Talk:Forward difference

What's the forward difference of one element? --Mwn3d 07:17, 11 January 2008 (MST)

With regard to pure mathematics I suppose it is undefined. It is natural, however, to extend it by definition so that the forward difference of a list of one element is the empty list. That's how the J code resolves it, too. --TBH 07:31, 11 January 2008 (MST)

I guess the FD of an empty list should just be another empty list then? These corner cases always get you. --Mwn3d 07:39, 11 January 2008 (MST)

Yes, that's the way to handle receiving an empty list. (A similar "corner case" has been discussed here.)
One of the things I appreciate about J is how many of these exception-situations have been resolved within the language itself. In this instance both the single-element and empty-list possibilities require no specific code. --TBH 09:45, 11 January 2008 (MST)

It is very nice to see the Python entry. Studying it has improved my grasp of that language. --TBH 09:45, 11 January 2008 (MST)

With regard to the replacement of ((}. - }:) ^:) by (2&(-/\)): I agree that a solution in the form of a verb is somewhat better than a solution that is an adverb, although the benefits strike me as subtle and minor. I think the original solution is worth retaining as an example because of its form. It is not only a different algorithm, it is another strong example of how tacit form allows one to "code the concept." These two solutions complement one another, so both should be included. Contrary to the comment upon replacement, the new program is not shorter than the first solution. This is demonstrated by the following J interaction:

   #;:'(}. - }:) ^:'
6
   #;:'2&(-/\)'
7

--TBH 21:13, 20 August 2008 (UTC)