Theorems · Theorem · field theory
inv_eq_of_root_of_coeff_zero_ne_zero
∀ {K : Type u_1} {L : Type u_2} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] {x : L} {p : Polynomial K},
(Polynomial.aeval x) p = 0 → p.coeff 0 ≠ 0 → x⁻¹ = -((Polynomial.aeval x) p.divX / (algebraMap K L) (p.coeff 0))- Defined in
- Mathlib.RingTheory.Algebraic.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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
- 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
- AlgHomstatement · cited by 3,236
- zero_addproof · cited by 2,366
- Polynomial.Xproof · cited by 1,639
- MulZeroClass.zero_mulproof · cited by 1,625
- Polynomial.Cproof · cited by 1,598
- map_mulproof · cited by 1,137
Cited by1
Results whose statement or proof uses this declaration.
- Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zeroproof · cited by 1