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ltis.m
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ltis.m
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% 1st order OE model with 5 samples
% y = filter([0 .2],[1 -.9],u)+e;
% [b1 f1 l1 l2 l3 l4]
u =[ -6.085574447383194 -7.370597716978055 -17.498793063876256 9.104825796471120 8.670825529473253];
y =[ 0.043995218887244 -1.206948645106605 -2.290789421143243 -5.928995765326843 -3.595561085051387];
strings{1}='y[2]+f[1]*y[1]-b[1]*u[1]-5*l[1]-5*l[2]*f[1]-5*f[1]^2*l[1]';
strings{2}='y[3]+f[1]*y[2]-b[1]*u[2]-5*l[2]-5*l[3]*f[1]-5*l[1]*f[1]-5*l[2]*f[1]^2';
strings{3}='y[4]+f[1]*y[3]-b[1]*u[3]-5*l[3]-5*l[4]*f[1]-5*l[2]*f[1]-5*l[3]*f[1]^2';
strings{4}='y[5]+f[1]*y[4]-b[1]*u[4]-5*l[4]-5*l[3]*f[1]-5*l[4]*f[1]^2';
strings{5}='l[1]*y[1]-5*l[1]^2*f[1]+l[2]*y[2]-5*l[2]*l[1]-5*l[2]^2*f[1]+l[3]*y[3]-5*l[3]*l[2]-5*l[3]^2*f[1]+l[4]*y[4]-5*l[4]*l[3]-5*l[4]^2*f[1]';
strings{6}='-l[1]*u[1]-l[2]*u[2]-l[3]*u[3]-l[4]*u[4]';
polysys = lti2polysys(strings,y,u,'nf',1,'nb',1,'nl',4);
Vstring='(5/2)*l[1]^2*f[1]^2+(5/2)*l[1]^2+5*l[1]*l[2]*f[1]+(5/2)*l[2]^2*f[1]^2+(5/2)*l[2]^2+5*l[2]*l[3]*f[1]+(5/2)*l[3]^2*f[1]^2+(5/2)*l[3]^2+5*l[3]*l[4]*f[1]+(5/2)*l[4]^2*f[1]^2+(5/2)*l[4]^2';
% 1st order OE model with 5 samples, all lagrange multipliers eliminated
u =[ -6.085574447383194 -7.370597716978055 -17.498793063876256 9.104825796471120 8.670825529473253];
y =[ 0.043995218887244 -1.206948645106605 -2.290789421143243 -5.928995765326843 -3.595561085051387];
% strings{1}='(1/5)*u[2]*f[1]*e[1]+(1/5)*y[3]*f[1]*u[2]+(1/5)*u[3]*f[1]^2*y[1]-(2/5)*b[1]*u[3]*f[1]*u[2]-(1/5)*u[3]*f[1]^2*e[1]-(1/5)*f[1]^3*y[1]*u[2]+(1/5)*f[1]^3*u[2]*e[1]+(1/5)*y[4]*f[1]*u[3]-(1/5)*y[4]*f[1]^2*u[2]-(2/5)*b[1]*u[4]*f[1]*u[3]-(1/5)*u[4]*f[1]^3*y[1]+(2/5)*b[1]*u[4]*f[1]^2*u[2]+(1/5)*u[4]*f[1]^3*e[1]+(1/5)*f[1]^4*u[3]*y[1]-(2/5)*f[1]^3*b[1]*u[3]*u[2]-(1/5)*f[1]^4*u[3]*e[1]-(1/5)*f[1]^5*y[1]*u[2]+(1/5)*f[1]^5*u[2]*e[1]+(1/5)*y[5]*f[1]*u[4]-(1/5)*y[5]*f[1]^2*u[3]+(1/5)*y[5]*f[1]^3*u[2]-(2/5)*b[1]*u[5]*f[1]*u[4]+(2/5)*b[1]*u[5]*f[1]^2*u[3]+(1/5)*u[5]*f[1]^4*y[1]-(2/5)*b[1]*u[5]*f[1]^3*u[2]-(1/5)*u[5]*f[1]^4*e[1]-(2/5)*f[1]^3*b[1]*u[4]*u[3]-(1/5)*f[1]^5*u[4]*y[1]+(2/5)*f[1]^4*b[1]*u[4]*u[2]+(1/5)*f[1]^5*u[4]*e[1]+(1/5)*f[1]^6*u[3]*y[1]-(2/5)*f[1]^5*b[1]*u[3]*u[2]-(1/5)*f[1]^6*u[3]*e[1]-(1/5)*f[1]^7*y[1]*u[2]+(1/5)*f[1]^7*u[2]*e[1]+(1/5)*b[1]*u[5]^2+(1/5)*b[1]*u[2]^2+(1/5)*b[1]*u[3]^2+(1/5)*b[1]*u[4]^2+(1/5)*f[1]^4*b[1]*u[2]^2+(1/5)*f[1]^6*b[1]*u[2]^2-(1/5)*y[4]*u[4]-(1/5)*y[3]*u[3]+(1/5)*f[1]^4*b[1]*u[3]^2-(1/5)*y[5]*u[5]+(1/5)*f[1]^2*b[1]*u[2]^2+(1/5)*f[1]^2*b[1]*u[4]^2-(1/5)*y[2]*u[2]+(1/5)*f[1]^2*b[1]*u[3]^2-(1/5)*f[1]*y[1]*u[2]';
% strings{2}='(4/5)*f[1]^3*b[1]*u[3]*y[1]-(3/5)*f[1]^2*b[1]^2*u[3]*u[2]-(4/5)*f[1]^3*b[1]*u[3]*e[1]-f[1]^4*y[1]*b[1]*u[2]+f[1]^4*b[1]*u[2]*e[1]+(1/5)*y[5]*b[1]*u[4]-(2/5)*y[5]*f[1]*b[1]*u[3]+(3/5)*y[5]*f[1]^2*b[1]*u[2]-(1/5)*b[1]^2*u[5]*u[4]+(2/5)*b[1]^2*u[5]*f[1]*u[3]+(4/5)*b[1]*u[5]*f[1]^3*y[1]-(3/5)*b[1]^2*u[5]*f[1]^2*u[2]-(4/5)*b[1]*u[5]*f[1]^3*e[1]-(3/5)*f[1]^2*b[1]^2*u[4]*u[3]-f[1]^4*b[1]*u[4]*y[1]+(4/5)*f[1]^3*b[1]^2*u[4]*u[2]+f[1]^4*b[1]*u[4]*e[1]+(6/5)*f[1]^5*b[1]*u[3]*y[1]-f[1]^4*b[1]^2*u[3]*u[2]-(6/5)*f[1]^5*b[1]*u[3]*e[1]-(7/5)*f[1]^6*y[1]*b[1]*u[2]+(7/5)*f[1]^6*b[1]*u[2]*e[1]+(1/5)*b[1]*u[2]*e[1]+(1/5)*y[3]*b[1]*u[2]+(2/5)*b[1]*u[3]*f[1]*y[1]-(1/5)*b[1]^2*u[3]*u[2]-(2/5)*b[1]*u[3]*f[1]*e[1]-(3/5)*f[1]^2*y[1]*b[1]*u[2]+(3/5)*f[1]^2*b[1]*u[2]*e[1]+(1/5)*y[4]*b[1]*u[3]-(2/5)*y[4]*f[1]*b[1]*u[2]-(1/5)*b[1]^2*u[4]*u[3]-(3/5)*b[1]*u[4]*f[1]^2*y[1]+(2/5)*b[1]^2*u[4]*f[1]*u[2]+(3/5)*b[1]*u[4]*f[1]^2*e[1]+(2/5)*f[1]^3*b[1]^2*u[3]^2-(2/5)*f[1]*y[1]*e[1]-(8/5)*f[1]^7*y[1]*e[1]-(6/5)*f[1]^5*y[1]*e[1]-(4/5)*f[1]^3*y[1]*e[1]+(2/5)*y[3]*f[1]*e[1]+(3/5)*y[4]*f[1]^2*y[1]-(2/5)*y[3]*f[1]*y[1]+(1/5)*f[1]*b[1]^2*u[2]^2-(3/5)*y[4]*f[1]^2*e[1]-(4/5)*y[5]*f[1]^3*y[1]-(1/5)*y[2]*e[1]+(2/5)*f[1]^3*b[1]^2*u[2]^2+(4/5)*y[5]*f[1]^3*e[1]+(1/5)*f[1]*b[1]^2*u[4]^2+(1/5)*y[2]*y[1]+(3/5)*f[1]^5*b[1]^2*u[2]^2+(1/5)*f[1]*b[1]^2*u[3]^2+(1/5)*f[1]*y[1]^2+(1/5)*f[1]*e[1]^2+(2/5)*f[1]^3*y[1]^2+(2/5)*f[1]^3*e[1]^2+(3/5)*f[1]^5*y[1]^2+(3/5)*f[1]^5*e[1]^2+(4/5)*f[1]^7*y[1]^2+(4/5)*f[1]^7*e[1]^2-(1/5)*y[1]*b[1]*u[2]';
% strings{3}='-(1/5)*f[1]^8*y[1]+(1/5)*f[1]*b[1]*u[2]-(1/5)*f[1]^2*b[1]*u[3]+(1/5)*f[1]^3*b[1]*u[2]+(1/5)*b[1]*u[4]*f[1]^3-(1/5)*f[1]^4*b[1]*u[3]+(1/5)*f[1]^5*b[1]*u[2]-(1/5)*b[1]*u[5]*f[1]^4+(1/5)*f[1]^5*b[1]*u[4]-(1/5)*f[1]^6*b[1]*u[3]+(1/5)*f[1]^7*b[1]*u[2]-(1/5)*f[1]*y[2]+(1/5)*y[3]*f[1]^2+(1/5)*y[5]*f[1]^4-(1/5)*f[1]^2*y[1]-(1/5)*f[1]^4*y[1]-(1/5)*y[4]*f[1]^3-(1/5)*f[1]^6*y[1]+(1/5)*f[1]^2*e[1]+(1/5)*f[1]^4*e[1]+(1/5)*f[1]^6*e[1]+(1/5)*f[1]^8*e[1]+(1/5)*e[1]';
strings{1}='(1/5)*y[3]*f[1]*u[2]+(1/5)*u[3]*f[1]^2*y[1]-(2/5)*b[1]*u[3]*f[1]*u[2]-(1/5)*u[3]*f[1]^2*e[1]-(1/5)*f[1]^3*y[1]*u[2]+(1/5)*f[1]^3*u[2]*e[1]+(1/5)*y[4]*f[1]*u[3]-(1/5)*y[4]*f[1]^2*u[2]-(2/5)*b[1]*u[4]*f[1]*u[3]-(1/5)*u[4]*f[1]^3*y[1]+(2/5)*b[1]*u[4]*f[1]^2*u[2]+(1/5)*u[4]*f[1]^3*e[1]+(1/5)*f[1]^4*u[3]*y[1]-(2/5)*f[1]^3*b[1]*u[3]*u[2]-(1/5)*f[1]^4*u[3]*e[1]-(1/5)*f[1]^5*y[1]*u[2]+(1/5)*f[1]^5*u[2]*e[1]+(1/5)*y[5]*f[1]*u[4]-(1/5)*y[5]*f[1]^2*u[3]+(1/5)*y[5]*f[1]^3*u[2]-(2/5)*b[1]*u[5]*f[1]*u[4]+(2/5)*b[1]*u[5]*f[1]^2*u[3]+(1/5)*u[5]*f[1]^4*y[1]-(2/5)*b[1]*u[5]*f[1]^3*u[2]-(1/5)*u[5]*f[1]^4*e[1]-(2/5)*f[1]^3*b[1]*u[4]*u[3]-(1/5)*f[1]^5*u[4]*y[1]+(2/5)*f[1]^4*b[1]*u[4]*u[2]+(1/5)*f[1]^5*u[4]*e[1]+(1/5)*f[1]^6*u[3]*y[1]-(2/5)*f[1]^5*b[1]*u[3]*u[2]-(1/5)*f[1]^6*u[3]*e[1]-(1/5)*f[1]^7*y[1]*u[2]+(1/5)*f[1]^7*u[2]*e[1]-(1/5)*f[1]*y[1]*u[2]+(1/5)*b[1]*u[2]^2+(1/5)*b[1]*u[3]^2+(1/5)*b[1]*u[4]^2+(1/5)*b[1]*u[5]^2+(1/5)*f[1]^2*b[1]*u[4]^2+(1/5)*f[1]^6*b[1]*u[2]^2-(1/5)*y[2]*u[2]+(1/5)*f[1]^4*b[1]*u[2]^2+(1/5)*f[1]^4*b[1]*u[3]^2-(1/5)*y[3]*u[3]-(1/5)*y[4]*u[4]+(1/5)*f[1]^2*b[1]*u[3]^2-(1/5)*y[5]*u[5]+(1/5)*f[1]^2*b[1]*u[2]^2+(1/5)*u[2]*f[1]*e[1]';
strings{2}='-(7/5)*f[1]^6*y[1]*b[1]*u[2]+(7/5)*f[1]^6*b[1]*u[2]*e[1]-(1/5)*y[1]*b[1]*u[2]+(1/5)*y[3]*b[1]*u[2]+(2/5)*b[1]*u[3]*f[1]*y[1]-(1/5)*b[1]^2*u[3]*u[2]-(2/5)*b[1]*u[3]*f[1]*e[1]-(3/5)*f[1]^2*y[1]*b[1]*u[2]+(3/5)*f[1]^2*b[1]*u[2]*e[1]+(1/5)*y[4]*b[1]*u[3]-(2/5)*y[4]*f[1]*b[1]*u[2]-(1/5)*b[1]^2*u[4]*u[3]-(3/5)*b[1]*u[4]*f[1]^2*y[1]+(2/5)*b[1]^2*u[4]*f[1]*u[2]+(3/5)*b[1]*u[4]*f[1]^2*e[1]+(4/5)*f[1]^3*b[1]*u[3]*y[1]-(3/5)*f[1]^2*b[1]^2*u[3]*u[2]-(4/5)*f[1]^3*b[1]*u[3]*e[1]-f[1]^4*y[1]*b[1]*u[2]+f[1]^4*b[1]*u[2]*e[1]+(1/5)*y[5]*b[1]*u[4]-(2/5)*y[5]*f[1]*b[1]*u[3]+(3/5)*y[5]*f[1]^2*b[1]*u[2]-(1/5)*b[1]^2*u[5]*u[4]+(2/5)*b[1]^2*u[5]*f[1]*u[3]+(4/5)*b[1]*u[5]*f[1]^3*y[1]-(3/5)*b[1]^2*u[5]*f[1]^2*u[2]-(4/5)*b[1]*u[5]*f[1]^3*e[1]-(3/5)*f[1]^2*b[1]^2*u[4]*u[3]-f[1]^4*b[1]*u[4]*y[1]+(4/5)*f[1]^3*b[1]^2*u[4]*u[2]+f[1]^4*b[1]*u[4]*e[1]+(6/5)*f[1]^5*b[1]*u[3]*y[1]-f[1]^4*b[1]^2*u[3]*u[2]-(6/5)*f[1]^5*b[1]*u[3]*e[1]+(2/5)*f[1]^3*b[1]^2*u[3]^2+(3/5)*f[1]^5*b[1]^2*u[2]^2+(2/5)*y[3]*f[1]*e[1]+(1/5)*y[2]*y[1]+(1/5)*f[1]*b[1]^2*u[2]^2-(2/5)*f[1]*y[1]*e[1]-(4/5)*f[1]^3*y[1]*e[1]+(1/5)*f[1]*b[1]^2*u[4]^2-(4/5)*y[5]*f[1]^3*y[1]-(6/5)*f[1]^5*y[1]*e[1]-(2/5)*y[3]*f[1]*y[1]+(2/5)*f[1]^3*b[1]^2*u[2]^2-(8/5)*f[1]^7*y[1]*e[1]-(3/5)*y[4]*f[1]^2*e[1]+(1/5)*f[1]*b[1]^2*u[3]^2+(4/5)*y[5]*f[1]^3*e[1]+(3/5)*y[4]*f[1]^2*y[1]-(1/5)*y[2]*e[1]+(1/5)*f[1]*y[1]^2+(1/5)*f[1]*e[1]^2+(2/5)*f[1]^3*y[1]^2+(2/5)*f[1]^3*e[1]^2+(3/5)*f[1]^5*y[1]^2+(3/5)*f[1]^5*e[1]^2+(4/5)*f[1]^7*y[1]^2+(4/5)*f[1]^7*e[1]^2+(1/5)*b[1]*u[2]*e[1]';
