Theorems · Theorem · commutative algebra
AdjoinRoot.minpoly_root
∀ {K : Type u_5} [inst : Field K] {f : Polynomial K},
f ≠ 0 → minpoly K (AdjoinRoot.root f) = f * Polynomial.C f.leadingCoeff⁻¹- Defined in
- Mathlib.RingTheory.AdjoinRoot
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 113 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.
Cites42
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHomstatement and proof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- add_zeroproof · cited by 2,707
- MulZeroClass.zero_mulproof · cited by 1,625
- map_zeroproof · cited by 1,614
- Polynomial.Cstatement and proof · cited by 1,598
- WithBotproof · cited by 1,498
- map_mulproof · cited by 1,137
- Polynomial.natDegreeproof · cited by 1,105
Cited by4
Results whose statement or proof uses this declaration.
- Irreducible.exists_dvd_monic_irreducible_of_isIntegralproof · cited by 2
- Polynomial.irreducible_compproof · cited by 1
- AdjoinRoot.minpoly_powerBasis_genproof · cited by 1
- AdjoinRoot.powerBasisAuxproof · cited by 1