Can we use the bound of the absolute values of the roots and that the constant coefficient is prime to show that $f(x)$ must be irreducible in $\mathbb Q[x]$
Yes, that is indeed exactly how we can prove the irreducibility of $x^j+x^k+2$, by more closely inspecting its (complex!) roots.
Fir...
I don't think SearchOnMath support keywords and multiple formulas - as Approach0 does. But take my words with grain of salt - I haven't really played around with SearchOnMath that much.
I should get some sleep, it is already past midnight in my part of the world. See you later!
@Sil My guess is they separate searching process into mathematical phase textual phase (as they state at the bottom of their search result page). And it seems they filter "irreducible" first and then filter that formula based on previous filtered results. Because there are too many documents having "irreducible" occurred, and the first phase returns a limited number of results, you may not find your post after applying that formula keyword.
@MartinSleziak I think they do, at least they claimed here: "SearchOnMath is able to search for mathematical formulas and/or text" (searchonmath.com/about).
Thanks for an edit. Maybe when I have a bit of time, I'll add at least one example with links to that bullet point. (One to search with |x| and one with search \left|x\right|.)
Quoted here: "This project was a part of my thesis. After I graduated I had to abandon it because I didn’t know how to make money with it and I didn’t have spare time to evolve it. "
Sounds a little doom for a new comer in this field :P I do have spare time due to doing PhD. research full time, but I admit not too many people pay attention to math-aware search and it may not be sustainable with current amount of users.
@MartinSleziak Got it. Yes, I am not sure on that.
@Sil You can see the score if you use browser's inspect tool, ahead of each DOM element of search result, there is a hidden <span> element with class "score", that is the corresponding result score.
Although I am not sure if it is better to show result scores. I imagine for most people, seeing a score around result is not intuitive, common search engines don't do that too.
"After I graduated I had to abandon it because I didn’t know how to make money with it and I didn’t have spare time to evolve it. " Why not open source it then...
"Good news, Linode has agreed to sponsor my hosting cost for one year." Does it mean better vps? :)
Even assuming you find a perfect threshold, is that really necessary to cut results under that score? I am open to discuss this. But I think hard code a threshold is not very robust because the way TF-IDF scoring works: The score in theory only makes sense to compare between results of same query.
@Sil Not really, it covers the cost of current 4 nodes for one year (5$ / 1 node / year).
Well what other search engines do is that they either cut it or first show you relevnant results and then state that following results may not be relevant or something
@Sil I will think about it. The way I understand text scoring part is that they are derived from Odds ratio or likelihood ratio and by thinking query q is fixed, something like P(R | d,q) = P(R|d)
I may not be just applying a threshold, I think they use other strategies, I will keep a note and think about it.
@Sil Because it uses p instead of n? And there are many p so my math scoring sums a much lower score? I am not sure, I will look into it locally to find out.
I think it is more detailed than what I can explain here in a few words. There is the exact scoring formula I use to score a math match.
@Sil It is hard to design a perfect score like that. Just like the most bottom result which you think is irrelevant, but it still share some matched parts.
like, does the length of MSE post influence score of a formula in it? even if the formula is the same? like having one post with 10000 characters and one with 100 charaters, but both sharing a formula
say you search x^2 and it returns a result containing x^2+1, the latter is a document formula, and its length is defined as the number leaves of its tree representation.
but if i search in "blablablablablablabla $x^2$" versus in "blablablablablablablablablablablablablablablablablablablabla $x^2$", the score should be the same?
the index mainly contains inverted lists and dictionary of the terms, there are other indices such as compressed document content indexed by id, they are used in a later stage when you highlight results.
@Sil Take your time, no worry, compared to many posts on MSE, it is easy to understand. I am sure you will grasp the idea very soon.
If later you want to inspect scores, you can paste this into your inspect tool console (e.g., under console tab in Chrome): $('span.score').each(function (i,r) { console.log(r) });
Can we use the bound of the absolute values of the roots and that the constant coefficient is prime to show that $f(x)$ must be irreducible in $\mathbb Q[x]$
Yes, that is indeed exactly how we can prove the irreducibility of $x^j+x^k+2$, by more closely inspecting its (complex!) roots.
Fir...
