Theorems · Theorem · commutative algebra
AdjoinRoot.minpoly_powerBasis_gen
∀ {K : Type u_5} [inst : Field K] {f : Polynomial K} (hf : f ≠ 0),
minpoly K (AdjoinRoot.powerBasis hf).gen = f * Polynomial.C f.leadingCoeff⁻¹- Defined in
- Mathlib.RingTheory.AdjoinRoot
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 125 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.
Cites12
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 · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Cstatement and proof · cited by 1,598
- Polynomial.leadingCoeffstatement and proof · cited by 498
- minpolystatement and proof · cited by 439
- AdjoinRootstatement and proof · cited by 177
- PowerBasis.genstatement · cited by 122
- AdjoinRoot.powerBasisstatement · cited by 9
- AdjoinRoot.minpoly_rootproof · cited by 3
- AdjoinRoot.powerBasis_genproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- AdjoinRoot.minpoly_powerBasis_gen_of_monicproof · cited by 0