# coding: utf-8

# # Monomial interpolation

# In[3]:

import numpy as np
import numpy.linalg as la
import matplotlib.pyplot as pt


# In[5]:

x = np.linspace(0, 1, 200)


# Now plot the monomial basis on the interval [0,1] up to $x^9$.

# In[6]:

for i in range(10):
    pt.plot(mesh, mesh**i)


# * How do the entries of the Vandermonde matrix relate to this plot?
# 
#   Hint: `pt.vlines(np.linspace(0, 1, 10), 0, 1)`

# ------------------
# * Guess the condition number of the Vandermonde matrix for $n=5,10,20$:

# In[19]:

n = 5
V = np.array([mesh**i for i in range(n)]).T
la.cond(V)