In-class and homework assignment for Tuesday, Sept. 11

You are encouraged (but not required) to work with a partner, in which case the two of you will turn in one paper with both your names on it (and both of you get the same grade).

Surface Meteorological Airways Format

The so-called METAR format is used to encode certain weather observations that are taken at ground level. Tables of these observations are updated hourly and can be downloaded from any National Weather Service web site. Here are the METAR data for stations in and near Arizona taken between 3 pm and 5 pm on Sept. 10, 2007.

Exercise 1. Write a Python script, metar.py, that reads metar.dat and produces a list of the form

station time pressure temperature dewpoint

One little challenge is to format an entry like 32/M01, which means that the ambient temperature is 32 degrees Celsius and the dewpoint is -1 degree Celsius. Some automated measurements omit the dewpoint temperature, in which case the corresponding entry looks like 32/ and you should write M for the missing dewpoint.

Atmospheric pressure in the United States is commonly reported in inches of mercury (Hg), but the international standard is hectoPascals (hPa), also known as millibars (mb). This conversion chart gives equivalent (in,hPa) pairs. Your Python script should read it in, along with the METAR data, to supply the conversion. You may assume that pressure data is reported to the nearest hundredth of an inch (when inches are used) and that the values lie within the range given in the conversion chart. (Suggestion: build a hash table from the conversion data so that an expression of the form hPa[inHg] yields the hectoPascal equivalent for a given reading, inHg, in inches of mercury. If you experience difficulties due to rounding, then convert inches of mercury to the nearest 4-digit integer value before placing it in the hash table.)

You may hardwire the name of the conversion file in your Python script as barometric.dat. Otherwise, your script must be runnable in the form

python metar.py < metar.dat

Integer division

1. a = bq + r
2. q has the same sign as ab
3. 0 ≤ |r| < |b|.

27 = 4×6 + 3 = 4×7 + (-1)

To obtain a unique quotient and remainder, a fourth condition is required. There are two reasonable possibilities.

• Convention Q. Choose the largest quotient in absolute value such that |bq| ≤ |a|.
• Convention R. Require r to have the same sign as b.

Exercise 2. Make a table of the values of q and r that each of the following expressions produces under Convention Q and under Convention R.

1. 21/6
2. -21/6
3. 21/(-6)
4. (-21)/(-6)

Exercise 3. Write a Python function, div_q(a,b) that returns the tuple (q,r) giving the quotient and remainder, respectively, according to Convention Q. (You may assume that a and b are integers and that b is nonzero; no error checking is required.)

Exercise 4. Write a Python function, div_r(a,b) that returns the tuple (q,r) giving the quotient and remainder, respectively, according to Convention R. (As above, no error checking is required.)

In the remaining problems, assume that a and b are integer variables and that b is not zero.

Exercise 5. Prove that Convention Q and Convention R produce the same values of q and r when a and b are both positive.

Exercise 6. True or false: Under Convention Q,

(-a)/b = -(a/b).

Exercise 7. True or false: Under Convention R, (-a)/b = -(a/b). As above, either write a proof or find a counterexample.

Submission instructions

• metar.py, containing your Python script for Exercise 1.
• division.py, containing your Python scripts for Exercises 3 and 4. Please include only the source code for div_q and div_r. All other testing code should be removed.
• remainder.txt or remainder.pdf containing either plain text or PDF, respectively, for your answers to the remaining exercises.

Package these files into a tar archive, hw4.tar, using the tar command as follows:

tar -cf hw4.tar metar.py division.py remainder.txt

Your_name MAT 420 HW4

Copyright(c) 2007 by Eric J. Kostelich. All rights reserved.