File size: 717 Bytes
dae740b | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 | 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
|