strings{3}='(1/5)*f[1]*b[1]*u[2]-(1/5)*f[1]^2*b[1]*u[3]+(1/5)*f[1]^3*b[1]*u[2]+(1/5)*b[1]*u[4]*f[1]^3-(1/5)*f[1]^4*b[1]*u[3]+(1/5)*f[1]^5*b[1]*u[2]-(1/5)*b[1]*u[5]*f[1]^4+(1/5)*f[1]^5*b[1]*u[4]-(1/5)*f[1]^6*b[1]*u[3]+(1/5)*f[1]^7*b[1]*u[2]+(1/5)*e[1]+(1/5)*y[5]*f[1]^4-(1/5)*f[1]^8*y[1]-(1/5)*f[1]^6*y[1]+(1/5)*y[3]*f[1]^2-(1/5)*f[1]^2*y[1]-(1/5)*f[1]*y[2]-(1/5)*y[4]*f[1]^3-(1/5)*f[1]^4*y[1]+(1/5)*f[1]^2*e[1]+(1/5)*f[1]^4*e[1]+(1/5)*f[1]^6*e[1]+(1/5)*f[1]^8*e[1]';
polysys = lti2polysys(strings,y,u,'nf',1,'nb',1,'ne',1);
Vstring='-(1/5)*f[1]^8*y[1]*e[1]-(1/5)*f[1]*y[1]*b[1]*u[2]+(1/5)*b[1]*u[2]*f[1]*e[1]+(1/5)*y[3]*f[1]*b[1]*u[2]+(1/5)*b[1]*u[3]*f[1]^2*y[1]-(1/5)*b[1]^2*u[3]*f[1]*u[2]-(1/5)*b[1]*u[3]*f[1]^2*e[1]-(1/5)*f[1]^3*y[1]*b[1]*u[2]+(1/5)*f[1]^3*b[1]*u[2]*e[1]+(1/5)*y[4]*f[1]*b[1]*u[3]-(1/5)*y[4]*f[1]^2*b[1]*u[2]-(1/5)*b[1]^2*u[4]*f[1]*u[3]-(1/5)*b[1]*u[4]*f[1]^3*y[1]+(1/5)*b[1]^2*u[4]*f[1]^2*u[2]+(1/5)*b[1]*u[4]*f[1]^3*e[1]+(1/5)*f[1]^4*b[1]*u[3]*y[1]-(1/5)*f[1]^3*b[1]^2*u[3]*u[2]-(1/5)*f[1]^4*b[1]*u[3]*e[1]-(1/5)*f[1]^5*y[1]*b[1]*u[2]+(1/5)*f[1]^5*b[1]*u[2]*e[1]+(1/5)*y[5]*f[1]*b[1]*u[4]-(1/5)*y[5]*f[1]^2*b[1]*u[3]+(1/5)*y[5]*f[1]^3*b[1]*u[2]-(1/5)*b[1]^2*u[5]*f[1]*u[4]+(1/5)*b[1]^2*u[5]*f[1]^2*u[3]+(1/5)*b[1]*u[5]*f[1]^4*y[1]-(1/5)*b[1]^2*u[5]*f[1]^3*u[2]-(1/5)*b[1]*u[5]*f[1]^4*e[1]-(1/5)*f[1]^3*b[1]^2*u[4]*u[3]-(1/5)*f[1]^5*b[1]*u[4]*y[1]+(1/5)*f[1]^4*b[1]^2*u[4]*u[2]+(1/5)*f[1]^5*b[1]*u[4]*e[1]+(1/5)*f[1]^6*b[1]*u[3]*y[1]-(1/5)*f[1]^5*b[1]^2*u[3]*u[2]-(1/5)*f[1]^6*b[1]*u[3]*e[1]-(1/5)*f[1]^7*y[1]*b[1]*u[2]+(1/5)*f[1]^7*b[1]*u[2]*e[1]-(1/5)*y[2]*f[1]*e[1]+(1/5)*y[3]*f[1]^2*e[1]-(1/5)*y[4]*b[1]*u[4]+(1/10)*f[1]^2*b[1]^2*u[4]^2+(1/10)*f[1]^6*b[1]^2*u[2]^2+(1/5)*y[5]*f[1]^4*e[1]+(1/10)*f[1]^4*b[1]^2*u[3]^2-(1/5)*f[1]^2*y[1]*e[1]+(1/10)*f[1]^2*b[1]^2*u[3]^2-(1/5)*y[2]*b[1]*u[2]-(1/5)*y[3]*f[1]^2*y[1]+(1/10)*f[1]^4*b[1]^2*u[2]^2-(1/5)*f[1]^4*y[1]*e[1]+(1/5)*y[4]*f[1]^3*y[1]-(1/5)*y[5]*f[1]^4*y[1]-(1/5)*y[4]*f[1]^3*e[1]+(1/5)*y[2]*f[1]*y[1]+(1/10)*f[1]^2*b[1]^2*u[2]^2-(1/5)*y[5]*b[1]*u[5]-(1/5)*y[3]*b[1]*u[3]-(1/5)*f[1]^6*y[1]*e[1]+(1/10)*b[1]^2*u[5]^2+(1/10)*f[1]^2*y[1]^2+(1/10)*b[1]^2*u[2]^2+(1/10)*f[1]^2*e[1]^2+(1/10)*y[3]^2+(1/10)*b[1]^2*u[3]^2+(1/10)*f[1]^4*y[1]^2+(1/10)*f[1]^4*e[1]^2+(1/10)*y[4]^2+(1/10)*b[1]^2*u[4]^2+(1/10)*f[1]^6*y[1]^2+(1/10)*f[1]^6*e[1]^2+(1/10)*y[5]^2+(1/10)*y[2]^2+(1/10)*f[1]^8*y[1]^2+(1/10)*f[1]^8*e[1]^2+(1/10)*e[1]^2';
% 2nd order OE with 7 samples, unconstrained, 5 extra unknowns
% l(1)=y(0), l(2)=y(-1), l(3)=u(0), l(4)=e(0), l(5)=e(-1)
u = [ -0.105715036001239 0.524840721552703 -0.961680965189235 0.462166156605002 1.410438100612864 3.279796646902768 5.330227374264688];
y = [ 0.010346930099179 -0.013874155866415 0.068104923542284 -0.056757269494429 -0.074267177564447 0.237870043104374 1.069957338248644];
e = [0.010346930099179 0.007268851333832 -0.003034409247860 0.002938714670967 -0.007872828037586 0.008883956317576 -0.011470701069692];
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strings{2}='-(4/7)*f[1]*b[1]^2*u[2]*f[2]*u[1]-2*f[1]^3*f[2]*b[1]^2*u[1]*u[2]+(6/7)*f[1]*f[2]^2*b[1]^2*u[1]*u[2]+(8/7)*f[1]^2*f[2]*b[1]^2*u[1]*u[3]-(2/7)*f[1]*f[2]*b[1]^2*u[1]*u[4]-(4/7)*f[2]*b[1]^2*u[2]*f[1]*u[3]+(39/7)*f[1]^3*f[2]^2*b[1]^2*u[1]*u[2]-(18/7)*f[1]^2*f[2]^2*b[1]^2*u[1]*u[3]-(32/7)*f[1]^5*f[2]*b[1]^2*u[1]*u[2]-2*f[1]^3*f[2]*b[1]^2*u[1]*u[4]+(22/7)*f[1]^4*f[2]*b[1]^2*u[1]*u[3]+(6/7)*f[1]^2*f[2]*b[1]^2*u[1]*u[5]+(6/7)*f[1]*f[2]^2*b[1]^2*u[2]*u[3]-(12/7)*f[1]*f[2]^3*b[1]^2*u[2]*u[1]+(8/7)*f[1]^2*f[2]*b[1]^2*u[2]*u[4]-2*f[1]^3*f[2]*b[1]^2*u[2]*u[3]-(2/7)*f[1]*f[2]*b[1]^2*u[2]*u[5]+(1/7)*b[1]^2*u[2]*f[1]*u[1]+(1/7)*b[1]^2*u[3]*f[1]*u[2]-(2/7)*b[1]^2*u[3]*f[1]^2*u[1]+(3/7)*f[1]^3*b[1]^2*u[2]*u[1]+(4/7)*f[1]^2*b[1]^2*u[1]^2*f[2]-(9/7)*f[1]^2*f[2]^2*b[1]^2*u[1]^2+(11/7)*f[1]^4*f[2]*b[1]^2*u[1]^2+(4/7)*f[1]^2*b[1]^2*u[2]^2*f[2]+(3/7)*f[1]^3*b[1]^2*u[2]*u[3]+(5/7)*f[1]^5*b[1]^2*u[2]*u[1]-(2/7)*f[1]^2*b[1]^2*u[2]*u[4]-(4/7)*f[1]^4*b[1]^2*u[3]*u[1]+(1/7)*f[1]*b[1]^2*u[3]*u[4]+(3/7)*f[1]^3*b[1]^2*u[1]*u[4]-(36/7)*f[1]^4*f[2]^2*b[1]^2*u[1]^2+(18/7)*f[1]^2*f[2]^3*b[1]^2*u[1]^2+(22/7)*f[1]^6*f[2]*b[1]^2*u[1]^2-(9/7)*f[1]^2*f[2]^2*b[1]^2*u[2]^2+(11/7)*f[1]^4*f[2]*b[1]^2*u[2]^2+(4/7)*f[2]*b[1]^2*u[3]^2*f[1]^2+f[1]^7*b[1]^2*u[2]*u[1]-(4/7)*f[1]^4*b[1]^2*u[2]*u[4]+(5/7)*f[1]^5*b[1]^2*u[2]*u[3]+(3/7)*f[1]^3*b[1]^2*u[2]*u[5]+(5/7)*f[1]^5*b[1]^2*u[1]*u[4]-(6/7)*f[1]^6*b[1]^2*u[1]*u[3]-(4/7)*f[1]^4*b[1]^2*u[1]*u[5]+(3/7)*f[1]^3*b[1]^2*u[4]*u[3]+(1/7)*f[1]*b[1]^2*u[4]*u[5]-(2/7)*f[1]^2*b[1]^2*u[3]*u[5]+(1/7)*b[1]*u[1]*f[1]*l[2]-(1/7)*b[1]*u[1]*f[1]*l[5]-(1/7)*f[1]^2*l[2]*b[1]*l[3]+(1/7)*f[1]^2*b[1]*l[3]*l[5]+(2/7)*b[1]*u[2]*f[1]*l[1]-(1/7)*b[1]*u[2]*f[1]^2*l[2]+(1/7)*b[1]*u[2]*f[1]^2*l[5]-(2/7)*b[1]*u[2]*f[1]*l[4]+(1/7)*f[1]^3*b[1]*u[1]*l[2]-(1/7)*f[1]^3*b[1]*u[1]*l[5]-(1/7)*f[1]^4*l[2]*b[1]*l[3]+(1/7)*f[1]^4*b[1]*l[3]*l[5]+(4/7)*f[1]*f[2]*l[5]*b[1]*u[3]-(3/7)*f[1]^2*l[1]*b[1]*u[3]+(2/7)*f[1]*b[1]^2*l[3]*u[3]-(2/7)*y[4]*f[1]*b[1]*l[3]-(4/7)*f[1]*f[2]*l[2]*b[1]*u[3]+(3/7)*f[1]^2*l[4]*b[1]*u[3]+(1/7)*f[1]^6*l[5]*b[1]*l[3]-(1/7)*f[1]^5*l[5]*b[1]*u[1]+(1/7)*f[1]^4*l[5]*b[1]*u[2]-(1/7)*f[1]^3*l[5]*b[1]*u[3]-(1/7)*f[1]^6*l[2]*b[1]*l[3]+(1/7)*f[1]^5*l[2]*b[1]*u[1]-(1/7)*f[1]^4*l[2]*b[1]*u[2]+(1/7)*f[1]^3*l[2]*b[1]*u[3]+(4/7)*f[1]^3*l[1]*b[1]*u[4]-(6/7)*f[1]*f[2]*l[1]*b[1]*u[4]+(3/7)*y[5]*f[1]^2*b[1]*l[3]+(6/7)*f[1]^2*f[2]*l[2]*b[1]*u[4]-(4/7)*f[1]^3*l[4]*b[1]*u[4]+(1/7)*f[1]^8*l[5]*b[1]*l[3]+(1/7)*f[1]^6*l[5]*b[1]*u[2]-(1/7)*f[1]^5*l[5]*b[1]*u[3]-(1/7)*f[1]^7*l[5]*b[1]*u[1]+(1/7)*f[1]^4*l[5]*b[1]*u[4]-(1/7)*f[1]^8*l[2]*b[1]*l[3]-(1/7)*f[1]^6*l[2]*b[1]*u[2]+(1/7)*f[1]^5*l[2]*b[1]*u[3]+(6/7)*y[6]*f[1]*f[2]*b[1]*l[3]-(4/7)*y[6]*f[1]^3*b[1]*l[3]+(6/7)*f[1]*f[2]*l[4]*b[1]*u[4]-(3/7)*f[1]^2*b[1]^2*l[3]*u[4]+(1/7)*f[1]^7*l[2]*b[1]*u[1]-(1/7)*f[1]^4*l[2]*b[1]*u[4]-(6/7)*f[1]^2*f[2]*l[5]*b[1]*u[4]-(5/7)*f[1]^4*l[1]*b[1]*u[5]+(12/7)*f[1]^2*f[2]*l[1]*b[1]*u[5]-(8/7)*f[1]^3*f[2]*l[2]*b[1]*u[5]+(5/7)*f[1]^4*l[4]*b[1]*u[5]+(1/7)*f[1]^10*l[5]*b[1]*l[3]+(1/7)*f[1]^8*l[5]*b[1]*u[2]-(1/7)*f[1]^9*l[5]*b[1]*u[1]+(1/7)*f[1]^6*l[5]*b[1]*u[4]-(1/7)*f[1]^7*l[5]*b[1]*u[3]-