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Theorems · Definition · commutative algebra

Polynomial.toSubring

{R : Type u_1} → [inst : Ring R] → (p : Polynomial R) → (T : Subring R) → ↑p.coeffs ⊆ ↑T → Polynomial ↥T

Given 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.

isIntegral_trans · cited by 15isIntegral_transFixedPoints.minpoly · cited by 9FixedPoints.minpolyIsAlgebraic.restrictScalars · cited by 6IsAlgebraic.restrictScala…Polynomial.map_toSubring · cited by 6Polynomial.map_toSubringPolynomial.coeff_toSubring · cited by 5Polynomial.coeff_toSubringPolynomial.monic_toSubring · cited by 3Polynomial.monic_toSubringIsSeparable.of_algebra_isSeparable_of_isSeparable · cited by 3IsSeparable.of_algebra_is…Polynomial.natDegree_toSubring · cited by 2Polynomial.natDegree_toSu…IntermediateField.adjoin_minpoly_coeff_of_exists_primitive_element · cited by 1IntermediateField.adjoin_…Polynomial.degree_toSubring · cited by 1Polynomial.degree_toSubri…Polynomial.coeff_toSubring' · cited by 1Polynomial.coeff_toSubrin…FixedPoints.minpoly.of_eval₂ · cited by 1minpoly.of_eval₂Polynomial.support_toSubring · cited by 1Polynomial.support_toSubr…Polynomial.toSubring.congr_simp · cited by 0toSubring.congr_simpPolynomial.toSubring_one · cited by 0Polynomial.toSubring_oneDFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetFinset · cited by 13712FinsetSetLike.coe · cited by 8199SetLike.coeRing · cited by 7463RingPolynomial · cited by 5681PolynomialFinset.sum · cited by 5195Finset.sumPolynomial.coeff · cited by 1045Polynomial.coeffSubring · cited by 602SubringPolynomial.monomial · cited by 256Polynomial.monomialPolynomial.support · cited by 237Polynomial.supportPolynomial.coeffs · cited by 41Polynomial.coeffsPolynomial.toSubringCITED BYCITES

Cites12

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Cited by16

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