Talk:K-regular sequence

Revising article

I have chosen to revise this article as part of a project for a course on automatic sequences. My goal is to make the article easier to read and understand by cleaning up the structure of the article and adding additional details. Please don't be alarmed if you see a large number of changes over the next little while. If you have any concerns, feel free to contact me.

Taylor J. Smith (talk) 17:42, 17 April 2017 (UTC)

Abstraction

Personally I think some of the recent revisions are unnecessarily abstract. My intent in writing the original article was to make it accessible to a wide audience. One can explain a regular sequence to someone who doesn't know what a Noetherian ring is. Since nearly all examples of regular sequences that have appeared in the literature are integer sequences, in my opinion it makes more sense to focus primarily on integer sequences and then mention that a more general definition exists.

Similarly, one can explain what a regular sequence is without saying "finite automaton with auxiliary storage". I think this phrasing is unnecessarily alienating, but I'd like to hear other opinions. Eric Rowland (talk) 21:14, 17 April 2017 (UTC)

Thanks for your feedback. I tried to bring this article more in line with the article on automatic sequences (since the two concepts are closely related), though I agree that some things could be rewritten to be more suitable for a general audience. I probably went a bit too far towards the mathematical side with my revisions. Though I feel like the definition should be the precise, mathematical definition, I believe a more accessible definition could be included in the introduction. I'm certainly not as familiar as you are with this topic, however, so I'm open to suggestions and corrections.

Taylor J. Smith (talk) 17:22, 18 April 2017 (UTC)

I'm not sure "the definition" is unique. The original 1990 paper defines regular sequences with entries in a ring containing a commutative Noetherian subring. Automatic Sequences: Theory, Applications, Generalizations only defines regular sequences with entries in a $\mathbb {Z}$-module. Presumably this was to make it easier on the reader, since the extra abstraction wasn't necessary. If we are just interested in integer sequences, we can get by with even less. So why not start as simple as possible, to have the widest audience, and then generalize?

If the Wikipedia entry does mention the generality of a Noetherian ring, it would be good to at least indicate why we need the Noetherian condition. Otherwise it heads in the direction of math entries that are only useful to the people who wrote them.

Eric Rowland (talk) 22:38, 18 April 2017 (UTC)