Theorems · Theorem · field theory
Polynomial.rootMultiplicity_expand_pow
∀ {R : Type u} [inst : CommRing R] {p n : ℕ} [ExpChar R p] {f : Polynomial R} {r : R},
Polynomial.rootMultiplicity r ((Polynomial.expand R (p ^ n)) f) = p ^ n * Polynomial.rootMultiplicity (r ^ p ^ n) f- Defined in
- Mathlib.Algebra.Polynomial.Expand
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
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
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement · cited by 3,236
- zero_addproof · cited by 2,366
- mul_commproof · cited by 2,262
- MulZeroClass.mul_zeroproof · cited by 2,091
- Polynomial.Xproof · cited by 1,639
- map_zeroproof · cited by 1,614
- Polynomial.Cproof · cited by 1,598
- map_mulproof · cited by 1,137
- eq_or_neproof · cited by 1,117
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.roots_expand_powproof · cited by 3
- Polynomial.rootMultiplicity_expandproof · cited by 0