#!/usr/bin/env wolframscript

(* prime.wl
 * Eric Zheng <ericzheng@cmu.edu>
 *
 * This is a partial solution to the Jones-Sato-Wada-Wiens polynomial,
 * witnessing the prime 2.
 *)

(* These are the variables that are small enough to
 * compute directly with. For constraints involving
 * c, d, r, and u, we have to do something more
 * sophisticated than quick maths.
*)
a = 7901690358098896161685556879749949186326380713409290912
b = 0
e = 32
f = 17
g = 0
h = 2
i = 0
j = 5
k = 1  (* note k = 0 in the polynomial, but k = 1 here *)
l = 1
m = a
n = 2
o = 8340353015645794683299462704812268882126086134656108363777
p = 3
q = 16
s = 1
t = 0
v = 2a - 3
w = 1
x = 2a^2 - 1
y = 2a
z = 9

(* These are the constraint equations, written in the form f(...) = 0. *)
eq1  = w z + h + j - q
eq2  = (g k + g + k)(h + j) + h - z
eq3  = (2k)^3 (2k + 2) (n + 1)^2 + 1 - f^2
eq4  = p + q + z + 2n - e
eq5  = e^3 (e + 2) (a + 1)^2 + 1 - o^2
eq6  = (a^2 - 1) y^2 - x^2 + 1
eq9  = (a^2 - 1) l^2 - m^2 + 1
eq10 = k + i (a - 1) - l
eq11 = n + l + v - y
eq12 = p + l (a - n - 1) + b (2a (n + 1) - (n + 1)^2 - 1) - m
eq13 = q + y (a - p - 1) + s (2a (p + 1) - (p + 1)^2 - 1) - x
eq14 = z + p l (a - p) + t (2a p - p^2 - 1) - p m

valid = AllTrue[{eq1, eq2, eq3, eq4, eq5, eq6, eq9, eq10, eq11, eq12,
                 eq13, eq14}, # == 0 &]
Print[If[valid, "All constraints passed!", "Failure."]]