(1/7)*f[1]^5*l[5]*b[1]*u[5]-(1/7)*f[1]^10*l[2]*b[1]*l[3]-(1/7)*f[1]^8*l[2]*b[1]*u[2]+(1/7)*f[1]^9*l[2]*b[1]*u[1]-(1/7)*f[1]^6*l[2]*b[1]*u[4]+(1/7)*f[1]^7*l[2]*b[1]*u[3]+(1/7)*f[1]^5*l[2]*b[1]*u[5]-(6/7)*f[1]*f[2]*b[1]^2*l[3]*u[5]+(4/7)*f[1]^3*b[1]^2*l[3]*u[5]-(12/7)*f[1]^2*f[2]*l[4]*b[1]*u[5]+(9/7)*f[1]*f[2]^2*l[2]*b[1]*u[5]-(9/7)*f[1]*f[2]^2*l[5]*b[1]*u[5]+(8/7)*f[1]^3*f[2]*l[5]*b[1]*u[5]-(2/7)*b[1]*u[2]*f[2]*l[5]+(1/7)*f[1]^5*l[1]*l[2]-(1/7)*f[1]^5*l[1]*l[5]-(1/7)*f[1]^5*l[2]*l[4]-(2/7)*f[1]^4*f[2]*l[2]*l[5]+(1/7)*f[1]*l[1]*l[2]-(1/7)*f[1]*l[1]*l[5]-(1/7)*l[2]*b[1]*l[3]-(1/7)*l[2]*f[1]*l[4]+(1/7)*b[1]*l[3]*l[5]+(1/7)*f[1]*l[4]*l[5]-(1/7)*y[2]*f[1]*l[2]+(1/7)*y[2]*f[1]*l[5]-(1/7)*l[1]*b[1]*u[1]+(1/7)*b[1]*u[1]*l[4]+(1/7)*f[1]^3*l[1]*l[2]-(1/7)*f[1]^3*l[1]*l[5]-(1/7)*f[1]^3*l[2]*l[4]-(2/7)*f[1]^2*f[2]*l[2]*l[5]+(1/7)*f[1]^3*l[4]*l[5]-(2/7)*f[1]^8*f[2]*l[5]*l[2]-(1/7)*f[1]^9*l[5]*l[1]+(1/7)*f[1]^9*l[5]*l[4]-(3/7)*f[2]^2*l[1]*b[1]*u[1]+(2/7)*f[2]*l[1]*b[1]*u[3]+(3/7)*f[2]^2*l[4]*b[1]*u[1]-(2/7)*f[2]*l[4]*b[1]*u[3]-(2/7)*f[1]^6*f[2]*l[5]*l[2]-(1/7)*f[1]^7*l[5]*l[1]+(1/7)*f[1]^7*l[5]*l[4]+(1/7)*f[1]^7*l[2]*l[1]-(1/7)*f[1]^7*l[2]*l[4]+(1/7)*f[1]^5*l[4]*l[5]-(3/7)*f[2]^2*l[2]*b[1]*l[3]+(3/7)*f[2]^2*b[1]*l[3]*l[5]+(4/7)*y[4]*f[1]*f[2]*l[2]-(3/7)*y[4]*f[1]^2*l[4]+(1/7)*y[4]*f[1]^3*l[5]-(1/7)*y[4]*f[1]^3*l[2]-(4/7)*y[4]*f[1]*f[2]*l[5]+(3/7)*y[4]*f[1]^2*l[1]-(2/7)*y[3]*f[1]*l[1]+(1/7)*y[3]*f[1]^2*l[2]-(1/7)*y[3]*f[1]^2*l[5]+(2/7)*y[3]*f[1]*l[4]+(1/7)*y[3]*b[1]*l[3]+(2/7)*b[1]*u[2]*f[2]*l[2]-(1/7)*b[1]^2*u[2]*l[3]-(1/7)*f[1]^11*l[5]*l[1]+(1/7)*f[1]^11*l[5]*l[4]+(1/7)*f[1]^11*l[2]*l[1]-(1/7)*f[1]^11*l[2]*l[4]+(3/7)*f[2]^2*l[5]*b[1]*u[4]+(8/7)*y[6]*f[1]^3*f[2]*l[2]-(5/7)*y[6]*f[1]^4*l[4]+(1/7)*y[6]*f[1]^5*l[5]-(1/7)*y[6]*f[1]^5*l[2]-(8/7)*y[6]*f[1]^3*f[2]*l[5]+(5/7)*y[6]*f[1]^4*l[1]-(12/7)*y[6]*f[1]^2*f[2]*l[1]+(12/7)*y[6]*f[1]^2*f[2]*l[4]-(9/7)*y[6]*f[1]*f[2]^2*l[2]+(9/7)*y[6]*f[1]*f[2]^2*l[5]-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b[1]^2*u[2]^2-(4/7)*f[1]^8*b[1]^2*u[1]^2-(1/7)*f[1]^2*b[1]^2*u[4]^2-(2/7)*f[1]^4*b[1]^2*u[3]^2-(1/7)*f[1]^2*b[1]^2*u[2]^2-(2/7)*f[1]^4*b[1]^2*u[1]^2-(2/7)*f[1]^4*b[1]^2*u[2]^2-(1/7)*f[1]^2*b[1]^2*u[3]^2-(3/7)*f[1]^6*b[1]^2*u[1]^2-(1/7)*f[1]^2*b[1]^2*u[1]^2';
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1]^6*f[2]^3*l[5]*b[1]-(8/7)*f[1]^8*f[2]^2*l[5]*b[1]-(1/7)*f[1]^10*f[2]*l[2]*b[1]-(24/7)*f[1]^4*f[2]^4*l[5]*b[1]+(8/7)*f[1]^8*f[2]^2*l[2]*b[1]+(24/7)*f[1]^4*f[2]^4*l[2]*b[1]-(22/7)*f[1]^6*f[2]^3*l[2]*b[1]-(6/7)*f[1]^2*f[2]^4*l[5]*b[1]+f[1]^7*b[1]*f[2]*l[1]-(16/7)*f[1]^5*b[1]*f[2]^2*l[1]+(13/7)*f[1]^3*f[2]^3*l[1]*b[1]-(3/7)*f[1]*f[2]^4*l[1]*b[1]+(3/7)*f[1]*f[2]^4*l[4]*b[1]+(6/7)*f[1]^6*f[2]^2*l[2]*b[1]+(6/7)*f[1]^2*f[2]^4*l[2]*b[1]+(12/7)*f[1]^2*f[2]^6*l[2]*b[1]-(12/7)*f[1]^2*f[2]^6*l[5]*b[1]-(4/7)*f[1]*f[2]^6*l[1]*b[1]-(86/7)*f[1]^5*f[2]^4*l[1]*b[1]+(34/7)*f[1]^3*f[2]^5*l[1]*b[1]-(34/7)*f[1]^3*f[2]^5*l[4]*b[1]+(46/7)*f[1]^4*f[2]^5*l[5]*b[1]+(11/7)*f[1]^11*b[1]*f[2]*l[1]-(46/7)*f[1]^9*b[1]*f[2]^2*l[1]+13*f[1]^7*b[1]*f[2]^3*l[1]-(37/7)*f[1]^8*f[2]^3*l[2]*b[1]-(11/7)*f[1]^11*f[2]*l[4]*b[1]+(86/7)*f[1]^5*f[2]^4*l[4]*b[1]-13*f[1]^7*f[2]^3*l[4]*b[1]+(46/7)*f[1]^9*f[2]^2*l[4]*b[1]+(1/7)*f[1]^12*f[2]*l[5]*b[1]-(62/7)*f[1]^6*f[2]^4*l[5]*b[1]+(37/7)*f[1]^8*f[2]^3*l[5]*b[1]-(10/7)*f[1]^10*f[2]^2*l[5]*b[1]-(1/7)*f[1]^12*f[2]*l[2]*b[1]+(10/7)*f[1]^10*f[2]^2*l[2]*b[1]-(46/7)*f[1]^4*f[2]^5*l[2]*b[1]+(62/7)*f[1]^6*f[2]^4*l[2]*b[1]+(3/7)*f[1]*f[2]^5*b[1]*l[1]-(3/7)*f[1]*f[2]^5*b[1]*l[4]+(4/7)*f[1]*f[2]^6*l[4]*b[1]';
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[2]^3*l[5]-(1/7)*f[1]^7*f[2]*l[2]-(2/7)*f[1]*f[2]^4*l[5]+(1/7)*f[1]^7*b[1]*l[3]-f[1]^3*f[2]^3*l[2]+(1/7)*f[2]^4*l[4]+(1/7)*f[1]^14*l[4]-(148/7)*f[1]^6*f[2]^4*l[1]+(1/7)*f[1]^12*l[4]-(9/7)*f[1]^2*f[2]^4*l[1]+(6/7)*f[1]^6*f[2]*l[1]+(6/7)*f[1]^2*f[2]^3*l[1]-8*f[1]^10*f[2]^2*l[1]-(37/7)*f[1]^8*f[2]^2*l[1]+(1/7)*f[1]^8*l[4]+(24/7)*f[1]^4*f[2]^3*l[1]-(16/7)*f[1]^2*f[2]^6*l[1]+(8/7)*f[1]^8*f[2]*l[1]+(1/7)*f[2]^6*l[4]+(12/7)*f[1]^2*f[2]^5*l[1]-(22/7)*f[1]^6*f[2]^2*l[1]+(1/7)*f[1]^10*l[4]+(80/7)*f[1]^4*f[2]^5*l[1]-(46/7)*f[1]^4*f[2]^4*l[1]-(11/7)*f[1]^4*f[2]^2*l[1]+(12/7)*f[1]^12*f[2]*l[1]+(62/7)*f[1]^6*f[2]^3*l[1]+(10/7)*f[1]^10*f[2]*l[1]+(128/7)*f[1]^8*f[2]^3*l[1]+(22/7)*f[1]^3*f[2]^4*b[1]*l[3]-f[1]^7*b[1]*l[3]*f[2]+(16/7)*f[1]^5*b[1]*l[3]*f[2]^2-(13/7)*f[1]^3*f[2]^3*b[1]*l[3]+(3/7)*f[1]*f[2]^4*b[1]*l[3]-(5/7)*f[1]^5*b[1]*l[3]*f[2]+f[1]^3*b[1]*l[3]*f[2]^2-(2/7)*f[1]*f[2]^3*b[1]*l[3]+(4/7)*f[1]*f[2]^6*b[1]*l[3]+(86/7)*f[1]^5*f[2]^4*b[1]*l[3]-(34/7)*f[1]^3*f[2]^5*b[1]*l[3]-(11/7)*f[1]^11*b[1]*l[3]*f[2]+(46/7)*f[1]^9*b[1]*l[3]*f[2]^2-13*f[1]^7*b[1]*l[3]*f[2]^3-(3/7)*f[1]*f[2]^5*b[1]*l[3]-(9/7)*f[1]^9*b[1]*l[3]*f[2]+(29/7)*f[1]^7*b[1]*l[3]*f[2]^2-(40/7)*f[1]^5*b[1]*l[3]*f[2]^3';
strings{8}='-(1/7)*f[1]*f[2]*b[1]*u[1]-(1/7)*f[1]^3*f[2]*b[1]*u[1]+(1/7)*f[1]^2*f[2]*b[1]*u[2]+(1/7)*f[1]*f[2]^2*b[1]*u[1]-(1/7)*f[1]^4*f[2]^2*l[2]+(1/7)*f[1]^5*f[2]*l[4]+(1/7)*f[1]^4*f[2]^2*l[5]-(1/7)*f[1]^5*f[2]*l[1]+(3/7)*f[1]^3*f[2]^2*l[1]-(3/7)*f[1]^3*f[2]^2*l[4]+(2/7)*f[1]^2*f[2]^3*l[2]-(2/7)*f[1]^2*f[2]^3*l[5]-(2/7)*f[1]*f[2]^3*l[1]+(2/7)*f[1]*f[2]^3*l[4]+(1/7)*f[2]^3*b[1]*l[3]+(1/7)*f[2]*b[1]*l[3]-(1/7)*f[1]^2*f[2]^2*l[2]+(1/7)*f[1]^3*f[2]*l[4]+(1/7)*f[1]^2*f[2]^2*l[5]-(1/7)*f[1]^3*f[2]*l[1]+(1/7)*f[1]*f[2]^2*l[1]-(1/7)*f[1]*f[2]^2*l[4]+(1/7)*f[1]*f[2]*l[4]-(1/7)*f[1]*f[2]*l[1]+(1/7)*f[1]^2*f[2]*b[1]*l[3]-(2/7)*f[1]^2*f[2]^2*b[1]*l[3]+(1/7)*f[1]^4*f[2]*b[1]*l[3]-(1/7)*f[2]^4*l[2]+(1/7)*f[2]^4*l[5]-(1/7)*f[2]^2*l[2]+(1/7)*f[2]^2*l[5]-(1/7)*f[2]^2*b[1]*u[2]-(1/7)*f[2]*y[1]-(1/7)*f[2]^8*l[2]-(1/7)*f[2]^6*l[2]+(13/7)*f[1]^3*f[2]^4*l[1]-(13/7)*f[1]^3*f[2]^4*l[4]+f[1]^7*f[2]^2*l[1]-f[1]^7*f[2]^2*l[4]-(6/7)*f[1]^2*f[2]^5*l[5]+(1/7)*f[1]^8*f[2]^2*l[5]+(5/7)*f[1]^5*f[2]^2*l[1]-(5/7)*f[1]^5*f[2]^2*l[4]+(2/7)*f[1]*f[2]^4*l[1]-(2/7)*f[1]*f[2]^4*l[4]+(1/7)*f[1]^6*f[2]^2*l[5]-(1/7)*f[1]^7*f[2]*l[1]+(1/7)*f[1]^7*f[2]*l[4]-(2/7)*y[4]*f[1]*f[2]^2+(1/7)*y[4]*f[1]^3*f[2]+f[1]^3*f[2]^3*l[4]-(4/7)*f[1]^4*f[2]^3*l[5]+(4/7)*f[1]^2*f[2]^4*l[5]-f[1]^3*f[2]^3*l[1]-(1/7)*y[3]*f[1]^2*f[2]+(1/7)*y[2]*f[1]*f[2]+(1/7)*f[2]^7*b[1]*l[3]-(34/7)*f[1]^3*f[2]^6*l[4]-(12/7)*f[1]^2*f[2]^7*l[5]-(4/7)*f[1]*f[2]^7*l[1]+(34/7)*f[1]^3*f[2]^6*l[1]+(46/7)*f[1]^9*f[2]^3*l[4]-(10/7)*f[1]^10*f[2]^3*l[5]+(37/7)*f[1]^8*f[2]^4*l[5]-(46/7)*f[1]^9*f[2]^3*l[1]+13*f[1]^7*f[2]^4*l[1]-13*f[1]^7*f[2]^4*l[4]-(62/7)*f[1]^6*f[2]^5*l[5]-(86/7)*f[1]^5*f[2]^5*l[1]+(86/7)*f[1]^5*f[2]^5*l[4]+(11/7)*f[1]^11*f[2]^2*l[1]-(11/7)*f[1]^11*f[2]^2*l[4]+(46/7)*f[1]^4*f[2]^6*l[5]+(1/7)*f[1]^12*f[2]^2*l[5]-(1/7)*f[1]^13*f[2]*l[1]+(1/7)*f[1]^13*f[2]*l[4]+(5/7)*y[7]*f[1]^4*f[2]^2-(1/7)*y[7]*f[1]^6*f[2]-(6/7)*y[7]*f[1]^2*f[2]^3+(9/7)*f[1]^2*f[2]^6*l[5]+(3/7)*f[1]*f[2]^6*l[1]-(3/7)*f[1]*f[2]^6*l[