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:: I think it is well-known at least for integers, rational, algebraic, and real numbers. I will do some digging for a reference sometime. (A few other additions to the articles need good references too, mainly the closure properties.) [[User:Caleb Stanford|Caleb Stanford]] ([[User talk:Caleb Stanford|talk]]) 19:11, 26 November 2021 (UTC)
== To-do list from [[Wikipedia:Peer review/Constant-recursive sequence/archive2|peer review]] (Jan 2022) ==
=== To do for [[Wikipedia:Content assessment/B-Class criteria|B-class]] ===
# {{tq|The article is suitably referenced, with inline citations.}}
#: I think this is the weak point of the article, and indeed of many Wikipedia articles about mathematical concepts. Not only are there important uncited statements in the article (although many of them can be verified by readers with sufficient mathematical background), as far as I can tell, all sources cited in the article are [[wp:primary|primary]]. The one thing that would improve the article most, in my opinion, is more [[wp:secondary source|secondary source]]s.
#:* Every citation should have an exact page if possible, a page range should only be used if the claim(s) cited cannot be verified by reading any single page (and even then it should be as short as possible). I haven't checked whether the article complies with this, I just wanted to mention that. I see that the ''Reachability Problems'' source is used several times, you can provide a separate page number for each of them by using {{tl|sfn}} or {{tl|r}} but given that the page range isn't long it may be more trouble that it's worth.
#:* It would be ideal if there were a source for every definition and every example, to verify that they are notable and therefore relevant to the article. Of particular interest would be a source for the fact that every eventually periodic sequence is constant-recursive, given that it causes a minor headache in [[Constant-recursive sequence#Definition|Definition]]. That said, I don't think it's necessary.
# {{tq|The article is reasonably well-written.}}
#: The prose is generally good, but it feels too textbook-like to me. Aside from the lead, the article uses a distinctive writing style that is more characteristic of a math textbook than of an encyclopedia.
#:* The use of the notation <math>s(n)</math> for an element of a sequence rather than the more common <math>s_n</math> can confuse readers, especially given that most (all?) articles linked from this one use the common notation. I propose changing <math>s(n)</math> to <math>s_n</math> and <math>F(n)</math> to <math>F_n</math>.
# {{tq|The article reasonably covers the topic, and does not contain obvious omissions or inaccuracies.}}
#: This one needs review from a subject-matter expert.
# {{tq|The article contains supporting materials where appropriate.}}
#:I think a video illustrating the concept would be helpful, but the article ought to pass this criterion even without one.
# {{tq|The article presents its content in an appropriately understandable way.}}
#: I think the [[wp:write one level down|write one level down]] rule is the best way to assess this, but I don't know at which level this subject is typically studied. If [[graduate school]], I'd say it passes. If [[undergraduate education#United States system|undergraduate]], it fails.
=== Done ===
:{{tick}} The article has a defined structure.
:{{tick}} The term "closed under" is used in the article without being wikilinked. Consider linking it in every section where it appears (the lead, [[Constant-recursive sequence#In terms of vector spaces|In terms of vector spaces]] and [[Constant-recursive sequence#Closure properties|Closure properties]]).
:{{tick}} The phrase "note that" is used in the article twice. Per [[MOS:NOTE]], it should be removed.
:{{tick}} In [[Constant-recursive sequence#Definition|Definition]], the phrase "eventually-periodic sequences... which are disallowed by some authors" makes it sound like said authors explicitly disallow them, which is not the case (rather, they require that <math>c_d \ne 0</math>, which incidentally disallows such sequences). I think this sentence and the next one could use a rewrite.
:{{tick}} Speaking of which, the citations in [[Constant-recursive sequence#Definition|Definition]] don't have a page number. I believe it should be page 66 in ''The Concrete Tetrahedron'' and page 1 in ''Skolem's Problem''.
:{{tick}} I've never seen the notation <math>s(n)_{n \geq 0}</math> before, it should be replaced by a more common notation such as <math>(s(n))_{n=0}^\infty</math>, or better yet, <math>(s_n)_{n=0}^\infty</math> (which mirrors the one used in the [[Sequence]] article). <math>(s_n)_{n\in\mathbb N}</math> is alright as long as you explain that <math>\mathbb N</math> includes zero.
:{{tick}} In the table in [[Constant-recursive sequence#Closure properties|Closure properties]], why is "Generating Function Equivalent" in title case?
:{{tick}} In [[Constant-recursive sequence#Decision problems|Decision problems]], "see closure properties" should be linked.
=== Discussion ===
Post any comments below. [[User:Caleb Stanford|Caleb Stanford]] ([[User talk:Caleb Stanford|talk]]) 18:03, 18 January 2022 (UTC)
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