text:
using AbstractAlgebra

@testset "Large testsets for f4" begin

    noon = Groebner.change_ordering(Groebner.noonn(4, ground=ZZ), :degrevlex)
    (x1, x2, x3, x4) = gens(parent(first(noon)))

    gb = Groebner.groebner(noon)

    sing_ans = [10*x1^2*x4 + 10*x2^2*x4 + 10*x3^2*x4 - 11*x4 + 10, 10*x1^2*x3 + 10*x2^2*x3 + 10*x3*x4^2 - 11*x3 + 10, 10*x1*x2^2 + 10*x1*x3^2 + 10*x1*x4^2 - 11*x1 + 10, 10*x1^2*x2 + 10*x2*x3^2 + 10*x2*x4^2 - 11*x2 + 10, x3^3*x4 - x3*x4^3 + x3 - x4, x2^3*x4 - x2*x4^3 + x2 - x4, 20*x2^2*x3^2 + 20*x2^2*x4^2 + 20*x3^2*x4^2 + 11*x1^2 - 11*x2^2 - 11*x3^2 - 11*x4^2 - 10*x1 + 10*x2 + 10*x3 + 10*x4, x2^3*x3 - x2*x3^3 + x2 - x3, 10*x1*x2*x3^2*x4 + 20*x1*x2*x4^3 - 11*x1*x2*x4 - 10*x1*x2 + 10*x1*x4 + 10*x2*x4, 200*x2*x3^4 + 200*x2*x3^2*x4^2 + 200*x2*x4^4 - 110*x2^3 - 220*x2*x3^2 - 220*x2*x4^2 - 100*x1*x2 + 100*x2^2 - 100*x2*x3 + 200*x3^2 - 100*x2*x4 + 200*x4^2 + 121*x2 - 110, 200*x1*x3^4 + 200*x1*x3^2*x4^2 + 200*x1*x4^4 - 110*x1^3 - 220*x1*x3^2 - 220*x1*x4^2 + 100*x1^2 - 100*x1*x2 - 100*x1*x3 + 200*x3^2 - 100*x1*x4 + 200*x4^2 + 121*x1 - 110, 20*x1*x2*x3^3 + 10*x1*x2*x3*x4^2 - 11*x1*x2*x3 - 10*x1*x2 + 10*x1*x3 + 10*x2*x3, 600*x3^2*x4^4 + 110*x1^4 + 110*x2^4 - 220*x3^4 - 660*x3^2*x4^2 - 220*x4^4 - 100*x1^3 - 100*x2^3 - 300*x1*x3^2 - 300*x2*x3^2 + 200*x3^3 - 300*x3^2*x4 - 300*x1*x4^2 - 300*x2*x4^2 + 300*x3*x4^2 + 200*x4^3 - 121*x1^2 - 121*x2^2 + 242*x3^2 + 242*x4^2 + 220*x1 + 220*x2 - 110*x3 - 110*x4 - 400, 600*x2^2*x4^4 + 110*x1^4 - 220*x2^4 + 110*x3^4 - 660*x2^2*x4^2 - 220*x4^4 - 100*x1^3 + 200*x2^3 - 300*x2^2*x3 + 300*x1*x3^2 - 100*x3^3 - 300*x2^2*x4 + 300*x2*x4^2 - 300*x3*x4^2 + 200*x4^3 - 121*x1^2 + 242*x2^2 - 121*x3^2 + 242*x4^2 - 110*x1 - 110*x2 + 220*x3 - 110*x4 - 100, 400*x2*x3^2*x4^3 + 200*x2*x4^5 - 220*x2*x3^2*x4 - 330*x2*x4^3 - 200*x2*x3^2 - 100*x1*x2*x4 + 100*x2^2*x4 + 100*x2*x3*x4 + 200*x3^2*x4 - 100*x2*x4^2 + 200*x4^3 + 121*x2*x4 + 110*x2 - 220*x4, 400*x1*x3^2*x4^3 + 200*x1*x4^5 - 220*x1*x3^2*x4 - 330*x1*x4^3 - 200*x1*x3^2 - 100*x1*x2*x4 - 100*x2^2*x4 + 100*x1*x3*x4 + 100*x3^2*x4 - 100*x1*x4^2 + 200*x4^3 + 121*x1*x4 + 110*x1 - 110*x4 - 100, 400*x2^2*x3*x4^3 + 200*x3*x4^5 - 220*x2^2*x3*x4 - 330*x3*x4^3 - 200*x2^2*x3 + 200*x2^2*x4 - 100*x1*x3*x4 + 100*x2*x3*x4 + 100*x3^2*x4 - 100*x3*x4^2 + 200*x4^3 + 121*x3*x4 + 110*x3 - 220*x4, 30*x1*x2*x3*x4^3 - 11*x1*x2*x3*x4 - 20*x1*x2*x3 + 10*x1*x2*x4 + 10*x1*x3*x4 + 10*x2*x3*x4, 2200*x3^6 - 2200*x4^6 - 2000*x3^5 - 4000*x1*x3^2*x4^2 - 4000*x2*x3^2*x4^2 + 4000*x3^2*x4^3 - 8000*x1*x4^4 - 8000*x2*x4^4 - 4000*x3*x4^4 + 2000*x4^5 - 3630*x3^4 + 3630*x4^4 + 2200*x1^3 + 2200*x2^3 + 1100*x1*x3^2 + 1100*x2*x3^2 + 2200*x3^3 - 3300*x3^2*x4 + 7700*x1*x4^2 + 7700*x2*x4^2 + 3300*x3*x4^2 - 2200*x4^3 - 2000*x1^2 + 4000*x1*x2 - 2000*x2^2 + 1000*x1*x3 + 1000*x2*x3 - 3669*x3^2 + 3000*x1*x4 + 3000*x2*x4 + 4000*x3*x4 - 16331*x4^2 - 2420*x1 - 2420*x2 + 4400, 2200*x2^6 - 2200*x4^6 - 2000*x2^5 - 4000*x2^2*x3*x4^2 + 4000*x1*x3^2*x4^2 + 4000*x2^2*x4^3 - 4000*x1*x4^4 - 4000*x2*x4^4 - 8000*x3*x4^4 + 2000*x4^5 - 3630*x2^4 + 3630*x4^4 + 2200*x1^3 + 2200*x2^3 + 1100*x2^2*x3 - 1100*x1*x3^2 + 2200*x3^3 - 3300*x2^2*x4 + 2200*x1*x4^2 + 3300*x2*x4^2 + 7700*x3*x4^2 - 2200*x4^3 - 2000*x1^2 + 1000*x1*x2 - 3669*x2^2 + 4000*x1*x3 + 1000*x2*x3 - 2000*x3^2 + 3000*x1*x4 + 4000*x2*x4 + 3000*x3*x4 - 12331*x4^2 - 1210*x1 - 2420*x3 + 3300, 2200*x1^6 - 2200*x4^6 - 2000*x1^5 + 4000*x2^2*x3*x4^2 + 4000*x2*x3^2*x4^2 - 4000*x2^2*x4^3 - 4000*x3^2*x4^3 - 4000*x1*x4^4 - 4000*x2*x4^4 - 4000*x3*x4^4 + 2000*x4^5 - 3630*x1^4 + 3630*x4^4 + 2200*x1^3 + 2200*x2^3 - 1100*x2^2*x3 - 1100*x2*x3^2 + 2200*x3^3 + 3300*x2^2*x4 + 3300*x3^2*x4 + 3300*x1*x4^2 + 2200*x2*x4^2 + 2200*x3*x4^2 + 2200*x4^3 - 3669*x1^2 + 1000*x1*x2 - 2000*x2^2 + 1000*x1*x3 + 4000*x2*x3 - 2000*x3^2 + 4000*x1*x4 + 3000*x2*x4 + 3000*x3*x4 - 12331*x4^2 - 1210*x2 - 1210*x3 - 3630*x4 + 5500, 66000*x4^7 + 180000*x1*x4^5 + 180000*x2*x4^5 + 180000*x3*x4^5 - 60000*x4^6 - 133100*x4^5 + 22000*x1^4 + 22000*x2^4 + 22000*x3^4 - 242000*x1*x4^3 - 242000*x2*x4^3 - 242000*x3*x4^3 + 44000*x4^4 - 20000*x1^3 - 20000*x2^3 - 20000*x3^3 - 60000*x1*x2*x4 - 60000*x1*x3*x4 - 60000*x2*x3*x4 - 120000*x1*x4^2 - 120000*x2*x4^2 - 120000*x3*x4^2 + 509860*x4^3 - 36300*x1^2 - 36300*x2^2 - 36300*x3^2 + 72600*x1*x4 + 72600*x2*x4 + 72600*x3*x4 + 24200*x4^2 + 88000*x1 + 88000*x2 + 88000*x3 - 311641*x4 - 96690, 6000*x3*x4^6 - 2200*x3^5 - 9900*x3*x4^4 - 4000*x1*x3^3 - 4000*x2*x3^3 + 2000*x3^4 - 3000*x1*x3*x4^2 - 3000*x2*x3*x4^2 + 3000*x3^2*x4^2 - 7000*x3*x4^3 + 6000*x4^4 + 3630*x3^3 + 3630*x3*x4^2 - 1100*x1^2 - 1100*x2^2 + 3300*x1*x3 + 3300*x2*x3 - 2200*x3^2 + 6600*x3*x4 - 7700*x4^2 + 1000*x1 + 1000*x2 - 4331*x3 - 3000*x4 + 1210, 6000*x2*x4^6 - 2200*x2^5 - 9900*x2*x4^4 + 2000*x2^4 + 4000*x1*x2*x3^2 - 4000*x2*x3^3 + 1000*x1*x2*x4^2 + 3000*x2^2*x4^2 - 3000*x2*x3*x4^2 - 7000*x2*x4^3 + 6000*x4^4 + 3630*x2^3 + 3630*x2*x4^2 - 1100*x1^2 - 1100*x1*x2 - 2200*x2^2 + 3300*x2*x3 - 1100*x3^2 + 6600*x2*x4 - 7700*x4^2 + 1000*x1 + 3669*x2 - 3000*x3 - 3000*x4 + 1210, 6000*x1*x4^6 - 2200*x1^5 - 9900*x1*x4^4 + 2000*x1^4 + 4000*x1*x2*x3^2 - 4000*x1*x3^3 + 1000*x1*x2*x4^2 - 3000*x2^2*x4^2 - 3000*x1*x3*x4^2 - 3000*x3^2*x4^2 - 7000*x1*x4^3 + 6000*x4^4 + 3630*x1^3 + 3630*x1*x4^2 - 2200*x1^2 - 1100*x1*x2 - 1100*x2^2 + 3300*x1*x3 - 1100*x3^2 + 6600*x1*x4 - 4400*x4^2 + 3669*x1 + 1000*x2 - 3000*x3 - 6000*x4 + 1210, 600*x2*x3*x4^5 - 550*x2*x3*x4^3 - 200*x2*x3^3 - 100*x1*x2*x3*x4 + 100*x2^2*x3*x4 + 100*x2*x3^2*x4 - 500*x2*x3*x4^2 + 400*x2*x4^3 + 400*x3*x4^3 + 121*x2*x3*x4 + 330*x2*x3 - 220*x2*x4 - 220*x3*x4 - 200*x3 + 200*x4, 600*x1*x3*x4^5 - 550*x1*x3*x4^3 - 200*x1*x3^3 - 100*x1*x2*x3*x4 - 100*x2^2*x3*x4 + 100*x1*x3^2*x4 - 500*x1*x3*x4^2 + 400*x1*x4^3 + 300*x3*x4^3 + 121*x1*x3*x4 + 330*x1*x3 - 220*x1*x4 - 110*x3*x4 - 200*x3 + 100*x4, 600*x1*x2*x4^5 - 550*x1*x2*x4^3 + 200*x1*x2*x3^2 - 100*x1*x2*x3*x4 - 100*x1*x3^2*x4 - 100*x2*x3^2*x4 - 300*x1*x2*x4^2 + 300*x1*x4^3 + 300*x2*x4^3 + 121*x1*x2*x4 + 110*x1*x2 - 110*x1*x4 - 110*x2*x4]

