Theorems · Theorem · field theory
Polynomial.coeff_contract
∀ {R : Type u} [inst : CommSemiring R] {p : ℕ},
p ≠ 0 → ∀ (f : Polynomial R) (n : ℕ), (Polynomial.contract p f).coeff n = f.coeff (n * p)- Defined in
- Mathlib.Algebra.Polynomial.Expand
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 99 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.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- mul_oneproof · cited by 3,885
- Finset.sum_congrproof · cited by 2,323
- le_reflproof · cited by 2,061
- Finset.rangeproof · cited by 1,341
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.coeffstatement and proof · cited by 1,045
- mul_le_mul'proof · cited by 274
- Polynomial.monomialproof · cited by 256
- Ne.bot_ltproof · cited by 116
Cited by6
Results whose statement or proof uses this declaration.
- Polynomial.expand_contractproof · cited by 2
- Polynomial.contract_addproof · cited by 1
- Polynomial.contract_mul_expandproof · cited by 1
- Polynomial.contract_oneproof · cited by 1
- Polynomial.map_contractproof · cited by 0
- Polynomial.contract_expandproof · cited by 0