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I saw this answer for a question about finding an ellipse from four points in general position; its centre and three points on its circumference, and wrote an edit with the following changes:

  • Define $C_{12}$ as twice its value in the original version; this adds two $/2$'s in its use in the initial matrix representation, but removes $21$ multiplications by $2$ elsewhere
  • restate the formulas for $C_{11},C_{22},C_{12}$ coefficients as a vector equality, to avoid duplicating division by $|M|$, and rewrite the numerators; they were arranged haphazardly previously (like the raw output of a CAS) rather than as a sum over cyclic index changes. From$$\begin{array}{ccl} C_{11}&=&\frac{y_2^22x_3y_3-2x_2y_2y_3^2+2x_1y_1y_3^2-y_1^22x_3y_3+y_1^22x_2y_2-2x_1y_1y_2^2}{|M|}\\C_{22}&=&\frac{2x_2y_2x_3^2-x_2^22x_3y_3+x_1^22x_3y_3-2x_1y_1x_3^2+2x_1y_1x_2^2-x_1^22x_2y_2}{|M|}\\C_{12}&=&\frac{x_2^2y_3^2-y_2^2x_3^2+y_1^2x_3^2-x_1^2y_3^2+x_1^2y_2^2-y_1^2x_2^2}{|M|} \end{array}$$to$$\begin{pmatrix}C_{11}\\C_{22}\\C_{12}\end{pmatrix}=\frac{\begin{pmatrix}x_1y_1(y_3^2-y_2^2)&+&x_2y_2(y_1^2-y_3^2)&+&x_3y_3(y_2^2-y_1^2)\\x_1y_1(x_2^2-x_3^2)&+&x_2y_2(x_3^2-x_1^2)&+&x_3y_3(x_1^2-x_2^2)\\x_1^2(y_2^2-y_3^2)&+&x_2^2(y_3^2-y_1^2)&+&x_3^2(y_1^2-y_2^2)\end{pmatrix}}{|M|}$$
  • Factorise $|M|$, from $$x_1^2(y_2^22x_3y_3-2x_2y_2y_3^2)+y_1^2(2x_2y_2x_3^2-x_2^22x_3y_3)+2x_1y_1(x_2^2y_3^2-y_2^2x_3^2)$$ to $$(x_1y_2-x_2y_1)(x_2y_3-x_3y_2)(x_3y_1-x_1y_3)$$
  • Change ellipse characterisation in terms of polar parameters, from $$\left(\frac{(b^2-a^2)\cos^2\theta}{a^2b^2}+\frac{1}{b^2}\right)x^2+\left(\frac{(a^2-b^2)\cos^2\theta}{a^2b^2}+\frac{1}{a^2}\right)y^2+\frac{2(a^2-b^2)\sin\theta\cos\theta}{a^2b^2}xy-1=0$$to$$\begin{aligned}0&=\left(\frac{\cos^2\theta}{a^2}+\frac{\sin^2\theta}{b^2}\right)x^2+\left(\frac{\cos^2\theta}{b^2}+\frac{\sin^2\theta}{a^2}\right)y^2+\left(\frac1{b^2}-\frac1{a^2}\right)\sin(2\theta)xy-1\\&=\left(\left(\frac1{a^2}-\frac1{b^2}\right)\cos^2\theta+\frac{1}{b^2}\right)x^2+\left(\left(\frac1{b^2}-\frac1{a^2}\right)\cos^2\theta+\frac{1}{a^2}\right)y^2+\left(\frac1{b^2}-\frac1{a^2}\right)\sin(2\theta)xy-1\end{aligned}$$I kept the original (minorly changed), because it's computationally more efficient if less straightforward to parse, though doing so felt somewhat verbose.

However, it was rejected by users amWhy and Another User, both using the default message,

The edit does not improve the quality of the post. Changes to the content are unnecessary or make the post more confusing.

which isn't specific as to which changes were objectionable. Each of these seems as though it reduces confusion, and I would hope they'd at least tell me how to salvage it from whatever didn't. Could anyone less invested explain in more detail?

I noticed a later answer used an equivalent matrix definition to the original version of this, is it a standard convention?

Also, unrelatedly, four other answers seem as though they should be deleted.

  • one answer on 2013-03-23 effectively restates the problem,
  • another on 2013-03-23 notes the aforementioned condition of 'in general position,' which could be merged into the question,
  • a third on 2015-11-08 gives a diagram (where two of the three specified circumference points are antipodal, so implied by each other; an infinitude satisfy this) and link to a prewritten answer to an entirely different question,
  • a fourth on 2015-11-09 (by the author of the third) states only two circumference points $B,C$ are necessary to find an ellipse (as $\left\{\begin{pmatrix}B\sin t\\C\cos t\end{pmatrix}: t\in[0,2\pi)\right\}$), which again fails to uniquely characterse it.
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    $\begingroup$ The general feeling around these parts is that you make edits to correct typos, bad formatting, stuff like that, but not to introduce things that don't align with the posters intentions. The poster intended $C_{12}$ be defined a certain way, and developed the whole post in accord with that intention. You changed the definition to something that may well be better than what OP had, but something that OP did not intend. I can't say whether that was the reason for the rejection of your proposed edit, but I wouldn't be surprised if that was the reason. $\endgroup$ Commented Oct 3, 2024 at 7:23
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    $\begingroup$ I think what you're expected to do in such a situation is to leave a comment along the lines of, "your exposition would become much simpler if you would write $(1/2)C_{12}$ where you now have $C_{12}$, so please make that change and the other changes that follow." If OP doesn't take you up on your suggestion, then you post your own answer, preface it by saying your answer is based on that other one but with the following simplifications, etc., etc. $\endgroup$ Commented Oct 3, 2024 at 7:27

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Thank you for taking some time to try to improve an existing answer. I'm sorry for the unfortunate experience you had.

