old_contents: import numpy as np
  import matplotlib.pylab as plt
  
  fig = plt.figure(figsize=(8, 8))
  ax = fig.add_subplot(111)
  
  M = 1000
  x = np.zeros(M + 1, dtype = np.float64)
  y_up = np.zeros(M + 1, dtype = np.float64)
  y_down = np.zeros(M + 1, dtype = np.float64)
  ## l1 norm
  for i in range(len(x)):
      x[i] = -1 + 2.0 * i / M
      y_up[i] = 1.0 - np.abs(x[i])
      y_down[i] = -y_up[i]
  ax.plot(np.append(x, np.fliplr([x])), np.append(y_up, np.fliplr([y_down])), label = "l1")    
  ## l2 norm
  for i in range(len(x)):
      y_up[i] = (1.0 - x[i] ** 2) ** (0.5)
      y_down[i] = -y_up[i]
  ax.plot(np.append(x, np.fliplr([x])), np.append(y_up, np.fliplr([y_down])), label = "l2")
  
  ## l10 norm
  for i in range(len(x)):
      y_up[i] = (1.0 - x[i] ** 10) ** (0.1)
      y_down[i] = -y_up[i]
  ax.plot(np.append(x, np.fliplr([x])), np.append(y_up, np.fliplr([y_down])), label = "l10")
  ## l infinity norm
  ax.plot([-1, 1, 1, -1, -1], [-1, -1, 1, 1, -1], label = "linf")
  ## legend
  ax.legend(loc = "upper right")
  ax.set_ylim(-1.5, 1.5)
  ax.set_xlim(-1.5, 1.5)
  
  plt.show()
new_contents: import numpy as np
  import matplotlib.pylab as plt
  
  fig = plt.figure(figsize=(8, 8))
  ax = fig.add_subplot(111)
  
  M = 1000
  x = np.zeros(M + 1, dtype = np.float64)
  y_up = np.zeros(M + 1, dtype = np.float64)
  y_down = np.zeros(M + 1, dtype = np.float64)
  ## l1 norm
  for i in range(len(x)):
      x[i] = -1 + 2.0 * i / M
      y_up[i] = 1.0 - np.abs(x[i])
      y_down[i] = -y_up[i]
  ax.plot(np.append(x, np.fliplr([x])), np.append(y_up, np.fliplr([y_down])), label = "l1-norm")
  ## l2 norm
  for i in range(len(x)):
      y_up[i] = (1.0 - x[i] ** 2) ** (0.5)
      y_down[i] = -y_up[i]
  ax.plot(np.append(x, np.fliplr([x])), np.append(y_up, np.fliplr([y_down])), label = "l2-norm")
  
  ## l10 norm
  for i in range(len(x)):
      y_up[i] = (1.0 - x[i] ** 10) ** (0.1)
      y_down[i] = -y_up[i]
  ax.plot(np.append(x, np.fliplr([x])), np.append(y_up, np.fliplr([y_down])), label = "l10-norm")
  ## l infinity norm
  ax.plot([-1, 1, 1, -1, -1], [-1, -1, 1, 1, -1], label = "linf-norm")
  ## legend
  ax.set_title("Unit circles under different lp-norms", fontsize = "large")
  ax.legend(loc = "upper right", fontsize = "medium")
  ax.set_xlabel("x", fontsize = "large")
  ax.set_ylabel("y", fontsize = "large")
  ax.set_ylim(-1.8, 1.8)
  ax.set_xlim(-1.8, 1.8)
  fig.savefig("norms.pdf")
  plt.show()
subject: Add labels.