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#Use this Julia module to generate barrier certificates.
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using MathOptInterface
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const MOI = MathOptInterface
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using JuMP
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using SumOfSquares
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using PolyJuMP
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using Base.Test
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using MultivariatePolynomials
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using SemialgebraicSets
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using Mosek
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import DynamicPolynomials.@polyvar
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@polyvar x[1:15]
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f = [-1.548546352724634*x[1]+-2.357154303962378*x[2]+-5.815071753763429*x[3]+1.7953191330495875*x[4]+4.076774205647443*x[5]+0.7755329752897628*x[6]+-1.1877927499253578*x[7]+-0.6184552197259104*x[8]+-1.6595382177324114*x[9]+4.147429366538116*x[10]+0.3668659814738049*x[11]+-0.060483558178587735*x[12]+-0.7543048442540582*x[13]+3.393499451990565*x[14]+1.594175130168944*x[15],0.0*x[1]+0.0*x[2]+1.0*x[3]+0.0*x[4]+0.0*x[5]+0.0*x[6]+0.0*x[7]+0.0*x[8]+0.0*x[9]+0.0*x[10]+0.0*x[11]+0.0*x[12]+0.0*x[13]+0.0*x[14]+0.0*x[15],3.1519685226285534*x[1]+-2.6348969175583914*x[2]+-7.113228428414966*x[3]+1.180669708519076*x[4]+6.931134777140352*x[5]+0.8663699580696483*x[6]+2.6118793992253604*x[7]+0.6802468854807752*x[8]+-1.6320891098662598*x[9]+4.080694551396657*x[10]+2.103058272479264*x[11]+0.1072185285967212*x[12]+1.1441094794158615*x[13]+2.7466840927642893*x[14]+2.2504006440586988*x[15],0.0*x[1]+0.0*x[2]+0.0*x[3]+0.0*x[4]+1.0*x[5]+0.0*x[6]+0.0*x[7]+0.0*x[8]+0.0*x[9]+0.0*x[10]+0.0*x[11]+0.0*x[12]+0.0*x[13]+0.0*x[14]+0.0*x[15],-5.93589008699051*x[1]+-2.9196710986470356*x[2]+-3.656719262168224*x[3]+-2.4724985506338184*x[4]+-5.6637148279673895*x[5]+1.5215952291102084*x[6]+-2.2651098911863428*x[7]+-1.6066051893710303*x[8]+0.7110599833813186*x[9]+-0.07890130422535852*x[10]+-3.1759299328642516*x[11]+2.6928198694179315*x[12]+-2.525419043226729*x[13]+2.5227046100659622*x[14]+-1.323035103894001*x[15],0.0*x[1]+0.0*x[2]+0.0*x[3]+0.0*x[4]+0.0*x[5]+0.0*x[6]+1.0*x[7]+0.0*x[8]+0.0*x[9]+0.0*x[10]+0.0*x[11]+0.0*x[12]+0.0*x[13]+0.0*x[14]+0.0*x[15],2.269797264250643*x[1]+3.3751816682908355*x[2]+4.4420956699262435*x[3]+3.1926967748398134*x[4]+1.6487163708569357*x[5]+-4.607927260164063*x[6]+-3.731196519963354*x[7]+1.9158524155276508*x[8]+0.753752446108976*x[9]+-0.3524177318571078*x[10]+3.6830070720785635*x[11]+-3.6433341134268575*x[12]+0.03307639331558998*x[13]+-2.305513275311999*x[14]+0.31755710677400006*x[15],0.0*x[1]+0.0*x[2]+0.0*x[3]+0.0*x[4]+0.0*x[5]+0.0*x[6]+0.0*x[7]+0.0*x[8]+1.0*x[9]+0.0*x[10]+0.0*x[11]+0.0*x[12]+0.0*x[13]+0.0*x[14]+0.0*x[15],-0.7337347439086874*x[1]+0.8355784528776233*x[2]+1.358128432951854*x[3]+-2.9614035651865924*x[4]+-0.4515172869836104*x[5]+3.1940141418549572*x[6]+3.1560954837123867*x[7]+-5.5667048429916*x[8]+-3.6362696392723315*x[9]+3.3102291157975783*x[10]+-2.021186726164213*x[11]+2.176428044242506*x[12]+4.360954981198082*x[13]+-0.15606382068809704*x[14]+0.8584331327897154*x[15],0.0*x[1]+0.0*x[2]+0.0*x[3]+0.0*x[4]+0.0*x[5]+0.0*x[6]+0.0*x[7]+0.0*x[8]+0.0*x[9]+0.0*x[10]+1.0*x[11]+0.0*x[12]+0.0*x[13]+0.0*x[14]+0.0*x[15],-0.7299046358172397*x[1]+-2.662458998316692*x[2]+-2.135058943942405*x[3]+1.3229240055567721*x[4]+1.279531673649941*x[5]+-1.0152171458254948*x[6]+-1.9633245606274352*x[7]+3.6855544053264193*x[8]+0.35034747704893743*x[9]+-4.817347253204286*x[10]+-3.3072433031618713*x[11]+-0.29582862529481124*x[12]+-2.394290068934123*x[13]+-1.7185157609708073*x[14]+-2.03676165880647*x[15],0.0*x[1]+0.0*x[2]+0.0*x[3]+0.0*x[4]+0.0*x[5]+0.0*x[6]+0.0*x[7]+0.0*x[8]+0.0*x[9]+0.0*x[10]+0.0*x[11]+0.0*x[12]+1.0*x[13]+0.0*x[14]+0.0*x[15],4.870317194109085*x[1]+1.5463677645404472*x[2]+0.8452886379481945*x[3]+1.3340313737269298*x[4]+-0.6562419157348112*x[5]+0.8132458483014668*x[6]+0.8136455619313883*x[7]+1.3801174148851225*x[8]+-1.4305906498296332*x[9]+-0.4015753125328754*x[10]+0.8378045154194953*x[11]+-4.336249138777637*x[12]+-4.384723508090271*x[13]+2.7099535063051445*x[14]+2.879350891091322*x[15],0.0*x[1]+0.0*x[2]+0.0*x[3]+0.0*x[4]+0.0*x[5]+0.0*x[6]+0.0*x[7]+0.0*x[8]+0.0*x[9]+0.0*x[10]+0.0*x[11]+0.0*x[12]+0.0*x[13]+0.0*x[14]+1.0*x[15],-5.868979525867747*x[1]+-0.8960440931189642*x[2]+-2.7181906516081478*x[3]+-1.5363273058443485*x[4]+0.8315450601706282*x[5]+0.6562001087025472*x[6]+-1.0867984938782644*x[7]+-0.673585046531207*x[8]+1.3805986669753516*x[9]+3.248755206442924*x[10]+1.0419647711575852*x[11]+4.136589619363765*x[12]+3.120942670577048*x[13]+-5.702022376419041*x[14]+-4.335368474476038*x[15]]
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