Wikipedia:Articles for deletion/Indeterminate system

The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was keep but rewrite . Beeblebrox (talk) 00:28, 5 December 2012 (UTC)[reply]

Indeterminate system

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Possible neologism--I can't find this term anywhere on google except in an unrelated context. Only one reference is given. The article is self-contradictory about the intended meaning of the title term: sometimes underdetermined (which means fewer equations than unknowns), sometimes infinitely many or no solutions (which permits either more or fewer or same number of equations as unknowns), sometimes fewer "unique" (another neologism) equations than unknowns. Subject matter is adequately covered elsewhere: System of linear equations, Underdetermined system. Duoduoduo (talk) 15:01, 20 November 2012 (UTC)[reply]

Redirect/Disambiguate I agree that the article is poorly written, contains insufficient references, and contains no content not already in other articles. "Indeterminate system" is not a neologism; http://www.encyclopediaofmath.org/index.php/Linear_algebraic_equation defines it as an system of linear equations having more than one solution and http://encyclopedia2.thefreedictionary.com/Statically+Indeterminate+System defines it as a mechanical system which cannot by solved for all forces and constraints using a static analysis alone. The term is also used in the context of linear Diophantine equations; http://www.jstor.org/stable/108738 is a reference from 1861. Given the indeterminate nature of "Indeterminate system", setting up a disambiguation page could be more helpful than simply deleting this article with no pointers. Mark viking (talk) 17:14, 20 November 2012 (UTC)[reply]

Note: This debate has been included in the list of Science-related deletion discussions. • Gene93k (talk) 14:36, 21 November 2012 (UTC)[reply]

Keep The article isn't perfect, but after reading both I'd say it's better-written than Underdetermined system; perhaps make that a redirect to this? DavidLeeLambert (talk) 14:36, 23 November 2012 (UTC)[reply]

But the meaning of "underdetermined system" is well-established and is stated clearly in that article, whereas there is no established meaning for "indeterminate system" and this article is self-contradictory about what meaning it wishes to assign to that term. Duoduoduo (talk) 16:29, 23 November 2012 (UTC)[reply]

Relisted to generate a more thorough discussion so a clearer consensus may be reached.

Please add new comments below this notice. Thanks, Vacation^nine 03:09, 27 November 2012 (UTC)[reply]

Redirect to Underdetermined system which is the much more common term. I'm not sure why DavidLeeLambert says that this article is better written than Underdetermined system (at least in the current versions). I don't think there is really anything useful here which hasn't already found its way to the other article, so no merge needed. Dingo1729 (talk) 19:19, 28 November 2012 (UTC)[reply]
Do not delete. The term is apparently used in the reference given in the article, and also in the sources dug up by Mark Viking, so I feel we should have something at "indeterminate system". What is not so relevant for AfD. Looking at the first revision of the article, it seems pretty clear to me that "indeterminate system" means a system of equations with no unique solution (so either it has no solutions or it has more than one). That's presumably the meaning in David Lay's book. The Springer Encyclopedia of Mathematics says "indeterminate system" means a system with more than one solution (which is also the meaning used in some non-reliable sources). So even within linear algebra, there are multiple meanings, but the term is not in wide use, which suggests to me that a disambiguation page as suggested by Mark Viking is the way forward. Underdetermined system is about systems with fewer equations than unknowns; this is yet another concept and not quite the same, so I feel redirecting there is not the best. -- Jitse Niesen (talk) 12:17, 29 November 2012 (UTC)[reply]
Drastically rewrite almost from scratch (from the original deletion proposer). I'm persuaded by the above arguments that instead of just deleting it we should have "Indeterminate system" go somewhere. But where? There appears to be no other term conveying the same meaning, so we can't just redirect it to somewhere, and there would be nothing to put on the disambiguation page after "Indeterminate system" can mean.... So how about if I drastically rewrite it, almost from scratch, with lede sentence "An indeterminate system of equations is an equation system that has more than one solution." I believe all of the definitions referenced by Mark Viking agree with that, as does the one referenced by Jitse Niesen. The definition that allows for either multiple solutions or no solution (1) is contrary to conventional mathematical usage of "indeterminate", and (2) is sourced nowhere (not even in the article; the reference at the bottom is not linked to from the article's definition). Duoduoduo (talk) 17:18, 29 November 2012 (UTC)[reply]