4]+(29/7)*f[1]^7*f[2]^3*l[4]-(8/7)*f[1]^8*f[2]^3*l[5]+(22/7)*f[1]^6*f[2]^4*l[5]-(29/7)*f[1]^7*f[2]^3*l[1]+(40/7)*f[1]^5*f[2]^4*l[1]-(40/7)*f[1]^5*f[2]^4*l[4]-(24/7)*f[1]^4*f[2]^5*l[5]+(9/7)*f[1]^9*f[2]^2*l[1]-(9/7)*f[1]^9*f[2]^2*l[4]-(22/7)*f[1]^3*f[2]^5*l[1]+(22/7)*f[1]^3*f[2]^5*l[4]+(1/7)*f[1]^10*f[2]^2*l[5]-(1/7)*f[1]^11*f[2]*l[1]+(1/7)*f[1]^11*f[2]*l[4]-(4/7)*y[6]*f[1]^3*f[2]^2+(1/7)*y[6]*f[1]^5*f[2]+(3/7)*y[6]*f[1]*f[2]^3+(1/7)*f[2]^5*b[1]*l[3]-(1/7)*f[2]^4*b[1]*u[2]+(1/7)*f[2]^3*b[1]*u[4]-(1/7)*f[1]^9*f[2]*l[1]+(1/7)*f[1]^9*f[2]*l[4]-(3/7)*f[1]*f[2]^5*l[1]+(3/7)*f[1]*f[2]^5*l[4]+(3/7)*y[5]*f[1]^2*f[2]^2-(1/7)*y[5]*f[1]^4*f[2]+(16/7)*f[1]^5*f[2]^3*l[4]-(6/7)*f[1]^6*f[2]^3*l[5]+(11/7)*f[1]^4*f[2]^4*l[5]-(16/7)*f[1]^5*f[2]^3*l[1]-(1/7)*f[2]^6*b[1]*u[2]+(1/7)*f[2]^5*b[1]*u[4]-(1/7)*f[2]^4*b[1]*u[6]+(4/7)*f[1]*f[2]^7*l[4]+(12/7)*f[1]^2*f[2]^7*l[2]+(1/7)*f[2]^8*l[5]-(9/7)*f[1]^2*f[2]^6*l[2]+(1/7)*y[7]*f[2]^4-(37/7)*f[1]^8*f[2]^4*l[2]+(10/7)*f[1]^10*f[2]^3*l[2]+(62/7)*f[1]^6*f[2]^5*l[2]-(46/7)*f[1]^4*f[2]^6*l[2]-(1/7)*f[1]^12*f[2]^2*l[2]-(1/7)*y[5]*f[2]^3-(11/7)*f[1]^4*f[2]^4*l[2]+(6/7)*f[1]^6*f[2]^3*l[2]+(6/7)*f[1]^2*f[2]^5*l[2]-(1/7)*f[1]^8*f[2]^2*l[2]+(1/7)*f[2]^6*l[5]-(22/7)*f[1]^6*f[2]^4*l[2]+(8/7)*f[1]^8*f[2]^3*l[2]+(24/7)*f[1]^4*f[2]^5*l[2]-(1/7)*f[1]^10*f[2]^2*l[2]-(4/7)*f[1]^2*f[2]^4*l[2]+(4/7)*f[1]^4*f[2]^3*l[2]-(1/7)*f[1]^6*f[2]^2*l[2]+(1/7)*y[3]*f[2]^2-(24/7)*f[1]^4*f[2]^4*b[1]*l[3]+(22/7)*f[1]^6*f[2]^3*b[1]*l[3]-f[1]^3*f[2]^3*b[1]*u[3]-(16/7)*f[1]^5*f[2]^3*b[1]*u[1]+f[1]^7*f[2]^2*b[1]*u[1]+(13/7)*f[1]^3*f[2]^4*b[1]*u[1]-(1/7)*f[2]^3*f[1]*b[1]*u[3]-(1/7)*f[1]^7*f[2]*b[1]*u[1]+(1/7)*f[1]^4*f[2]*b[1]*u[4]+(2/7)*f[1]*f[2]^4*b[1]*u[1]-(6/7)*f[1]^6*f[2]^2*b[1]*l[3]-(6/7)*f[1]^2*f[2]^4*b[1]*l[3]+(11/7)*f[1]^4*f[2]^3*b[1]*l[3]-(4/7)*f[1]^4*f[2]^2*b[1]*u[2]+(4/7)*f[1]^2*f[2]^3*b[1]*u[2]+(3/7)*f[1]^3*f[2]^2*b[1]*u[3]-(3/7)*f[1]^2*f[2]^2*b[1]*u[4]+(1/7)*f[1]^8*f[2]*b[1]*l[3]+(1/7)*f[1]^6*f[2]*b[1]*u[2]-(1/7)*f[1]^5*f[2]*b[1]*u[3]-f[1]^3*f[2]^3*b[1]*u[1]+(5/7)*f[1]^5*f[2]^2*b[1]*u[1]-(4/7)*f[1]^4*f[2]^2*b[1]*l[3]+(4/7)*f[1]^2*f[2]^3*b[1]*l[3]-(2/7)*f[1]*f[2]^3*b[1]*u[1]+(3/7)*f[1]^3*f[2]^2*b[1]*u[1]-(2/7)*f[1]^2*f[2]^2*b[1]*u[2]+(2/7)*f[1]*f[2]^2*b[1]*u[3]+(1/7)*f[1]^6*f[2]*b[1]*l[3]-(1/7)*f[1]^5*f[2]*b[1]*u[1]+(1/7)*f[1]^4*f[2]*b[1]*u[2]-(1/7)*f[1]^3*f[2]*b[1]*u[3]-(1/7)*f[1]^7*f[2]*b[1]*u[5]+(1/7)*f[1]^8*f[2]*b[1]*u[4]-(1/7)*f[1]^11*f[2]*b[1]*u[1]+(1/7)*f[1]^10*f[2]*b[1]*u[2]-(1/7)*f[1]^9*f[2]*b[1]*u[3]+(1/7)*f[1]^6*f[2]*b[1]*u[6]+(37/7)*f[1]^8*f[2]^3*b[1]*l[3]+(5/7)*f[1]^5*f[2]^2*b[1]*u[5]-(6/7)*f[1]^6*f[2]^2*b[1]*u[4]+(11/7)*f[1]^4*f[2]^3*b[1]*u[4]-(5/7)*f[1]^4*f[2]^2*b[1]*u[6]+(1/7)*f[1]^12*f[2]*b[1]*l[3]+(3/7)*f[1]*f[2]^6*b[1]*u[1]-(10/7)*f[1]^10*f[2]^2*b[1]*l[3]+(46/7)*f[1]^4*f[2]^5*b[1]*l[3]-(62/7)*f[1]^6*f[2]^4*b[1]*l[3]-(24/7)*f[1]^4*f[2]^4*b[1]*u[2]+(9/7)*f[1]^2*f[2]^5*b[1]*u[2]-(16/7)*f[1]^5*f[2]^3*b[1]*u[3]+f[1]^7*f[2]^2*b[1]*u[3]+(13/7)*f[1]^3*f[2]^4*b[1]*u[3]-(2/7)*f[1]*f[2]^5*b[1]*u[3]-(29/7)*f[1]^7*f[2]^3*b[1]*u[1]+(9/7)*f[1]^9*f[2]^2*b[1]*u[1]+(40/7)*f[1]^5*f[2]^4*b[1]*u[1]-(22/7)*f[1]^3*f[2]^5*b[1]*u[1]+(22/7)*f[1]^6*f[2]^3*b[1]*u[2]-(8/7)*f[1]^8*f[2]^2*b[1]*u[2]+(9/7)*f[1]^2*f[2]^5*b[1]*l[3]+(3/7)*f[1]*f[2]^4*b[1]*u[3]-(3/7)*f[1]*f[2]^5*b[1]*u[1]+(3/7)*f[1]^2*f[2]^3*b[1]*u[4]-(3/7)*f[1]*f[2]^3*b[1]*u[5]-(4/7)*f[1]^4*f[2]^2*b[1]*u[4]+(5/7)*f[1]^5*f[2]^2*b[1]*u[3]+(4/7)*f[1]^3*f[2]^2*b[1]*u[5]+(1/7)*f[1]^10*f[2]*b[1]*l[3]+(1/7)*f[1]^8*f[2]*b[1]*u[2]-(1/7)*f[1]^9*f[2]*b[1]*u[1]+(1/7)*f[1]^6*f[2]*b[1]*u[4]-(1/7)*f[1]^7*f[2]*b[1]*u[3]-(1/7)*f[1]^5*f[2]*b[1]*u[5]+(11/7)*f[1]^4*f[2]^3*b[1]*u[2]-(6/7)*f[1]^6*f[2]^2*b[1]*u[2]-(6/7)*f[1]^2*f[2]^4*b[1]*u[2]-(8/7)*f[1]^8*f[2]^2*b[1]*l[3]+(1/7)*f[2]^4*f[1]*b[1]*u[5]-(12/7)*f[1]^2*f[2]^6*b[1]*l[3]-(6/7)*f[1]^3*f[2]^3*b[1]*u[5]-f[1]^2*f[2]^4*b[1]*u[4]+(6/7)*f[1]^2*f[2]^3*b[1]*u[6]';
polysys = lti2polysys(strings,y,u,'nf',2,'nb',1,'nl',5);
% 2nd order OE with 5 samples, Ljung cannot estimate
% ARMAX N=7, na=2 nb=1 nc=1
u = [5.376671395461000 18.338850145950865 -22.588468610036479 8.621733203681206 3.187652398589808 -13.076882963052734 -4.335920223056836];
e = [ 0.084037552975391 -0.088803208232901 0.010009283313932 -0.054452892999055 0.030352079464935 -0.060032656213373 0.048996532117395];
y = [0.084037552975391 1.057962990888381 5.362329081952093 3.058485891740889 1.916642933798528 0.899310014334141 -2.788271756479185];
% y = filter([0 .2],[1 -1.6 .89],u)+filter([1 -.75],[1 -1.6 .89],e);
strings{1}='y[3]+a[1]*y[2]+a[2]*y[1]-b[1]*u[2]-7*l[1]-7*l[2]*c[1]-7*c[1]^2*l[1]';
strings{2}='y[4]+a[1]*y[3]+a[2]*y[2]-b[1]*u[3]-7*l[2]-7*l[3]*c[1]-7*l[1]*c[1]-7*l[2]*c[1]^2';
strings{3}='y[5]+a[1]*y[4]+a[2]*y[3]-b[1]*u[4]-7*l[3]-7*l[4]*c[1]-7*l[2]*c[1]-7*l[3]*c[1]^2';
strings{4}='y[6]+a[1]*y[5]+a[2]*y[4]-b[1]*u[5]-7*l[4]-7*l[5]*c[1]-7*l[3]*c[1]-7*l[4]*c[1]^2';
strings{5}='y[7]+a[1]*y[6]+a[2]*y[5]-b[1]*u[6]-7*l[5]-7*l[4]*c[1]-7*l[5]*c[1]^2';
strings{6}='l[1]*y[2]+l[2]*y[3]+l[3]*y[4]+l[4]*y[5]+l[5]*y[6]';
strings{7}='l[1]*y[1]+l[2]*y[2]+l[3]*y[3]+l[4]*y[4]+l[5]*y[5]';
strings{8}='-l[1]*u[2]-l[2]*u[3]-l[3]*u[4]-l[4]*u[5]-l[5]*u[6]';
strings{9}='-7*l[1]^2*c[1]-7*l[2]*l[1]-7*l[2]^2*c[1]-7*l[3]*l[2]-7*l[3]^2*c[1]-7*l[4]*l[3]-7*l[4]^2*c[1]-7*l[5]*l[4]-7*l[5]^2*c[1]';
polysys = lti2polysys(strings,y,u,'na',2,'nb',1,'nc',1,'nl',5);
Vstring='(7/2)*l[1]^2*c[1]^2+(7/2)*l[1]^2+7*l[1]*l[2]*c[1]+(7/2)*l[2]^2*c[1]^2+(7/2)*l[2]^2+7*l[2]*l[3]*c[1]+(7/2)*l[3]^2*c[1]^2+(7/2)*l[3]^2+7*l[3]*l[4]*c[1]+(7/2)*l[4]^2*c[1]^2+(7/2)*l[4]^2+7*l[4]*l[5]*c[1]+(7/2)*l[5]^2*c[1]^2+(7/2)*l[5]^2';
% ARMAX N=6, na=2 nb=1 nc=1, ljung cannot handle
u = [0.105219541681517 0.083164231586952 -0.732361627452833 -0.316986997635078 3.377954632877850 6.993296474977185];
y = [0.058117232267592 -0.198199583660287 -0.181624931008854 -0.076723073431271 -0.338561567715224 0.402196073315222];
% y = filter([0 .2],[1 -1.6 .89],u)+filter([1 -.75],[1 -1.6 .89],e);
e = [0.058117232267592 -0.219243491996590 -0.231928030664330 0.007993371029844 -0.094848098357051 0.041149062142337];
strings{1}='y[3]+a[1]*y[2]+a[2]*y[1]-b[1]*u[2]-6*l[1]-6*l[2]*c[1]-6*c[1]^2*l[1]';
strings{2}='y[4]+a[1]*y[3]+a[2]*y[2]-b[1]*u[3]-6*l[2]-6*l[3]*c[1]-6*l[1]*c[1]-6*l[2]*c[1]^2';
strings{3}='y[5]+a[1]*y[4]+a[2]*y[3]-b[1]*u[4]-6*l[3]-6*l[4]*c[1]-6*l[2]*c[1]-6*l[3]*c[1]^2';
strings{4}='y[6]+a[1]*y[5]+a[2]*y[4]-b[1]*u[5]-6*l[4]-6*l[3]*c[1]-6*l[4]*c[1]^2';
strings{5}='l[1]*y[2]+l[2]*y[3]+l[3]*y[4]+l[4]*y[5]';
strings{6}='l[1]*y[1]+l[2]*y[2]+l[3]*y[3]+l[4]*y[4]';
strings{7}='-l[1]*u[2]-l[2]*u[3]-l[3]*u[4]-l[4]*u[5]';
strings{8}='-6*l[1]^2*c[1]-6*l[2]*l[1]-6*l[2]^2*c[1]-6*l[3]*l[2]-6*l[3]^2*c[1]-6*l[4]*l[3]-6*l[4]^2*c[1]';
polysys = lti2polysys(strings,y,u,'na',2,'nb',1,'nc',1,'nl',4);
Vstring='3*l[1]^2*c[1]^2+3*l[1]^2+6*l[1]*l[2]*c[1]+3*l[2]^2*c[1]^2+3*l[2]^2+6*l[2]*l[3]*c[1]+3*l[3]^2*c[1]^2+3*l[3]^2+6*l[3]*l[4]*c[1]+3*l[4]^2*c[1]^2+3*l[4]^2';
% 2nd order OE N=6, nf=2,nb=1, no white noise input
% y = filter([0 .2],[1 -1.6 .89],uf)+e;
u = [ -0.047729189400468 0.135937653716237 0.093185670161992 -0.878660683496810 1.399702362976676 3.142798207529186];
y = [ -0.018053733513861 0.009040091605463 0.005868889247353 0.047229231184944 -0.106791082029198 0.060085925807587];
% uf = [4.669144356847000 2.105096537274933 8.146490454423697 9.164114038995697 -2.049972800570083 7.647242790797150];
% y = [ 0.058117232267592 0.714585379372810 1.683217470981696 3.870416569029461 6.213372329776512 6.286750540822362];
% e = [ 0.058117232267592 -0.219243491996590 -0.231928030664330 0.007993371029844 -0.094848098357051 0.041149062142337];
strings{1}='y[3]+f[1]*y[2]+f[2]*y[1]-b[1]*u[2]-6*l[1]-6*l[2]*f[1]-6*l[3]*f[2]-6*l[1]*f[1]^2-6*f[1]*l[2]*f[2]-6*f[2]^2*l[1]';
strings{2}='y[4]+f[1]*y[3]+f[2]*y[2]-b[1]*u[3]-6*l[2]-6*l[3]*f[1]-6*l[4]*f[2]-6*l[1]*f[1]-6*l[2]*f[1]^2-6*f[1]*l[3]*f[2]-6*f[2]*l[1]*f[1]-6*l[2]*f[2]^2';
strings{3}='y[5]+f[1]*y[4]+f[2]*y[3]-b[1]*u[4]-6*l[3]-6*l[4]*f[1]-6*l[2]*f[1]-6*l[3]*f[1]^2-6*f[1]*l[4]*f[2]-6*l[1]*f[2]-6*f[1]*l[2]*f[2]-6*l[3]*f[2]^2';
strings{4}='y[6]+f[1]*y[5]+f[2]*y[4]-b[1]*u[5]-6*l[4]-6*l[3]*f[1]-6*l[4]*f[1]^2-6*l[2]*f[2]-6*f[1]*l[3]*f[2]-6*l[4]*f[2]^2';
strings{5}='l[1]*y[2]-6*l[1]^2*f[1]-6*l[1]*l[2]*f[2]+l[2]*y[3]-6*l[2]*l[1]-6*l[2]^2*f[1]-6*l[2]*l[3]*f[2]+l[3]*y[4]-6*l[3]*l[2]-6*l[3]^2*f[1]-6*l[3]*l[4]*f[2]+l[4]*y[5]-6*l[4]*l[3]-6*l[4]^2*f[1]';
strings{6}='l[1]*y[1]-6*l[1]^2*f[2]+l[2]*y[2]-6*l[2]*l[1]*f[1]-6*l[2]^2*f[2]+l[3]*y[3]-6*l[3]*l[1]-6*l[3]*l[2]*f[1]-6*l[3]^2*f[2]+l[4]*y[4]-6*l[4]*l[2]-6*l[4]*l[3]*f[1]-6*l[4]^2*f[2]';
strings{7}='-l[1]*u[2]-l[2]*u[3]-l[3]*u[4]-l[4]*u[5]';
polysys = lti2polysys(strings,y,u,'nb',1,'nf',2,'nl',4);
Vstring='3*l[1]^2*f[2]^2+3*l[1]^2*f[1]^2+6*l[1]*f[1]*l[2]*f[2]+3*l[2]^2*f[2]^2+3*l[1]^2+6*l[2]*l[1]*f[1]+6*l[1]*l[3]*f[2]+3*l[2]^2*f[1]^2+6*l[2]*f[1]*l[3]*f[2]+3*l[3]^2*f[2]^2+3*l[2]^2+6*l[3]*l[2]*f[1]+6*l[2]*l[4]*f[2]+3*l[3]^2*f[1]^2+6*l[3]*f[1]*l[4]*f[2]+3*l[4]^2*f[2]^2+3*l[3]^2+6*l[4]*l[3]*f[1]+3*l[4]^2*f[1]^2+3*l[4]^2';
% OE N=7, nf=2, nb=1
u = [5.376671395461000 18.338850145950865 -22.588468610036479 8.621733203681206 3.187652398589808 -13.076882963052734 -4.335920223056836];
e = [ 0.097601458525137 -0.065840933270162 0.078317019931183 -0.102600253803208 0.055591506772292 -0.085708556912590 -0.086229282617519];
y = [ 0.097601458525137 1.009493345822039 5.466621895668876 3.043946316977745 2.018821321351514 0.892563178137079 -2.883645634124104];
% y = filter([0 .2],[1 -1.6 .89],u) +e;
% filtered white noise input, noise level 1000 smaller than input
u = [ -0.105715036001239 0.524840721552703 -0.961680965189235 0.462166156605002 1.410438100612864 3.279796646902768 5.330227374264688];
y = [ 0.010346930099179 -0.013874155866415 0.068104923542284 -0.056757269494429 -0.074267177564447 0.237870043104374 1.069957338248644];
e = [0.010346930099179 0.007268851333832 -0.003034409247860 0.002938714670967 -0.007872828037586 0.008883956317576 -0.011470701069692];
strings{1} = 'y[3]+f[1]*y[2]+f[2]*y[1]-b[1]*u[2]-7*l[1]-7*l[2]*f[1]-7*l[3]*f[2]-7*l[1]*f[1]^2-7*f[1]*l[2]*f[2]-7*f[2]^2*l[1]';
strings{2} = 'y[4]+f[1]*y[3]+f[2]*y[2]-b[1]*u[3]-7*l[2]-7*l[3]*f[1]-7*l[4]*f[2]-7*l[1]*f[1]-7*l[2]*f[1]^2-7*f[1]*l[3]*f[2]-7*f[2]*l[1]*f[1]-7*l[2]*f[2]^2';
strings{3} = 'y[5]+f[1]*y[4]+f[2]*y[3]-b[1]*u[4]-7*l[3]-7*l[4]*f[1]-7*l[5]*f[2]-7*l[2]*f[1]-7*l[3]*f[1]^2-7*f[1]*l[4]*f[2]-7*l[1]*f[2]-7*f[1]*l[2]*f[2]-7*l[3]*f[2]^2';
strings{4} = 'y[6]+f[1]*y[5]+f[2]*y[4]-b[1]*u[5]-7*l[4]-7*l[5]*f[1]-7*l[3]*f[1]-7*l[4]*f[1]^2-7*f[1]*l[5]*f[2]-7*l[2]*f[2]-7*f[1]*l[3]*f[2]-7*l[4]*f[2]^2';
strings{5} = 'y[7]+f[1]*y[6]+f[2]*y[5]-b[1]*u[6]-7*l[5]-7*l[4]*f[1]-7*l[5]*f[1]^2-7*l[3]*f[2]-7*f[1]*l[4]*f[2]-7*l[5]*f[2]^2';
strings{6} = 'l[1]*y[2]-7*l[1]^2*f[1]-7*l[1]*l[2]*f[2]+l[2]*y[3]-7*l[2]*l[1]-7*l[2]^2*f[1]-7*l[2]*l[3]*f[2]+l[3]*y[4]-7*l[3]*l[2]-7*l[3]^2*f[1]-7*l[3]*l[4]*f[2]+l[4]*y[5]-7*l[4]*l[3]-7*l[4]^2*f[1]-7*l[4]*l[5]*f[2]+l[5]*y[6]-7*l[5]*l[4]-7*l[5]^2*f[1]';
strings{7} = 'l[1]*y[1]-7*l[1]^2*f[2]+l[2]*y[2]-7*l[2]*l[1]*f[1]-7*l[2]^2*f[2]+l[3]*y[3]-7*l[3]*l[1]-7*l[3]*l[2]*f[1]-7*l[3]^2*f[2]+l[4]*y[4]-7*l[4]*l[2]-7*l[4]*l[3]*f[1]-7*l[4]^2*f[2]+l[5]*y[5]-7*l[5]*l[3]-7*l[5]*l[4]*f[1]-7*l[5]^2*f[2]';
strings{8} = '-l[1]*u[2]-l[2]*u[3]-l[3]*u[4]-l[4]*u[5]-l[5]*u[6]';
polysys = lti2polysys(strings,y,u,'nf',2,'nb',1,'nl',5);
Vstring='(7/2)*l[1]^2+(7/2)*l[2]^2+7*l[5]*l[4]*f[1]+7*l[2]*l[1]*f[1]+7*l[3]*l[2]*f[1]+7*l[4]*l[3]*f[1]+7*l[1]*f[1]*l[2]*f[2]+7*l[2]*f[1]*l[3]*f[2]+7*l[3]*f[1]*l[4]*f[2]+7*l[4]*f[1]*l[5]*f[2]+7*l[3]*l[5]*f[2]+7*l[1]*l[3]*f[2]+7*l[2]*l[4]*f[2]+(7/2)*l[1]^2*f[2]^2+(7/2)*l[1]^2*f[1]^2+(7/2)*l[2]^2*f[2]^2+(7/2)*l[2]^2*f[1]^2+(7/2)*l[3]^2*f[2]^2+(7/2)*l[3]^2*f[1]^2+(7/2)*l[4]^2*f[2]^2+(7/2)*l[4]^2*f[1]^2+(7/2)*l[5]^2*f[2]^2+(7/2)*l[5]^2*f[1]^2+(7/2)*l[5]^2+(7/2)*l[4]^2+(7/2)*l[3]^2';
% OE N=100, nf=2, nb=1
% y = filter([0 .2],[1 -1.6 .89],u) +e;
u=100*randn(1,100);
e = .1*randn(1,100);
y = filter([0 .2],[1 -1.6 .89],u) +e;
strings{1}='y[3]+f[1]*y[2]+f[2]*y[1]-b[1]*u[2]-100*l[1]-100*l[2]*f[1]-100*l[3]*f[2]-100*l[1]*f[1]^2-100*f[1]*l[2]*f[2]-100*f[2]^2*l[1]';
strings{2}='y[4]+f[1]*y[3]+f[2]*y[2]-b[1]*u[3]-100*l[2]-100*l[3]*f[1]-100*l[4]*f[2]-100*l[1]*f[1]-100*l[2]*f[1]^2-100*f[1]*l[3]*f[2]-100*f[2]*l[1]*f[1]-100*l[2]*f[2]^2';
strings{3}='y[5]+f[1]*y[4]+f[2]*y[3]-b[1]*u[4]-100*l[3]-100*l[4]*f[1]-100*l[5]*f[2]-100*l[2]*f[1]-100*l[3]*f[1]^2-100*f[1]*l[4]*f[2]-100*l[1]*f[2]-100*f[1]*l[2]*f[2]-100*l[3]*f[2]^2';
strings{4}='y[6]+f[1]*y[5]+f[2]*y[4]-b[1]*u[5]-100*l[4]-100*l[5]*f[1]-100*l[6]*f[2]-100*l[3]*f[1]-100*l[4]*f[1]^2-100*f[1]*l[5]*f[2]-100*l[2]*f[2]-100*f[1]*l[3]*f[2]-100*l[4]*f[2]^2';
strings{5}='y[7]+f[1]*y[6]+f[2]*y[5]-b[1]*u[6]-100*l[5]-100*l[6]*f[1]-100*l[7]*f[2]-100*l[4]*f[1]-100*l[5]*f[1]^2-100*f[1]*l[6]*f[2]-100*l[3]*f[2]-100*f[1]*l[4]*f[2]-100*l[5]*f[2]^2';
strings{6}='y[8]+f[1]*y[7]+f[2]*y[6]-b[1]*u[7]-100*l[6]-100*l[7]*f[1]-100*l[8]*f[2]-100*l[5]*f[1]-100*l[6]*f[1]^2-100*f[1]*l[7]*f[2]-100*l[4]*f[2]-100*f[1]*l[5]*f[2]-100*l[6]*f[2]^2';
strings{7}='y[9]+f[1]*y[8]+f[2]*y[7]-b[1]*u[8]-100*l[7]-100*l[8]*f[1]-100*l[9]*f[2]-100*l[6]*f[1]-100*l[7]*f[1]^2-100*f[1]*l[8]*f[2]-100*l[5]*f[2]-100*f[1]*l[6]*f[2]-100*l[7]*f[2]^2';
strings{8}='y[10]+f[1]*y[9]+f[2]*y[8]-b[1]*u[9]-100*l[8]-100*l[9]*f[1]-100*l[10]*f[2]-100*l[7]*f[1]-100*l[8]*f[1]^2-100*f[1]*l[9]*f[2]-100*l[6]*f[2]-100*f[1]*l[7]*f[2]-100*l[8]*f[2]^2';
strings{9}='y[11]+f[1]*y[10]+f[2]*y[9]-b[1]*u[10]-100*l[9]-100*l[10]*f[1]-100*l[11]*f[2]-100*l[8]*f[1]-100*l[9]*f[1]^2-100*f[1]*l[10]*f[2]-100*l[7]*f[2]-100*f[1]*l[8]*f[2]-100*l[9]*f[2]^2';
