Rank-one coupling · biquartic pencil — instance data

Definition

HodgeComputerRankOneBiquartic

by benediamond · Nov 5, 2026 · Mathlib 0df444a (Lean v4.33.1)

algebraic-geometryhodge-computerrank-one-biquartic

The exact fixed polynomials and pole parameter for “Rank-one coupling · biquartic pencil”, over $\mathbb C$ with coordinates $X_0,X_1,X_2,Y_0,Y_1,Y_2$ :

F=f(X_0,X_1,X_2)+g(Y_0,Y_1,Y_2)+t\cdot L^2\cdot M.

q=1,\qquad A=X_{0}^{3} \cdot Y_{0}^{3}.

where

\begin{aligned} t&=\frac57 \\ f(a,b,c)&=a^6+b^6+c^6+t\cdot(a^5\cdot b+2\cdot b^5\cdot c+3\cdot c^5\cdot a+a^2\cdot b^3\cdot c) \\ g(a,b,c)&=a^6+b^6+c^6+t\cdot(2\cdot a^5\cdot b+3\cdot b^5\cdot c+c^5\cdot a+2\cdot a^3\cdot b\cdot c^2) \\ L&=X_{0}^{2} + X_{0} \cdot X_{1} + 2 \cdot X_{1} \cdot X_{2} + 3 \cdot X_{2}^{2} \\ M&=Y_{0}^{2} + Y_{0} \cdot Y_{1} + 2 \cdot Y_{1} \cdot Y_{2} + 3 \cdot Y_{2}^{2} \end{aligned}

