Theorems · Definition · commutative algebra
Polynomial.int
{K : Type u_1} → [inst : Field K] → (R : Subring K) → (P : Polynomial K) → (∀ (n : ℕ), P.coeff n ∈ R) → Polynomial ↥RGiven a polynomial in K[X] such that all coefficients belong to the subring R,
Polynomial.int is the corresponding polynomial in R[X].
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Polynomial.coeffstatement and proof · cited by 1,045
- Subringstatement and proof · cited by 602
- Polynomial.supportproof · cited by 237
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.int_leadingCoeff_eqstatement · cited by 1
- Polynomial.int_monic_iffstatement and proof · cited by 0
- Polynomial.int_natDegreestatement · cited by 0
- Polynomial.int_coeff_eqstatement · cited by 0
- Polynomial.int_eval₂_eqstatement and proof · cited by 0