problem0():
  Plot a Gaussian prime spiral.

  Graphics saved as "problem0.png"

problem1():
  Define matrix A, verify that A*A = I

  A*A =  [[ 1.00000000e+00  8.32667268e-17 -1.66533454e-16  1.38777878e-16
   5.55111512e-17]
 [ 8.32667268e-17  1.00000000e+00  5.55111512e-17  2.77555756e-17
  -1.94289029e-16]
 [-1.66533454e-16  5.55111512e-17  1.00000000e+00 -5.55111512e-17
   1.94289029e-16]
 [ 1.38777878e-16  2.77555756e-17 -5.55111512e-17  1.00000000e+00
  -4.44089210e-16]
 [ 5.55111512e-17 -1.94289029e-16  1.94289029e-16 -4.44089210e-16
   1.00000000e+00]]

problem2():
  Draw a hexagonal figure divided into colored triangles.

  Graphics saved as "problem2.png"

problem3():
  Draw a triangular grid of blue dots.

  Graphics saved as "problem3.png"

problem4():
  plot the sinc function, with a "cutoff" line..

  Graphics saved as "problem4.png"

problem5():
  Complex arithmetic

  a =  (-5+4j)
  b =  (2-3j)
  c =  (2+23j)
  ar =  6.4031242374328485   br =  3.605551275463989   cr =  23.08679276123039
  cr =  23.08679276123039   ar * br =  23.086792761230388
  at =  2.4668517113662407   bt =  -0.982793723247329   ct =  1.4840579881189115
  ct =  1.4840579881189115   at + bt =  1.4840579881189115
  ap =  (-5+3.9999999999999996j)   bp =  (2-3j)   cp =  (1.9999999999999991+23j)

problem6():
  Find minimum and maximum of f(x) over an interval.

  minimum occurs at x =  0.85  where y =  -12.890117720183559
  maximum occurs at x =  0.6  where y =  17.03688115426212

problem7():
  Write a one line statement that is:
  * True if vector x is monotonically increasing. 
  * True if vector x is strictly monotonically increasing.

  np.diff(x) returns the successive difference of entries in x
  What condition must this difference vector satisfy?
  Hill Q6.1.10, page 226.

  Test on the following:
  1) x = [  1, 2, 3, 6, 8 ]
  2) y = [ -1, 2, 3, 3, 7 ]
  3) z = [  1, 3, 7, 2, 9 ]
  x monotonic          is  True
  x strictly monotonic is  True
  y monotonic          is  True
  y strictly monotonic is  False
  z monotonic          is  False
  z strictly monotonic is  False

problem8():
  Area of a polygon (Hill P6.1.2.
  Use for() loops and a list.

  Area =  6.0

problem9():
  Use indexing.

  Area =  6.0