Theorems · Theorem · field theory
minpoly.zero
∀ (A : Type u_1) (B : Type u_2) [inst : Field A] [inst_1 : Ring B] [inst_2 : Algebra A B] [Nontrivial B], minpoly A 0 = Polynomial.X
The minimal polynomial of 0 is X.
- Defined in
- Mathlib.FieldTheory.Minpoly.Field
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldRingAlgebraNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- add_zeroproof · cited by 2,707
- Nontrivialstatement and proof · cited by 2,416
- Polynomial.Xstatement and proof · cited by 1,639
- map_zeroproof · cited by 1,614
- Polynomial.Cproof · cited by 1,598
- sub_eq_add_negproof · cited by 1,023
- neg_zeroproof · cited by 542
Cited by2
Results whose statement or proof uses this declaration.
- spectralNorm_zeroproof · cited by 1
- minpoly.coeff_zero_eq_zeroproof · cited by 0