# tohecz

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bio website kmlinux.fjfi.cvut.cz/… location Prague, Czech Republic age 27 member for 2 years, 2 months seen 17 hours ago profile views 133

Math PhD student at Czech Technical University in Prague and at LIAFA in Paris. At the same time, I'm a typesetter (and partly the copy editor) of one scientific journal (done in LaTeX, of course).

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# 338 Actions

 Nov22 suggested approved edit on Integral value of z Nov19 awarded Informed Nov19 awarded Nice Answer Nov18 comment SageMath: Embed all roots of a polynomial You can identify the roots in another way. You may do qRoot=L.polynomial().complex_roots()[0] and redefine L as L. = NumberField(q, embedding=qRoot). Then f.roots(L) give 3 roots, and when you .N() them, you see that they are gamma, gammabar and the real root in some order. They will permute depending on which qRoot you choose. Nov18 answered Show that $x \mapsto \frac{f(x)}{x}$ is strictly increasing on (0,1) given that f '(x) is strictly increasing on (0,1) and that f(0)=0 Nov18 answered Is it true that $E[X^2]-E[Y^2] = 0?$ Nov18 accepted SageMath: Embed all roots of a polynomial Nov18 comment SageMath: Embed all roots of a polynomial @hardmath btw, I posted a comment like 2 hours ago, but it seems to get lost on its way. I said that galois_closure() seems to be what I was looking for, so you can make it an answer, even though it's not completely general. I know only need to find out how things work further, but manuals should help with that. Nov18 comment SageMath: Embed all roots of a polynomial @hardmath I asked a question exactly about it just before asking this one. However, your explanation doesn't seem to be enough, since I don't see why complex conjugation cannot fix a non-real field of degree $3$. Nov18 comment Nesting big-O with big-Omega $O(g(\Omega(h(n))))$: is it $O$ for all $\Omega$ or for one $\Omega$? I don't have a ref, but think if any function would be $o(\mathcal O(x))$ in "$\exists\forall$" interpretation ;) For me, $o(\mathcal O(x))=o(x)$, because $x\in O(x)$, but for you $o(\mathcal O(x))=\emptyset$ because $(x\mapsto0)\in O(x)$. As I said, avoid unclear notation, it cannot be useful. Just write it out as I did. Nov18 comment SageMath: Embed all roots of a polynomial I don't know what you mean by "splitting", but yes, I obviously need to work over $\mathbb Q$, since I basically want to express $\mathbb Q(\gamma, \overline\gamma)$ as $\mathbb Q(\alpha)$ for some $\alpha$. Nov18 comment $\lim_{x \to 0} \frac{x^n}{\cos\sin x -\cos x}=l$, find $n$ such that $l$ is non zero finite real One should be quite carefull when writing $\sin x\approx x-x^3/6$ instead of $\sin x=x-x^3/6+\mathcal{O}(x^5)$, it takes some good 6th sense to be sure you can do it ;) Nov18 revised $\lim_{x \to 0} \frac{x^n}{\cos\sin x -\cos x}=l$, find $n$ such that $l$ is non zero finite real Improved formatting. Nov18 answered $\lim_{x \to 0} \frac{x^n}{\cos\sin x -\cos x}=l$, find $n$ such that $l$ is non zero finite real Nov18 comment The sign of $0$ is both positive and negative or neither positive nor negative? I mean examples like this: "The derivative of $x\mapsto |x|$ is $+1$ for positive $x$ and $-1$ for negative $x$. Nov18 suggested approved edit on $\lim_{x \to 0} \frac{x^n}{\cos\sin x -\cos x}=l$, find $n$ such that $l$ is non zero finite real Nov18 comment The sign of $0$ is both positive and negative or neither positive nor negative? If $0$ is both positive and negative, how do you define $\operatorname{sgn}0$? Nov18 revised Nesting big-O with big-Omega $O(g(\Omega(h(n))))$: is it $O$ for all $\Omega$ or for one $\Omega$? added 85 characters in body Nov18 answered Nesting big-O with big-Omega $O(g(\Omega(h(n))))$: is it $O$ for all $\Omega$ or for one $\Omega$? Nov18 answered Notation for translating vectors