# Should there be a simultaneous equations tag?

There do seem to be a number of these questions - linear ones come under various headings, but there are quadratic and cubic ones around. I wanted to retag a post with , and discovered it wasn't there. Any views on whether this tag would be useful?

• The way I'd gone about it once was to determine if there are at least ten questions that could be tagged with this new tag. I suppose that since there are more than ten questions on simultaneous equations, as well as that the methods for linear and nonlinear simultaneous equations are a bit more elaborate than in the univariate case, this tag's justified. Jun 17, 2013 at 0:50
• @J.M.: "...for linear and nonlinear..." isn't the linear case already covered by linear algebra? But I agree with the sentiment in the rest. Jun 17, 2013 at 8:10
• @Willie, ah, linear-algebra would be much more suitable in the linear case, yes. I'm slipping. :D Jun 17, 2013 at 9:11
• I recall once being surprised for their not being a tag for systems of equations. In some cases they could fall under the umbrella of analytic-geometry, in particular if the variables are real numbers. Or was that for a parametrized curve? May be two occasions have coalesced into one in my fuzzy brain? Jun 17, 2013 at 16:01
• @JyrkiLahtonen Indeed - another place for systems of equations would be algebraic geometry, but I was thinking of some of the elementary questions. Jun 17, 2013 at 16:53
• To check the Ｊ.M.'s requirement of at least 10 questions, I have collected some question where the tag might be suitable here. Feel free to add more questions, if you find some. Jun 17, 2013 at 17:51
• @Willie Wong, it is not a good idea of just using the linear-algebra tag for simultaneous linear algebraic equations as they will still fall into the deep ocean of the linear-algebra tag and difficult to find them. Tagging them for example as simultaneous-algebraic-equations will have no such problem. Jun 18, 2013 at 5:01
• @Jyrki Lahtonen, it is important to note that if the algebraic-geometry tag is using for the simultaneous-type equations, only the questions about simultaneous algebraic equations and simultaneous transcendental equations that analysing in graphical approach are suitable. Jun 18, 2013 at 5:12

This is just to post a counterargument to that advanced by user pau2357paul:

I think the attempt to compare with the [algebra] tag is a false analogy. A better tag to compare to would be the tag, which describes a general concept but which has different manifestations in introductory real analysis, general topology, functional analysis, and so forth. Another similar tag is .

Note that each question is allowed to have five tags. It would be reasonable to read the tag combinations

• (simultaneous-equations) (pde) to mean simultaneous partial differential equations
• (simultaneous-equations) (differential-equations) to mean simultaneous ODEs
• (simultaneous-equations) (linear-algebra) to mean simultaneous linear algebraic equations
• (simultaneous-equations) (analytic-geomety) to mean simultaneous equations arising from a geometric context
• (simultaneous-equations) (polynomials) for the case of solving nonlinear, algebraic equations
• ...

Also, as an aside, I would personally prefer (systems-of-equations) to (simultaneous-equations), but that is just an irrational personal preference and I won't make too big a deal of it.

• Agree with this. Sounds like a good solution. I particularly agree with the last paragraph. Simultaneity carries, for me at least, the overtone of there being some kind of dependence on time and/or relation to physics. I suppose it would sound better in some contexts, so I also agree with not making a big deal about the choice of term here. Jun 18, 2013 at 9:51
• @JyrkiLahtonen: in particular, they can always be synonyms. Jun 18, 2013 at 10:16
• I could get behind with having systems-of-equations as the primary tag and simultaneous-equations as the synonym... Jun 18, 2013 at 10:54
• For the record: I added [tag: systems-of-equations] to this question. Partly prompted by Calvin Lin. Is this how it's supposed to get started, or was my action premature? Jun 21, 2013 at 18:54
• @JyrkiLahtonen: while you are at it, do you mind adding the tag to the questions mentioned by Martin? I'll enter in the synonym a bit later. (It is best to have more than 1 question tagged so that the tag doesn't get auto-removed after a few months..) Jun 24, 2013 at 8:09
• @Willie: Working on it. Splitting it to a couple of session in the interest of keeping the number of bumps down. Jun 24, 2013 at 8:40
• Well. I forgot that retagging does not (appear to) bump. Done. All the questions in Martin's list involved systems of polynomial and/or algebraic equations. So we are still lacking DE/PDE questions with this tag. Jun 24, 2013 at 8:51
• @JyrkiLahtonen: I'll add the DE/PDE ones as I see them pop up. Jun 24, 2013 at 9:07
• Found one on the front page :-) Jun 24, 2013 at 9:08

I'd prefer to keep the discussion about system of equations in one place (and I don't think this will generate enough discussion to deserve a separate question). So I'll point out here that there exists a tag called . (I only noticed it now.)

What should we do with this tag. Should it by made synonym of the newly created ?

If we keep the two tags separate, the usage of should be clarified. (Tag-wiki and tag-excerpt are empty at the moment.)

• Upvote to express support of making it a synonym (at least a majority of the 15 questions in nonlinear-system would fit perfectly in systems-of-equations). Jun 24, 2013 at 17:13
• Oh dear. May be I was a bit trigger happy in creating the tag? Anyway, while retagging I did notice this tag. I would have thought that nonlinear-systems is meant to be a subset of dynamical-systems, but should have asked. I'm neutral about making them synonyms. I don't know enough! Jun 24, 2013 at 19:10
• I can merge, but there are a few question for which removing (nonlinear-system) and replacing with (systems-of-equations) would lose meaning. (For example, there's one currently tagged with the only other tag (matrices)...) Jun 25, 2013 at 13:44
• While we are at it, there's also algebraic-systems. Jun 25, 2013 at 13:45
• @WillieWong I did not notice (algebraic-systems). But moth of those questions seem to fit (systems-of-equations). As far the questions tagged (nonlinear-system) are concerned, I've posted here how I would tag them. Jun 25, 2013 at 14:24

It is a good idea of having the specific tags for simultaneous-type equations, as questions about simultaneous-type equations are often more advanced than that of non-simultaneous-type equations, but you should note that the term "equations" itself is in fact too vague, as the types of equations contain at least algebraic equations, transcendental equations, diophantine equations, ordinary differential equations, partial differential equations, difference equations, integral equations, and any composite types of them as http://en.wikipedia.org/wiki/Equation#Types_of_equations classified, so as the simultaneous-type equations.

It is lucky that in MSE nobody has created the tag so that the arguments like The use of the [algebra] tag not appeared in the equation-types tags. If you create the tag, the arguments like The use of the [algebra] tag will appear again, the tag names about equations will become inequality and eventually brings the inappropriate culture of tagging. So if you want to create the specific tags for simultaneous-type equations, please create the tags like , , , etc.

• One technical comment, there's something like a 25 character length limit to tags. So your ODE and PDE ones would be cut-off somewhere around the e of equations. Jun 18, 2013 at 8:40