Comment I wouldn't want to discourage you from re-writing, but I would point out that the encyclopedias referenced here are all open source (including the Springer one). So we are short on reliable sources. I note that the Springer encyclopedia is based on a translation of a Russian encyclopedia, so the use of 'indeterminate' may simply be originally a case of the translator not realizing that 'underdetermined' is the common english usage. Cases like that are quite common in translated papers. 'Indeterminate' seems to be synonymous with 'underdetermined' when used for linear systems (at least for characteristic zero). When we come to non-linear equations (and other rings) there are numerous annoying special cases. But the generic case is still the same. I agree that a disambiguation page is a non-starter (see WP:DISAMBIG). I still think that a simple redirect to Underdetermined system is the way to go, together with possibly a short comment there if we think that there are slight consistent differences between 'indeterminate' and 'underdetermined'. Dingo1729 (talk) 18:32, 29 November 2012 (UTC)[reply]

Comment For linear equations "underdetermined" and "has multiple solutions" are overlapping sets. x+y+z=1, x+y+z=2 is underdetermined but has no solution; x+y=1, 2x+2y=2, 3x+3y=3 is overdetermined but has an infinitude of solutions. I think redirecting to underdetermined system would muddy the waters since it would not allow discussion of the overdetermined possibility. Duoduoduo (talk) 19:10, 29 November 2012 (UTC)[reply]

Comment I agree that a rewrite is a good solution here--thanks for taking the initiative. If there are not suitable targets, then a rewrite is superior to a disambiguation page. Mark viking (talk) 18:54, 29 November 2012 (UTC)[reply]

@duoduoduo. Do you have a reliable source for definitions of overdetermined and underdetermined? I looked briefly on-line and in the library here but couldn't find anything. I think that what matters is the rank of the coefficient matrix. That would make your example rank 1 and underdetermined rather than 3 equations and overdetermined. People (and wikipedia) are often careless about this sort of thing. The rank is, of course, less than or equal to the number of equations. So fewer equations than variables implies underdetermined, but you can still be underdetermined with more equations. Dingo1729 (talk) 20:41, 29 November 2012 (UTC)[reply]

Good question. While the article underdetermined system doesn't contain one, overdetermined system has a reference to planetmath that says

An overdetermined system of linear equations has more equations than unknowns. In general, overdetermined systems have no solution. In some cases, linear least squares may be used to find an approximate solution.

The first sentence seems unequivocal, and the corresponding definition of "underdetermined" follows directly. But the second sentence is a little vague (does "in general" mean "in every case" or "you cannot say the contrary is always true"?). More clearly, planetmath here says (and I can put this cite into our article):

An under determined system of linear equations has more unknowns than equations. It can be consistent with infinitely many solutions, or have no solution.

The historical authors of overdetermined system seem to be very sure about it -- its definition has been there since inception on 20 March 2007‎, and the section "An example in two dimensions" has covered it at great graphical length ever since 15:51, 30 May 2007. Duoduoduo (talk) 22:17, 29 November 2012 (UTC)[reply]

I agree with what you've said, but of course planetmath is yet another crowdsourced website and not Reliable. And even that says An overdetermined system of linear equations has more equations than unknowns. (which I don't disagree with) not A system with more equations than unknowns is overdetermined. And I'm sure you'll agree that just having been in the articles for 5 years doesn't make things true. I'm feeling that there's a lack of solid ground. Dingo1729 (talk) 22:42, 29 November 2012 (UTC)[reply]

I agree, I'm somewhat uncomfortable about it too. I found this on mathworld:

If k<n [fewer unknowns than equations], then the system is (in general) overdetermined and there is no solution.

There's that "in general" again -- here I think it means "usually". But I interpret this passage to mean that "overdetermined" is the same thing as "no solution". So yes, I'm uncomfortable. Duoduoduo (talk) 23:08, 29 November 2012 (UTC)[reply]

But our article System of polynomial equations#Basic properties and definitions says

A system is overdetermined if the number of equations is higher than the number of variables. A system is inconsistent if it has no solutions.... Most but not all overdetermined systems are inconsistent. For example the system x³ − 1 = 0, x² − 1 = 0 is overdetermined but not inconsistent.

A system is underdetermined if the number of equations is lower than the number of the variables. An underdetermined system is either inconsistent or has infinitely many solutions in an algebraically closed extension K of k.

Duoduoduo (talk) 23:13, 29 November 2012 (UTC)[reply]

Least squares says

The method of least squares is a standard approach to the approximate solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns.

Duoduoduo (talk) 23:22, 29 November 2012 (UTC)[reply]

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.