strings{10}='y[12]+f[1]*y[11]+f[2]*y[10]-b[1]*u[11]-100*l[10]-100*l[11]*f[1]-100*l[12]*f[2]-100*l[9]*f[1]-100*l[10]*f[1]^2-100*f[1]*l[11]*f[2]-100*l[8]*f[2]-100*f[1]*l[9]*f[2]-100*l[10]*f[2]^2';
strings{11}='y[13]+f[1]*y[12]+f[2]*y[11]-b[1]*u[12]-100*l[11]-100*l[12]*f[1]-100*l[13]*f[2]-100*l[10]*f[1]-100*l[11]*f[1]^2-100*f[1]*l[12]*f[2]-100*l[9]*f[2]-100*f[1]*l[10]*f[2]-100*l[11]*f[2]^2';
strings{12}='y[14]+f[1]*y[13]+f[2]*y[12]-b[1]*u[13]-100*l[12]-100*l[13]*f[1]-100*l[14]*f[2]-100*l[11]*f[1]-100*l[12]*f[1]^2-100*f[1]*l[13]*f[2]-100*l[10]*f[2]-100*f[1]*l[11]*f[2]-100*l[12]*f[2]^2';
strings{13}='y[15]+f[1]*y[14]+f[2]*y[13]-b[1]*u[14]-100*l[13]-100*l[14]*f[1]-100*l[15]*f[2]-100*l[12]*f[1]-100*l[13]*f[1]^2-100*f[1]*l[14]*f[2]-100*l[11]*f[2]-100*f[1]*l[12]*f[2]-100*l[13]*f[2]^2';
strings{14}='y[16]+f[1]*y[15]+f[2]*y[14]-b[1]*u[15]-100*l[14]-100*l[15]*f[1]-100*l[16]*f[2]-100*l[13]*f[1]-100*l[14]*f[1]^2-100*f[1]*l[15]*f[2]-100*l[12]*f[2]-100*f[1]*l[13]*f[2]-100*l[14]*f[2]^2';
strings{15}='y[17]+f[1]*y[16]+f[2]*y[15]-b[1]*u[16]-100*l[15]-100*l[16]*f[1]-100*l[17]*f[2]-100*l[14]*f[1]-100*l[15]*f[1]^2-100*f[1]*l[16]*f[2]-100*l[13]*f[2]-100*f[1]*l[14]*f[2]-100*l[15]*f[2]^2';
strings{16}='y[18]+f[1]*y[17]+f[2]*y[16]-b[1]*u[17]-100*l[16]-100*l[17]*f[1]-100*l[18]*f[2]-100*l[15]*f[1]-100*l[16]*f[1]^2-100*f[1]*l[17]*f[2]-100*l[14]*f[2]-100*f[1]*l[15]*f[2]-100*l[16]*f[2]^2';
strings{17}='y[19]+f[1]*y[18]+f[2]*y[17]-b[1]*u[18]-100*l[17]-100*l[18]*f[1]-100*l[19]*f[2]-100*l[16]*f[1]-100*l[17]*f[1]^2-100*f[1]*l[18]*f[2]-100*l[15]*f[2]-100*f[1]*l[16]*f[2]-100*l[17]*f[2]^2';
strings{18}='y[20]+f[1]*y[19]+f[2]*y[18]-b[1]*u[19]-100*l[18]-100*l[19]*f[1]-100*l[20]*f[2]-100*l[17]*f[1]-100*l[18]*f[1]^2-100*f[1]*l[19]*f[2]-100*l[16]*f[2]-100*f[1]*l[17]*f[2]-100*l[18]*f[2]^2';
strings{19}='y[21]+f[1]*y[20]+f[2]*y[19]-b[1]*u[20]-100*l[19]-100*l[20]*f[1]-100*l[21]*f[2]-100*l[18]*f[1]-100*l[19]*f[1]^2-100*f[1]*l[20]*f[2]-100*l[17]*f[2]-100*f[1]*l[18]*f[2]-100*l[19]*f[2]^2';
strings{20}='y[22]+f[1]*y[21]+f[2]*y[20]-b[1]*u[21]-100*l[20]-100*l[21]*f[1]-100*l[22]*f[2]-100*l[19]*f[1]-100*l[20]*f[1]^2-100*f[1]*l[21]*f[2]-100*l[18]*f[2]-100*f[1]*l[19]*f[2]-100*l[20]*f[2]^2';
strings{21}='y[23]+f[1]*y[22]+f[2]*y[21]-b[1]*u[22]-100*l[21]-100*l[22]*f[1]-100*l[23]*f[2]-100*l[20]*f[1]-100*l[21]*f[1]^2-100*f[1]*l[22]*f[2]-100*l[19]*f[2]-100*f[1]*l[20]*f[2]-100*l[21]*f[2]^2';
strings{22}='y[24]+f[1]*y[23]+f[2]*y[22]-b[1]*u[23]-100*l[22]-100*l[23]*f[1]-100*l[24]*f[2]-100*l[21]*f[1]-100*l[22]*f[1]^2-100*f[1]*l[23]*f[2]-100*l[20]*f[2]-100*f[1]*l[21]*f[2]-100*l[22]*f[2]^2';
strings{23}='y[25]+f[1]*y[24]+f[2]*y[23]-b[1]*u[24]-100*l[23]-100*l[24]*f[1]-100*l[25]*f[2]-100*l[22]*f[1]-100*l[23]*f[1]^2-100*f[1]*l[24]*f[2]-100*l[21]*f[2]-100*f[1]*l[22]*f[2]-100*l[23]*f[2]^2';
strings{24}='y[26]+f[1]*y[25]+f[2]*y[24]-b[1]*u[25]-100*l[24]-100*l[25]*f[1]-100*l[26]*f[2]-100*l[23]*f[1]-100*l[24]*f[1]^2-100*f[1]*l[25]*f[2]-100*l[22]*f[2]-100*f[1]*l[23]*f[2]-100*l[24]*f[2]^2';
strings{25}='y[27]+f[1]*y[26]+f[2]*y[25]-b[1]*u[26]-100*l[25]-100*l[26]*f[1]-100*l[27]*f[2]-100*l[24]*f[1]-100*l[25]*f[1]^2-100*f[1]*l[26]*f[2]-100*l[23]*f[2]-100*f[1]*l[24]*f[2]-100*l[25]*f[2]^2';
strings{26}='y[28]+f[1]*y[27]+f[2]*y[26]-b[1]*u[27]-100*l[26]-100*l[27]*f[1]-100*l[28]*f[2]-100*l[25]*f[1]-100*l[26]*f[1]^2-100*f[1]*l[27]*f[2]-100*l[24]*f[2]-100*f[1]*l[25]*f[2]-100*l[26]*f[2]^2';
strings{27}='y[29]+f[1]*y[28]+f[2]*y[27]-b[1]*u[28]-100*l[27]-100*l[28]*f[1]-100*l[29]*f[2]-100*l[26]*f[1]-100*l[27]*f[1]^2-100*f[1]*l[28]*f[2]-100*l[25]*f[2]-100*f[1]*l[26]*f[2]-100*l[27]*f[2]^2';
strings{28}='y[30]+f[1]*y[29]+f[2]*y[28]-b[1]*u[29]-100*l[28]-100*l[29]*f[1]-100*l[30]*f[2]-100*l[27]*f[1]-100*l[28]*f[1]^2-100*f[1]*l[29]*f[2]-100*l[26]*f[2]-100*f[1]*l[27]*f[2]-100*l[28]*f[2]^2';
strings{29}='y[31]+f[1]*y[30]+f[2]*y[29]-b[1]*u[30]-100*l[29]-100*l[30]*f[1]-100*l[31]*f[2]-100*l[28]*f[1]-100*l[29]*f[1]^2-100*f[1]*l[30]*f[2]-100*l[27]*f[2]-100*f[1]*l[28]*f[2]-100*l[29]*f[2]^2';
strings{30}='y[32]+f[1]*y[31]+f[2]*y[30]-b[1]*u[31]-100*l[30]-100*l[31]*f[1]-100*l[32]*f[2]-100*l[29]*f[1]-100*l[30]*f[1]^2-100*f[1]*l[31]*f[2]-100*l[28]*f[2]-100*f[1]*l[29]*f[2]-100*l[30]*f[2]^2';
strings{31}='y[33]+f[1]*y[32]+f[2]*y[31]-b[1]*u[32]-100*l[31]-100*l[32]*f[1]-100*l[33]*f[2]-100*l[30]*f[1]-100*l[31]*f[1]^2-100*f[1]*l[32]*f[2]-100*l[29]*f[2]-100*f[1]*l[30]*f[2]-100*l[31]*f[2]^2';
strings{32}='y[34]+f[1]*y[33]+f[2]*y[32]-b[1]*u[33]-100*l[32]-100*l[33]*f[1]-100*l[34]*f[2]-100*l[31]*f[1]-100*l[32]*f[1]^2-100*f[1]*l[33]*f[2]-100*l[30]*f[2]-100*f[1]*l[31]*f[2]-100*l[32]*f[2]^2';
strings{33}='y[35]+f[1]*y[34]+f[2]*y[33]-b[1]*u[34]-100*l[33]-100*l[34]*f[1]-100*l[35]*f[2]-100*l[32]*f[1]-100*l[33]*f[1]^2-100*f[1]*l[34]*f[2]-100*l[31]*f[2]-100*f[1]*l[32]*f[2]-100*l[33]*f[2]^2';
strings{34}='y[36]+f[1]*y[35]+f[2]*y[34]-b[1]*u[35]-100*l[34]-100*l[35]*f[1]-100*l[36]*f[2]-100*l[33]*f[1]-100*l[34]*f[1]^2-100*f[1]*l[35]*f[2]-100*l[32]*f[2]-100*f[1]*l[33]*f[2]-100*l[34]*f[2]^2';
strings{35}='y[37]+f[1]*y[36]+f[2]*y[35]-b[1]*u[36]-100*l[35]-100*l[36]*f[1]-100*l[37]*f[2]-100*l[34]*f[1]-100*l[35]*f[1]^2-100*f[1]*l[36]*f[2]-100*l[33]*f[2]-100*f[1]*l[34]*f[2]-100*l[35]*f[2]^2';
strings{36}='y[38]+f[1]*y[37]+f[2]*y[36]-b[1]*u[37]-100*l[36]-100*l[37]*f[1]-100*l[38]*f[2]-100*l[35]*f[1]-100*l[36]*f[1]^2-100*f[1]*l[37]*f[2]-100*l[34]*f[2]-100*f[1]*l[35]*f[2]-100*l[36]*f[2]^2';
strings{37}='y[39]+f[1]*y[38]+f[2]*y[37]-b[1]*u[38]-100*l[37]-100*l[38]*f[1]-100*l[39]*f[2]-100*l[36]*f[1]-100*l[37]*f[1]^2-100*f[1]*l[38]*f[2]-100*l[35]*f[2]-100*f[1]*l[36]*f[2]-100*l[37]*f[2]^2';
strings{38}='y[40]+f[1]*y[39]+f[2]*y[38]-b[1]*u[39]-100*l[38]-100*l[39]*f[1]-100*l[40]*f[2]-100*l[37]*f[1]-100*l[38]*f[1]^2-100*f[1]*l[39]*f[2]-100*l[36]*f[2]-100*f[1]*l[37]*f[2]-100*l[38]*f[2]^2';
strings{39}='y[41]+f[1]*y[40]+f[2]*y[39]-b[1]*u[40]-100*l[39]-100*l[40]*f[1]-100*l[41]*f[2]-100*l[38]*f[1]-100*l[39]*f[1]^2-100*f[1]*l[40]*f[2]-100*l[37]*f[2]-100*f[1]*l[38]*f[2]-100*l[39]*f[2]^2';
strings{40}='y[42]+f[1]*y[41]+f[2]*y[40]-b[1]*u[41]-100*l[40]-100*l[41]*f[1]-100*l[42]*f[2]-100*l[39]*f[1]-100*l[40]*f[1]^2-100*f[1]*l[41]*f[2]-100*l[38]*f[2]-100*f[1]*l[39]*f[2]-100*l[40]*f[2]^2';
strings{41}='y[43]+f[1]*y[42]+f[2]*y[41]-b[1]*u[42]-100*l[41]-100*l[42]*f[1]-100*l[43]*f[2]-100*l[40]*f[1]-100*l[41]*f[1]^2-100*f[1]*l[42]*f[2]-100*l[39]*f[2]-100*f[1]*l[40]*f[2]-100*l[41]*f[2]^2';
strings{42}='y[44]+f[1]*y[43]+f[2]*y[42]-b[1]*u[43]-100*l[42]-100*l[43]*f[1]-100*l[44]*f[2]-100*l[41]*f[1]-100*l[42]*f[1]^2-100*f[1]*l[43]*f[2]-100*l[40]*f[2]-100*f[1]*l[41]*f[2]-100*l[42]*f[2]^2';
strings{43}='y[45]+f[1]*y[44]+f[2]*y[43]-b[1]*u[44]-100*l[43]-100*l[44]*f[1]-100*l[45]*f[2]-100*l[42]*f[1]-100*l[43]*f[1]^2-100*f[1]*l[44]*f[2]-100*l[41]*f[2]-100*f[1]*l[42]*f[2]-100*l[43]*f[2]^2';
