x_1, x_2, x_3, x_4, 
3*x_1^3+2*x_1+x_3
9*x_1^4+6*x_1^2+1
4*x_1^2+4*x_1*x_2+x_2^2
3*x_1^3+x_1+2*x_2+2*x_4
6*x_1^3+3*x_1^2*x_2+2*x_1+x_2
