Finally, I find out the answer, it seems matlab will do some approximations, the true system is
eqstrue=[ u6*(3*u5 - 1) - u4 - u1 - 3*u2*u3 - 3*u5*u6 + 3*u3*(u2 - 1) + 1/24, u2^2*u3*(u2 - 1) - 2*u5^3*u6 - u2*u3*(u2 - 1)^2 - (2*u4)/27 - u5*u6*(3*u5 - 1)^2 + u5^2*u6*(3*u5 - 1) + 1/360, 1/1260 - 2*u5^4*u6 - 2*u5^2*u6*(3*u5 - 1)^2 - 2*u2^2*u3*(u2 - 1)^2 - (2*u4)/81, u5^2*u6*(3*u5 - 1)^3 - 3*u5^5*u6 - u4/81 - 4*u5^3*u6*(3*u5 - 1)^2 + 4*u5^4*u6*(3*u5 - 1) + 1/2880, 9*u5^4*u6*(3*u5 - 1) - 3*u5^3*u6*(3*u5 - 1)^2 + 1/6720, u5^3*u6*(3*u5 - 1)^3 - 6*u5^4*u6*(3*u5 - 1)^2 - 3*u5^4*u6*(3*u5 - 1)^3 - 6*u5^5*u6*(3*u5 - 1)^2 + 9*u5^5*u6*(3*u5 - 1) - 3*u5^6*u6*(3*u5 - 1) + 1/21600, u5^3*u6*(3*u5 - 1)^3 - 6*u5^4*u6*(3*u5 - 1)^2 + u5^4*u6*(3*u5 - 1)^3 + 2*u5^5*u6*(3*u5 - 1)^2 + 9*u5^5*u6*(3*u5 - 1) + u5^6*u6*(3*u5 - 1) + 11/226800]
after I make
matlab solves the approximatied system
eqs=[ u6*(3*u5 - 1) - u4 - u1 - 3*u2*u3 - 3*u5*u6 + 3*u3*(u2 - 1) + 1/24, u2^2*u3*(u2 - 1) - 2*u5^3*u6 - u2*u3*(u2 - 1)^2 - (2*u4)/27 - u5*u6*(3*u5 - 1)^2 + u5^2*u6*(3*u5 - 1) + 1/360, 1/1260 - 2*u5^4*u6 - 2*u5^2*u6*(3*u5 - 1)^2 - 2*u2^2*u3*(u2 - 1)^2 - (2*u4)/81, u5^2*u6*(3*u5 - 1)^3 - 3*u5^5*u6 - u4/81 - 4*u5^3*u6*(3*u5 - 1)^2 + 4*u5^4*u6*(3*u5 - 1) + 1/2880, 9*u5^4*u6*(3*u5 - 1) - 3*u5^3*u6*(3*u5 - 1)^2 + 1/6720, u5^3*u6*(3*u5 - 1)^3 - 6*u5^4*u6*(3*u5 - 1)^2 - 3*u5^4*u6*(3*u5 - 1)^3 - 6*u5^5*u6*(3*u5 - 1)^2 + 9*u5^5*u6*(3*u5 - 1) - 3*u5^6*u6*(3*u5 - 1) + 34433922270924495617/743772721051969121157120, u5^3*u6*(3*u5 - 1)^3 - 6*u5^4*u6*(3*u5 - 1)^2 + u5^4*u6*(3*u5 - 1)^3 + 2*u5^5*u6*(3*u5 - 1)^2 + 9*u5^5*u6*(3*u5 - 1) + u5^6*u6*(3*u5 - 1) + 37713343439583972437/743772721051969121157120];
so it gives me an answer, I don't know why it does this. In the last equation.
vpa(11/226800 - 37713343439583972437/743772721051969121157120)
ans = -0.0000022045855379188659798651850341144609
It's a bad approximation.
Best Answer