Definition code

import Definitions.Def_DiamondCertificate

set_option autoImplicit false
noncomputable section
namespace HodgeComputer.RankOneBiquartic
def n : ℕ := 5
def d : ℕ := 6
def F : HodgeComputer.AmbientPoly n := (((((((((((((((((((((((((((((((((((((((((((((((((((((((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (6 : ℕ)) + ((((5 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (5 : ℕ))) * (MvPolynomial.X (R := ℂ) (1 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((((5 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (4 : ℕ))) * ((MvPolynomial.X (R := ℂ) (3 : Fin 6)) ^ (2 : ℕ))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + (((((5 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (4 : ℕ))) * (MvPolynomial.X (R := ℂ) (3 : Fin 6))) * (MvPolynomial.X (R := ℂ) (4 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + (((((10 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (4 : ℕ))) * (MvPolynomial.X (R := ℂ) (4 : Fin 6))) * (MvPolynomial.X (R := ℂ) (5 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((((15 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (4 : ℕ))) * ((MvPolynomial.X (R := ℂ) (5 : Fin 6)) ^ (2 : ℕ))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + (((((10 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (3 : ℕ))) * (MvPolynomial.X (R := ℂ) (1 : Fin 6))) * ((MvPolynomial.X (R := ℂ) (3 : Fin 6)) ^ (2 : ℕ))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((((((10 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (3 : ℕ))) * (MvPolynomial.X (R := ℂ) (1 : Fin 6))) * (MvPolynomial.X (R := ℂ) (3 : Fin 6))) * (MvPolynomial.X (R := ℂ) (4 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((((((20 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (3 : ℕ))) * (MvPolynomial.X (R := ℂ) (1 : Fin 6))) * (MvPolynomial.X (R := ℂ) (4 : Fin 6))) * (MvPolynomial.X (R := ℂ) (5 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + (((((30 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (3 : ℕ))) * (MvPolynomial.X (R := ℂ) (1 : Fin 6))) * ((MvPolynomial.X (R := ℂ) (5 : Fin 6)) ^ (2 : ℕ))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + (((((5 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (2 : ℕ))) * ((MvPolynomial.X (R := ℂ) (1 : Fin 6)) ^ (3 : ℕ))) * (MvPolynomial.X (R := ℂ) (2 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + (((((5 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (2 : ℕ))) * ((MvPolynomial.X (R := ℂ) (1 : Fin 6)) ^ (2 : ℕ))) * ((MvPolynomial.X (R := ℂ) (3 : Fin 6)) ^ (2 : ℕ))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((((((5 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (2 : ℕ))) * ((MvPolynomial.X (R := ℂ) (1 : Fin 6)) ^ (2 : ℕ))) * (MvPolynomial.X (R := ℂ) (3 : Fin 6))) * (MvPolynomial.X (R := ℂ) (4 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((((((10 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (2 : ℕ))) * ((MvPolynomial.X (R := ℂ) (1 : Fin 6)) ^ (2 : ℕ))) * (MvPolynomial.X (R := ℂ) (4 : Fin 6))) * (MvPolynomial.X (R := ℂ) (5 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + (((((15 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (2 : ℕ))) * ((MvPolynomial.X (R := ℂ) (1 : Fin 6)) ^ (2 : ℕ))) * ((MvPolynomial.X (R := ℂ) (5 : Fin 6)) ^ (2 : ℕ))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((((((20 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (2 : ℕ))) * (MvPolynomial.X (R := ℂ) (1 : Fin 6))) * (MvPolynomial.X (R := ℂ) (2 : Fin 6))) * ((MvPolynomial.X (R := ℂ) (3 : Fin 6)) ^ (2 : ℕ))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + (((((((20 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (2 : ℕ))) * (MvPolynomial.X (R := ℂ) (1 : Fin 6))) * (MvPolynomial.X (R := ℂ) (2 : Fin 6))) * (MvPolynomial.X (R := ℂ) (3 : Fin 6))) * (MvPolynomial.X (R := ℂ) (4 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + (((((((40 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (2 : ℕ))) * (MvPolynomial.X (R := ℂ) (1 : Fin 6))) * (MvPolynomial.X (R := ℂ) (2 : Fin 6))) * (MvPolynomial.X (R := ℂ) (4 : Fin 6))) * (MvPolynomial.X (R := ℂ) (5 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((((((60 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (2 : ℕ))) * (MvPolynomial.X (R := ℂ) (1 : Fin 6))) * (MvPolynomial.X (R := ℂ) (2 : Fin 6))) * ((MvPolynomial.X (R := ℂ) (5 : Fin 6)) ^ (2 : ℕ))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + (((((30 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (2 : ℕ))) * ((MvPolynomial.X (R := ℂ) (2 : Fin 6)) ^ (2 : ℕ))) * ((MvPolynomial.X (R := ℂ) (3 : Fin 6)) ^ (2 : ℕ))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((((((30 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (2 : ℕ))) * ((MvPolynomial.X (R := ℂ) (2 : Fin 6)) ^ (2 : ℕ))) * (MvPolynomial.X (R := ℂ) (3 : Fin 6))) * (MvPolynomial.X (R := ℂ) (4 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((((((60 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (2 : ℕ))) * ((MvPolynomial.X (R := ℂ) (2 : Fin 6)) ^ (2 : ℕ))) * (MvPolynomial.X (R := ℂ) (4 : Fin 6))) * (MvPolynomial.X (R := ℂ) (5 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + (((((90 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (2 : ℕ))) * ((MvPolynomial.X (R := ℂ) (2 : Fin 6)) ^ (2 : ℕ))) * ((MvPolynomial.X (R := ℂ) (5 : Fin 6)) ^ (2 : ℕ))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((((((20 : MvPolynomial (Fin 6) ℂ) * (MvPolynomial.X (R := ℂ) (0 : Fin 6))) * ((MvPolynomial.X (R := ℂ) (1 : Fin 6)) ^ (2 : ℕ))) * (MvPolynomial.X (R := ℂ) (2 : Fin 6))) * ((MvPolynomial.X (R := ℂ) (3 : Fin 6)) ^ (2 : ℕ))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + (((((((20 : MvPolynomial (Fin 6) ℂ) * (MvPolynomial.X (R := ℂ) (0 : Fin 6))) * ((MvPolynomial.X (R := ℂ) (1 : Fin 6)) ^ (2 : ℕ))) * (MvPolynomial.X (R := ℂ) (2 : Fin 6))) * (MvPolynomial.X (R := ℂ) (3 : Fin 6))) * (MvPolynomial.X (R := ℂ) (4 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + (((((((40 : MvPolynomial (Fin 6) ℂ) * (MvPolynomial.X (R := ℂ) (0 : Fin 