strings{44}='y[46]+f[1]*y[45]+f[2]*y[44]-b[1]*u[45]-100*l[44]-100*l[45]*f[1]-100*l[46]*f[2]-100*l[43]*f[1]-100*l[44]*f[1]^2-100*f[1]*l[45]*f[2]-100*l[42]*f[2]-100*f[1]*l[43]*f[2]-100*l[44]*f[2]^2';
strings{45}='y[47]+f[1]*y[46]+f[2]*y[45]-b[1]*u[46]-100*l[45]-100*l[46]*f[1]-100*l[47]*f[2]-100*l[44]*f[1]-100*l[45]*f[1]^2-100*f[1]*l[46]*f[2]-100*l[43]*f[2]-100*f[1]*l[44]*f[2]-100*l[45]*f[2]^2';
strings{46}='y[48]+f[1]*y[47]+f[2]*y[46]-b[1]*u[47]-100*l[46]-100*l[47]*f[1]-100*l[48]*f[2]-100*l[45]*f[1]-100*l[46]*f[1]^2-100*f[1]*l[47]*f[2]-100*l[44]*f[2]-100*f[1]*l[45]*f[2]-100*l[46]*f[2]^2';
strings{47}='y[49]+f[1]*y[48]+f[2]*y[47]-b[1]*u[48]-100*l[47]-100*l[48]*f[1]-100*l[49]*f[2]-100*l[46]*f[1]-100*l[47]*f[1]^2-100*f[1]*l[48]*f[2]-100*l[45]*f[2]-100*f[1]*l[46]*f[2]-100*l[47]*f[2]^2';
strings{48}='y[50]+f[1]*y[49]+f[2]*y[48]-b[1]*u[49]-100*l[48]-100*l[49]*f[1]-100*l[50]*f[2]-100*l[47]*f[1]-100*l[48]*f[1]^2-100*f[1]*l[49]*f[2]-100*l[46]*f[2]-100*f[1]*l[47]*f[2]-100*l[48]*f[2]^2';
strings{49}='y[51]+f[1]*y[50]+f[2]*y[49]-b[1]*u[50]-100*l[49]-100*l[50]*f[1]-100*l[51]*f[2]-100*l[48]*f[1]-100*l[49]*f[1]^2-100*f[1]*l[50]*f[2]-100*l[47]*f[2]-100*f[1]*l[48]*f[2]-100*l[49]*f[2]^2';
strings{50}='y[52]+f[1]*y[51]+f[2]*y[50]-b[1]*u[51]-100*l[50]-100*l[51]*f[1]-100*l[52]*f[2]-100*l[49]*f[1]-100*l[50]*f[1]^2-100*f[1]*l[51]*f[2]-100*l[48]*f[2]-100*f[1]*l[49]*f[2]-100*l[50]*f[2]^2';
strings{51}='y[53]+f[1]*y[52]+f[2]*y[51]-b[1]*u[52]-100*l[51]-100*l[52]*f[1]-100*l[53]*f[2]-100*l[50]*f[1]-100*l[51]*f[1]^2-100*f[1]*l[52]*f[2]-100*l[49]*f[2]-100*f[1]*l[50]*f[2]-100*l[51]*f[2]^2';
strings{52}='y[54]+f[1]*y[53]+f[2]*y[52]-b[1]*u[53]-100*l[52]-100*l[53]*f[1]-100*l[54]*f[2]-100*l[51]*f[1]-100*l[52]*f[1]^2-100*f[1]*l[53]*f[2]-100*l[50]*f[2]-100*f[1]*l[51]*f[2]-100*l[52]*f[2]^2';
strings{53}='y[55]+f[1]*y[54]+f[2]*y[53]-b[1]*u[54]-100*l[53]-100*l[54]*f[1]-100*l[55]*f[2]-100*l[52]*f[1]-100*l[53]*f[1]^2-100*f[1]*l[54]*f[2]-100*l[51]*f[2]-100*f[1]*l[52]*f[2]-100*l[53]*f[2]^2';
strings{54}='y[56]+f[1]*y[55]+f[2]*y[54]-b[1]*u[55]-100*l[54]-100*l[55]*f[1]-100*l[56]*f[2]-100*l[53]*f[1]-100*l[54]*f[1]^2-100*f[1]*l[55]*f[2]-100*l[52]*f[2]-100*f[1]*l[53]*f[2]-100*l[54]*f[2]^2';
strings{55}='y[57]+f[1]*y[56]+f[2]*y[55]-b[1]*u[56]-100*l[55]-100*l[56]*f[1]-100*l[57]*f[2]-100*l[54]*f[1]-100*l[55]*f[1]^2-100*f[1]*l[56]*f[2]-100*l[53]*f[2]-100*f[1]*l[54]*f[2]-100*l[55]*f[2]^2';
strings{56}='y[58]+f[1]*y[57]+f[2]*y[56]-b[1]*u[57]-100*l[56]-100*l[57]*f[1]-100*l[58]*f[2]-100*l[55]*f[1]-100*l[56]*f[1]^2-100*f[1]*l[57]*f[2]-100*l[54]*f[2]-100*f[1]*l[55]*f[2]-100*l[56]*f[2]^2';
strings{57}='y[59]+f[1]*y[58]+f[2]*y[57]-b[1]*u[58]-100*l[57]-100*l[58]*f[1]-100*l[59]*f[2]-100*l[56]*f[1]-100*l[57]*f[1]^2-100*f[1]*l[58]*f[2]-100*l[55]*f[2]-100*f[1]*l[56]*f[2]-100*l[57]*f[2]^2';
strings{58}='y[60]+f[1]*y[59]+f[2]*y[58]-b[1]*u[59]-100*l[58]-100*l[59]*f[1]-100*l[60]*f[2]-100*l[57]*f[1]-100*l[58]*f[1]^2-100*f[1]*l[59]*f[2]-100*l[56]*f[2]-100*f[1]*l[57]*f[2]-100*l[58]*f[2]^2';
strings{59}='y[61]+f[1]*y[60]+f[2]*y[59]-b[1]*u[60]-100*l[59]-100*l[60]*f[1]-100*l[61]*f[2]-100*l[58]*f[1]-100*l[59]*f[1]^2-100*f[1]*l[60]*f[2]-100*l[57]*f[2]-100*f[1]*l[58]*f[2]-100*l[59]*f[2]^2';
strings{60}='y[62]+f[1]*y[61]+f[2]*y[60]-b[1]*u[61]-100*l[60]-100*l[61]*f[1]-100*l[62]*f[2]-100*l[59]*f[1]-100*l[60]*f[1]^2-100*f[1]*l[61]*f[2]-100*l[58]*f[2]-100*f[1]*l[59]*f[2]-100*l[60]*f[2]^2';
strings{61}='y[63]+f[1]*y[62]+f[2]*y[61]-b[1]*u[62]-100*l[61]-100*l[62]*f[1]-100*l[63]*f[2]-100*l[60]*f[1]-100*l[61]*f[1]^2-100*f[1]*l[62]*f[2]-100*l[59]*f[2]-100*f[1]*l[60]*f[2]-100*l[61]*f[2]^2';
strings{62}='y[64]+f[1]*y[63]+f[2]*y[62]-b[1]*u[63]-100*l[62]-100*l[63]*f[1]-100*l[64]*f[2]-100*l[61]*f[1]-100*l[62]*f[1]^2-100*f[1]*l[63]*f[2]-100*l[60]*f[2]-100*f[1]*l[61]*f[2]-100*l[62]*f[2]^2';
strings{63}='y[65]+f[1]*y[64]+f[2]*y[63]-b[1]*u[64]-100*l[63]-100*l[64]*f[1]-100*l[65]*f[2]-100*l[62]*f[1]-100*l[63]*f[1]^2-100*f[1]*l[64]*f[2]-100*l[61]*f[2]-100*f[1]*l[62]*f[2]-100*l[63]*f[2]^2';
strings{64}='y[66]+f[1]*y[65]+f[2]*y[64]-b[1]*u[65]-100*l[64]-100*l[65]*f[1]-100*l[66]*f[2]-100*l[63]*f[1]-100*l[64]*f[1]^2-100*f[1]*l[65]*f[2]-100*l[62]*f[2]-100*f[1]*l[63]*f[2]-100*l[64]*f[2]^2';
strings{65}='y[67]+f[1]*y[66]+f[2]*y[65]-b[1]*u[66]-100*l[65]-100*l[66]*f[1]-100*l[67]*f[2]-100*l[64]*f[1]-100*l[65]*f[1]^2-100*f[1]*l[66]*f[2]-100*l[63]*f[2]-100*f[1]*l[64]*f[2]-100*l[65]*f[2]^2';
strings{66}='y[68]+f[1]*y[67]+f[2]*y[66]-b[1]*u[67]-100*l[66]-100*l[67]*f[1]-100*l[68]*f[2]-100*l[65]*f[1]-100*l[66]*f[1]^2-100*f[1]*l[67]*f[2]-100*l[64]*f[2]-100*f[1]*l[65]*f[2]-100*l[66]*f[2]^2';
strings{67}='y[69]+f[1]*y[68]+f[2]*y[67]-b[1]*u[68]-100*l[67]-100*l[68]*f[1]-100*l[69]*f[2]-100*l[66]*f[1]-100*l[67]*f[1]^2-100*f[1]*l[68]*f[2]-100*l[65]*f[2]-100*f[1]*l[66]*f[2]-100*l[67]*f[2]^2';
strings{68}='y[70]+f[1]*y[69]+f[2]*y[68]-b[1]*u[69]-100*l[68]-100*l[69]*f[1]-100*l[70]*f[2]-100*l[67]*f[1]-100*l[68]*f[1]^2-100*f[1]*l[69]*f[2]-100*l[66]*f[2]-100*f[1]*l[67]*f[2]-100*l[68]*f[2]^2';
strings{69}='y[71]+f[1]*y[70]+f[2]*y[69]-b[1]*u[70]-100*l[69]-100*l[70]*f[1]-100*l[71]*f[2]-100*l[68]*f[1]-100*l[69]*f[1]^2-100*f[1]*l[70]*f[2]-100*l[67]*f[2]-100*f[1]*l[68]*f[2]-100*l[69]*f[2]^2';
strings{70}='y[72]+f[1]*y[71]+f[2]*y[70]-b[1]*u[71]-100*l[70]-100*l[71]*f[1]-100*l[72]*f[2]-100*l[69]*f[1]-100*l[70]*f[1]^2-100*f[1]*l[71]*f[2]-100*l[68]*f[2]-100*f[1]*l[69]*f[2]-100*l[70]*f[2]^2';
strings{71}='y[73]+f[1]*y[72]+f[2]*y[71]-b[1]*u[72]-100*l[71]-100*l[72]*f[1]-100*l[73]*f[2]-100*l[70]*f[1]-100*l[71]*f[1]^2-100*f[1]*l[72]*f[2]-100*l[69]*f[2]-100*f[1]*l[70]*f[2]-100*l[71]*f[2]^2';
strings{72}='y[74]+f[1]*y[73]+f[2]*y[72]-b[1]*u[73]-100*l[72]-100*l[73]*f[1]-100*l[74]*f[2]-100*l[71]*f[1]-100*l[72]*f[1]^2-100*f[1]*l[73]*f[2]-100*l[70]*f[2]-100*f[1]*l[71]*f[2]-100*l[72]*f[2]^2';
strings{73}='y[75]+f[1]*y[74]+f[2]*y[73]-b[1]*u[74]-100*l[73]-100*l[74]*f[1]-100*l[75]*f[2]-100*l[72]*f[1]-100*l[73]*f[1]^2-100*f[1]*l[74]*f[2]-100*l[71]*f[2]-100*f[1]*l[72]*f[2]-100*l[73]*f[2]^2';
strings{74}='y[76]+f[1]*y[75]+f[2]*y[74]-b[1]*u[75]-100*l[74]-100*l[75]*f[1]-100*l[76]*f[2]-100*l[73]*f[1]-100*l[74]*f[1]^2-100*f[1]*l[75]*f[2]-100*l[72]*f[2]-100*f[1]*l[73]*f[2]-100*l[74]*f[2]^2';
strings{75}='y[77]+f[1]*y[76]+f[2]*y[75]-b[1]*u[76]-100*l[75]-100*l[76]*f[1]-100*l[77]*f[2]-100*l[74]*f[1]-100*l[75]*f[1]^2-100*f[1]*l[76]*f[2]-100*l[73]*f[2]-100*f[1]*l[74]*f[2]-100*l[75]*f[2]^2';
strings{76}='y[78]+f[1]*y[77]+f[2]*y[76]-b[1]*u[77]-100*l[76]-100*l[77]*f[1]-100*l[78]*f[2]-100*l[75]*f[1]-100*l[76]*f[1]^2-100*f[1]*l[77]*f[2]-100*l[74]*f[2]-100*f[1]*l[75]*f[2]-100*l[76]*f[2]^2';
strings{77}='y[79]+f[1]*y[78]+f[2]*y[77]-b[1]*u[78]-100*l[77]-100*l[78]*f[1]-100*l[79]*f[2]-100*l[76]*f[1]-100*l[77]*f[1]^2-100*f[1]*l[78]*f[2]-100*l[75]*f[2]-100*f[1]*l[76]*f[2]-100*l[77]*f[2]^2';
