Theorems · Definition · field theory
Polynomial.expand
(R : Type u) → [inst : CommSemiring R] → ℕ → Polynomial R →ₐ[R] Polynomial R
Expand the polynomial by a factor of p, so ∑ aₙ xⁿ becomes ∑ aₙ xⁿᵖ.
- Defined in
- Mathlib.Algebra.Polynomial.Expand
- Cited by
- 90 results in Mathlib
- Foundations
- Depth 106 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.
Cites7
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
- RingHomproof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement · cited by 3,236
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Polynomial.eval₂RingHomproof · cited by 19
Cited by95
Results whose statement or proof uses this declaration.
- Polynomial.expand_Cstatement · cited by 12
- Polynomial.expand_Xstatement · cited by 12
- Polynomial.coeff_expandstatement · cited by 11
- Polynomial.expand_onestatement and proof · cited by 10
- isPurelyInseparable_iff_pow_memproof · cited by 10
- Polynomial.IsSeparableContractionproof · cited by 7
- Polynomial.map_expandstatement and proof · cited by 7
- Polynomial.natDegree_expandstatement and proof · cited by 7
- Polynomial.coeff_expand_mulstatement · cited by 5
- Irreducible.hasSeparableContractionproof · cited by 4
- IsIntegral.of_powproof · cited by 4
- Polynomial.expand_aevalstatement and proof · cited by 4