6))) * ((MvPolynomial.X (R := ℂ) (1 : Fin 6)) ^ (2 : ℕ))) * (MvPolynomial.X (R := ℂ) (2 : Fin 6))) * (MvPolynomial.X (R := ℂ) (4 : Fin 6))) * (MvPolynomial.X (R := ℂ) (5 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((((((60 : MvPolynomial (Fin 6) ℂ) * (MvPolynomial.X (R := ℂ) (0 : Fin 6))) * ((MvPolynomial.X (R := ℂ) (1 : Fin 6)) ^ (2 : ℕ))) * (MvPolynomial.X (R := ℂ) (2 : Fin 6))) * ((MvPolynomial.X (R := ℂ) (5 : Fin 6)) ^ (2 : ℕ))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((((((30 : MvPolynomial (Fin 6) ℂ) * (MvPolynomial.X (R := ℂ) (0 : Fin 6))) * (MvPolynomial.X (R := ℂ) (1 : Fin 6))) * ((MvPolynomial.X (R := ℂ) (2 : Fin 6)) ^ (2 : ℕ))) * ((MvPolynomial.X (R := ℂ) (3 : Fin 6)) ^ (2 : ℕ))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + (((((((30 : MvPolynomial (Fin 6) ℂ) * (MvPolynomial.X (R := ℂ) (0 : Fin 6))) * (MvPolynomial.X (R := ℂ) (1 : Fin 6))) * ((MvPolynomial.X (R := ℂ) (2 : Fin 6)) ^ (2 : ℕ))) * (MvPolynomial.X (R := ℂ) (3 : Fin 6))) * (MvPolynomial.X (R := ℂ) (4 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + (((((((60 : MvPolynomial (Fin 6) ℂ) * (MvPolynomial.X (R := ℂ) (0 : Fin 6))) * (MvPolynomial.X (R := ℂ) (1 : Fin 6))) * ((MvPolynomial.X (R := ℂ) (2 : Fin 6)) ^ (2 : ℕ))) * (MvPolynomial.X (R := ℂ) (4 : Fin 6))) * (MvPolynomial.X (R := ℂ) (5 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((((((90 : MvPolynomial (Fin 6) ℂ) * (MvPolynomial.X (R := ℂ) (0 : Fin 6))) * (MvPolynomial.X (R := ℂ) (1 : Fin 6))) * ((MvPolynomial.X (R := ℂ) (2 : Fin 6)) ^ (2 : ℕ))) * ((MvPolynomial.X (R := ℂ) (5 : Fin 6)) ^ (2 : ℕ))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((((15 : MvPolynomial (Fin 6) ℂ) * (MvPolynomial.X (R := ℂ) (0 : Fin 6))) * ((MvPolynomial.X (R := ℂ) (2 : Fin 6)) ^ (5 : ℕ))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((MvPolynomial.X (R := ℂ) (1 : Fin 6)) ^ (6 : ℕ))) + ((((10 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (1 : Fin 6)) ^ (5 : ℕ))) * (MvPolynomial.X (R := ℂ) (2 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + (((((20 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (1 : Fin 6)) ^ (2 : ℕ))) * ((MvPolynomial.X (R := ℂ) (2 : Fin 6)) ^ (2 : ℕ))) * ((MvPolynomial.X (R := ℂ) (3 : Fin 6)) ^ (2 : ℕ))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((((((20 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (1 : Fin 6)) ^ (2 : ℕ))) * ((MvPolynomial.X (R := ℂ) (2 : Fin 6)) ^ (2 : ℕ))) * (MvPolynomial.X (R := ℂ) (3 : Fin 6))) * (MvPolynomial.X (R := ℂ) (4 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((((((40 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (1 : Fin 6)) ^ (2 : ℕ))) * ((MvPolynomial.X (R := ℂ) (2 : Fin 6)) ^ (2 : ℕ))) * (MvPolynomial.X (R := ℂ) (4 : Fin 6))) * (MvPolynomial.X (R := ℂ) (5 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + (((((60 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (1 : Fin 6)) ^ (2 : ℕ))) * ((MvPolynomial.X (R := ℂ) (2 : Fin 6)) ^ (2 : ℕ))) * ((MvPolynomial.X (R := ℂ) (5 : Fin 6)) ^ (2 : ℕ))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + (((((60 : MvPolynomial (Fin 6) ℂ) * (MvPolynomial.X (R := ℂ) (1 : Fin 6))) * ((MvPolynomial.X (R := ℂ) (2 : Fin 6)) ^ (3 : ℕ))) * ((MvPolynomial.X (R := ℂ) (3 : Fin 6)) ^ (2 : ℕ))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((((((60 : MvPolynomial (Fin 6) ℂ) * (MvPolynomial.X (R := ℂ) (1 : Fin 6))) * ((MvPolynomial.X (R := ℂ) (2 : Fin 6)) ^ (3 : ℕ))) * (MvPolynomial.X (R := ℂ) (3 : Fin 6))) * (MvPolynomial.X (R := ℂ) (4 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((((((120 : MvPolynomial (Fin 6) ℂ) * (MvPolynomial.X (R := ℂ) (1 : Fin 6))) * ((MvPolynomial.X (R := ℂ) (2 : Fin 6)) ^ (3 : ℕ))) * (MvPolynomial.X (R := ℂ) (4 : Fin 6))) * (MvPolynomial.X (R := ℂ) (5 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + (((((180 : MvPolynomial (Fin 6) ℂ) * (MvPolynomial.X (R := ℂ) (1 : Fin 6))) * ((MvPolynomial.X (R := ℂ) (2 : Fin 6)) ^ (3 : ℕ))) * ((MvPolynomial.X (R := ℂ) (5 : Fin 6)) ^ (2 : ℕ))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((MvPolynomial.X (R := ℂ) (2 : Fin 6)) ^ (6 : ℕ))) + ((((45 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (2 : Fin 6)) ^ (4 : ℕ))) * ((MvPolynomial.X (R := ℂ) (3 : Fin 6)) ^ (2 : ℕ))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + (((((45 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (2 : Fin 6)) ^ (4 : ℕ))) * (MvPolynomial.X (R := ℂ) (3 : Fin 6))) * (MvPolynomial.X (R := ℂ) (4 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + (((((90 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (2 : Fin 6)) ^ (4 : ℕ))) * (MvPolynomial.X (R := ℂ) (4 : Fin 6))) * (MvPolynomial.X (R := ℂ) (5 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((((135 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (2 : Fin 6)) ^ (4 : ℕ))) * ((MvPolynomial.X (R := ℂ) (5 : Fin 6)) ^ (2 : ℕ))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((MvPolynomial.X (R := ℂ) (3 : Fin 6)) ^ (6 : ℕ))) + ((((10 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (3 : Fin 6)) ^ (5 : ℕ))) * (MvPolynomial.X (R := ℂ) (4 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + (((((10 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (3 : Fin 6)) ^ (3 : ℕ))) * (MvPolynomial.X (R := ℂ) (4 : Fin 6))) * ((MvPolynomial.X (R := ℂ) (5 : Fin 6)) ^ (2 : ℕ))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((((5 : MvPolynomial (Fin 6) ℂ) * (MvPolynomial.X (R := ℂ) (3 : Fin 6))) * ((MvPolynomial.X (R := ℂ) (5 : Fin 6)) ^ (5 : ℕ))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((MvPolynomial.X (R := ℂ) (4 : Fin 6)) ^ (6 : ℕ))) + ((((15 : MvPolynomial (Fin 6) ℂ) * ((MvPolynomial.X (R := ℂ) (4 : Fin 6)) ^ (5 : ℕ))) * (MvPolynomial.X (R := ℂ) (5 : Fin 6))) * MvPolynomial.C (σ := Fin 6) (1 / 7 : ℂ))) + ((MvPolynomial.X (R := ℂ) (5 : Fin 6)) ^ (6 : ℕ)))
def A : HodgeComputer.AmbientPoly n := (((MvPolynomial.X (R := ℂ) (0 : Fin 6)) ^ (3 : ℕ)) * ((MvPolynomial.X (R := ℂ) (3 : Fin 6)) ^ (3 : ℕ)))
def q : ℕ := 1
end HodgeComputer.RankOneBiquartic

