Theorems · Theorem · field theory
Polynomial.natSepDegree_mul_eq_iff
∀ {F : Type u} [inst : Field F] (f g : Polynomial F),
(f * g).natSepDegree = f.natSepDegree + g.natSepDegree ↔ f = 0 ∧ g = 0 ∨ IsCoprime f g- Defined in
- Mathlib.FieldTheory.SeparableDegree
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 180 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.coeproof · cited by 62,936
- CommRingproof · cited by 17,173
- Algebraproof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- Finset.cardproof · cited by 2,327
- mul_commproof · cited by 2,262
- IsDomainproof · cited by 2,196
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.natSepDegree_mul_of_isCoprimeproof · cited by 1