problem0():
  Compute planetary density using a dict.
{'Earth': [5.972e+24, 6371],
 'Jupiter': [1.899e+27, 69911],
 'Mars': [6.417e+23, 3390],
 'Mercury': [3.301e+23, 2440],
 'Neptune': [1.024e+26, 24622],
 'Saturn': [5.685e+26, 58232],
 'Sun': [1.988e+30, 695500],
 'Uranus': [8.682e+25, 25362],
 'Venus': [4.867e+24, 6052]}
Sun 1.988e+30 695500 1410705526697.2375
Mercury 3.301e+23 2440 5424846275125.448
Venus 4.867e+24 6052 5241746077656.206
Earth 5.972e+24 6371 5513258738589.094
Mars 6.417e+23 3390 3932279103238.88
Jupiter 1.899e+27 69911 1326782738207.952
Saturn 5.685e+26 58232 687316453662.8875
Uranus 8.682e+25 25362 1270517576645.7202
Neptune 1.024e+26 24622 1637726462393.788

problem1():
  Create a dict() that records word lengths in a text.
{1: 1, 2: 3, 3: 9, 4: 3, 5: 5, 6: 1, 7: 4, 9: 3, 11: 1}

problem2():
  Use a dict() to translate English to Morse code.

  Plain message:
END OF SEMESTER IS COMING
  Morse code version:
. -. -.. / --- ..-. / ... . -- . ... - . .-. / .. ... / -.-. --- -- .. -. --. 

problem3():
  Use roots_legendre() for approximate integration.
  n =  1   e =  0.6399892584925493
  n =  2   e =  0.09462965794454914
  n =  3   e =  0.002792922371481543
  n =  4   e =  0.0028275243989659415
  n =  5   e =  0.0009539081732152788
  n =  6   e =  0.0001739791298585036
  n =  7   e =  1.473657900530334e-05
  n =  8   e =  2.345621630039929e-06
  n =  9   e =  1.2626401459936432e-06
  n =  10   e =  2.83505651177407e-07
  n =  11   e =  3.532922221438639e-08
  n =  12   e =  4.4715253721960835e-10
  n =  13   e =  1.4897874045516346e-09
  n =  14   e =  4.233546846421632e-10
  n =  15   e =  6.795652929270091e-11

problem4():
  Use quad() to estimate an integral.

  exact integral =  1.582232963729673
  estimate       =  1.5822329637296728
  error          =  2.220446049250313e-16

problem5():
  Use minimize_scalar() to minimize a function.

  minimizer is    -1.0574527467194874
  f(x) =          16.970492717458466

  minimizer is    0.930403370197514
  f(x) =          18.966502983430757

problem6():
  use minimize() to minimize a function of two variables.
  xy_start is    [1.5 0.5]
  f(xy_start) =  2.1656249999999986

  Using Nelder-Mead method:
  xy_min is    [1.60712295 0.56866213]
  f(xy_min) =  2.1042503125266885

  Using Powell method:
  xy_min is    [-0.08983771  0.71268588]
  f(xy_min) =  -1.031628446172904

problem7():
  Use brentq() to find a root of a function.


  left endpoint a   2.0
  f(a) =            1.1814051463486366
  right endpoint b  6.0
  f(b) =            -0.4411690036021483
  estimated root    5.846278223000454
  f(x) =            9.992007221626409e-16

problem8(): interpolation
  Use interp1d() to interpolate data.
  Graphics saved as "problem8.png"

problem9():
  fft.
  ||x-ifft(fft(x))|| =  9.879748754926199e-15