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/* Problem: Chemical equilibrium of hydrocarbon combustion @Article{MeintjesMorgan1992, author = {K. Meintjes and A. P. Morgan}, title = {Chemical equilibrium systems as numerical test problems}, year = {1990}, journal = {ACM TOMS}, volume = {16}, number = {2}, pages = {143--151} } Although the total degree equals 108, there are only 4 real and 12 complex solutions and an infinite number of solutions at infinity. */ Variables x1 in [0,1.0e8], x2 in [0,1.0e8], x3 in [0,1.0e8], x4 in [0,1.0e8], x5 in [0,1.0e8] ; Constants R = 10, R5 = 0.193, R6 = 0.002597/sqrt(40), R7 = 0.003448/sqrt(40), R8 = 0.00001799/40, R9 = 0.0002155/sqrt(40), R10 = 0.00003846/40 ; Constraints 3*x5 = x1*(x2 + 1), x3*(x2*(2*x3+R7) + 2*R5*x3 + R6) = 8*x5, x4*(R9*x2 + 2*x4) = 4*R*x5, x2*(2*x1 + x3*(x3+R7) + R8 + 2*R10*x2 + R9*x4) + x1 = R*x5, x2*(x1 + R10*x2 + x3*(x3+R7) + R8 + R9*x4) + x1 + x3*(R5*x3 + R6) + x4^2 = 1 ;
The result is: