Does "you" mean me? As best I can recall, the answer is no. But it's
never too late for our book -- even though it's "published" (and has been
for 4 years), we're constantly making improvements, ranging from fixing
typos to replacing interacts with prettier or more effective ones for the
same tasks. And when there is a cube root or nth root function that
includes x<0 in the domain, we'll take advantage of that -- although it's
not critical to our mission. We haven't bothered with revision numbers
(bad practice, I know), and "version" (which we're about to drop) refers to
the technology required. We have just posted our (final?) version,
entirely Sage and MathJax based, no longer with any external CAS required.
You can see the result at calculuscourse.maa.org, where the only links are
to Full Text and Sample Chapters. The Sample is open to the public, while
Full is behind a pay wall. However, until next Monday, you can see the
full text at calculuscourse.maa.org/main2/ -- and comments are welcome. My
sincere thanks to all who have helped us get up to speed on Sage interacts
and responded to our requests for additional features. DAS
On Tuesday, July 8, 2014 10:30:09 PM UTC-4, kcrisman wrote:
>
> Ah, I missed all this. Did you ever open a ticket (with this or Nils' or
> other code)? I guess it's too late for your book (well, the 1st print
> edition, on the internet revision means something different, as a recent
> article I read on lit crit was pointing out...)
>
>
>
>
>> def nth_real_root( x, n ):
>> """Note: n must be a positive integer. However, x is any real number.
>> (Otherwise this explanation will make no sense.)
>> For odd values of n, we return the unique real number y such
>> that y^n = x.
>> For even values of n, if x<0, there is no real number y such
>> that y^n = x and so we throw an exception.
>> For even values of n, if x=>0, then we return the unique real
>> number y such that y^n = x."""
>>
>> if ((n in ZZ)==false):
>> raise RuntimeError('nth_real_root(x,n) requires n to be a
>> positive integer. Your n is not an integer.')
>>
>> if (n<=0):
>> raise RuntimeError('nth_real_root(x,n) requires n to be a
>> positive integer. Your n is not positive.')
>>
>> assert (n in ZZ)
>> assert (n>0)
>>
>> if ((n%2) == 0):
>> # n is even
>> if (x<0):
>> raise RuntimeError('There is no nth real root (of a
>> negative number x) when n is even.')
>> else:
>> return x^(1/n)
>>
>> assert ((n%2)==1)
>> # n is odd
>> return sign(x)*(abs(x))^(1/n)
>>
>>
> By the way, apparently it's better to use a try/except clause than an
> assert, so that we have a meaningful error message, or so I have heard, I'm
> not a PEP guru.
>
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