Question

I was watching lecture 4 in the spring 2011 series and I am a little confused about the findRoot function in the handout.
Specifically, in the findRoot function, the line:
if isEven(pwr) and val < 0:

If I understand this line correctly, the code returns a None value if the value is negative and the pwr is even, so you can calculate the cube root of a negative number for example, but not the square root or fourth root. Is there a reason for this limitation, or am I missing something
Thanks

Answer 1

This is the code:

def isEven(i):
"""assumes i a positive int
returns True if i is even, otherwise False"""
return i%2 == 0

def findRoot(pwr, val, epsilon):
"""assumes pwr an int; val, epsilon floats
pwr and epsilon > 0
if it exists,
returns a value within epsilon of val**pwr
otherwise returns None"""
assert type(pwr) == int and type(val) == float\
and type(epsilon) == float
assert pwr > 0 and epsilon > 0
if isEven(pwr) and val < 0:
return None
low = -abs(val)
high = max(abs(val), 1.0)
ans = (high + low)/2.0
while not withinEpsilon(ans**pwr, val, epsilon):
print ('ans =', ans, 'low =', low, 'high =', high)
if ans**pwr < val:
low = ans
else:
high = ans
ans = (high + low)/2.0
return ans

Answer 2

sorry, you also need this to make it all work:

def withinEpsilon(x, y, epsilon):
"""x,y,epsilon ints or floats. epsilon > 0.0
returns True if x is within epsilon of y"""
return abs(x - y) <= epsilon

Answer 3

The function is operating in the real numbers. Therefore, it does not attempt to calculate complex conjugates.

Answer 4

\(\sqrt{-1}=i\) and \(\sqrt{9}=\pm 3\)
\(\sqrt{-9}\implies \sqrt{9}\sqrt{-1}=\pm 3i\)

Answer 5

Also, when you paste code blocks as basic text, they can not be properly copied. They collapse into one line when pasted. If you put ``` on a separate line above and below the code, it changes it into a preformatted block. You can also use a code pasting service to get a similar effect, which is better for longer bits of code.

For example, try copying and pasting these:

def withinEpsilon(x, y, epsilon):
"""x,y,epsilon ints or floats. epsilon > 0.0
returns True if x is within epsilon of y"""
return abs(x - y) <= epsilon

```
def withinEpsilon(x, y, epsilon):
"""x,y,epsilon ints or floats. epsilon > 0.0
returns True if x is within epsilon of y"""
return abs(x - y) <= epsilon
```
And here are some free paste services:
http://gist.github.com/
http://pastebin.com/
http://dpaste.com/

Dpaste is the fastest to use, but not intended for long term items.

Answer 6

Funny how working through this course has forced me to brush up on my math skills while learning programming skills!
Thanks

Answer 7

Well, computers don't speak English. They speak math. \(\ddot \smile\)