Source

https://github.com/hodge-computer/sextics/blob/83fbf5c9a0afe9136ce4f1ed324d085a2c899bd0/data/rank-one-biquartic/instance.rec

Read-back

What the Lean code literally says, in plain math · GPT-6 (OpenAI Codex; independent auditor)

$n$ . The natural number $n$ is defined to be $5$ .

$d$ . The natural number $d$ is defined to be $6$ .

$F$ . In the polynomial ring $R=\mathbb C[X_0,X_1,X_2,Y_0,Y_1,Y_2]$ , with the six indeterminates corresponding, in that order, to the indices $0,1,2,3,4,5$ , the polynomial $F$ is defined by

\begin{aligned} F={}&X_0^6+X_1^6+X_2^6+Y_0^6+Y_1^6+Y_2^6\\ &+\frac{5}{7}\Bigl[X_0^5X_1+X_0^2X_1^3X_2+3X_0X_2^5+2X_1^5X_2\\ &\qquad+2Y_0^5Y_1+2Y_0^3Y_1Y_2^2+Y_0Y_2^5+3Y_1^5Y_2\\ &\qquad+(X_0^2+X_0X_1+2X_1X_2+3X_2^2)^2(Y_0^2+Y_0Y_1+2Y_1Y_2+3Y_2^2)\Bigr]. \end{aligned}

$A$ . In the polynomial ring $R=\mathbb C[X_0,X_1,X_2,Y_0,Y_1,Y_2]$ , with the six indeterminates corresponding, in that order, to the indices $0,1,2,3,4,5$ , the polynomial $A$ is defined to be $X_0^3Y_0^3$ .

$q$ . The natural number $q$ is defined to be $1$ .

Human review

Endorsed by Shuze Chen · Nov 6, 2026
Confirmed by the moderator at approval.
Endorsed by benediamond · Nov 6, 2026
Confirmed by the mission captain (proposal self-audit).

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