Wouldn't Python be much faster if its code ran directly on a native machine?
What are advantages of bytecode over native code?
font set problems in beamer i want to set the main font in my beamer as "Consolas" i do like this :  \documentclass{beamer} \usepackage{fontspec} \usetheme{Warsaw} \begin{document} \setmainfont{Consolas} \begin{frame} we discuss the ambiguities of existing security definitions and then provide a general framework for defining AKE security when involve strong adversary capabilities \end{frame} \end{document}   but after compile it , the font doesn't change, it is the same with that before the main font was set. what's the reason? Finding a basis for a certain vector space of periodic polynomials I am having a little bit of trouble solving an homework question.  I found that $S={ p(x) \in R_4[x]} \big| p(x)=p(x-1) $ is a vector space.  Now I need to find some set, K that holds ${span(k)=S}$  My idea was to substitute: $ a+bx+cx^{2}+dx^{3}+ex^{4}=a+b(x-1)+c(x-1)^{2}+d(x-1)^{3}+e(x-1)^{4}$  But here I get something that seems a little bit weird, I'd like to look if I have any mistakes that I did not notice. and if I had mistakes, how to make my answer right. I calculated the right side of the equation and I got to  :  $a+b(x-1)+c(x-1)^{2}+d(x-1)^{3}+e(x-1)^{4}=a+bx-b+cx^{2}-2cx+c+dx^{3}-3dx^{2}+3dx-d+ex^{4}-4ex^{3}+6ex^{2}-4ex+e= (a-b+c-d+e)+(b-2c+3d-4e)x+(c-3d+6e)x^{2}+(d-4e)x^{3}+ex^{4}  $  From here, $ (a-b+c-d+e)+(b-2c+3d-4e)x+(c-3d+6e)x^{2}+(d-4e)x^{3}+ex^{4}=a+b(x-1)+c(x-1)^{2}+d(x-1)^{3}+e(x-1)^{4}\Rightarrow $  $(-b+c-d+e)+(-2c+3d-4e)x+(-3d+6e)x^{2}+(d-4e)x^{3}=0+0x+0x^{2}+0x^{3}+0x^{4}$  And the solution to this equation is only whan $a=b=c=d=e=0$.  I think that I am maybe not in the right direction. Do you have any Idea how to find a set $K\Rightarrow span(K)=S$ ?  Thanks in advance. Is there something I can do from the terminal when a program freezes up and Ubuntu becomes unresponsive? Numerical Approximation of Differential Equations with Midpoint Method How could I adjust the size and placement of chapter heading in my custom class? I am using report class as my base. When I used titlesec package inside my custom class, it threw error     ! Package titlesec Error: Not allowed in `easy'   settings. I'm adding a title clock in the foot line of a beamer slide, if I compile it with pdfLaTeX it works fine; while the clock doesn't align in the middle vertically if compiling with XeLaTeX. How can I fix this.  Here is my MWE:  \documentclass[10pt]{beamer} \usepackage[font=Times,timeinterval=1]{tdclock} \usetheme{Madrid} \title{Title} \author{Authors} \institute{Institute} \date[\initclock\tddate\ \ \tdtime]{\today} \begin{document} \frame{\titlepage} \end{document} Rounding Percentages How to turn a ruled pattern into a multivariable function How to convert a column number (e.g. 127) into an Excel column (e.g. AA) grep a file, but show several surrounding lines? How to create a color of the same brightness and saturation? Let's consider three colors: Red, Green and Blue. For blue I created a specific shade, something like #F2F5F7. If you see this color, it has a certain level of shade, brightness and saturation value of blue.  I want to create the same equivalent color but for Green and Red, how to get that? Diamond moderator privileges vs. 10k rep privileges? As we are in election period, I don't get the difference between getting to 10k reputation point and the diamond. What additional controls do you earn with the diamond ? of Stack Overflow, all content posted on Stack Exchange sites by their users (i.e. you wonderful people) has been provided to the whole universe under . For my fellow non-lawyers, that license basically means:   Anyone can use any Stack Exchange posts at any time without having to ask for permission Making money off of the copied content is permitted You don't even have to copy stuff from here verbatim; you can just use it as a starting point and make whatever edits you want There are just two rules you have to follow:   You have to provide . Simple links to the original post and author info are just fine. You have to  and allow other people to use your content, as long as they follow these very same rules. How meta!    (If you ever forget any of that, and want to refresh your memory, the license info is linked to in the footer of every page.)  