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Theorems · Definition · commutative algebra

PowerBasis.minpolyGen

{S : Type u_2} →
  [inst : Ring S] → {A : Type u_4} → [inst_1 : CommRing A] → [inst_2 : Algebra A S] → PowerBasis A S → Polynomial A

pb.minpolyGen is the minimal polynomial for pb.gen.

Defined in
Mathlib.RingTheory.PowerBasis
Cited by
9 results in Mathlib
Foundations
Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RingCommRingAlgebra
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

PowerBasis.isIntegral_gen · cited by 4PowerBasis.isIntegral_genPowerBasis.minpolyGen_eq · cited by 4PowerBasis.minpolyGen_eqPowerBasis.degree_minpolyGen · cited by 3PowerBasis.degree_minpoly…PowerBasis.minpolyGen_monic · cited by 3PowerBasis.minpolyGen_mon…PowerBasis.aeval_minpolyGen · cited by 3PowerBasis.aeval_minpolyG…PowerBasis.natDegree_minpolyGen · cited by 2PowerBasis.natDegree_minp…PowerBasis.minpolyGen_map · cited by 1PowerBasis.minpolyGen_mapPowerBasis.leftMulMatrix · cited by 0PowerBasis.leftMulMatrixAlgebra.adjoin.powerBasis'_minpoly_gen · cited by 0adjoin.powerBasis'_minpol…DFunLike.coe · cited by 62936DFunLike.coeCommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraRing · cited by 7463RingPolynomial · cited by 5681PolynomialFinset.sum · cited by 5195Finset.sumFinset.univ · cited by 3473Finset.univPolynomial.X · cited by 1639Polynomial.XPolynomial.C · cited by 1598Polynomial.CModule.Basis.repr · cited by 498Basis.reprPowerBasis.gen · cited by 122PowerBasis.genPowerBasis · cited by 115PowerBasisPowerBasis.dim · cited by 74PowerBasis.dimPowerBasis.basis · cited by 54PowerBasis.basisPowerBasis.minpolyGenCITED BYCITES

Cites14

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by9

Results whose statement or proof uses this declaration.