Kin2 Problem (polynomial system) go icos AMPL = -1, <= 1; var x2 >= -1, <= 1; var x3 >= -1, <= 1; var x4 >= -1, <= 1; var x5 >= -1, <= 1; var x6 >= -1, <= 1; var x7 >= -1, <= 1; var x8 >= -1, <= 1; # Constants param a11 := -0.24915068; param a12 := 0.12501635; param a13 := -0.63555007; param a14 := 1.4894773; param a21 := 1.6091354; param a22 := -0.68660736; param a23 := -0.11571992; param a24 := 0.23062341; param a31 := 0.27942343; param a32 := -0.11922812; param a33 := -0.66640448; param a34 := 1.3281073; param a41 := 1.4348016; param a42 := -0.71994047; param a43 := 0.11036211; param a44 := -0.25864503; param a51 := 0.0; param a52 := -0.43241927; param a53 := 0.29070203; param a54 := 1.1651720; param a61 := 0.40026384; param a62 := 0.0; param a63 := 1.2587767; param a64 := -0.26908494; param a71 := -0.80052768; param a72 := 0.0; param a73 := -0.62938836; param a74 := 0.53816987; param a81 := 0.0; param a82 := -0.86483855; param a83 := 0.58140406; param a84 := 0.58258598; param a91 := 0.074052388; param a92 := -0.037157270; param a93 := 0.19594662; param a94 := -0.20816985; param a101 := -0.083050031; param a102 := 0.035436896; param a103 := -1.2280342; param a104 := 2.6868320; param a111 := -0.38615961; param a112 := 0.085383482; param a113 := 0.0; param a114 := -0.69910317; param a121 := -0.75526603; param a122 := 0.0; param a123 := -0.079034221; param a124 := 0.35744413; param a131 := 0.50420168; param a132 := -0.039251967; param a133 := 0.026387877; param a134 := 1.2499117; param a141 := -1.0916287; param a142 := 0.0; param a143 := -0.057131430; param a144 := 1.4677360; param a151 := 0.0; param a152 := -0.43241927; param a153 := -1.1628081; param a154 := 1.1651720; param a161 := 0.049207290; param a162 := 0.0; param a163 := 1.2587767; param a164 := 1.0763397; param a171 := 0.049207290; param a172 := 0.013873010; param a173 := 2.1625750; param a174 := -0.69686809; subject to cons1 : x1^2 + x2^2 = 1; cons2 : x3^2 + x4^2 = 1; cons3 : x5^2 + x6^2 = 1; cons4 : x7^2 + x8^2 = 1; cons5 : x3*(a11*x1 + a31*x2 + a111) +x4*(a21*x1 + a41*x2 + a121) +x8*(a61*x5 + a161) +x6*(a71*x7 + a141) +a91*x1 + a101*x2 + a131*x5 + a171 = 0; cons6 : x3*(a12*x1 + a32*x2 + a112) +x4*(a22*x1 + a42*x2) +x7*(a52*x5 + a152) +a92*x1 + a102*x2 + a132*x5 + a82*x6*x8 + a172 = 0; cons7 : x3*(a13*x1 + a33*x2) +x4*(a23*x1 + a43*x2 + a123) +x7*(a53*x5 + a73*x6 + a153) +x8*(a63*x5 + a83*x6 + a163) +a93*x1 + a103*x2 + a133*x5 + a143*x6 + a173 = 0; cons8 : x3*(a14*x1 + a34*x2 + a114) +x4*(a24*x1 + a44*x2 + a124) +x7*(a54*x5 + a74*x6 + a154) +x8*(a64*x5 + a84*x6 + a164) +a94*x1 + a104*x2 + a134*x5 + a144*x6 + a174 = 0; ]]> This is the kin2 problem taken from the ICOS distribution. It has 10 solutions.