There are, in fact, a lot of people who republish varying amounts of our content for assorted reasons. Unfortunately, there are some Stack Content Republishers Attributing Poorly and/or Excelling at Ranking (SCRAPERs, for short).  In this context, "attributing poorly" means any use that doesn't follow our attribution rules or make any other reasonable attempt at give credit. This can get pretty egregious; I've seen SCRAPERs that not only don't link back to SE originals, but also use fake author info and post dates to make it harder to find originals. By "excelling at ranking," I'm referring to copycat sites that end up higher in Google results than the original SE sites do for the same content. That's not necessarily wrong, but in some cases, it indicates inappropriate SEO hackery.  So, the question is: what can you do if you spot a SCRAPER? I am afraid that listing doesn't support javascript.  \begin{lstlisting}[language=javascript] ... \end{lstlisting}   What am I doing wrong? I want to prove:  $$\int_{0}^{2\pi}\frac{1}{a^{2}\cos^2t+b^{2}\sin^{2}t}dt=\frac{2\pi}{ab}$$  by the deformation theorem of complex variable.  Then I consider a parameterization $\gamma:[0,2\pi]\rightarrow A$, traveled in the opposite direction of the clock hand, of the ellipse (in $\mathbb{C}$):  $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$  I thought of searching for a function $f:A\rightarrow \mathbb{C}$ (analytic in $A$) and a curve $\lambda:[0,2\pi]\rightarrow A$ (homotopic to $\gamma$) and use the deformation theorem:  $$\int_{\gamma}f = \int_{\lambda}f$$  But I can not find a function $f(z)$ that meets what I need, can you help me to find the f?   P.D: Necessarily I have to use the theorem of deformation How do I show that:  $$\frac{1}{\sin^{2}\frac{\pi}{14}} + \frac{1}{\sin^{2}\frac{3\pi}{14}} + \frac{1}{\sin^{2}\frac{5\pi}{14}} = 24$$  This is actually problem B $4371$ given at this . Looks like a very interesting problem.   My attempts: Well, I have been thinking about this for the whole day, and I have got some insights. I don't believe my insights will lead me to a $\text{complete}$ solution.   First, I wrote $\sin\frac{5\pi}{14}$ as $\sin\frac{9 \pi}{14}$ so that if I put $A = \frac{\pi}{14}$ so that the given equation becomes, $$\frac{1}{\sin^{2}{A}} + \frac{1}{\sin^{2}{3A}} + \frac{1}{\sin^{2}{9A}} =24$$ Then I tried working with this by taking $\text{lcm}$ and multiplying and doing something, which appeared futile. Next, I actually didn't work it out, but I think we have to look for a equation which has roots as $\sin$ and then use $\text{sum of roots}$ formulas to get $24$. I think I haven't explained this clearly.         $\text{Thirdly, is there a trick proving such type of identities using Gauss sums ?}$ One post related to this is:  I don't know how this will help as I haven't studied anything yet regarding Gauss sums. What makes the inside of a shape the inside? What's the weight of the earth? What's the weight of the earth?  That is, what's the weight of the earth in the gravitational field of the sun? I imagine it's either   $0$, because there's no net fall toward the sun, so the downward component of acceleration is $0$ and $F=ma=0$, or $Gm_1m_2/r^2\approx7\cdot10^{-11}\cdot6\cdot10^{24}\cdot2\cdot10^{30}/(1.5\cdot10^{11})^2\approx4\cdot10^{22}$ Newtons,   but which, and why? I was surprised to find that standalone package can not compile a document with an equation:  \documentclass{standalone} \begin{document} \begin{equation} % not working! F(V, T) = E(V) + D(T) \end{equation} \end{document}   Is there an option or some workaround that allows this? The current error is something like:   ! Missing $ inserted.   in line 4. (The idea of course is that the including (main) document can just \input the standalone without knowing if is going to be an equation or something else) Drawing a triangle from medians Is it possible to draw a triangle, if the length of its medians $(m_1, m_2, m_3)$ are given only?  Someone asked me this question, but I can not see it. Is it really possible?  UPDATE  Apart from the algebraic solution given by JimmyK4542, can anyone give me a direct construction?  I mean, it should sound like:     Draw a line segment sufficiently long. Cut the length of $m_1$ from it. Then $\ldots$