Wikipedia:Reference desk/Archives/Mathematics/2016 May 21

= May 21 =

Polynomial optimization problem
Description of the problem: Given $$f: \mathbb{C} \rightarrow \mathbb{R}$$ and $$a \in \mathbb{R}$$, find a polynomial $$p$$ with integer coefficients such that $$p$$ has a root $$r$$ with $$f(r) = a$$ (and constrain the degree and range of coefficients). What kind of algorithms exist to find a set of coefficients within the range such that $$|f(r) - a|$$ is minimized, beyond bruteforce? 24.255.17.182 (talk) 01:35, 21 May 2016 (UTC)
 * I naively expect this problem to be reducible to one of integer programming, which however I know to be NP-hard.--Jasper Deng (talk) 06:06, 21 May 2016 (UTC)
 * The goal of f(r) = a is probably hopeless since there are uncountably many possible a's and only finitely many possible r's. For the minimization problem you would probably need some additional information about f. For example is f known to be continuous, analytic or a polynomial? The problem sounds tricky even if f is the identity (i.e. f(x)=x). --RDBury (talk) 07:22, 21 May 2016 (UTC)

Using

 * 1) How do I make a multiplication table? For: Commons:File:125x4.jpg
 * 2) This: Commons:File:Paramètre R.JPG does not display like this: LaTeX/Mathematics —User 000 name 05:20, 21 May 2016 (UTC)
 * Using TeX is skill that takes some time to learn an this image looks a bit tricky to duplicate. If you want to learn TeX you could start with help:math. In this case you could also replace the image with a wiki table. But since the image is only used once, I wouldn't be overly concerned. Yet another possibility is just to remove or replace it in the article where is used; if 20 other versions of the article can get by without it then I'm sure the Germans can do without it as well.
 * Again, only used in one article. I would just go ahead and replace the image with the proposed replacement since it looks fine, just trivial differences in typography. --RDBury (talk) 08:02, 21 May 2016 (UTC)
 * For future reference, if you need to type a tag without invoking the tag itself, use the  tag. E.g. "Using    ", not "Using  ". I've fixed that in the title, it was causing problems. -- Meni Rosenfeld (talk) 19:55, 23 May 2016 (UTC)

\begin{matrix} \color{Gray} {}^1 & \color{Gray} {}^2 \\ 1&2&5 \\ \times& &4\\ \hline 5&0&0 \end{matrix}
 * These are not very good solution, but I hope at least they resemble what you need: $$

\qquad

\begin{array}{l} \color{Gray} {}^1\, {}^2 \\ 125 \\ \times\ 4\\ \hline 500 \end{array}

\qquad \qquad

R=\sum_{i=i}^S \left( \frac {(i-1)C_i}C \right) $$ CiaPan (talk) 13:16, 24 May 2016 (UTC)