    @test gb == sing_ans

    noon = Groebner.change_ordering(Groebner.noonn(5, ground=ZZ), :degrevlex)
    (x1, x2, x3, x4, x5) = gens(parent(first(noon)))

    gb = Groebner.groebner(noon)
    sing_ans = [10*x1^2*x5 + 10*x2^2*x5 + 10*x3^2*x5 + 10*x4^2*x5 - 11*x5 + 10, 10*x1^2*x4 + 10*x2^2*x4 + 10*x3^2*x4 + 10*x4*x5^2 - 11*x4 + 10, 10*x1^2*x3 + 10*x2^2*x3 + 10*x3*x4^2 + 10*x3*x5^2 - 11*x3 + 10, 10*x1*x2^2 + 10*x1*x3^2 + 10*x1*x4^2 + 10*x1*x5^2 - 11*x1 + 10, 10*x1^2*x2 + 10*x2*x3^2 + 10*x2*x4^2 + 10*x2*x5^2 - 11*x2 + 10, x4^3*x5 - x4*x5^3 + x4 - x5, x3^3*x5 - x3*x5^3 + x3 - x5, x2^3*x5 - x2*x5^3 + x2 - x5, x3^3*x4 - x3*x4^3 + x3 - x4, x2^3*x4 - x2*x4^3 + x2 - x4, 20*x2^2*x3^2 + 20*x2^2*x4^2 + 20*x3^2*x4^2 + 20*x2^2*x5^2 + 20*x3^2*x5^2 + 20*x4^2*x5^2 + 11*x1^2 - 11*x2^2 - 11*x3^2 - 11*x4^2 - 11*x5^2 - 10*x1 + 10*x2 + 10*x3 + 10*x4 + 10*x5, x2^3*x3 - x2*x3^3 + x2 - x3, 10*x1*x2*x3^2*x5 + 10*x1*x2*x4^2*x5 + 20*x1*x2*x5^3 - 11*x1*x2*x5 - 10*x1*x2 + 10*x1*x5 + 10*x2*x5, 10*x1*x2*x3^2*x4 + 20*x1*x2*x4^3 + 10*x1*x2*x4*x5^2 - 11*x1*x2*x4 - 10*x1*x2 + 10*x1*x4 + 10*x2*x4, 200*x2*x3^4 + 200*x2*x3^2*x4^2 + 200*x2*x4^4 + 200*x2*x3^2*x5^2 + 200*x2*x4^2*x5^2 + 200*x2*x5^4 - 110*x2^3 - 220*x2*x3^2 - 220*x2*x4^2 - 220*x2*x5^2 - 100*x1*x2 + 100*x2^2 - 100*x2*x3 + 200*x3^2 - 100*x2*x4 + 200*x4^2 - 100*x2*x5 + 200*x5^2 + 121*x2 - 110, 200*x1*x3^4 + 200*x1*x3^2*x4^2 + 200*x1*x4^4 + 200*x1*x3^2*x5^2 + 200*x1*x4^2*x5^2 + 200*x1*x5^4 - 110*x1^3 - 220*x1*x3^2 - 220*x1*x4^2 - 220*x1*x5^2 + 100*x1^2 - 100*x1*x2 - 100*x1*x3 + 200*x3^2 - 100*x1*x4 + 200*x4^2 - 100*x1*x5 + 200*x5^2 + 121*x1 - 110, 20*x1*x2*x3^3 + 10*x1*x2*x3*x4^2 + 10*x1*x2*x3*x5^2 - 11*x1*x2*x3 - 10*x1*x2 + 10*x1*x3 + 10*x2*x3, 200*x2*x3^2*x4^2*x5 + 400*x2*x3^2*x5^3 + 400*x2*x4^2*x5^3 + 200*x2*x5^5 - 220*x2*x3^2*x5 - 220*x2*x4^2*x5 - 330*x2*x5^3 - 200*x2*x3^2 - 200*x2*x4^2 - 100*x1*x2*x5 + 100*x2^2*x5 + 100*x2*x3*x5 + 200*x3^2*x5 + 100*x2*x4*x5 + 200*x4^2*x5 - 100*x2*x5^2 + 200*x5^3 + 121*x2*x5 + 110*x2 - 220*x5, 200*x1*x3^2*x4^2*x5 + 400*x1*x3^2*x5^3 + 400*x1*x4^2*x5^3 + 200*x1*x5^5 - 220*x1*x3^2*x5 - 220*x1*x4^2*x5 - 330*x1*x5^3 - 200*x1*x3^2 - 200*x1*x4^2 - 100*x1*x2*x5 - 100*x2^2*x5 + 100*x1*x3*x5 + 100*x3^2*x5 + 100*x1*x4*x5 + 100*x4^2*x5 - 100*x1*x5^2 + 200*x5^3 + 121*x1*x5 + 110*x1 - 110*x5 - 100, 200*x2^2*x3*x4^2*x5 + 400*x2^2*x3*x5^3 + 400*x3*x4^2*x5^3 + 200*x3*x5^5 - 220*x2^2*x3*x5 - 220*x3*x4^2*x5 - 330*x3*x5^3 - 200*x2^2*x3 - 200*x3*x4^2 + 200*x2^2*x5 - 100*x1*x3*x5 + 100*x2*x3*x5 + 100*x3^2*x5 + 100*x3*x4*x5 + 200*x4^2*x5 - 100*x3*x5^2 + 200*x5^3 + 121*x3*x5 + 110*x3 - 220*x5, 10*x1*x2*x3*x4^2*x5 + 30*x1*x2*x3*x5^3 - 11*x1*x2*x3*x5 - 20*x1*x2*x3 + 10*x1*x2*x5 + 10*x1*x3*x5 + 10*x2*x3*x5, 600*x3^2*x4^4 + 600*x3^2*x4^2*x5^2 + 600*x3^2*x5^4 + 600*x4^2*x5^4 + 110*x1^4 + 110*x2^4 - 220*x3^4 - 660*x3^2*x4^2 - 220*x4^4 - 660*x3^2*x5^2 - 660*x4^2*x5^2 - 220*x5^4 - 100*x1^3 - 100*x2^3 - 300*x1*x3^2 - 300*x2*x3^2 + 200*x3^3 - 300*x3^2*x4 - 300*x1*x4^2 - 300*x2*x4^2 + 300*x3*x4^2 + 200*x4^3 - 300*x3^2*x5 - 300*x4^2*x5 - 300*x1*x5^2 - 300*x2*x5^2 + 300*x3*x5^2 + 300*x4*x5^2 + 200*x5^3 - 121*x1^2 - 121*x2^2 + 242*x3^2 + 242*x4^2 + 242*x5^2 + 220*x1 + 220*x2 - 110*x3 - 110*x4 - 110*x5 - 500, 600*x2^2*x4^4 + 600*x2^2*x4^2*x5^2 + 600*x2^2*x5^4 + 600*x4^2*x5^4 + 110*x1^4 - 220*x2^4 + 110*x3^4 - 660*x2^2*x4^2 - 220*x4^4 - 660*x2^2*x5^2 - 660*x4^2*x5^2 - 220*x5^4 - 100*x1^3 + 200*x2^3 - 300*x2^2*x3 + 300*x1*x3^2 - 100*x3^3 - 300*x2^2*x4 + 300*x2*x4^2 - 300*x3*x4^2 + 200*x4^3 - 300*x2^2*x5 - 300*x4^2*x5 + 300*x2*x5^2 - 300*x3*x5^2 + 300*x4*x5^2 + 200*x5^3 - 121*x1^2 + 242*x2^2 - 121*x3^2 + 242*x4^2 + 242*x5^2 - 110*x1 - 110*x2 + 220*x3 - 110*x4 - 110*x5 - 200, 400*x2*x3^2*x4^3 + 200*x2*x4^5 + 200*x2*x3^2*x4*x5^2 + 400*x2*x4*x5^4 - 220*x2*x3^2*x4 - 330*x2*x4^3 - 220*x2*x4*x5^2 - 200*x2*x3^2 - 100*x1*x2*x4 + 100*x2^2*x4 + 100*x2*x3*x4 + 200*x3^2*x4 - 100*x2*x4^2 + 200*x4^3 - 300*x2*x4*x5 + 200*x2*x5^2 + 200*x4*x5^2 + 121*x2*x4 + 110*x2 - 220*x4, 400*x1*x3^2*x4^3 + 200*x1*x4^5 + 200*x1*x3^2*x4*x5^2 + 400*x1*x4*x5^4 - 220*x1*x3^2*x4 - 330*x1*x4^3 - 220*x1*x4*x5^2 - 200*x1*x3^2 - 100*x1*x2*x4 - 100*x2^2*x4 + 100*x1*x3*x4 + 100*x3^2*x4 - 100*x1*x4^2 + 200*x4^3 - 300*x1*x4*x5 + 200*x1*x5^2 + 100*x4*x5^2 + 121*x1*x4 + 110*x1 - 110*x4 - 100, 400*x2^2*x3*x4^3 + 200*x3*x4^5 + 200*x2^2*x3*x4*x5^2 + 400*x3*x4*x5^4 - 220*x2^2*x3*x4 - 330*x3*x4^3 - 220*x3*x4*x5^2 - 200*x2^2*x3 + 200*x2^2*x4 - 100*x1*x3*x4 + 100*x2*x3*x4 + 100*x3^2*x4 - 100*x3*x4^2 + 200*x4^3 - 300*x3*x4*x5 + 200*x3*x5^2 + 200*x4*x5^2 + 121*x3*x4 + 110*x3 - 220*x4, 30*x1*x2*x3*x4^3 + 10*x1*x2*x3*x4*x5^2 - 11*x1*x2*x3*x4 - 20*x1*x2*x3 + 10*x1*x2*x4 + 10*x1*x3*x4 + 10*x2*x3*x4, 12000*x3^2*x4^2*x5^3 + 6000*x3^2*x5^5 + 6000*x4^2*x5^5 - 6600*x3^2*x4^2*x5 - 9900*x3^2*x5^3 - 9900*x4^2*x5^3 - 2200*x5^5 - 6000*x3^2*x4^2 - 3000*x1*x3^2*x5 - 3000*x2*x3^2*x5 + 3000*x3^2*x4*x5 - 3000*x1*x4^2*x5 - 3000*x2*x4^2*x5 + 3000*x3*x4^2*x5 - 3000*x3^2*x5^2 - 3000*x4^2*x5^2 - 4000*x1*x5^3 - 4000*x2*x5^3 + 5000*x3*x5^3 + 5000*x4*x5^3 + 2000*x5^4 + 3630*x3^2*x5 + 3630*x4^2*x5 + 3630*x5^3 - 1100*x1^2 - 1100*x2^2 + 2200*x3^2 + 2200*x4^2 + 3300*x1*x5 + 3300*x2*x5 - 3300*x3*x5 - 3300*x4*x5 - 2200*x5^2 + 1000*x1 + 1000*x2 - 2000*x3 - 2000*x4 - 4331*x5 + 1210, 600*x2*x3*x4^2*x5^3 + 600*x2*x3*x5^5 - 220*x2*x3*x4^2*x5 - 550*x2*x3*x5^3 - 200*x2*x3^3 - 400*x2*x3*x4^2 - 100*x1*x2*x3*x5 + 100*x2^2*x3*x5 + 100*x2*x3^2*x5 + 100*x2*x3*x4*x5 + 200*x2*x4^2*x5 + 200*x3*x4^2*x5 - 500*x2*x3*x5^2 + 400*x2*x5^3 + 400*x3*x5^3 + 121*x2*x3*x5 + 330*x2*x3 - 220*x2*x5 - 220*x3*x5 - 200*x3 + 200*x5, 600*x1*x3*x4^2*x5^3 + 600*x1*x3*x5^5 - 220*x1*x3*x4^2*x5 - 550*x1*x3*x5^3 - 200*x1*x3^3 - 400*x1*x3*x4^2 - 100*x1*x2*x3*x5 - 100*x2^2*x3*x5 + 100*x1*x3^2*x5 + 100*x1*x3*x4*x5 + 200*x1*x4^2*x5 + 100*x3*x4^2*x5 - 500*x1*x3*x5^2 + 400*x1*x5^3 + 300*x3*x5^3 + 121*x1*x3*x5 + 330*x1*x3 - 220*x1*x5 - 110*x3*x5 - 200*x3 + 100*x5, 12000*x2^2*x4^2*x5^3 + 6000*x2^2*x5^5 + 6000*x4^2*x5^5 - 6600*x2^2*x4^2*x5 - 9900*x2^2*x5^3 - 9900*x4^2*x5^3 - 2200*x5^5 - 6000*x2^2*x4^2 - 3000*x2^2*x3*x5 + 3000*x1*x3^2*x5 + 3000*x2^2*x4*x5 + 3000*x2*x4^2*x5 - 3000*x3*x4^2*x5 - 3000*x2^2*x5^2 - 3000*x4^2*x5^2 - 1000*x1*x5^3 + 5000*x2*x5^3 - 4000*x3*x5^3 + 5000*x4*x5^3 + 2000*x5^4 + 3630*x2^2*x5 + 3630*x4^2*x5 + 3630*x5^3 - 1100*x1^2 + 2200*x2^2 - 1100*x3^2 + 2200*x4^2 - 3300*x2*x5 + 3300*x3*x5 - 3300*x4*x5 - 2200*x5^2 + 1000*x1 - 2000*x2 + 1000*x3 - 2000*x4 - 1331*x5 + 1210, 600*x1*x2*x4^2*x5^3 + 600*x1*x2*x5^5 - 220*x1*x2*x4^2*x5 - 550*x1*x2*x5^3 + 200*x1*x2*x3^2 - 200*x1*x2*x4^2 - 100*x1*x2*x3*x5 - 100*x1*x3^2*x5 - 100*x2*x3^2*x5 + 100*x1*x2*x4*x5 + 100*x1*x4^2*x5 + 100*x2*x4^2*x5 - 300*x1*x2*x5^2 + 300*x1*x5^3 + 300*x2*x5^3 + 121*x1*x2*x5 + 110*x1*x2 - 110*x1*x5 - 110*x2*x5, 600*x2*x3^2*x4*x5^3 + 600*x2*x4*x5^5 - 220*x2*x3^2*x4*x5 - 550*x2*x4*x5^3 - 400*x2*x3^2*x4 - 200*x2*x4^3 + 200*x2*x3^2*x5 - 100*x1*x2*x4*x5 + 100*x2^2*x4*x5 + 100*x2*x3*x4*x5 + 200*x3^2*x4*x5 + 100*x2*x4^2*x5 - 500*x2*x4*x5^2 + 400*x2*x5^3 + 400*x4*x5^3 + 121*x2*x4*x5 + 330*x2*x4 - 220*x2*x5 - 220*x4*x5 - 200*x4 + 200*x5, 600*x1*x3^2*x4*x5^3 + 600*x1*x4*x5^5 - 220*x1*x3^2*x4*x5 - 550*x1*x4*x5^3 - 400*x1*x3^2*x4 - 200*x1*x4^3 + 200*x1*x3^2*x5 - 100*x1*x2*x4*x5 - 100*x2^2*x4*x5 + 100*x1*x3*x4*x5 + 100*x3^2*x4*x5 + 100*x1*x4^2*x5 - 500*x1*x4*x5^2 + 400*x1*x5^3 + 300*x4*x5^3 + 121*x1*x4*x5 + 330*x1*x4 - 220*x1*x5 - 110*x4*x5 - 200*x4 + 100*x5, 600*x2^2*x3*x4*x5^3 + 600*x3*x4*x5^5 - 220*x2^2*x3*x4*x5 - 550*x3*x4*x5^3 - 400*x2^2*x3*x4 - 200*x3*x4^3 + 200*x2^2*x3*x5 + 200*x2^2*x4*x5 - 100*x1*x3*x4*x5 + 100*x2*x3*x4*x5 + 100*x3^2*x4*x5 + 100*x3*x4^2*x5 - 500*x3*x4*x5^2 + 400*x3*x5^3 + 400*x4*x5^3 + 121*x3*x4*x5 + 330*x3*x4 - 220*x3*x5 - 220*x4*x5 - 200*x4 + 200*x5, 40*x1*x2*x3*x4*x5^3 - 11*x1*x2*x3*x4*x5 - 30*x1*x2*x3*x4 + 10*x1*x2*x3*x5 + 10*x1*x2*x4*x5 + 10*x1*x3*x4*x5 + 10*x2*x3*x4*x5, 6000*x3*x4^6 + 12000*x3*x4^2*x5^4 + 6000*x3*x5^6 - 2200*x3^5 - 9900*x3*x4^4 - 6600*x3*x4^2*x5^2 - 9900*x3*x5^4 - 4000*x1*x3^3 - 4000*x2*x3^3 + 2000*x3^4 - 3000*x1*x3*x4^2 - 3000*x2*x3*x4^2 + 3000*x3^2*x4^2 - 7000*x3*x4^3 + 6000*x4^4 - 9000*x3*x4^2*x5 - 3000*x1*x3*x5^2 - 3000*x2*x3*x5^2 + 3000*x3^2*x5^2 + 3000*x3*x4*x5^2 + 6000*x4^2*x5^2 - 7000*x3*x5^3 + 6000*x5^4 + 3630*x3^3 + 3630*x3*x4^2 + 3630*x3*x5^2 - 1100*x1^2 - 1100*x2^2 + 3300*x1*x3 + 3300*x2*x3 - 2200*x3^2 + 6600*x3*x4 - 7700*x4^2 + 6600*x3*x5 - 7700*x5^2 + 1000*x1 + 1000*x2 - 2331*x3 - 3000*x4 - 3000*x5 + 1210, 6000*x2*x4^6 + 12000*x2*x4^2*x5^4 + 6000*x2*x5^6 - 2200*x2^5 - 9900*x2*x4^4 - 6600*x2*x4^2*x5^2 - 9900*x2*x5^4 + 2000*x2^4 + 4000*x1*x2*x3^2 - 4000*x2*x3^3 + 1000*x1*x2*x4^2 + 3000*x2^2*x4^2 - 3000*x2*x3*x4^2 - 7000*x2*x4^3 + 6000*x4^4 - 9000*x2*x4^2*x5 + 1000*x1*x2*x5^2 + 3000*x2^2*x5^2 - 3000*x2*x3*x5^2 + 3000*x2*x4*x5^2 + 6000*x4^2*x5^2 - 7000*x2*x5^3 + 6000*x5^4 + 3630*x2^3 + 3630*x2*x4^2 + 3630*x2*x5^2 - 1100*x1^2 - 1100*x1*x2 - 2200*x2^2 + 3300*x2*x3 - 1100*x3^2 + 6600*x2*x4 - 7700*x4^2 + 6600*x2*x5 - 7700*x5^2 + 1000*x1 + 5669*x2 - 3000*x3 - 3000*x4 - 3000*x5 + 1210, 6000*x1*x4^6 + 12000*x1*x4^2*x5^4 + 6000*x1*x5^6 - 2200*x1^5 - 9900*x1*x4^4 - 6600*x1*x4^2*x5^2 - 9900*x1*x5^4 + 2000*x1^4 + 4000*x1*x2*x3^2 - 4000*x1*x3^3 + 1000*x1*x2*x4^2 - 3000*x2^2*x4^2 - 3000*x1*x3*x4^2 - 3000*x3^2*x4^2 - 7000*x1*x4^3 + 6000*x4^4 - 9000*x1*x4^2*x5 + 1000*x1*x2*x5^2 - 3000*x2^2*x5^2 - 3000*x1*x3*x5^2 - 3000*x3^2*x5^2 + 3000*x1*x4*x5^2 - 7000*x1*x5^3 + 6000*x5^4 + 3630*x1^3 + 3630*x1*x4^2 + 3630*x1*x5^2 - 2200*x1^2 - 1100*x1*x2 - 1100*x2^2 + 3300*x1*x3 - 1100*x3^2 + 6600*x1*x4 - 4400*x4^2 + 6600*x1*x5 - 4400*x5^2 + 5669*x1 + 1000*x2 - 3000*x3 - 6000*x4 - 6000*x5 + 1210, 600*x2*x3*x4^5 + 600*x2*x3*x4*x5^4 - 550*x2*x3*x4^3 - 220*x2*x3*x4*x5^2 - 200*x2*x3^3 - 100*x1*x2*x3*x4 + 100*x2^2*x3*x4 + 100*x2*x3^2*x4 - 500*x2*x3*x4^2 + 400*x2*x4^3 + 400*x3*x4^3 - 500*x2*x3*x4*x5 + 200*x2*x3*x5^2 + 200*x2*x4*x5^2 + 200*x3*x4*x5^2 + 121*x2*x3*x4 + 330*x2*x3 - 220*x2*x4 - 220*x3*x4 - 200*x3 + 200*x4, 600*x1*x3*x4^5 + 600*x1*x3*x4*x5^4 - 550*x1*x3*x4^3 - 220*x1*x3*x4*x5^2 - 200*x1*x3^3 - 100*x1*x2*x3*x4 - 100*x2^2*x3*x4 + 100*x1*x3^2*x4 - 500*x1*x3*x4^2 + 400*x1*x4^3 + 300*x3*x4^3 - 500*x1*x3*x4*x5 + 200*x1*x3*x5^2 + 200*x1*x4*x5^2 + 100*x3*x4*x5^2 + 121*x1*x3*x4 + 330*x1*x3 - 220*x1*x4 - 110*x3*x4 - 200*x3 + 100*x4, 600*x1*x2*x4^5 + 600*x1*x2*x4*x5^4 - 550*x1*x2*x4^3 - 220*x1*x2*x4*x5^2 + 200*x1*x2*x3^2 - 100*x1*x2*x3*x4 - 100*x1*x3^2*x4 - 100*x2*x3^2*x4 - 300*x1*x2*x4^2 + 300*x1*x4^3 + 300*x2*x4^3 - 500*x1*x2*x4*x5 + 400*x1*x2*x5^2 + 100*x1*x4*x5^2 + 100*x2*x4*x5^2 + 121*x1*x2*x4 + 110*x1*x2 - 110*x1*x4 - 110*x2*x4, 24000*x4^2*x5^6 + 2200*x1^6 + 2200*x2^6 + 2200*x3^6 - 6600*x4^6 - 39600*x4^2*x5^4 - 6600*x5^6 - 2000*x1^5 - 2000*x2^5 - 2000*x3^5 - 16000*x1*x4^4 - 16000*x2*x4^4 - 16000*x3*x4^4 + 6000*x4^5 - 12000*x1*x4^2*x5^2 - 12000*x2*x4^2*x5^2 - 12000*x3*x4^2*x5^2 - 28000*x4^2*x5^3 - 16000*x1*x5^4 - 16000*x2*x5^4 - 16000*x3*x5^4 + 20000*x4*x5^4 + 6000*x5^5 - 3630*x1^4 - 3630*x2^4 - 3630*x3^4 + 10890*x4^4 + 14520*x4^2*x5^2 + 10890*x5^4 + 6600*x1^3 + 6600*x2^3 + 6600*x3^3 + 13200*x1*x4^2 + 13200*x2*x4^2 + 13200*x3*x4^2 - 2200*x4^3 + 26400*x4^2*x5 + 13200*x1*x5^2 + 13200*x2*x5^2 + 13200*x3*x5^2 - 13200*x4*x5^2 - 2200*x5^3 - 9669*x1^2 + 6000*x1*x2 - 9669*x2^2 + 6000*x1*x3 + 6000*x2*x3 - 9669*x3^2 + 10000*x1*x4 + 10000*x2*x4 + 10000*x3*x4 - 34993*x4^2 + 10000*x1*x5 + 10000*x2*x5 + 10000*x3*x5 - 14000*x4*x5 - 38993*x5^2 - 3630*x1 - 3630*x2 - 3630*x3 - 3630*x4 - 3630*x5 + 19800, 24000*x3^2*x5^6 + 2200*x1^6 + 2200*x2^6 - 6600*x3^6 + 2200*x4^6 - 39600*x3^2*x5^4 - 6600*x5^6 - 2000*x1^5 - 2000*x2^5 + 6000*x3^5 + 16000*x1*x3^2*x4^2 + 16000*x2*x3^2*x4^2 - 16000*x3^2*x4^3 + 16000*x1*x4^4 + 16000*x2*x4^4 - 2000*x4^5 + 4000*x1*x3^2*x5^2 + 4000*x2*x3^2*x5^2 - 12000*x3^2*x4*x5^2 + 16000*x1*x4^2*x5^2 + 16000*x2*x4^2*x5^2 - 28000*x3^2*x5^3 + 20000*x3*x5^4 - 16000*x4*x5^4 + 6000*x5^5 - 3630*x1^4 - 3630*x2^4 + 10890*x3^4 - 3630*x4^4 + 14520*x3^2*x5^2 + 10890*x5^4 - 2200*x1^3 - 2200*x2^3 - 4400*x1*x3^2 - 4400*x2*x3^2 - 2200*x3^3 + 13200*x3^2*x4 - 17600*x1*x4^2 - 17600*x2*x4^2 + 6600*x4^3 + 26400*x3^2*x5 - 4400*x1*x5^2 - 4400*x2*x5^2 - 13200*x3*x5^2 + 13200*x4*x5^2 - 2200*x5^3 - 1669*x1^2 - 10000*x1*x2 - 1669*x2^2 + 2000*x1*x3 + 2000*x2*x3 + 13007*x3^2 - 2000*x1*x4 - 2000*x2*x4 - 6000*x3*x4 + 22331*x4^2 + 2000*x1*x5 + 2000*x2*x5 - 14000*x3*x5 + 10000*x4*x5 - 6993*x5^2 + 6050*x1 + 6050*x2 - 3630*x3 - 3630*x4 - 3630*x5 + 2200, 24000*x2^2*x5^6 + 2200*x1^6 - 6600*x2^6 + 2200*x3^6 + 2200*x4^6 - 39600*x2^2*x5^4 - 6600*x5^6 - 2000*x1^5 + 6000*x2^5 - 2000*x3^5 + 16000*x2^2*x3*x4^2 - 16000*x1*x3^2*x4^2 - 16000*x2^2*x4^3 + 16000*x3*x4^4 - 2000*x4^5 + 4000*x2^2*x3*x5^2 - 4000*x1*x3^2*x5^2 - 12000*x2^2*x4*x5^2 - 4000*x1*x4^2*x5^2 + 16000*x3*x4^2*x5^2 - 28000*x2^2*x5^3 - 4000*x1*x5^4 + 20000*x2*x5^4 - 16000*x4*x5^4 + 6000*x5^5 - 3630*x1^4 + 10890*x2^4 - 3630*x3^4 - 3630*x4^4 + 14520*x2^2*x5^2 + 10890*x5^4 - 2200*x1^3 - 2200*x2^3 - 4400*x2^2*x3 + 4400*x1*x3^2 - 2200*x3^3 + 13200*x2^2*x4 + 4400*x1*x4^2 - 17600*x3*x4^2 + 6600*x4^3 + 26400*x2^2*x5 + 4400*x1*x5^2 - 13200*x2*x5^2 - 4400*x3*x5^2 + 13200*x4*x5^2 - 2200*x5^3 - 1669*x1^2 + 2000*x1*x2 + 13007*x2^2 - 10000*x1*x3 + 2000*x2*x3 - 1669*x3^2 - 2000*x1*x4 - 6000*x2*x4 - 2000*x3*x4 + 6331*x4^2 + 2000*x1*x5 - 14000*x2*x5 + 2000*x3*x5 + 10000*x4*x5 - 10993*x5^2 + 1210*x1 - 3630*x2 + 6050*x3 - 3630*x4 - 3630*x5 + 6600, 18000*x3*x4^2*x5^5 + 6000*x3*x5^7 - 16500*x3*x4^2*x5^3 - 12100*x3*x5^5 - 6000*x3*x4^4 - 3000*x1*x3*x4^2*x5 - 3000*x2*x3*x4^2*x5 + 3000*x3^2*x4^2*x5 - 15000*x3*x4^2*x5^2 - 7000*x1*x3*x5^3 - 7000*x2*x3*x5^3 + 5000*x3^2*x5^3 + 8000*x3*x4*x5^3 + 12000*x4^2*x5^3 - 7000*x3*x5^4 + 6000*x5^5 + 3630*x3*x4^2*x5 + 7260*x3*x5^3 + 2200*x3^3 + 9900*x3*x4^2 + 3300*x1*x3*x5 + 3300*x2*x3*x5 - 3300*x3^2*x5 - 3300*x3*x4*x5 - 6600*x4^2*x5 + 8800*x3*x5^2 - 9900*x5^3 + 4000*x1*x3 + 4000*x2*x3 - 2000*x3^2 + 1000*x3*x4 - 6000*x4^2 - 3000*x1*x5 - 3000*x2*x5 - 1331*x3*x5 + 3000*x4*x5 - 3000*x5^2 - 3630*x3 + 3630*x5 + 1100, 18000*x2*x4^2*x5^5 + 6000*x2*x5^7 - 16500*x2*x4^2*x5^3 - 12100*x2*x5^5 - 6000*x2*x4^4 - 3000*x1*x2*x4^2*x5 + 3000*x2^2*x4^2*x5 - 3000*x2*x3*x4^2*x5 - 15000*x2*x4^2*x5^2 - 7000*x1*x2*x5^3 + 5000*x2^2*x5^3 - 7000*x2*x3*x5^3 + 8000*x2*x4*x5^3 + 12000*x4^2*x5^3 - 7000*x2*x5^4 + 6000*x5^5 + 3630*x2*x4^2*x5 + 7260*x2*x5^3 + 2200*x2^3 + 9900*x2*x4^2 + 3300*x1*x2*x5 - 3300*x2^2*x5 + 3300*x2*x3*x5 - 3300*x2*x4*x5 - 6600*x4^2*x5 + 8800*x2*x5^2 - 9900*x5^3 + 4000*x1*x2 - 2000*x2^2 + 4000*x2*x3 + 1000*x2*x4 - 6000*x4^2 - 3000*x1*x5 - 1331*x2*x5 - 3000*x3*x5 + 3000*x4*x5 - 3000*x5^2 - 3630*x2 + 3630*x5 + 1100, 18000*x1*x4^2*x5^5 + 6000*x1*x5^7 - 16500*x1*x4^2*x5^3 - 12100*x1*x5^5 - 6000*x1*x4^4 - 3000*x1*x2*x4^2*x5 - 3000*x2^2*x4^2*x5 - 3000*x1*x3*x4^2*x5 - 3000*x3^2*x4^2*x5 - 15000*x1*x4^2*x5^2 - 7000*x1*x2*x5^3 - 5000*x2^2*x5^3 - 7000*x1*x3*x5^3 - 5000*x3^2*x5^3 + 8000*x1*x4*x5^3 + 4000*x4^2*x5^3 - 7000*x1*x5^4 + 6000*x5^5 + 3630*x1*x4^2*x5 + 7260*x1*x5^3 + 2200*x1^3 + 9900*x1*x4^2 + 3300*x1*x2*x5 + 3300*x2^2*x5 + 3300*x1*x3*x5 + 3300*x3^2*x5 - 3300*x1*x4*x5 + 8800*x1*x5^2 - 4400*x5^3 - 2000*x1^2 + 4000*x1*x2 + 4000*x1*x3 + 1000*x1*x4 - 6000*x4^2 - 1331*x1*x5 - 3000*x2*x5 - 3000*x3*x5 - 8000*x5^2 - 3630*x1 + 4400, 18000*x3^2*x4*x5^5 + 6000*x4*x5^7 - 16500*x3^2*x4*x5^3 - 12100*x4*x5^5 - 6000*x3^2*x4^3 - 3000*x1*x3^2*x4*x5 - 3000*x2*x3^2*x4*x5 + 3000*x3^2*x4^2*x5 - 15000*x3^2*x4*x5^2 + 12000*x3^2*x5^3 - 7000*x1*x4*x5^3 - 7000*x2*x4*x5^3 + 8000*x3*x4*x5^3 + 5000*x4^2*x5^3 - 7000*x4*x5^4 + 6000*x5^5 + 3630*x3^2*x4*x5 + 7260*x4*x5^3 + 9900*x3^2*x4 + 2200*x4^3 - 6600*x3^2*x5 + 3300*x1*x4*x5 + 3300*x2*x4*x5 - 3300*x3*x4*x5 - 3300*x4^2*x5 + 8800*x4*x5^2 - 9900*x5^3 + 4000*x1*x4 + 4000*x2*x4 - 5000*x3*x4 - 2000*x4^2 - 3000*x1*x5 - 3000*x2*x5 + 3000*x3*x5 - 1331*x4*x5 - 3000*x5^2 - 3630*x4 + 3630*x5 + 1100, 1200*x2*x3*x4*x5^5 - 770*x2*x3*x4*x5^3 - 600*x2*x3*x4^3 - 100*x1*x2*x3*x4*x5 + 100*x2^2*x3*x4*x5 + 100*x2*x3^2*x4*x5 + 100*x2*x3*x4^2*x5 - 1100*x2*x3*x4*x5^2 + 600*x2*x3*x5^3 + 600*x2*x4*x5^3 + 600*x3*x4*x5^3 + 121*x2*x3*x4*x5 + 550*x2*x3*x4 - 220*x2*x3*x5 - 220*x2*x4*x5 - 220*x3*x4*x5 + 200*x2*x3 - 400*x2*x4 - 400*x3*x4 + 200*x2*x5 + 200*x3*x5 + 200*x4*x5, 1200*x1*x3*x4*x5^5 - 770*x1*x3*x4*x5^3 - 600*x1*x3*x4^3 - 100*x1*x2*x3*x4*x5 - 100*x2^2*x3*x4*x5 + 100*x1*x3^2*x4*x5 + 100*x1*x3*x4^2*x5 - 1100*x1*x3*x4*x5^2 + 600*x1*x3*x5^3 + 600*x1*x4*x5^3 + 400*x3*x4*x5^3 + 121*x1*x3*x4*x5 + 550*x1*x3*x4 - 220*x1*x3*x5 - 220*x1*x4*x5 - 110*x3*x4*x5 + 200*x1*x3 - 400*x1*x4 - 300*x3*x4 + 200*x1*x5 + 100*x3*x5 + 100*x4*x5, 18000*x2^2*x4*x5^5 + 6000*x4*x5^7 - 16500*x2^2*x4*x5^3 - 12100*x4*x5^5 - 6000*x2^2*x4^3 - 3000*x2^2*x3*x4*x5 + 3000*x1*x3^2*x4*x5 + 3000*x2^2*x4^2*x5 - 15000*x2^2*x4*x5^2 + 12000*x2^2*x5^3 - 1000*x1*x4*x5^3 + 8000*x2*x4*x5^3 - 7000*x3*x4*x5^3 + 5000*x4^2*x5^3 - 7000*x4*x5^4 + 6000*x5^5 + 3630*x2^2*x4*x5 + 7260*x4*x5^3 + 9900*x2^2*x4 + 2200*x4^3 - 6600*x2^2*x5 - 3300*x2*x4*x5 + 3300*x3*x4*x5 - 3300*x4^2*x5 + 8800*x4*x5^2 - 9900*x5^3 + 1000*x1*x4 - 5000*x2*x4 + 4000*x3*x4 - 2000*x4^2 + 3000*x2*x5 - 3000*x3*x5 + 1669*x4*x5 - 3000*x5^2 - 3630*x4 + 3630*x5 + 1100, 1200*x1*x2*x4*x5^5 - 770*x1*x2*x4*x5^3 - 600*x1*x2*x4^3 - 100*x1*x2*x3*x4*x5 - 100*x1*x3^2*x4*x5 - 100*x2*x3^2*x4*x5 + 100*x1*x2*x4^2*x5 - 1100*x1*x2*x4*x5^2 + 600*x1*x2*x5^3 + 400*x1*x4*x5^3 + 400*x2*x4*x5^3 + 121*x1*x2*x4*x5 + 550*x1*x2*x4 - 220*x1*x2*x5 - 110*x1*x4*x5 - 110*x2*x4*x5 + 200*x1*x2 - 300*x1*x4 - 300*x2*x4 + 100*x1*x5 + 100*x2*x5, 18000*x2*x3^2*x5^5 + 6000*x2*x5^7 - 16500*x2*x3^2*x5^3 - 12100*x2*x5^5 + 6000*x2*x3^2*x4^2 + 6000*x2*x4^4 - 3000*x2*x3^2*x4*x5 + 3000*x1*x2*x4^2*x5 - 3000*x2^2*x4^2*x5 - 3000*x3^2*x4^2*x5 - 9000*x2*x3^2*x5^2 + 6000*x2*x4^2*x5^2 - 1000*x1*x2*x5^3 + 2000*x2^2*x5^3 + 8000*x2*x3*x5^3 + 9000*x3^2*x5^3 - 7000*x2*x4*x5^3 - 3000*x4^2*x5^3 - 1000*x2*x5^4 + 6000*x5^5 + 3630*x2*x3^2*x5 + 7260*x2*x5^3 - 1100*x2^3 + 3300*x2*x3^2 - 6600*x2*x4^2 - 3300*x2*x3*x5 - 3300*x3^2*x5 + 3300*x2*x4*x5 + 3300*x4^2*x5 + 2200*x2*x5^2 - 8250*x5^3 - 2000*x1*x2 + 1000*x2^2 - 2000*x2*x3 + 1000*x2*x4 + 6000*x4^2 + 1500*x1*x5 - 2831*x2*x5 + 1500*x3*x5 - 4500*x4*x5 + 1500*x5^2 + 1815*x5 - 550, 18000*x1*x3^2*x5^5 + 6000*x1*x5^7 - 16500*x1*x3^2*x5^3 - 12100*x1*x5^5 + 6000*x1*x3^2*x4^2 + 6000*x1*x4^4 - 3000*x1*x3^2*x4*x5 + 3000*x1*x2*x4^2*x5 + 3000*x2^2*x4^2*x5 - 9000*x1*x3^2*x5^2 + 6000*x1*x4^2*x5^2 - 1000*x1*x2*x5^3 - 2000*x2^2*x5^3 + 8000*x1*x3*x5^3 + 7000*x3^2*x5^3 - 7000*x1*x4*x5^3 - 2000*x4^2*x5^3 - 1000*x1*x5^4 + 6000*x5^5 + 3630*x1*x3^2*x5 + 7260*x1*x5^3 - 1100*x1^3 + 3300*x1*x3^2 - 6600*x1*x4^2 - 3300*x1*x3*x5 - 3300*x3^2*x5 + 3300*x1*x4*x5 + 2200*x1*x5^2 - 6050*x5^3 + 1000*x1^2 - 2000*x1*x2 - 2000*x1*x3 + 1000*x1*x4 + 6000*x4^2 - 2831*x1*x5 + 1500*x2*x5 + 1500*x3*x5 - 1500*x4*x5 - 500*x5^2 + 1815*x5 - 550, 18000*x2^2*x3*x5^5 + 6000*x3*x5^7 - 16500*x2^2*x3*x5^3 - 12100*x3*x5^5 + 6000*x2^2*x3*x4^2 + 6000*x3*x4^4 - 3000*x2^2*x3*x4*x5 - 3000*x2^2*x4^2*x5 + 3000*x1*x3*x4^2*x5 - 3000*x3^2*x4^2*x5 - 9000*x2^2*x3*x5^2 + 6000*x3*x4^2*x5^2 + 9000*x2^2*x5^3 - 1000*x1*x3*x5^3 + 8000*x2*x3*x5^3 + 2000*x3^2*x5^3 - 7000*x3*x4*x5^3 - 3000*x4^2*x5^3 - 1000*x3*x5^4 + 6000*x5^5 + 3630*x2^2*x3*x5 + 7260*x3*x5^3 + 3300*x2^2*x3 - 1100*x3^3 - 6600*x3*x4^2 - 3300*x2^2*x5 - 3300*x2*x3*x5 + 3300*x3*x4*x5 + 3300*x4^2*x5 + 2200*x3*x5^2 - 8250*x5^3 - 2000*x1*x3 - 2000*x2*x3 + 1000*x3^2 + 1000*x3*x4 + 6000*x4^2 + 1500*x1*x5 + 1500*x2*x5 - 2831*x3*x5 - 4500*x4*x5 + 1500*x5^2 + 1815*x5 - 550, 1200*x1*x2*x3*x5^5 - 770*x1*x2*x3*x5^3 + 300*x1*x2*x3*x4^2 - 100*x1*x2*x3*x4*x5 - 100*x1*x2*x4^2*x5 - 100*x1*x3*x4^2*x5 - 100*x2*x3*x4^2*x5 - 800*x1*x2*x3*x5^2 + 400*x1*x2*x5^3 + 400*x1*x3*x5^3 + 400*x2*x3*x5^3 + 121*x1*x2*x3*x5 + 220*x1*x2*x3 - 110*x1*x2*x5 - 110*x1*x3*x5 - 110*x2*x3*x5, 66000*x4^8 - 66000*x5^8 - 60000*x4^7 - 360000*x1*x4^2*x5^4 - 360000*x2*x4^2*x5^4 - 360000*x3*x4^2*x5^4 + 180000*x4^2*x5^5 - 360000*x1*x5^6 - 360000*x2*x5^6 - 360000*x3*x5^6 - 180000*x4*x5^6 + 60000*x5^7 - 133100*x4^6 + 133100*x5^6 + 66000*x1^5 + 66000*x2^5 + 66000*x3^5 + 55000*x1*x4^4 + 55000*x2*x4^4 + 55000*x3*x4^4 + 44000*x4^5 + 198000*x1*x4^2*x5^2 + 198000*x2*x4^2*x5^2 + 198000*x3*x4^2*x5^2 - 242000*x4^2*x5^3 + 539000*x1*x5^4 + 539000*x2*x5^4 + 539000*x3*x5^4 + 242000*x4*x5^4 - 44000*x5^5 - 60000*x1^4 - 60000*x2^4 - 240000*x1*x2*x3^2 + 240000*x1*x3^3 + 240000*x2*x3^3 - 60000*x3^4 - 120000*x1*x2*x4^2 + 120000*x1*x3*x4^2 + 120000*x2*x3*x4^2 + 70000*x1*x4^3 + 70000*x2*x4^3 + 70000*x3*x4^3 - 90140*x4^4 + 210000*x1*x4^2*x5 + 210000*x2*x4^2*x5 + 210000*x3*x4^2*x5 + 240000*x1*x3*x5^2 + 240000*x2*x3*x5^2 - 30000*x1*x4*x5^2 - 30000*x2*x4*x5^2 - 30000*x3*x4*x5^2 - 540000*x4^2*x5^2 + 350000*x1*x5^3 + 350000*x2*x5^3 + 350000*x3*x5^3 + 360000*x4*x5^3 - 1169860*x5^4 - 108900*x1^3 - 108900*x2^3 - 108900*x3^3 - 36300*x1*x4^2 - 36300*x2*x4^2 - 36300*x3*x4^2 + 48400*x4^3 + 72600*x4^2*x5 - 181500*x1*x5^2 - 181500*x2*x5^2 - 181500*x3*x5^2 - 72600*x4*x5^2 - 48400*x5^3 + 132000*x1^2 + 66000*x1*x2 + 132000*x2^2 - 198000*x1*x3 - 198000*x2*x3 + 132000*x3^2 - 88000*x1*x4 - 88000*x2*x4 - 88000*x3*x4 + 436359*x4^2 - 308000*x1*x5 - 308000*x2*x5 - 308000*x3*x5 - 242000*x4*x5 + 993641*x5^2 - 230070*x1 - 230070*x2 + 249930*x3 + 63380*x4 + 656620*x5 - 108900, 66000*x3^8 - 66000*x5^8 - 60000*x3^7 - 360000*x1*x3^2*x5^4 - 360000*x2*x3^2*x5^4 - 360000*x3^2*x4*x5^4 + 180000*x3^2*x5^5 - 360000*x1*x5^6 - 360000*x2*x5^6 - 180000*x3*x5^6 - 360000*x4*x5^6 + 60000*x5^7 - 133100*x3^6 + 133100*x5^6 + 66000*x1^5 + 66000*x2^5 + 44000*x3^5 - 55000*x1*x3^2*x4^2 - 55000*x2*x3^2*x4^2 + 55000*x3^2*x4^3 - 55000*x1*x4^4 - 55000*x2*x4^4 + 66000*x4^5 + 143000*x1*x3^2*x5^2 + 143000*x2*x3^2*x5^2 + 198000*x3^2*x4*x5^2 - 55000*x1*x4^2*x5^2 - 55000*x2*x4^2*x5^2 - 242000*x3^2*x5^3 + 484000*x1*x5^4 + 484000*x2*x5^4 + 242000*x3*x5^4 + 539000*x4*x5^4 - 44000*x5^5 - 60000*x1^4 - 60000*x2^4 - 120000*x1*x2*x3^2 + 70000*x1*x3^3 + 70000*x2*x3^3 - 90140*x3^4 + 120000*x1*x3^2*x4 + 120000*x2*x3^2*x4 - 240000*x1*x2*x4^2 + 240000*x1*x4^3 + 240000*x2*x4^3 + 70000*x3*x4^3 - 60000*x4^4 + 210000*x1*x3^2*x5 + 210000*x2*x3^2*x5 + 210000*x3^2*x4*x5 - 30000*x1*x3*x5^2 - 30000*x2*x3*x5^2 - 540000*x3^2*x5^2 + 240000*x1*x4*x5^2 + 240000*x2*x4*x5^2 - 30000*x3*x4*x5^2 + 350000*x1*x5^3 + 350000*x2*x5^3 + 360000*x3*x5^3 + 350000*x4*x5^3 - 1169860*x5^4 - 78650*x1^3 - 78650*x2^3 + 24200*x1*x3^2 + 24200*x2*x3^2 + 48400*x3^3 - 36300*x3^2*x4 + 60500*x1*x4^2 + 60500*x2*x4^2 - 108900*x4^3 + 72600*x3^2*x5 - 121000*x1*x5^2 - 121000*x2*x5^2 - 72600*x3*x5^2 - 181500*x4*x5^2 - 48400*x5^3 + 104500*x1^2 + 121000*x1*x2 + 104500*x2^2 - 60500*x1*x3 - 60500*x2*x3 + 271359*x3^2 - 170500*x1*x4 - 170500*x2*x4 - 33000*x3*x4 + 22000*x4^2 - 280500*x1*x5 - 280500*x2*x5 - 242000*x3*x5 - 308000*x4*x5 + 883641*x5^2 - 263345*x1 - 263345*x2 - 6620*x3 + 319930*x4 + 656620*x5 - 48400, 66000*x2^8 - 66000*x5^8 - 60000*x2^7 - 360000*x2^2*x3*x5^4 + 360000*x1*x3^2*x5^4 - 360000*x2^2*x4*x5^4 + 360000*x1*x4^2*x5^4 + 180000*x2^2*x5^5 - 180000*x2*x5^6 - 360000*x3*x5^6 - 360000*x4*x5^6 + 60000*x5^7 - 133100*x2^6 + 133100*x5^6 + 66000*x1^5 + 44000*x2^5 + 66000*x3^5 - 55000*x2^2*x3*x4^2 + 55000*x1*x3^2*x4^2 + 55000*x2^2*x4^3 - 55000*x3*x4^4 + 66000*x4^5 + 143000*x2^2*x3*x5^2 - 143000*x1*x3^2*x5^2 + 198000*x2^2*x4*x5^2 - 143000*x1*x4^2*x5^2 - 55000*x3*x4^2*x5^2 - 242000*x2^2*x5^3 - 55000*x1*x5^4 + 242000*x2*x5^4 + 484000*x3*x5^4 + 539000*x4*x5^4 - 44000*x5^5 - 60000*x1^4 - 90140*x2^4 - 70000*x1*x2*x3^2 + 120000*x1*x3^3 + 70000*x2*x3^3 - 60000*x3^4 + 120000*x2^2*x3*x4 - 120000*x1*x3^2*x4 - 70000*x1*x2*x4^2 - 120000*x1*x3*x4^2 + 120000*x1*x4^3 + 70000*x2*x4^3 + 240000*x3*x4^3 - 60000*x4^4 + 210000*x2^2*x3*x5 - 210000*x1*x3^2*x5 + 210000*x2^2*x4*x5 - 210000*x1*x4^2*x5 - 100000*x1*x2*x5^2 - 540000*x2^2*x5^2 + 120000*x1*x3*x5^2 - 30000*x2*x3*x5^2 + 120000*x1*x4*x5^2 - 30000*x2*x4*x5^2 + 240000*x3*x4*x5^2 + 140000*x1*x5^3 + 360000*x2*x5^3 + 350000*x3*x5^3 + 350000*x4*x5^3 - 809860*x5^4 - 78650*x1^3 + 48400*x2^3 + 24200*x2^2*x3 - 24200*x1*x3^2 - 78650*x3^3 - 36300*x2^2*x4 - 24200*x1*x4^2 + 60500*x3*x4^2 - 108900*x4^3 + 72600*x2^2*x5 + 12100*x1*x5^2 - 72600*x2*x5^2 - 121000*x3*x5^2 - 181500*x4*x5^2 - 48400*x5^3 + 104500*x1^2 + 16500*x1*x2 + 271359*x2^2 - 11000*x1*x3 - 60500*x2*x3 + 104500*x3^2 - 38500*x1*x4 - 33000*x2*x4 - 170500*x3*x4 + 77000*x4^2 - 49500*x1*x5 - 242000*x2*x5 - 280500*x3*x5 - 308000*x4*x5 + 740641*x5^2 - 236725*x1 - 146620*x2 - 73345*x3 + 199930*x4 + 446620*x5 - 72600, 66000*x1^8 - 66000*x5^8 - 60000*x1^7 + 360000*x2^2*x3*x5^4 + 360000*x2*x3^2*x5^4 + 360000*x2^2*x4*x5^4 + 360000*x3^2*x4*x5^4 + 360000*x2*x4^2*x5^4 + 360000*x3*x4^2*x5^4 - 180000*x2^2*x5^5 - 180000*x3^2*x5^5 - 180000*x4^2*x5^5 - 180000*x1*x5^6 + 60000*x5^7 - 133100*x1^6 + 133100*x5^6 + 44000*x1^5 + 66000*x2^5 + 66000*x3^5 + 55000*x2^2*x3*x4^2 + 55000*x2*x3^2*x4^2 - 55000*x2^2*x4^3 - 55000*x3^2*x4^3 + 66000*x4^5 - 143000*x2^2*x3*x5^2 - 143000*x2*x3^2*x5^2 - 198000*x2^2*x4*x5^2 - 198000*x3^2*x4*x5^2 - 143000*x2*x4^2*x5^2 - 143000*x3*x4^2*x5^2 + 242000*x2^2*x5^3 + 242000*x3^2*x5^3 + 242000*x4^2*x5^3 + 242000*x1*x5^4 - 55000*x2*x5^4 - 55000*x3*x5^4 - 110000*x4*x5^4 + 154000*x5^5 - 90140*x1^4 - 60000*x2^4 - 70000*x1*x2*x3^2 + 70000*x1*x3^3 + 120000*x2*x3^3 - 60000*x3^4 - 120000*x2^2*x3*x4 - 120000*x2*x3^2*x4 - 70000*x1*x2*x4^2 - 120000*x2*x3*x4^2 + 70000*x1*x4^3 + 120000*x2*x4^3 + 120000*x3*x4^3 - 60000*x4^4 - 210000*x2^2*x3*x5 - 210000*x2*x3^2*x5 - 210000*x2^2*x4*x5 - 210000*x3^2*x4*x5 - 210000*x2*x4^2*x5 - 210000*x3*x4^2*x5 - 100000*x1*x2*x5^2 + 540000*x2^2*x5^2 - 30000*x1*x3*x5^2 + 120000*x2*x3*x5^2 + 540000*x3^2*x5^2 - 30000*x1*x4*x5^2 + 120000*x2*x4*x5^2 + 120000*x3*x4*x5^2 + 540000*x4^2*x5^2 + 360000*x1*x5^3 + 140000*x2*x5^3 + 140000*x3*x5^3 + 140000*x4*x5^3 - 269860*x5^4 + 48400*x1^3 - 78650*x2^3 - 24200*x2^2*x3 - 24200*x2*x3^2 - 78650*x3^3 + 36300*x2^2*x4 + 36300*x3^2*x4 - 24200*x2*x4^2 - 24200*x3*x4^2 - 48400*x4^3 - 72600*x2^2*x5 - 72600*x3^2*x5 - 72600*x4^2*x5 - 72600*x1*x5^2 + 12100*x2*x5^2 + 12100*x3*x5^2 + 72600*x4*x5^2 - 314600*x5^3 + 271359*x1^2 + 16500*x1*x2 + 104500*x2^2 - 60500*x1*x3 - 11000*x2*x3 + 104500*x3^2 - 33000*x1*x4 - 38500*x2*x4 - 38500*x3*x4 + 77000*x4^2 - 242000*x1*x5 - 49500*x2*x5 - 49500*x3*x5 - 22000*x4*x5 - 7359*x5^2 - 146620*x1 - 236725*x2 - 46725*x3 + 40000*x4 + 646480*x5 - 133100, 2640000*x5^9 + 9600000*x1*x5^7 + 9600000*x2*x5^7 + 9600000*x3*x5^7 + 9600000*x4*x5^7 - 2400000*x5^8 - 6050000*x5^7 + 660000*x1^6 + 660000*x2^6 + 660000*x3^6 + 660000*x4^6 - 16500000*x1*x5^5 - 16500000*x2*x5^5 - 16500000*x3*x5^5 - 16500000*x4*x5^5 + 440000*x5^6 - 600000*x1^5 - 600000*x2^5 - 600000*x3^5 - 600000*x4^5 - 8000000*x1*x2*x5^3 - 8000000*x1*x3*x5^3 - 8000000*x2*x3*x5^3 - 8000000*x1*x4*x5^3 - 8000000*x2*x4*x5^3 - 8000000*x3*x4*x5^3 - 13200000*x1*x5^4 - 13200000*x2*x5^4 - 13200000*x3*x5^4 - 13200000*x4*x5^4 + 38058500*x5^5 - 1331000*x1^4 - 1331000*x2^4 - 1331000*x3^4 - 1331000*x4^4 + 8470000*x1*x5^3 + 8470000*x2*x5^3 + 8470000*x3*x5^3 + 8470000*x4*x5^3 + 4719000*x5^4 + 3080000*x1^3 + 3080000*x2^3 + 3080000*x3^3 + 3080000*x4^3 + 3300000*x1*x2*x5 + 3300000*x1*x3*x5 + 3300000*x2*x3*x5 + 3300000*x1*x4*x5 + 3300000*x2*x4*x5 + 3300000*x3*x4*x5 + 13200000*x1*x5^2 + 13200000*x2*x5^2 + 13200000*x3*x5^2 + 13200000*x4*x5^2 - 38094100*x5^3 - 3301400*x1^2 + 5000000*x1*x2 - 3301400*x2^2 + 5000000*x1*x3 + 5000000*x2*x3 - 3301400*x3^2 + 5000000*x1*x4 + 5000000*x2*x4 + 5000000*x3*x4 - 3301400*x4^2 - 2331000*x1*x5 - 2331000*x2*x5 - 2331000*x3*x5 - 2331000*x4*x5 - 31828900*x5^2 - 3509000*x1 - 3509000*x2 - 3509000*x3 - 3509000*x4 + 8147051*x5 + 9863590, 240000*x4*x5^8 - 66000*x4^7 - 484000*x4*x5^6 - 180000*x1*x4^5 - 180000*x2*x4^5 - 180000*x3*x4^5 + 60000*x4^6 - 280000*x1*x4*x5^4 - 280000*x2*x4*x5^4 - 280000*x3*x4*x5^4 + 200000*x4^2*x5^4 - 460000*x4*x5^5 + 240000*x5^6 + 133100*x4^5 + 290400*x4*x5^4 - 22000*x1^4 - 22000*x2^4 - 22000*x3^4 + 242000*x1*x4^3 + 242000*x2*x4^3 + 242000*x3*x4^3 - 44000*x4^4 + 132000*x1*x4*x5^2 + 132000*x2*x4*x5^2 + 132000*x3*x4*x5^2 - 132000*x4^2*x5^2 + 682000*x4*x5^3 - 418000*x5^4 + 20000*x1^3 + 20000*x2^3 + 20000*x3^3 + 60000*x1*x2*x4 + 60000*x1*x3*x4 + 60000*x2*x3*x4 + 120000*x1*x4^2 + 120000*x2*x4^2 + 120000*x3*x4^2 - 449860*x4^3 + 220000*x1*x4*x5 + 220000*x2*x4*x5 + 220000*x3*x4*x5 - 140000*x4^2*x5 - 120000*x1*x5^2 - 120000*x2*x5^2 - 120000*x3*x5^2 + 6760*x4*x5^2 - 280000*x5^3 + 36300*x1^2 + 36300*x2^2 + 36300*x3^2 - 72600*x1*x4 - 72600*x2*x4 - 72600*x3*x4 - 24200*x4^2 - 217800*x4*x5 + 181500*x5^2 - 88000*x1 - 88000*x2 - 88000*x3 + 69641*x4 + 286000*x5 + 116690, 240000*x3*x5^8 - 66000*x3^7 - 484000*x3*x5^6 + 60000*x3^6 + 360000*x1*x3*x4^4 + 360000*x2*x3*x4^4 - 180000*x3*x4^5 + 180000*x1*x3*x4^2*x5^2 + 180000*x2*x3*x4^2*x5^2 + 80000*x1*x3*x5^4 + 80000*x2*x3*x5^4 + 200000*x3^2*x5^4 - 280000*x3*x4*x5^4 - 460000*x3*x5^5 + 240000*x5^6 + 133100*x3^5 + 290400*x3*x5^4 - 22000*x1^4 - 22000*x2^4 - 55000*x1*x3^3 - 55000*x2*x3^3 - 44000*x3^4 - 198000*x1*x3*x4^2 - 198000*x2*x3*x4^2 + 242000*x3*x4^3 - 22000*x4^4 - 66000*x1*x3*x5^2 - 66000*x2*x3*x5^2 - 132000*x3^2*x5^2 + 132000*x3*x4*x5^2 + 682000*x3*x5^3 - 418000*x5^4 + 20000*x1^3 + 20000*x2^3 - 120000*x1*x2*x3 + 30000*x1*x3^2 + 30000*x2*x3^2 + 90140*x3^3 - 210000*x1*x3*x4 - 210000*x2*x3*x4 - 60000*x3^2*x4 + 180000*x1*x4^2 + 180000*x2*x4^2 + 450000*x3*x4^2 - 160000*x4^3 - 50000*x1*x3*x5 - 50000*x2*x3*x5 - 140000*x3^2*x5 + 220000*x3*x4*x5 + 60000*x1*x5^2 + 60000*x2*x5^2 + 276760*x3*x5^2 - 120000*x4*x5^2 - 280000*x5^3 + 36300*x1^2 + 36300*x2^2 + 36300*x1*x3 + 36300*x2*x3 - 24200*x3^2 - 72600*x3*x4 + 36300*x4^2 - 217800*x3*x5 + 181500*x5^2 + 11000*x1 + 11000*x2 - 469359*x3 + 154000*x4 + 286000*x5 + 26690, 240000*x2*x5^8 - 66000*x2^7 - 484000*x2*x5^6 + 60000*x2^6 + 360000*x1*x2*x4^4 + 360000*x2*x3*x4^4 - 180000*x2*x4^5 + 180000*x1*x2*x4^2*x5^2 + 180000*x2*x3*x4^2*x5^2 + 80000*x1*x2*x5^4 + 200000*x2^2*x5^4 + 80000*x2*x3*x5^4 - 280000*x2*x4*x5^4 - 460000*x2*x5^5 + 240000*x5^6 + 133100*x2^5 + 290400*x2*x5^4 - 22000*x1^4 - 44000*x2^4 + 55000*x1*x2*x3^2 - 55000*x2*x3^3 - 22000*x3^4 - 143000*x1*x2*x4^2 - 198000*x2*x3*x4^2 + 242000*x2*x4^3 - 22000*x4^4 - 11000*x1*x2*x5^2 - 132000*x2^2*x5^2 - 66000*x2*x3*x5^2 + 132000*x2*x4*x5^2 + 682000*x2*x5^3 - 418000*x5^4 + 20000*x1^3 + 90140*x2^3 - 120000*x1*x2*x3 + 30000*x2^2*x3 - 30000*x1*x3^2 + 20000*x3^3 - 210000*x1*x2*x4 - 60000*x2^2*x4 - 210000*x2*x3*x4 + 150000*x1*x4^2 + 450000*x2*x4^2 + 180000*x3*x4^2 - 160000*x4^3 - 50000*x1*x2*x5 - 140000*x2^2*x5 - 50000*x2*x3*x5 + 220000*x2*x4*x5 + 30000*x1*x5^2 + 276760*x2*x5^2 + 60000*x3*x5^2 - 120000*x4*x5^2 - 280000*x5^3 + 36300*x1^2 - 24200*x1*x2 - 24200*x2^2 + 36300*x2*x3 + 36300*x3^2 - 72600*x2*x4 + 36300*x4^2 - 217800*x2*x5 + 181500*x5^2 + 44000*x1 - 359359*x2 - 44000*x3 + 154000*x4 + 286000*x5 - 3310, 240000*x1*x5^8 - 66000*x1^7 - 484000*x1*x5^6 + 60000*x1^6 + 360000*x1*x2*x4^4 + 360000*x1*x3*x4^4 - 180000*x1*x4^5 + 180000*x1*x2*x4^2*x5^2 + 180000*x1*x3*x4^2*x5^2 + 80000*x1*x2*x5^4 - 200000*x2^2*x5^4 + 80000*x1*x3*x5^4 - 200000*x3^2*x5^4 - 280000*x1*x4*x5^4 - 200000*x4^2*x5^4 - 460000*x1*x5^5 + 240000*x5^6 + 133100*x1^5 + 290400*x1*x5^4 - 44000*x1^4 - 22000*x2^4 + 55000*x1*x2*x3^2 - 55000*x1*x3^3 - 22000*x3^4 - 143000*x1*x2*x4^2 - 198000*x1*x3*x4^2 + 242000*x1*x4^3 - 22000*x4^4 - 11000*x1*x2*x5^2 + 132000*x2^2*x5^2 - 66000*x1*x3*x5^2 + 132000*x3^2*x5^2 + 132000*x1*x4*x5^2 + 132000*x4^2*x5^2 + 682000*x1*x5^3 - 198000*x5^4 + 90140*x1^3 + 20000*x2^3 - 120000*x1*x2*x3 - 30000*x2^2*x3 - 30000*x2*x3^2 + 20000*x3^3 - 210000*x1*x2*x4 + 60000*x2^2*x4 - 210000*x1*x3*x4 + 60000*x3^2*x4 + 450000*x1*x4^2 + 150000*x2*x4^2 + 150000*x3*x4^2 - 160000*x4^3 - 50000*x1*x2*x5 + 140000*x2^2*x5 - 50000*x1*x3*x5 + 140000*x3^2*x5 + 220000*x1*x4*x5 + 140000*x4^2*x5 + 276760*x1*x5^2 + 30000*x2*x5^2 + 30000*x3*x5^2 - 60000*x4*x5^2 - 480000*x5^3 - 24200*x1^2 - 24200*x1*x2 + 36300*x2^2 + 36300*x1*x3 + 36300*x3^2 - 72600*x1*x4 + 36300*x4^2 - 217800*x1*x5 + 36300*x5^2 - 359359*x1 + 44000*x2 - 11000*x3 + 88000*x4 + 264000*x5 + 166690, 24000*x3*x4*x5^7 - 28600*x3*x4*x5^5 - 6000*x3*x4^5 - 10000*x1*x3*x4*x5^3 - 10000*x2*x3*x4*x5^3 + 8000*x3^2*x4*x5^3 + 8000*x3*x4^2*x5^3 - 40000*x3*x4*x5^4 + 18000*x3*x5^5 + 18000*x4*x5^5 + 10890*x3*x4*x5^3 + 12100*x3*x4^3 + 3300*x1*x3*x4*x5 + 3300*x2*x3*x4*x5 - 3300*x3^2*x4*x5 - 3300*x3*x4^2*x5 + 25300*x3*x4*x5^2 - 16500*x3*x5^3 - 16500*x4*x5^3 + 7000*x1*x3*x4 + 7000*x2*x3*x4 - 5000*x3^2*x4 + 1000*x3*x4^2 - 6000*x4^3 - 3000*x1*x3*x5 - 3000*x2*x3*x5 + 3000*x3^2*x5 - 3000*x1*x4*x5 - 3000*x2*x4*x5 + 13669*x3*x4*x5 + 3000*x4^2*x5 - 15000*x3*x5^2 - 15000*x4*x5^2 + 12000*x5^3 - 7260*x3*x4 + 3630*x3*x5 + 3630*x4*x5 - 2200*x3 + 9900*x4 - 6600*x5, 24000*x2*x4*x5^7 - 28600*x2*x4*x5^5 - 6000*x2*x4^5 - 10000*x1*x2*x4*x5^3 + 8000*x2^2*x4*x5^3 - 10000*x2*x3*x4*x5^3 + 8000*x2*x4^2*x5^3 - 40000*x2*x4*x5^4 + 18000*x2*x5^5 + 18000*x4*x5^5 + 10890*x2*x4*x5^3 + 12100*x2*x4^3 + 3300*x1*x2*x4*x5 - 3300*x2^2*x4*x5 + 3300*x2*x3*x4*x5 - 3300*x2*x4^2*x5 + 25300*x2*x4*x5^2 - 16500*x2*x5^3 - 16500*x4*x5^3 + 7000*x1*x2*x4 - 5000*x2^2*x4 + 7000*x2*x3*x4 + 1000*x2*x4^2 - 6000*x4^3 - 3000*x1*x2*x5 + 3000*x2^2*x5 - 3000*x2*x3*x5 - 3000*x1*x4*x5 + 13669*x2*x4*x5 - 3000*x3*x4*x5 + 3000*x4^2*x5 - 15000*x2*x5^2 - 15000*x4*x5^2 + 12000*x5^3 - 7260*x2*x4 + 3630*x2*x5 + 3630*x4*x5 - 2200*x2 + 9900*x4 - 6600*x5, 24000*x1*x4*x5^7 - 28600*x1*x4*x5^5 - 6000*x1*x4^5 - 10000*x1*x2*x4*x5^3 - 8000*x2^2*x4*x5^3 - 10000*x1*x3*x4*x5^3 - 8000*x3^2*x4*x5^3 + 8000*x1*x4^2*x5^3 - 40000*x1*x4*x5^4 + 18000*x1*x5^5 + 10000*x4*x5^5 + 10890*x1*x4*x5^3 + 12100*x1*x4^3 + 3300*x1*x2*x4*x5 + 3300*x2^2*x4*x5 + 3300*x1*x3*x4*x5 + 3300*x3^2*x4*x5 - 3300*x1*x4^2*x5 + 25300*x1*x4*x5^2 - 16500*x1*x5^3 - 4400*x4*x5^3 + 7000*x1*x2*x4 + 5000*x2^2*x4 + 7000*x1*x3*x4 + 5000*x3^2*x4 + 1000*x1*x4^2 - 6000*x4^3 - 3000*x1*x2*x5 - 3000*x2^2*x5 - 3000*x1*x3*x5 - 3000*x3^2*x5 + 13669*x1*x4*x5 - 3000*x2*x4*x5 - 3000*x3*x4*x5 - 15000*x1*x5^2 - 10000*x4*x5^2 + 4000*x5^3 - 7260*x1*x4 + 3630*x1*x5 - 2200*x1 + 4400*x4 + 2000, 24000*x2*x3*x5^7 - 28600*x2*x3*x5^5 + 12000*x2*x3*x4^4 + 6000*x2*x3*x4^2*x5^2 - 10000*x1*x2*x3*x5^3 + 8000*x2^2*x3*x5^3 + 8000*x2*x3^2*x5^3 - 10000*x2*x3*x4*x5^3 - 28000*x2*x3*x5^4 + 18000*x2*x5^5 + 18000*x3*x5^5 + 10890*x2*x3*x5^3 + 2200*x2*x3^3 - 6600*x2*x3*x4^2 + 3300*x1*x2*x3*x5 - 3300*x2^2*x3*x5 - 3300*x2*x3^2*x5 + 3300*x2*x3*x4*x5 + 18700*x2*x3*x5^2 - 16500*x2*x5^3 - 16500*x3*x5^3 + 4000*x1*x2*x3 - 2000*x2^2*x3 - 2000*x2*x3^2 - 2000*x2*x3*x4 + 6000*x2*x4^2 + 6000*x3*x4^2 - 3000*x1*x2*x5 + 3000*x2^2*x5 - 3000*x1*x3*x5 + 4669*x2*x3*x5 + 3000*x3^2*x5 - 3000*x2*x4*x5 - 3000*x3*x4*x5 - 9000*x2*x5^2 - 9000*x3*x5^2 + 12000*x5^3 - 3630*x2*x3 + 3630*x2*x5 + 3630*x3*x5 + 1100*x2 + 3300*x3 - 6600*x5, 24000*x1*x3*x5^7 - 28600*x1*x3*x5^5 + 12000*x1*x3*x4^4 + 6000*x1*x3*x4^2*x5^2 - 10000*x1*x2*x3*x5^3 - 8000*x2^2*x3*x5^3 + 8000*x1*x3^2*x5^3 - 10000*x1*x3*x4*x5^3 - 8000*x3*x4^2*x5^3 - 28000*x1*x3*x5^4 + 18000*x1*x5^5 + 10000*x3*x5^5 + 10890*x1*x3*x5^3 + 2200*x1*x3^3 - 6600*x1*x3*x4^2 + 3300*x1*x2*x3*x5 + 3300*x2^2*x3*x5 - 3300*x1*x3^2*x5 + 3300*x1*x3*x4*x5 + 3300*x3*x4^2*x5 + 18700*x1*x3*x5^2 - 16500*x1*x5^3 - 4400*x3*x5^3 + 4000*x1*x2*x3 + 2000*x2^2*x3 - 2000*x1*x3^2 - 2000*x1*x3*x4 + 6000*x1*x4^2 + 8000*x3*x4^2 - 3000*x1*x2*x5 - 3000*x2^2*x5 + 4669*x1*x3*x5 - 3000*x2*x3*x5 - 3000*x1*x4*x5 - 3000*x3*x4*x5 - 3000*x4^2*x5 - 9000*x1*x5^2 - 7000*x3*x5^2 + 4000*x5^3 - 3630*x1*x3 + 3630*x1*x5 + 1100*x1 + 1100*x3 - 1000, 24000*x1*x2*x5^7 - 28600*x1*x2*x5^5 + 12000*x1*x2*x4^4 + 6000*x1*x2*x4^2*x5^2 - 10000*x1*x2*x3*x5^3 - 8000*x1*x3^2*x5^3 - 8000*x2*x3^2*x5^3 - 10000*x1*x2*x4*x5^3 - 8000*x1*x4^2*x5^3 - 8000*x2*x4^2*x5^3 - 28000*x1*x2*x5^4 + 10000*x1*x5^5 + 10000*x2*x5^5 + 10890*x1*x2*x5^3 - 2200*x1*x2*x3^2 - 8800*x1*x2*x4^2 + 3300*x1*x2*x3*x5 + 3300*x1*x3^2*x5 + 3300*x2*x3^2*x5 + 3300*x1*x2*x4*x5 + 3300*x1*x4^2*x5 + 3300*x2*x4^2*x5 + 16500*x1*x2*x5^2 - 4400*x1*x5^3 - 4400*x2*x5^3 + 4000*x1*x2*x3 + 2000*x1*x3^2 + 2000*x2*x3^2 - 2000*x1*x2*x4 + 8000*x1*x4^2 + 8000*x2*x4^2 + 4669*x1*x2*x5 - 3000*x1*x3*x5 - 3000*x2*x3*x5 - 3000*x3^2*x5 - 3000*x1*x4*x5 - 3000*x2*x4*x5 - 3000*x4^2*x5 - 7000*x1*x5^2 - 7000*x2*x5^2 - 4000*x5^3 - 1210*x1*x2 - 1100*x1 - 1100*x2 + 3300*x5 + 1000]

