In [2]:

    

using SymPy


    

In [4]:

    

x_1, x_2 = @syms x_1, x_2


    

    
Out[4]:





(x_1,x_2)

In [21]:

    

X = [x_1, x_2]


    

    
Out[21]:





\begin{bmatrix}x_{1}\\x_{2}\end{bmatrix}

In [22]:

    

f_1 = -x_1 + x_2


    

    
Out[22]:





$$- x_{1} + x_{2}$$

In [23]:

    

f_2 = 1//10 * x_1 - 2 * x_2 - x_1 ^ 2 - 1//10 * x_1 ^ 3


    

    
Out[23]:





$$- \frac{x_{1}^{3}}{10} - x_{1}^{2} + \frac{x_{1}}{10} - 2 x_{2}$$

In [24]:

    

F = [f_1,f_2]


    

    
Out[24]:





\begin{bmatrix}- x_{1} + x_{2}\\- \frac{x_{1}^{3}}{10} - x_{1}^{2} + \frac{x_{1}}{10} - 2 x_{2}\end{bmatrix}

In [32]:

    

A = [diff(f_1,x_1) diff(f_1,x_2);diff(f_2,x_1) diff(f_2,x_2)]


    

    
Out[32]:





\begin{bmatrix}-1&1\\- \frac{3 x_{1}^{2}}{10} - 2 x_{1} + \frac{1}{10}&-2\end{bmatrix}

In [35]:

    

solve([f_1,f_2],[x_1,x_])


    

    
Out[35]:





3-element Array{Any,1}:
 Dict{AbstractString,SymPy.Sym}("x_1"=>0,"x_2"=>0)                      
 Dict{AbstractString,SymPy.Sym}("x_1"=>-5 - sqrt(6),"x_2"=>-5 - sqrt(6))
 Dict{AbstractString,SymPy.Sym}("x_1"=>-5 + sqrt(6),"x_2"=>-5 + sqrt(6))

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