| import Mathlib | |
| namespace OAI | |
| noncomputable section | |
| namespace ComplexCancellation | |
| abbrev P := MvPolynomial (Fin 5) ℂ | |
| def p : P := MvPolynomial.X 0 | |
| def s : P := MvPolynomial.X 1 | |
| def u : P := MvPolynomial.X 2 | |
| def F : P := MvPolynomial.X 3 | |
| def J : P := MvPolynomial.X 4 | |
| def x : P := s ^ 2 + u ^ 3 + p ^ 2 * F | |
| def H : P := x ^ 2 * F - (1 + 2 * s * x) * J - p ^ 2 * J ^ 2 - p * u | |
| abbrev A := P ⧸ Ideal.span {H} | |
| def MainStatement : Prop := | |
| Algebra.FiniteType ℂ A ∧ IsDomain A ∧ ringKrullDim A = 4 ∧ | |
| Nonempty (Polynomial A ≃ₐ[ℂ] MvPolynomial (Fin 5) ℂ) ∧ | |
| ¬ Nonempty (A ≃ₐ[ℂ] MvPolynomial (Fin 4) ℂ) | |
| theorem main : MainStatement := by | |
| sorry | |
| end ComplexCancellation | |
| end | |
| end OAI | |