaleRootsstatement · cited by 56
- WithBot.unbotDproof · cited by 49
- Polynomial.degree_scaleRootsproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- Polynomial.leadingCoeff_scaleRootsproof · cited by 2
- den_dvd_of_is_rootproof · cited by 2
- Polynomial.scaleRoots.isWeaklyEisensteinAtproof · cited by 1
- Polynomial.dvd_pow_natDegree_of_eval₂_eq_zeroproof · cited by 1
- Polynomial.resultant_scaleRootsproof · cited by 1
- Polynomial.scaleRoots_mulproof · cited by 1
- Polynomial.resultant_integralNormalizationproof · cited by 0