CS414 Spring 2017: Lab #2

Due Wednesday, February 9, 2017, before midnight

Late penalty: Fri 5%, Sat 10%, Sun 100%

Before You Begin:

• Create a folder on your computer where your files will be kept.
• Download the following four files, and save them into the folder you just created. You should modify them. At the end of the lab session, submit your work so far, for the record.
  1. answers1and2.txt : Your typed answers to the first two questions.
  2. demorgan.py
  3. quadratic.py
  4. tenperline.py
• You can re-submit your work, up until midnight tonight, with no late penalty.

Questions:

1. In python, how big a number can be stored in a float? For example, 2.0**100 evaluates to 1.2676506002282294e+30, but 2.0**10000 gives an overflow error. Run IDLE, and experiment to find the biggest exponent n such that 2.0**n evaluates without overflow.

2. Floats:

   1. Consider this code:

                  root2 = 2**0.5
                  two = root2 * root2
                  shouldBeTrue = (two == 2)
                  print shouldBeTrue
                

      Type it into IDLE. What is printed? Why?

   2. Extend the above code, with these two lines:

                  zero = two - 2
                  print zero
                

      Type them into IDLE. What is printed? Why?

3. Demorgan's theorem states that, if A and B are booleans, the following will both always be True:

           not (A and B) == (not A) or  (not B)
           not (A or  B) == (not A) and (not B)
         

   Prove it using python. To do this, write a program demorgan.py with code like this:

           print "A:", A, "B:", B, "not(A and B)==(not A) or (not B):", not(A and B)==(not A) or (not B)
         

   and repeat this code, each time setting A and B to one of the four possible combinations of True and False. Repeat for the second part of DeMorgan's theorem.

4. Write a program quadratic.py that accepts three numbers a, b, and c, and prints the real roots of the quadratic polynomial ax²+bx+c. Your program should be robust: it should not crash. Instead, print messages indicating how many real roots exist (there may be no real roots).

   Crash course in quadratic equations:
   Here is the quadratic equation: ax²+bx+c .
   Compute the discriminant: d = b² - 4ac
   Don't forget to use * to multiply values!
   If d is negative, there are no real roots.
   If d is zero, there is one root: x = -b / (2a) .
   If d is positive, there are two roots:
   x₁ = (-b - d^0.5) / (2a) , and
   x₂ = (-b + d^0.5) / (2a).
   Don't forget to use ** to compute an exponent.

5. (Bonus 10%): Write a program tenperline.py that prints the numbers 1 through 100 (inclusive), with ten integers per line. Method: use a for-loop, and print each number with a trailing comma (to avoid advancing to a new line). To advance to a new line, (print by itself). Do this when the number's remainder, on division by 10, has a specific value. Use number % 10 to get that remainder.