1,452 reputation
319
bio website kmlinux.fjfi.cvut.cz/…
location Prague, Czech Republic
age 27
visits member for 2 years, 2 months
seen 17 hours ago

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).

Code licence details applicable on my posts on TeX.SX.

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Nov
22
suggested approved edit on Integral value of z
Nov
19
awarded  Informed
Nov
19
awarded  Nice Answer
Nov
18
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.<gg> = 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.
Nov
18
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
Nov
18
answered Is it true that $E[X^2]-E[Y^2] = 0?$
Nov
18
accepted SageMath: Embed all roots of a polynomial
Nov
18
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.
Nov
18
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 $3$.
Nov
18
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.
Nov
18
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 $\alpha$.
Nov
18
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 ;)
Nov
18
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.
Nov
18
answered $\lim_{x \to 0} \frac{x^n}{\cos\sin x -\cos x}=l$, find $n$ such that $l$ is non zero finite real
Nov
18
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 $x$.
Nov
18
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
Nov
18
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 $\operatorname{sgn}0$?
Nov
18
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
Nov
18
answered Nesting big-O with big-Omega $O(g(\Omega(h(n))))$: is it $O$ for all $\Omega$ or for one $\Omega$?
Nov
18
answered Notation for translating vectors