    @test gb == sing_ans

    kat = Groebner.change_ordering(Groebner.katsuran(6, ground=ZZ), :degrevlex)
    (x1, x2, x3, x4, x5, x6, x7) = gens(parent(first(kat)))

    gb = Groebner.groebner(kat)

    sing_ans = [
    x1 + 2*x2 + 2*x3 + 2*x4 + 2*x5 + 2*x6 + 2*x7 - 1, 26*x4*x5 + 28*x5^2 + 26*x3*x6 + 56*x4*x6 + 90*x5*x6 + 64*x6^2 + 26*x2*x7 + 56*x3*x7 + 90*x4*x7 + 128*x5*x7 + 170*x6*x7 + 108*x7^2 - x2 - 4*x3 - 9*x4 - 16*x5 - 25*x6 - 36*x7, 13*x4^2 + 26*x3*x5 - 15*x5^2 + 26*x2*x6 - 30*x4*x6 - 64*x5*x6 - 51*x6^2 - 52*x2*x7 - 82*x3*x7 - 116*x4*x7 - 154*x5*x7 - 196*x6*x7 - 147*x7^2 + x2 + 4*x3 + 9*x4 + 16*x5 + 25*x6 + 49*x7, 2*x3*x4 + 2*x2*x5 - 4*x2*x6 - 4*x3*x6 - 4*x4*x6 - 4*x5*x6 - 4*x6^2 + 2*x2*x7 - 4*x6*x7 + x6, 13*x3^2 + 26*x2*x4 - 52*x2*x5 - 52*x3*x5 + 4*x5^2 + 26*x2*x6 + 52*x3*x6 + 112*x4*x6 + 128*x5*x6 + 128*x6^2 + 52*x2*x7 + 138*x3*x7 + 180*x4*x7 + 204*x5*x7 + 340*x6*x7 + 216*x7^2 - 2*x2 - 8*x3 - 18*x4 - 19*x5 - 50*x6 - 72*x7, 26*x2*x3 - 52*x2*x4 + 78*x2*x5 + 104*x3*x5 - 4*x5^2 - 26*x3*x6 - 164*x4*x6 - 180*x5*x6 - 180*x6^2 - 104*x2*x7 - 216*x3*x7 - 310*x4*x7 - 360*x5*x7 - 548*x6*x7 - 372*x7^2 + 2*x2 + 8*x3 + 31*x4 + 32*x5 + 76*x6 + 124*x7, 13*x2^2 + 26*x2*x4 - 26*x3*x5 + 8*x5^2 + 42*x4*x6 + 48*x5*x6 + 48*x6^2 + 52*x2*x7 + 68*x3*x7 + 100*x4*x7 + 122*x5*x7 + 160*x6*x7 + 120*x7^2 - 4*x2 - 3*x3 - 10*x4 - 12*x5 - 22*x6 - 40*x7, 270*x5^2*x7 + 540*x4*x6*x7 + 1152*x5*x6*x7 + 918*x6^2*x7 + 540*x3*x7^2 + 1152*x4*x7^2 + 1836*x5*x7^2 + 2592*x6*x7^2 + 1710*x7^3 + x5^2 + 2*x4*x6 + 6*x5*x6 + 6*x6^2 - 18*x2*x7 - 70*x3*x7 - 156*x4*x7 - 276*x5*x7 - 430*x6*x7 - 633*x7^2 + 6*x2 + 11*x3 + 15*x4 + 18*x5 + 20*x6 + 21*x7, 64800*x5^2*x6 + 129600*x4*x6^2 + 276480*x5*x6^2 + 220320*x6^3 + 129600*x3*x6*x7 + 276480*x4*x6*x7 + 591804*x5*x6*x7 + 782136*x6^2*x7 + 151164*x4*x7^2 + 320112*x5*x7^2 + 917244*x6*x7^2 + 355680*x7^3 + 532*x5^2 - 4320*x2*x6 - 17280*x3*x6 - 37816*x4*x6 - 65928*x5*x6 - 104808*x6^2 - 4446*x2*x7 - 16720*x3*x7 - 36822*x4*x7 - 64752*x5*x7 - 256030*x6*x7 - 152076*x7^2 + 1437*x2 + 5852*x3 + 7980*x4 + 9576*x5 + 10640*x6 + 11172*x7, 1053000*x3*x5*x6 + 842400*x2*x6^2 + 898560*x3*x6^2 + 795600*x4*x6^2 + 861120*x5*x6^2 + 608400*x6^3 + 631800*x2*x5*x7 + 1797120*x3*x5*x7 + 168480*x2*x6*x7 + 1172340*x3*x6*x7 + 313560*x4*x6*x7 + 1140516*x5*x6*x7 + 1370304*x6^2*x7 - 985140*x2*x7^2 - 393120*x3*x7^2 + 57096*x4*x7^2 + 971568*x5*x7^2 + 1112436*x6*x7^2 + 411840*x7^3 + 14040*x2*x4 - 33930*x2*x5 - 163800*x3*x5 + 39568*x5^2 - 128700*x2*x6 - 265590*x3*x6 - 63604*x4*x6 - 19992*x5*x6 - 172092*x6^2 + 5616*x2*x7 - 202600*x3*x7 - 34968*x4*x7 - 151368*x5*x7 - 271000*x6*x7 - 187104*x7^2 + 8673*x2 + 21068*x3 + 14370*x4 + 24264*x5 + 46655*x6 + 16608*x7, 1170000*x2*x5*x6 - 530400*x2*x6^2 - 926640*x3*x6^2 - 2152800*x4*x6^2 - 2695680*x5*x6^2 - 2371200*x6^3 + 1170000*x2*x4*x7 - 1060800*x2*x5*x7 - 1853280*x3*x5*x7 + 1541280*x2*x6*x7 - 1007760*x3*x6*x7 + 165360*x4*x6*x7 - 1196364*x5*x6*x7 - 3897816*x6^2*x7 + 1756560*x2*x7^2 + 2976480*x3*x7^2 + 3106116*x4*x7^2 + 2712528*x5*x7^2 + 1755156*x6*x7^2 + 2845440*x7^3 - 95160*x2*x4 - 20280*x2*x5 + 109200*x3*x5 - 27172*x5^2 - 93600*x2*x6 + 188760*x3*x6 + 228016*x4*x6 + 258168*x5*x6 + 850968*x6^2 - 285714*x2*x7 - 136400*x3*x7 - 428778*x4*x7 - 317328*x5*x7 + 244750*x6*x7 - 1052484*x7^2 - 7617*x2 - 30572*x3 - 17580*x4 - 30456*x5 - 21620*x6 + 34668*x7, 327600*x5^3 - 655200*x3*x6^2 - 2795520*x4*x6^2 - 3325920*x5*x6^2 - 3138720*x6^3 + 655200*x3*x5*x7 - 655200*x2*x6*x7 - 4193280*x3*x6*x7 - 8895120*x4*x6*x7 - 12666108*x5*x6*x7 - 15459912*x6^2*x7 - 1397760*x2*x7^2 - 4455360*x3*x7^2 - 9533628*x4*x7^2 - 12227904*x5*x7^2 - 24840348*x6*x7^2 - 12673440*x7^3 - 21840*x2*x5 - 87360*x3*x5 - 141524*x5^2 + 48360*x2*x6 + 390000*x3*x6 + 851072*x4*x6 + 885576*x5*x6 + 1670256*x6^2 + 322062*x2*x7 + 917840*x3*x7 + 1787334*x4*x7 + 2144304*x5*x7 + 6088430*x6*x7 + 5278092*x7^2 - 31509*x2 - 91924*x3 - 124500*x4 - 188712*x5 - 264280*x6 - 351204*x7, 12285000*x3*x5^2 - 3931200*x2*x6^2 - 4651920*x3*x6^2 - 3494400*x4*x6^2 + 2988960*x5*x6^2 + 5834400*x6^3 - 24570000*x2*x4*x7 - 7862400*x2*x5*x7 - 9303840*x3*x5*x7 - 39017160*x2*x6*x7 - 23030280*x3*x6*x7 - 43300920*x4*x6*x7 - 44663892*x5*x6*x7 - 20070648*x6^2*x7 - 6235320*x2*x7^2 - 38689560*x3*x7^2 - 59641452*x4*x7^2 - 75774816*x5*x7^2 - 86197332*x6*x7^2 - 53707680*x7^3 + 1294020*x2*x4 + 660660*x2*x5 + 54600*x3*x5 - 1050916*x5^2 + 3365700*x2*x6 + 2340780*x3*x6 + 578248*x4*x6 - 2194896*x5*x6 - 3653496*x6^2 + 5511558*x2*x7 + 7058800*x3*x7 + 9850566*x4*x7 + 10807416*x5*x7 + 12994750*x6*x7 + 21800748*x7^2 - 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16280*x6*x7^2 - 23712*x7^3 - 224*x2*x6 - 416*x3*x6 - 576*x4*x6 - 704*x5*x6 - 800*x6^2 + 224*x2*x7 + 912*x3*x7 + 1254*x4*x7 + 1520*x5*x7 + 846*x6*x7 + 1824*x7^2 - x2, 707719615200*x5*x6^2*x7 + 749350180800*x6^3*x7 + 707719615200*x4*x6*x7^2 + 1196626672800*x6^2*x7^2 - 1498700361600*x4*x7^3 - 2352631132800*x5*x7^3 - 1631226729600*x6*x7^3 - 2165077512000*x7^4 + 3809332800*x4*x6^2 + 12019307040*x5*x6^2 + 15444056160*x6^3 - 20815282800*x2*x6*x7 - 77547132000*x3*x6*x7 - 161033240160*x4*x6*x7 - 294410760228*x5*x6*x7 - 453957338952*x6^2*x7 + 24376528800*x2*x7^2 + 101315448000*x3*x7^2 + 221420412252*x4*x7^2 + 379186428816*x5*x7^2 - 110014529508*x6*x7^2 + 832832900640*x7^3 - 6666332400*x2*x5 - 12380331600*x3*x5 - 2461514524*x5^2 + 14245840440*x2*x6 + 43161262560*x3*x6 + 72299905312*x4*x6 + 77853438696*x5*x6 + 88875947856*x6^2 + 9191457522*x2*x7 + 4544407840*x3*x7 + 38769924954*x4*x7 + 31851802464*x5*x7 + 127684259410*x6*x7 + 32318628132*x7^2 - 538622259*x2 - 2384020364*x3 - 5495722260*x4 - 10023266232*x5 - 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3741333828106321356330564*x6*x7^2 - 5156346182740012202679360*x7^3 + 87905353113080506238040*x2*x4 - 21015412513775591656680*x2*x5 - 52566646604988875860800*x3*x5 - 11910758606743831473532*x5^2 + 142963189486971495899400*x2*x6 + 154262017092437729593560*x3*x6 + 270140558654485351741096*x4*x6 + 236532122026388960476008*x5*x6 + 208527847299173086682808*x6^2 + 74283947898623382534966*x2*x7 - 1108137280306685827400*x3*x7 + 45013053968152169775582*x4*x7 + 187817790529342334656032*x5*x7 + 691730883317631934902250*x6*x7 + 1193385145621286498158596*x7^2 - 10083748747131810001077*x2 - 13181186628077305152932*x3 - 36042321215831696355480*x4 - 35666875635415993199736*x5 - 72714390106558639868720*x6 - 95025180652045199448492*x7, 11709223669916496523800000*x3*x7^5 - 2459920939058087505000000*x7^6 - 380655540572743636200000*x2*x7^4 - 2783509948076911113060000*x3*x7^4 + 372379009321073898000000*x4*x7^4 + 1254770377859486789730000*x5*x7^4 + 1125826736807434275900000*x6*x7^4 + 1862705393862785978220000*x7^5 + 22703750068891011120000*x6^4 + 74289206809519132860000*x6^3*x7 - 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3434763247012176874470*x2*x5 - 2718613367900473252950*x3*x5 - 1020458922153876501328*x5^2 + 19730333788087551062850*x2*x6 + 40834694078304015236490*x3*x6 + 55123511449159483078984*x4*x6 + 60164881779312679711332*x5*x6 + 55202136314762527873032*x6^2 - 3245176408048760227536*x2*x7 - 39942581339718649283600*x3*x7 - 65290531151752543280472*x4*x7 - 60325409391745552280922*x5*x7 + 4098373374657188968000*x6*x7 - 64358353956064115802516*x7^2 - 1011685625985017629383*x2 - 2320646184431820277553*x3 - 3769910292728590265670*x4 - 4778751198022899582294*x5 - 8685971954071407757505*x6 - 11206869794816131549668*x7, 6393236123774407101994800000*x2*x7^5 + 1515311298459781903080000000*x7^6 - 1092356626137293234718000000*x2*x7^4 + 749246471963087291313120000*x3*x7^4 + 1277754257554237338876000000*x4*x7^4 + 1327677124187649266871840000*x5*x7^4 + 1339338715187169326830200000*x6*x7^4 + 769863374477413898441760000*x7^5 - 7062929402554522617120000*x6^4 - 47737071299430524531520000*x6^3*x7 + 710668297336002243638400000*x2*x4*x7^2 - 362806305987446359475580000*x2*x5*x7^2 - 996106170733829155592280000*x3*x5*x7^2 + 208838625720376349865960000*x2*x6*x7^2 - 112829090601530019379747500*x3*x6*x7^2 + 852609421581546160673505000*x4*x6*x7^2 - 136769060781284565198825000*x6^2*x7^2 + 848172606859056606509947500*x2*x7^3 + 1360108019646223407492660000*x3*x7^3 + 888824889304010434627897500*x4*x7^3 + 12459156444693045923940000*x5*x7^3 - 199604887659440747065530000*x6*x7^3 - 465095436446213412374340000*x7^4 + 9129170070484867889460000*x2*x4*x6 + 59734933761963901318207200*x2*x6^2 + 13021813598483579191492320*x3*x6^2 + 19199881327312801576562400*x4*x6^2 + 32667731676928410030951840*x5*x6^2 + 16484350711483753187169600*x6^3 - 40398257181734269194195000*x2*x4*x7 - 10444891368230404908094350*x2*x5*x7 + 73000284498591561460079640*x3*x5*x7 - 4421996657708926547677140*x2*x6*x7 + 47809136447963840460758130*x3*x6*x7 + 5014849571933248549763820*x4*x6*x7 + 33433608254049362615442732*x5*x6*x7 + 55591861753985973055897608*x6^2*x7 - 62992650109339083214936530*x2*x7^2 + 67814959580235779517365760*x3*x7^2 + 11697571732557072753217242*x4*x7^2 + 236312981572539691979009136*x5*x7^2 + 242770630678297411274391222*x6*x7^2 + 215185443618084832750787280*x7^3 - 4327220481695280507225420*x2*x4 + 1763728452343009468066140*x2*x5 + 2147165259467299081475400*x3*x5 + 650152272481695824104486*x5^2 + 5346118566658815053460300*x2*x6 + 12462512905844946994065120*x3*x6 + 15244953956809355822047292*x4*x6 + 23212063076849437155467316*x5*x6 + 21194139688896427353854916*x6^2 - 14332664821561816688507718*x2*x7 - 52749685777766515811887300*x3*x7 - 65356955577998062138493886*x4*x7 - 85541420127204870019406736*x5*x7 - 60753627690555295760201125*x6*x7 - 84151548930587395236322458*x7^2 + 212312398870574592881271*x2 + 684766942020229187664686*x3 + 1774296765154899525816915*x4 + 1996889296060073185141428*x5 + 4734882875090237823046685*x6 + 5626444410753850382035566*x7, 490487285309857856031052497456000000*x7^7 - 230332184169245603682474765528000000*x7^6 + 67606722290137285348757961897600000*x2*x7^4 + 203476859404587414143723890304640000*x3*x7^4 + 364802241816546725541495175430400000*x4*x7^4 + 478089566314416212006471204263680000*x5*x7^4 + 509726806292962092675026549563200000*x6*x7^4 + 454251205279980690451113340015920000*x7^5 + 5967866400538906910229002820000000*x6^4 + 7675532399025941695555635725400000*x6^3*x7 + 1294877498764641250339365685200000*x2*x4*x7^2 + 2827174304473390387376081947440000*x2*x5*x7^2 + 6226065093418532389943728502040000*x3*x5*x7^2 + 9400628863180557225938726465220000*x2*x6*x7^2 + 16065546447129988058871556447980000*x3*x6*x7^2 + 35399102390676089008834881561480000*x4*x6*x7^2 + 26088017212503339469638165455760000*x6^2*x7^2 - 11646456407284585051703257848180000*x2*x7^3 - 46891369182916638451378420331400000*x3*x7^3 - 139559753356111318520834303383260000*x4*x7^3 - 205157580341181328997323797406680000*x5*x7^3 - 205769431879092277109251195656240000*x6*x7^3 - 304814995372801409259950627725440000*x7^4 + 200010927710729147488480503720000*x2*x4*x6 + 407301864504298086139205050958400*x2*x6^2 - 59420742140110347180970026096960*x3*x6^2 - 257908412804004044527476657787200*x4*x6^2 - 97454741870010032667128646911520*x5*x6^2 + 339207546082849521498264034807200*x6^3 + 62966417579836747295208795360000*x2*x4*x7 - 380574995316177531467111164513200*x2*x5*x7 - 163549285845366083896768596253920*x3*x5*x7 - 1522530517734889587881283471796080*x2*x6*x7 - 4548742744949586901344489239510640*x3*x6*x7 - 7469843418697774038545750671254960*x4*x6*x7 - 11939705109268620035467027569015996*x5*x6*x7 - 16683293480265219931346927958798024*x6^2*x7 + 714323689609980552531635492385840*x2*x7^2 + 4742387983467818237051009955162720*x3*x7^2 + 12064461073610139126363638715764724*x4*x7^2 + 21724728039074529786704060987934192*x5*x7^2 + 10396729520195074857073399208899284*x6*x7^2 + 57324702791175745885248561223592160*x7^3 + 8771161156153704199558756823760*x2*x4 - 197795322986199641692148607055920*x2*x5 - 308674760743308253904341410931200*x3*x5 - 137016009200243205590444927417108*x5^2 + 544880599941877902161483841975600*x2*x6 + 1487460381258460364959775899850640*x3*x6 + 2338888181668000450235936077851824*x4*x6 + 2499644293726457786808999213160152*x5*x6 + 2898688553140598788307735881688352*x6^2 - 29103531506215859973307888942146*x2*x7 - 529779780740722076501106070141600*x3*x7 + 205263867960413498063379472359558*x4*x7 - 177778086061360723802715262573392*x5*x7 + 3290583895677503205513069003743750*x6*x7 + 606277615092370362716298353169324*x7^2 - 15772641642434959283774654187213*x2 - 60197373549482648100492329161708*x3 - 137915100965321904395651572093620*x4 - 255031510221343654583843624334984*x5 - 415209119922756093620278917053680*x6 - 615052252138533091728635488833348*x7
    ]

    @test gb == sing_ans

end


text:
cd(@__DIR__)
println("building...")
println(@__DIR__)

#unpack dats
cd("../dats/pbesol/v1.2/")
run(`tar -xf els.tar`)
run(`tar -xf binary.tar`)
cd(@__DIR__)

#unpack pseudos
cd("../pseudo/gbrv_pbesol/")
run(`tar -xf all.tar.gz`)
cd(@__DIR__)

ext: jl


text:
"""
```
macro ofu_str(unit)
```

String macro to easily recall oil-field units located in the `UnitfulOfu`
package. Although all unit symbols in that package are suffixed with `_ofu`,
the suffix should not be used when using this macro.

Note that what goes inside must be parsable as a valid Julia expression.

Examples:

```jldoctest
julia> 1.0ofu"lbf"
4.45 N

julia> 5.0ofu"rpm" - 1//60u"Hz"
4.0 Hz
```
"""
macro ofu_str(unit)
    ex = parse(unit)
    esc(replace_value(ex))
end

const allowed_funcs = [:*, :/, :^, :sqrt, :√, :+, :-, ://]
function replace_value(ex::Expr)
    if ex.head == :call
        ex.args[1] in allowed_funcs ||
            error("""$(ex.args[1]) is not a valid function call when parsing a unit.
             Only the following functions are allowed: $allowed_funcs""")
        for i=2:length(ex.args)
            if typeof(ex.args[i])==Symbol || typeof(ex.args[i])==Expr
                ex.args[i]=replace_value(ex.args[i])
            end
        end
        return ex
    elseif ex.head == :tuple
        for i=1:length(ex.args)
            if typeof(ex.args[i])==Symbol
                ex.args[i]=replace_value(ex.args[i])
            else
                error("only use symbols inside the tuple.")
            end
        end
        return ex
    else
        error("Expr head $(ex.head) must equal :call or :tuple")
    end
end

dottify(s, t, u...) = dottify(Expr(:(.), s, QuoteNode(t)), u...)
dottify(s) = s

function replace_value(sym::Symbol)
    s = Symbol(sym, :_us)
    if !isdefined(UnitfulOfu, s)
        error("Symbol $s could not be found in UnitfulUS.")
    end

    expr = Expr(:(.), dottify(fullname(UnitfulOfu)...), QuoteNode(s))
    return :(UnitfulOfu.ustrcheck($expr))
end

replace_value(literal::Number) = literal

ustrcheck(x::Unitful.Unitlike) = x
ustrcheck(x::Unitful.Quantity) = x
ustrcheck(x) = error("Symbol $x is not a unit or quantity.")


text:
#!/usr/bin/env julia

using PyCall
@pyimport matplotlib as mpl
mpl.rc("text", usetex=true)
mpl.use("Agg")
using PyPlot
using JLD2
using FileIO
using ArgParse

function singleplot(filename::String, name::String, compare::String = "")
    d = load(filename*".jld2")
  if compare == ""
    comptimes = d[name]
    ylab = "computional time [s]"
  else
    comptimes = d[name]./d[compare]
    ylab = "speedup"
  end
  x = d["x"]
  t = d["t"]
  m = d["m"]
  mpl.rc("font", family="serif", size = 7)
  fig, ax = subplots(figsize = (2.5, 2.))
  col = ["red", "blue", "black", "green", "yellow", "orange"]
  marker = [":s", ":o", ":v", ":<", ":>", ":d"]
  for i in 1:size(comptimes, 2)
    tt = t[i]
    ax[:plot](d[x], comptimes[:,i], marker[i], label= "t = $tt", color = col[i], markersize=2.5, linewidth = 1)
  end
  PyPlot.ylabel(ylab, labelpad = -1.8)
  PyPlot.xlabel(x, labelpad = -2)
  if maximum(comptimes) > 10
    f = matplotlib[:ticker][:ScalarFormatter]()
    f[:set_powerlimits]((-3, 2))
  else
    f = matplotlib[:ticker][:FormatStrFormatter]("%.1f")
  end
  ax[:yaxis][:set_major_formatter](f)
  ax[:legend](fontsize = 6, loc = 2, ncol = 1)
  subplots_adjust(left = 0.15, bottom = 0.12,top=0.92)
  fig[:savefig](name*filename*".pdf")
end

"""
  pltspeedup(comptimes::Array{Float}, m::Int, n::Vector{Int}, T::Vector{Int}, label::String)

Returns a figure in .pdf format of the computional speedup of cumulants function

"""

function pltspeedup(filename::String)
  d = load(filename)
  filename = replace(filename, ".jld2"=>"")
  for f in d["functions"]
    singleplot(filename::String, f...)
  end
end

function main(args)
  s = ArgParseSettings("description")
  @add_arg_table s begin
    "file"
    help = "the file name"
    arg_type = String
  end
  parsed_args = parse_args(s)
  pltspeedup(parsed_args["file"])
end

main(ARGS)


text:
@testset "testing TICR" begin

@testset "ticr! on data frame, on tree" begin
truenet1 = readTopology("((((D:0.4,C:0.4):4.8,((A:0.8,B:0.8):2.2)#H1:2.2::0.7):4.0,(#H1:0::0.3,E:3.0):6.2):2.0,O:11.2);");
setGamma!(truenet1.edge[9],0.0);
truenet2 = deepcopy(truenet1);
df = CSV.read(joinpath(@__DIR__,"..","examples","buckyCF.csv"));
#df = CSV.read(joinpath(Pkg.dir("PhyloNetworks"),"examples","buckyCF.csv"));
#without optimizing branch lengthes
result1 = ticr!(truenet1,df,false);
@test result1[2] ≈ 25.962962962962965463 # chi-squared statistic obtained from R
@test result1[1] ≈ 9.7092282251534852702e-06 # p-value obtained from R
@test result1[3] ≈ 48.152697007372566418 # pseudo log-lik obtained from R
@test result1[4] ≈ 10.576940922426542713 atol=1e-5 # alpha obtained from R
#with optimizing branch lengthes
result2 = ticr!(truenet2,df,true);
setGamma!(result2[6].edge[9],0.0);
result3 = ticr!(result2[6],df,false);
@test result3[2] ≈ 25.962962962962965463 # chi-squared statistic obtained from R
@test result3[1] ≈ 9.7092282251534852702e-06 # p-value obtained from R
@test result3[3] ≈ 54.449883693197676848 # pseudo log-lik obtained from R
@test result3[4] ≈ 20.694991969052374259 atol=1e-6 # alpha obtained from R
end

@testset "ticr! on data frame, on network" begin
truenet3 = readTopology("((((D:0.4,C:0.4):4.8,((A:0.8,B:0.8):2.2)#H1:2.2::0.7):4.0,(#H1:0::0.3,E:3.0):6.2):2.0,O:11.2);");
#without optimizing branch lengths
netresult1 = ticr!(truenet3,df,false);
#setGamma!(netresult1[6].edge[9],0.0);
#netresult2 = ticr!(netresult1[6],netCF1,false);
@test netresult1[2] ≈ 2.851851851851852 # chi-squared statistic
@test netresult1[1] ≈ 0.41503515532593677 # p-value
@test netresult1[3] ≈ 68.03708830981597 # pseudo log-lik
@test netresult1[4] ≈ 29.34808731515701 atol=1e-5 # alpha
end

end