strings{78}='y[80]+f[1]*y[79]+f[2]*y[78]-b[1]*u[79]-100*l[78]-100*l[79]*f[1]-100*l[80]*f[2]-100*l[77]*f[1]-100*l[78]*f[1]^2-100*f[1]*l[79]*f[2]-100*l[76]*f[2]-100*f[1]*l[77]*f[2]-100*l[78]*f[2]^2';
strings{79}='y[81]+f[1]*y[80]+f[2]*y[79]-b[1]*u[80]-100*l[79]-100*l[80]*f[1]-100*l[81]*f[2]-100*l[78]*f[1]-100*l[79]*f[1]^2-100*f[1]*l[80]*f[2]-100*l[77]*f[2]-100*f[1]*l[78]*f[2]-100*l[79]*f[2]^2';
strings{80}='y[82]+f[1]*y[81]+f[2]*y[80]-b[1]*u[81]-100*l[80]-100*l[81]*f[1]-100*l[82]*f[2]-100*l[79]*f[1]-100*l[80]*f[1]^2-100*f[1]*l[81]*f[2]-100*l[78]*f[2]-100*f[1]*l[79]*f[2]-100*l[80]*f[2]^2';
strings{81}='y[83]+f[1]*y[82]+f[2]*y[81]-b[1]*u[82]-100*l[81]-100*l[82]*f[1]-100*l[83]*f[2]-100*l[80]*f[1]-100*l[81]*f[1]^2-100*f[1]*l[82]*f[2]-100*l[79]*f[2]-100*f[1]*l[80]*f[2]-100*l[81]*f[2]^2';
strings{82}='y[84]+f[1]*y[83]+f[2]*y[82]-b[1]*u[83]-100*l[82]-100*l[83]*f[1]-100*l[84]*f[2]-100*l[81]*f[1]-100*l[82]*f[1]^2-100*f[1]*l[83]*f[2]-100*l[80]*f[2]-100*f[1]*l[81]*f[2]-100*l[82]*f[2]^2';
strings{83}='y[85]+f[1]*y[84]+f[2]*y[83]-b[1]*u[84]-100*l[83]-100*l[84]*f[1]-100*l[85]*f[2]-100*l[82]*f[1]-100*l[83]*f[1]^2-100*f[1]*l[84]*f[2]-100*l[81]*f[2]-100*f[1]*l[82]*f[2]-100*l[83]*f[2]^2';
strings{84}='y[86]+f[1]*y[85]+f[2]*y[84]-b[1]*u[85]-100*l[84]-100*l[85]*f[1]-100*l[86]*f[2]-100*l[83]*f[1]-100*l[84]*f[1]^2-100*f[1]*l[85]*f[2]-100*l[82]*f[2]-100*f[1]*l[83]*f[2]-100*l[84]*f[2]^2';
strings{85}='y[87]+f[1]*y[86]+f[2]*y[85]-b[1]*u[86]-100*l[85]-100*l[86]*f[1]-100*l[87]*f[2]-100*l[84]*f[1]-100*l[85]*f[1]^2-100*f[1]*l[86]*f[2]-100*l[83]*f[2]-100*f[1]*l[84]*f[2]-100*l[85]*f[2]^2';
strings{86}='y[88]+f[1]*y[87]+f[2]*y[86]-b[1]*u[87]-100*l[86]-100*l[87]*f[1]-100*l[88]*f[2]-100*l[85]*f[1]-100*l[86]*f[1]^2-100*f[1]*l[87]*f[2]-100*l[84]*f[2]-100*f[1]*l[85]*f[2]-100*l[86]*f[2]^2';
strings{87}='y[89]+f[1]*y[88]+f[2]*y[87]-b[1]*u[88]-100*l[87]-100*l[88]*f[1]-100*l[89]*f[2]-100*l[86]*f[1]-100*l[87]*f[1]^2-100*f[1]*l[88]*f[2]-100*l[85]*f[2]-100*f[1]*l[86]*f[2]-100*l[87]*f[2]^2';
strings{88}='y[90]+f[1]*y[89]+f[2]*y[88]-b[1]*u[89]-100*l[88]-100*l[89]*f[1]-100*l[90]*f[2]-100*l[87]*f[1]-100*l[88]*f[1]^2-100*f[1]*l[89]*f[2]-100*l[86]*f[2]-100*f[1]*l[87]*f[2]-100*l[88]*f[2]^2';
strings{89}='y[91]+f[1]*y[90]+f[2]*y[89]-b[1]*u[90]-100*l[89]-100*l[90]*f[1]-100*l[91]*f[2]-100*l[88]*f[1]-100*l[89]*f[1]^2-100*f[1]*l[90]*f[2]-100*l[87]*f[2]-100*f[1]*l[88]*f[2]-100*l[89]*f[2]^2';
strings{90}='y[92]+f[1]*y[91]+f[2]*y[90]-b[1]*u[91]-100*l[90]-100*l[91]*f[1]-100*l[92]*f[2]-100*l[89]*f[1]-100*l[90]*f[1]^2-100*f[1]*l[91]*f[2]-100*l[88]*f[2]-100*f[1]*l[89]*f[2]-100*l[90]*f[2]^2';
strings{91}='y[93]+f[1]*y[92]+f[2]*y[91]-b[1]*u[92]-100*l[91]-100*l[92]*f[1]-100*l[93]*f[2]-100*l[90]*f[1]-100*l[91]*f[1]^2-100*f[1]*l[92]*f[2]-100*l[89]*f[2]-100*f[1]*l[90]*f[2]-100*l[91]*f[2]^2';
strings{92}='y[94]+f[1]*y[93]+f[2]*y[92]-b[1]*u[93]-100*l[92]-100*l[93]*f[1]-100*l[94]*f[2]-100*l[91]*f[1]-100*l[92]*f[1]^2-100*f[1]*l[93]*f[2]-100*l[90]*f[2]-100*f[1]*l[91]*f[2]-100*l[92]*f[2]^2';
strings{93}='y[95]+f[1]*y[94]+f[2]*y[93]-b[1]*u[94]-100*l[93]-100*l[94]*f[1]-100*l[95]*f[2]-100*l[92]*f[1]-100*l[93]*f[1]^2-100*f[1]*l[94]*f[2]-100*l[91]*f[2]-100*f[1]*l[92]*f[2]-100*l[93]*f[2]^2';
strings{94}='y[96]+f[1]*y[95]+f[2]*y[94]-b[1]*u[95]-100*l[94]-100*l[95]*f[1]-100*l[96]*f[2]-100*l[93]*f[1]-100*l[94]*f[1]^2-100*f[1]*l[95]*f[2]-100*l[92]*f[2]-100*f[1]*l[93]*f[2]-100*l[94]*f[2]^2';
strings{95}='y[97]+f[1]*y[96]+f[2]*y[95]-b[1]*u[96]-100*l[95]-100*l[96]*f[1]-100*l[97]*f[2]-100*l[94]*f[1]-100*l[95]*f[1]^2-100*f[1]*l[96]*f[2]-100*l[93]*f[2]-100*f[1]*l[94]*f[2]-100*l[95]*f[2]^2';
strings{96}='y[98]+f[1]*y[97]+f[2]*y[96]-b[1]*u[97]-100*l[96]-100*l[97]*f[1]-100*l[98]*f[2]-100*l[95]*f[1]-100*l[96]*f[1]^2-100*f[1]*l[97]*f[2]-100*l[94]*f[2]-100*f[1]*l[95]*f[2]-100*l[96]*f[2]^2';
strings{97}='y[99]+f[1]*y[98]+f[2]*y[97]-b[1]*u[98]-100*l[97]-100*l[98]*f[1]-100*l[96]*f[1]-100*l[97]*f[1]^2-100*f[1]*l[98]*f[2]-100*l[95]*f[2]-100*f[1]*l[96]*f[2]-100*l[97]*f[2]^2';
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100*l[57]*l[56]*f[1]-100*l[58]*l[57]*f[1]-100*l[59]*l[58]*f[1]-100*l[60]*l[59]*f[1]-100*l[61]*l[60]*f[1]-100*l[62]*l[61]*f[1]-100*l[63]*l[62]*f[1]-100*l[64]*l[63]*f[1]-100*l[65]*l[64]*f[1]-100*l[66]*l[65]*f[1]-100*l[67]*l[66]*f[1]-100*l[68]*l[67]*f[1]-100*l[69]*l[68]*f[1]-100*l[70]*l[69]*f[1]-100*l[71]*l[70]*f[1]-100*l[72]*l[71]*f[1]-100*l[73]*l[72]*f[1]-100*l[74]*l[73]*f[1]-100*l[75]*l[74]*f[1]-100*l[76]*l[75]*f[1]-100*l[77]*l[76]*f[1]-100*l[78]*l[77]*f[1]-100*l[79]*l[78]*f[1]-100*l[80]*l[79]*f[1]-100*l[8]*l[7]*f[1]-100*l[9]*l[8]*f[1]-100*l[10]*l[9]*f[1]-100*l[11]*l[10]*f[1]-100*l[12]*l[11]*f[1]-100*l[13]*l[12]*f[1]-100*l[14]*l[13]*f[1]-100*l[15]*l[14]*f[1]-100*l[16]*l[15]*f[1]-100*l[17]*l[16]*f[1]-100*l[18]*l[17]*f[1]-100*l[19]*l[18]*f[1]-100*l[20]*l[19]*f[1]-100*l[21]*l[20]*f[1]-100*l[22]*l[21]*f[1]-100*l[23]*l[22]*f[1]-100*l[24]*l[23]*f[1]-100*l[25]*l[24]*f[1]-100*l[26]*l[25]*f[1]-100*l[27]*l[26]*f[1]-100*l[28]*l[27]*f[1]-100*l[29]*l[28]*f[1]-100*l[30]*l[29]*f[1]-100*l[31]*l[30]*f[1]-100*l[32]*l[31]*f[1]-100*l[33]*l[32]*f[1]-100*l[34]*l[33]*f[1]-100*l[35]*l[34]*f[1]-100*l[36]*l[35]*f[1]-100*l[37]*l[36]*f[1]-100*l[38]*l[37]*f[1]-100*l[39]*l[38]*f[1]-100*l[40]*l[39]*f[1]-100*l[41]*l[40]*f[1]-100*l[42]*l[41]*f[1]-100*l[43]*l[42]*f[1]-100*l[3]*l[2]*f[1]-100*l[2]*l[1]*f[1]-100*l[4]*l[3]*f[1]-100*l[5]*l[4]*f[1]-100*l[6]*l[5]*f[1]-100*l[7]*l[6]*f[1]';
strings{101}='-l[91]*u[92]-l[92]*u[93]-l[93]*u[94]-l[94]*u[95]-l[95]*u[96]-l[96]*u[97]-l[97]*u[98]-l[98]*u[99]-l[71]*u[72]-l[72]*u[73]-l[73]*u[74]-l[74]*u[75]-l[75]*u[76]-l[76]*u[77]-l[77]*u[78]-l[78]*u[79]-l[79]*u[80]-l[80]*u[81]-l[81]*u[82]-l[82]*u[83]-l[83]*u[84]-l[84]*u[85]-l[85]*u[86]-l[86]*u[87]-l[87]*u[88]-l[88]*u[89]-l[89]*u[90]-l[90]*u[91]-l[50]*u[51]-l[51]*u[52]-l[52]*u[53]-l[53]*u[54]-l[54]*u[55]-l[55]*u[56]-l[56]*u[57]-l[57]*u[58]-l[58]*u[59]-l[59]*u[60]-l[60]*u[61]-l[61]*u[62]-l[62]*u[63]-l[63]*u[64]-l[64]*u[65]-l[65]*u[66]-l[66]*u[67]-l[67]*u[68]-l[68]*u[69]-l[69]*u[70]-l[70]*u[71]-l[30]*u[31]-l[31]*u[32]-l[32]*u[33]-l[33]*u[34]-l[34]*u[35]-l[35]*u[36]-l[36]*u[37]-l[37]*u[38]-l[38]*u[39]-l[39]*u[40]-l[40]*u[41]-l[41]*u[42]-l[42]*u[43]-l[43]*u[44]-l[44]*u[45]-l[45]*u[46]-l[46]*u[47]-l[47]*u[48]-l[48]*u[49]-l[49]*u[50]-l[9]*u[10]-l[10]*u[11]-l[11]*u[12]-l[12]*u[13]-l[13]*u[14]-l[14]*u[15]-l[15]*u[16]-l[16]*u[17]-l[17]*u[18]-l[18]*u[19]-l[19]*u[20]-l[20]*u[21]-l[21]*u[22]-l[22]*u[23]-l[23]*u[24]-l[24]*u[25]-l[25]*u[26]-l[26]*u[27]-l[27]*u[28]-l[28]*u[29]-l[29]*u[30]-l[1]*u[2]-l[2]*u[3]-l[3]*u[4]-l[4]*u[5]-l[5]*u[6]-l[6]*u[7]-l[7]*u[8]-l[8]*u[9]';
polysys = lti2polysys(strings,y,u,'nf',2,'nb',1,'nl',98);