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;
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This is the kin2 problem taken from the ICOS distribution.
It has 10 solutions.