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This is a followup question to Appropriate Reaction to a Failed Reference Request on MO related to Reference Request for Integer factorization with LP/ILP

I'm about to prepare an answer that contains my way of formulating integer factorization as an optimization problem that can be solved with the integer variant of the simplex method.

Now I have the options of either presenting the answer with just enough detail to understand it and judge its correctness and/or its practical relevance, or I could also supply some background information, that would have a more "entertaining" quality, e.g. what was the original motivation, difficulties encountered, etc.
The background information could of course be supplied well separated from the "technical" part.

I would like to get some opinions on the usefulness and desirability of documenting such background information.
Also replies related to other mathematical results, for which background information is available or not, are welcome.

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    $\begingroup$ My gut feeling is this: given that Dima expressed some mild skepticism with regard to your question, it might be good to test the waters first by starting with the concise version. If the community is encouraging in the form of upvotes, you should feel free to edit in further information. (Your third paragraph suggests to me that maybe you are not 100% certain of the correctness or practical relevance, so maybe it would be good to hold back and get community feedback first, before launching on a longer disquisition.) $\endgroup$ – Todd Trimble Dec 29 '13 at 17:08
  • $\begingroup$ Thanks for your advice, Todd. I will follow it and restrict my answer accordingly. $\endgroup$ – Manfred Weis Dec 29 '13 at 18:30
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    $\begingroup$ I don't quite understand what you are planning to do, but it is inappropriate to use MO to publicize your work or to ask for feedback on a new theorem. This holds even if you have a sort of "fig-leaf" question -- it's usually pretty clear if a question is an honest query or a veil for self-promotion. $\endgroup$ – Andy Putman Dec 29 '13 at 18:55
  • $\begingroup$ @AndyPutman That's a good point. There's really not enough information at hand to give more than somewhat generic advice. $\endgroup$ – Todd Trimble Dec 29 '13 at 19:06
  • $\begingroup$ @Andy, how would a question of the following form be received? "I have applied the following methods X,Y and Z in working on problem Q. A seemingly novel aspect is the (100 word description here). Is this aspect, or even the combination of X,Y and Z, addressed or discussed in the literature? For those wanting more detail, I have (linked PDF) available." $\endgroup$ – The Masked Avenger Dec 30 '13 at 0:50
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    $\begingroup$ @TheMaskedAvenger : My guess is that it would be poorly received. It is fine to ask whether a specific thing is known (as long as it is at the appropriate level and you have done a reasonable literature search before asking), but in general I think that one should mention one's own work only in answers to other people's questions (and then only when it directly answers those questions, which is extremely rare). $\endgroup$ – Andy Putman Dec 30 '13 at 1:05
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    $\begingroup$ (here's an example of an answer I wrote that referred to my own work and was well-received : mathoverflow.net/a/52407/317). $\endgroup$ – Andy Putman Dec 30 '13 at 1:06
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    $\begingroup$ As I commented under your question it is an undergraduate exercise (I literally mean it, I do give similar exercises to my students) to write any NP problem as an IP problem and prove the correctness of the reduction from the NP problem to IP. This is not research level unless you have very strong theoretical or experimental (e.g. breaking RSA factoring challenges) evidence to support that your reduction is considerably better than other standard reductions from factoring to IP. $\endgroup$ – Kaveh Dec 30 '13 at 8:50
  • $\begingroup$ ps: it seems to me that you have some confusion and misconception about understanding the difference between LP and IP, you cannot use Simplex or other LP algorithms to solve IP as that implies P=NP. $\endgroup$ – Kaveh Dec 30 '13 at 8:54
  • $\begingroup$ @Kaveh I definitely don't confuse LP and IP; applying LP can give integer solutions in certain special cases, e.g. in case of total unimodularity or, for the matching problem. My MO question was asking for a reference to either IP or LP formulations and I got no feedback. Now I had already asked how to react to such a failed request and was encouraged to share my ideas; but how can I provide a better solution to something that doesn't exist. In my opinion an IP or LP formulation could give new means of studying the complexity of Factoring Problem - but apparently that isn't appreciated. $\endgroup$ – Manfred Weis Dec 30 '13 at 11:08
  • $\begingroup$ @Kaveh please give your undergraduate students the task of formulating the integer factoring problem as either an IP or an LP and provide me their solutions so I can compare or, provide the missing pointer to the "other standard reductions from factoring to IP" $\endgroup$ – Manfred Weis Dec 30 '13 at 11:13
  • $\begingroup$ @AndyPutman what then is the button "Answer your Question" good for; I thought that sharing new knowledge is a noble idea and, what is evil about checking first, whether something is already known, before providing it as an answer. I have checked the internet for a long time and also asked for references, both without result and so I guess my ideas could be new. $\endgroup$ – Manfred Weis Dec 30 '13 at 13:28
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    $\begingroup$ It doesn't matter whether sharing "new" knowledge is noble. That's simply not the purpose of MO (it also isn't meant to feed the hungry, clothe the naked, etc). Attempts at self-promotion will be downvoted, closed, and deleted. Please find some other venue (eg a blog) for this. $\endgroup$ – Andy Putman Dec 30 '13 at 15:03
  • $\begingroup$ OK, understood; my solution won't appear on MO and neither a link to anything I publish in that respect. $\endgroup$ – Manfred Weis Dec 30 '13 at 16:05
  • $\begingroup$ I don't know your background but I should say that on the first look it looks like an amateur trying to promote or check publishable of some kind of algorithm for factoring. Your question hasn't got an answer because it is not clear what you are asking exactly. If I explain to you that it is easy to formulate factoring as IP would that answer your question? If you are claiming that you have found some new interesting formulation of factoring as an IP or LP $\endgroup$ – Kaveh Jan 1 '14 at 0:46

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