Theorems · Definition · commutative algebra
Polynomial.toSubring
{R : Type u_1} → [inst : Ring R] → (p : Polynomial R) → (T : Subring R) → ↑p.coeffs ⊆ ↑T → Polynomial ↥TGiven a polynomial p and a subring T that contains the coefficients of p,
return the corresponding polynomial whose coefficients are in T.
- Defined in
- Mathlib.RingTheory.Polynomial.Subring
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Finsetstatement · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Finset.sumproof · cited by 5,195
- Polynomial.coeffproof · cited by 1,045
- Subringstatement and proof · cited by 602
- Polynomial.monomialproof · cited by 256
- Polynomial.supportproof · cited by 237
- Polynomial.coeffsstatement and proof · cited by 41
Cited by16
Results whose statement or proof uses this declaration.
- isIntegral_transproof · cited by 15
- FixedPoints.minpolyproof · cited by 9
- IsAlgebraic.restrictScalarsproof · cited by 6
- Polynomial.map_toSubringstatement · cited by 6
- Polynomial.coeff_toSubringstatement · cited by 5
- Polynomial.monic_toSubringstatement and proof · cited by 3
- IsSeparable.of_algebra_isSeparable_of_isSeparableproof · cited by 3
- Polynomial.natDegree_toSubringstatement · cited by 2
- IntermediateField.adjoin_minpoly_coeff_of_exists_primitive_elementproof · cited by 1
- Polynomial.degree_toSubringstatement · cited by 1
- Polynomial.coeff_toSubring'statement · cited by 1
- FixedPoints.minpoly.of_eval₂proof · cited by 1