Theorems · Theorem · field theory
minpoly.add_algebraMap
∀ {A : Type u_1} [inst : Field A] {B : Type u_3} [inst_1 : CommRing B] [inst_2 : Algebra A B] (x : B) (a : A),
minpoly A (x + (algebraMap A B) a) = (minpoly A x).comp (Polynomial.X - Polynomial.C a)- Defined in
- Mathlib.FieldTheory.Minpoly.Field
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites40
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
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- mul_oneproof · cited by 3,885
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- WithBotproof · cited by 1,498
- Polynomial.natDegreeproof · cited by 1,105
Cited by4
Results whose statement or proof uses this declaration.
- IsConjRoot.add_algebraMapproof · cited by 2
- minpoly_add_algebraMap_splitsproof · cited by 2
- IsPrimitiveRoot.minpoly_sub_one_eq_cyclotomic_compproof · cited by 1
- minpoly.sub_algebraMapproof · cited by 0