Unfortunately, the culture on this site can often be unfriendly towards edits that improve an answer written by someone other than the editor. It is my opinion that editing to improve others' answers is beneficial, but most on this site disagree with me. I think this culture is well-intentioned but misguided and overall detrimental to the mission of the site (to be a repository of knowledge), but my opinion is a minority opinion.

I think one of the reasons often cited for disliking such edits is the risk that edits can introduce errors. Verifying that the changes don't increase errors takes some work and can be error-prone. So, I think some members of the community feel uncomfortable with the prospect that an edit might introduce an error that wasn't previously there. They might feel comfortable with an edit to change a minor and obvious typo, but not the kind of sweeping change you made.

I also suspect some users feel that whoever originally wrote the answer should have a kind of "moral ownership" or "moral agency" over the answer, and others should not edit "their words" without permission. That is an understandable view. It's not how Stack Exchange works (see https://math.stackexchange.com/help/editing), but I realize the Stack Exchange approach is counterintuitive and unfamiliar for many folks. So I can understand why people might come from that perspective.

What should you do about it? It's up to you. I can't tell you what to do. My approach has been to exercise caution about making anything more than de minimis changes. If I am making a clear improvement that does not change the meaning or style of the answer (e.g., fix a typo, improve formatting in a way that is unambiguously an improvement), and my change is very narrowly scoped and obviously unobjectionable, then I think there is a reasonable chance it will be accepted (but no guarantees! sometimes even that is unwelcome). In contrast, if I make a major revision, there is a very significant risk that such an edit will trigger some backlash and unhappiness. Therefore, I have decided not to waste my valuable time on an activity that is likely to be unappreciated and reversed; there are plenty of other useful ways I can spend my time.

At the same time, I would completely respect anyone who, out of principle, continues to try to submit major revisions if they improve an answer, even knowing that they might be rejected. I admire that attitude of doing what is right even though it might not be appreciated by others.

Another possibility is to write your own answer. Personally I often feel hesitation about that if it's going to largely duplicate an existing answer, but it seems to be an "approved" way to handle these things (i.e., approved by site culture).

So only you can decide how you want to handle this. I apologize in advance that you have to make these kinds of calculations. But I wanted you to be aware of the considerations.

Thank you for your effort to improve the site and make it more useful for others. I appreciate that.

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    $\begingroup$ I don't generally have a problem with this, but one reason that proactive edits can be received poorly is that it denies the original writer's agency. Rational or not, they might prefer to be informed first of the deficiency, and arrive at their own way of remedying it (if they agree it's a deficiency). After all (from their point of view), they know best how their original post was organized, so they should know best how to re-organize it to suit an updated purpose. (I realize you've already mentioned some of this, but I tend to prefer "agency" over "moral ownership" as an explanation.) $\endgroup$ Commented Oct 6, 2024 at 5:44
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    $\begingroup$ @BrianTung, Thank you for articulating that perspective in greater detail and better than I did. $\endgroup$ Commented Oct 7, 2024 at 4:39
  • $\begingroup$ @D.W. This is a really good answer, but you being someone who has seen a lot of other websites on SE, I'd like you to explain what those sites do well that allows editing culture to be more free, and also what counters something like Brian's argument on other websites. $\endgroup$ Commented Oct 7, 2024 at 9:24
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    $\begingroup$ @SarveshRavichandranIyer, My apologies. I don't have any great insights. Maybe others will have some perspectives. My impression is that the primary difference in other sites is that they are more welcoming and accepting of edits (so edits are less likely to be rejected on grounds of "you're not the author", and on meta, people are more likely to educate other about SE norms that encourage edits, and focus more on building a high-quality knowledge archive and less on protecting the original author). $\endgroup$ Commented Oct 7, 2024 at 16:04
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    $\begingroup$ Stack Overflow has an interesting policy that largely encourages edits, but warns to take special care about editing code and largely discourages editing code, and reviewers may reject some edits that make too large of a change to code (because, much like it can be hard to check edits to math to make sure it hasn't inadvertently introduced errors, it can be hard to check edits to code in the same way): meta.stackoverflow.com/q/303219/781723, meta.stackoverflow.com/q/260245/781723 $\endgroup$ Commented Oct 7, 2024 at 16:05
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    $\begingroup$ Some example reading: meta.stackexchange.com/q/15839/160917, meta.stackoverflow.com/q/367885/781723, meta.stackoverflow.com/q/269995/781723, meta.stackoverflow.com/q/288987/781723, meta.stackoverflow.com/q/416012/781723, meta.stackoverflow.com/q/381353/781723, meta.stackoverflow.com/q/272486/781723, meta.stackoverflow.com/q/404191/781723, meta.stackoverflow.com/q/338662/781723, meta.stackoverflow.com/q/263115/781723 $\endgroup$ Commented Oct 7, 2024 at 16:12
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    $\begingroup$ But I have no special insight. And there are lots of other users who participate on multiple SE sites. Hopefully others will be able to give a more helpful perspective. Sorry that this wasn't particularly useful. $\endgroup$ Commented Oct 7, 2024 at 16:14
  • $\begingroup$ @D.W. No problem, thanks for the input. There is good discussion here and there, but a very healthy population represents your opinion on other websites (unlike here). $\endgroup$ Commented Oct 8, 2024 at 7:09

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