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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Jacobiana
$$\frac{dx}{dt}=a_{1}x-b_{1}x^{2}+c_{1}xy$$
$$\frac{dy}{dt}=a_{2}y-b_{2}y^{2}+c_{1}xy$$
$$\frac{dx}{dt}=(1-x-y)x$$
$$\frac{dy}{dt}=(4-7x-3y)y$$
Step1:  Equilibrios
Step2:  Jacobiana
Step3:  Evaluada en un punto de equilibrio
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Python Code:
import numpy as np
# importamos bibliotecas para plotear
import matplotlib
import matplotlib.pyplot as plt
# para desplegar los plots en el notebook
%matplotlib inline
# para cómputo simbólico
from sympy import *
init_printing()
x, y = symbols('x y')
f = (1-x-y)*x
f
g = (4-7*x-3*y)*y
g
Explanation: Jacobiana
$$\frac{dx}{dt}=a_{1}x-b_{1}x^{2}+c_{1}xy$$
$$\frac{dy}{dt}=a_{2}y-b_{2}y^{2}+c_{1}xy$$
$$\frac{dx}{dt}=(1-x-y)x$$
$$\frac{dy}{dt}=(4-7x-3y)y$$
End of explanation
solve(f, x)
solve(g, y)
Y = solve(g, y)[1]
solve(f.subs(y, Y),x)
solve(g.subs(x, -y + 1), y)
Explanation: Equilibrios
End of explanation
J = symbols("J")
J = Matrix([[diff(f, x), diff(f, y)], 
            [diff(g, x), diff(g, y)]])
J
Explanation: Jacobiana
End of explanation
J = J.subs({x: 1/4, y:3/4})
J
J.det(), J.trace()
Explanation: Evaluada en un punto de equilibrio
End of explanation
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