from numpy import *
from matplotlib.pyplot import *
from mpl_toolkits.axes_grid.axislines import SubplotZero

xlim,ylim = 10,10
x1 = linspace(-xlim,-sqrt(5.))
x2 = linspace(-sqrt(4.99),sqrt(4.99))
x3 = linspace(sqrt(5.01),xlim)
y = lambda x: .5*(x**3 - 2.*x) / (x**2 - 5.)

fig = figure(figsize=(5,5))
ax = SubplotZero(fig,111)
fig.add_subplot(ax)

for direction in ["xzero","yzero"]:
        ax.axis[direction].set_visible(True)
        ax.axis[direction].set_axisline_style("->")
for direction in ["top","bottom","left","right"]:
        ax.axis[direction].set_visible(False)
ax.axis["yzero"].set_axis_direction("left")
ax.grid(False)
ax.minorticks_on()

ax.plot(x1,y(x1),'b')
ax.plot(x2,y(x2),'b')
ax.plot(x3,y(x3),'b')
ax.arrow(-10,-5,20,10,color='k',lw=.5,ls='dashed')
ax.arrow(-sqrt(5.),-ylim,0.,2.*ylim+1,color='k',lw=.5,ls='dashed')
ax.arrow(sqrt(5.),-ylim,0.,2.*ylim+1,color='k',lw=.5,ls='dashed')
ax.set_ylim(-ylim,ylim)

fig.savefig("RationalDegree3.svg",bbox_inches="tight",pad_inches=.15)