# **************************************************************************
# Kinematics2: Inverse position problem for a six-revolute-joint problem
#              in mechanics (dense system)
# 
# References :
# @book{Numerica,
# author       = "P. {Van Hentenryck} and L. Michel and Y. Deville",
# title        = "{N}umerica: a {M}odeling {L}anguage for {G}lobal {O}ptimization",
# publisher    = "MIT Press",
# year         = 1997
# }
# 
# A. Morgan and A. Sommese 
# `Computing all solutions to polynomial systems
#  using homotopy continuation',
#  Appl. Math. Comput., Vol. 24, pp 115-138, 1987.
# 
# 
# Solution 1 [7.96e-10]
# x1 = [0.847673005425..0.847673006201]
# x2 = [0.530519061668..0.530519062465]
# x3 = [0.985262164217..0.985262164748]
# x4 = [-0.17105106633..-0.171051066016]
# x5 = [0.490021055296..0.490021055511]
# x6 = [-0.871710597238..-0.871710597151]
# x7 = [-0.551930866067..-0.551930866017]
# x8 = [-0.833889872294..-0.833889872288]
# 
# Solution 2 [2.16e-14]
# x1 = [0.945504605289..0.94550460529]
# x2 = [0.325608724354..0.325608724355]
# x3 = [0.938561247378..0.938561247379]
# x4 = [0.345112713354..0.345112713355]
# x5 = [-0.939144701771..-0.93914470177]
# x6 = [-0.343521803002..-0.343521803001]
# x7 = [0.870774471403..0.870774471404]
# x8 = [0.4916826415..0.491682641501]
# 
# Solution 3 [1.07e-13]
# x1 = [0.977921858273..0.977921858274]
# x2 = [0.208970904937..0.208970904938]
# x3 = [0.0261132902624..0.0261132902626]
# x4 = [0.999658989891..0.999658989892]
# x5 = [-0.0978686112838..-0.0978686112837]
# x6 = [0.995199344315..0.995199344316]
# x7 = [0.0770736104145..0.0770736104146]
# x8 = [-0.997025405182..-0.997025405181]
# 
# 
# Solution 4 [6.34e-12]
# x1 = [0.980793884335..0.980793884338]
# x2 = [0.195047062133..0.19504706214]
# x3 = [-0.99411033624..-0.994110336236]
# x4 = [-0.108372687451..-0.108372687444]
# x5 = [0.884452311754..0.884452311758]
# x6 = [0.466630590755..0.466630590757]
# x7 = [0.294340361574..0.294340361575]
# x8 = [-0.955700660013..-0.955700660012]
# 
# Solution 5 [3.69e-14]
# x1 = [0.952758034456..0.952758034457]
# x2 = [0.303730353733..0.303730353734]
# x3 = [-0.790526544347..-0.790526544346]
# x4 = [0.612427777524..0.612427777525]
# x5 = [0.241511523754..0.241511523755]
# x6 = [0.970397951303..0.970397951304]
# x7 = [0.237359796077..0.237359796078]
# x8 = [-0.971421807047..-0.971421807046]
# 
# Solution 6 [9.63e-11]
# x1 = [-0.554195147306..-0.554195147277]
# x2 = [0.832386772303..0.832386772319]
# x3 = [0.562636008201..0.562636008298]
# x4 = [0.826704737002..0.82670473705]
# x5 = [0.82857143958..0.828571439594]
# x6 = [-0.559883353483..-0.559883353471]
# x7 = [-0.690854676776..-0.690854676766]
# x8 = [-0.722993648373..-0.722993648368]
# 
# Solution 7 [1.76e-14]
# x1 = [-0.541927920626..-0.541927920625]
# x2 = [0.840424969194..0.840424969195]
# x3 = [0.467043194447..0.467043194448]
# x4 = [0.884234501996..0.884234501997]
# x5 = [-0.836719093531..-0.83671909353]
# x6 = [-0.54763232056..-0.547632320559]
# x7 = [0.895144039691..0.895144039692]
# x8 = [0.445777016237..0.445777016238]
# 
# Solution 8 [5.11e-15]
# x1 = [-0.767519772512..-0.767519772511]
# x2 = [0.641025271579..0.64102527158]
# x3 = [0.696416041868..0.696416041869]
# x4 = [-0.717638277009..-0.717638277008]
# x5 = [-0.999979248148..-0.999979248147]
# x6 = [-0.00644230346531..-0.0064423034653]
# x7 = [0.814950634523..0.814950634524]
# x8 = [0.579530381679..0.57953038168]
# 
# Solution 9 [1.53e-14]
# x1 = [-0.83325829747..-0.833258297469]
# x2 = [-0.55288390255..-0.552883902549]
# x3 = [-0.954937653973..-0.954937653972]
# x4 = [0.29680646392..0.296806463921]
# x5 = [0.864628314645..0.864628314646]
# x6 = [-0.502412059483..-0.502412059482]
# x7 = [-0.233473572586..-0.233473572585]
# x8 = [-0.972363147649..-0.972363147648]
# 
# Solution 10 [1.64e-14]
# x1 = [-0.974997904471..-0.97499790447]
# x2 = [-0.222214055087..-0.222214055086]
# x3 = [-0.993879628586..-0.993879628585]
# x4 = [-0.110468474607..-0.110468474606]
# x5 = [-0.999992079505..-0.999992079504]
# x6 = [0.00398006627132..0.00398006627133]
# x7 = [0.998339814129..0.99833981413]
# x8 = [-0.0575987458603..-0.0575987458602]
# **************************************************************************




# Domains
var x1 >= -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;




#  SYSTEME ORIGINAL
# x1*(a11*x3 + a21*x4 + a91)  +
# x2*(a31*x3 + a41*x4 + a101) +
# x5*(a51*x7 + a61*x8 + a131) +
# x6*(a71*x7 + a81*x8 + a141) +
# a111*x3 + a121*x4 + a151*x7 + a161*x8 + a171 = 0,
# 
# x1*(a12*x3 + a22*x4 + a92)  +
# x2*(a32*x3 + a42*x4 + a102) +
# x5*(a52*x7 + a62*x8 + a132) +
# x6*(a72*x7 + a82*x8 + a142) +
# a112*x3 + a122*x4 + a152*x7 + a162*x8 + a172 = 0,
# 
# x1*(a13*x3 + a23*x4 + a93)  +
# x2*(a33*x3 + a43*x4 + a103) +
# x5*(a53*x7 + a63*x8 + a133) +
# x6*(a73*x7 + a83*x8 + a143) +
# a113*x3 + a123*x4 + a153*x7 + a163*x8 + a173 = 0,
# 
# x1*(a14*x3 + a24*x4 + a94)  +
# x2*(a34*x3 + a44*x4 + a104) +
# x5*(a54*x7 + a64*x8 + a134) +
# x6*(a74*x7 + a84*x8 + a144) +
# a114*x3 + a124*x4 + a154*x7 + a164*x8 + a174 = 0
# 



solve;
display x1, x2, x3, x4, x5, x6, x7, x8;