#!/usr/bin/python
# -*- coding: utf8 -*-

import matplotlib.pyplot as plt
import matplotlib as mpl
import numpy as np
from math import *

code_website = 'https://commons.wikimedia.org/wiki/User:Geek3/mplwp'
try:
    import mplwp
except ImportError, er:
    print 'ImportError:', er
    print 'You need to download mplwp.py from', code_website
    exit(1)

name = 'mplwp_Steiners_problem.svg'
fig = mplwp.fig_standard(mpl)

xlim = 0, 10; fig.gca().set_xlim(xlim)
ylim = -0.3, 1.8; fig.gca().set_ylim(ylim)
mplwp.mark_axeszero(fig.gca())

x = np.linspace(xlim[0], xlim[1], 5001)
y = x ** (x ** -1)
plt.plot(x, y, label=r'$x^{1/x}$')
plt.plot([exp(1)], [exp(1) ** (exp(1) ** -1)], 'ob')

plt.legend(loc='upper right', borderaxespad=1.5)
plt.savefig(name)
mplwp.postprocess(name)