Let $f$ be a polynomial in the variables $x_1, \ldots, x_n$, where $n &gt; 1$, and with coefficients in $\mathbb{Z}$.   Are there convenient assumptions on $f$ to make the following implication? Assume that $f$ is irreducible in the ring ${\mathbb Z}[x_1, \ldots, x_n]$, then $f$ is irreducible in $\mathbb{Q}[x_1, \ldots, x_n]$.   For instance, if $n = 1$, you would require that the leading coefficient of $f$ is equal to $1$ (Gauss lemma). Are you aware of a similar condition in case $n &gt; 1$ ? Thank you.
Gauss's Lemma for polynomials claims that a non-constant polynomial in $\mathbb{Z}[X]$ is irreducible in $\mathbb{Z}[X]$ if and only if it is both irreducible in $\mathbb{Q}[X]$ and primitive in $\mathbb{Z}[X]$.   I wonder if this holds for multivariable case.      Is it true that a non-constant polynomial in $\mathbb{Z}[X_1,\dots,X_n]$ is irreducible in $\mathbb{Z}[X_1,\dots,X_n]$ if and only if it is both irreducible in $\mathbb{Q}[X_1,\dots,X_n]$ and primitive in $\mathbb{Z}[X_1,\dots,X_n]$?    Thank you for your help.
Featured On Meta section doesn't list MSE posts on meta sites When hyperref is loaded I receive the following error:     TeX capacity exceeded, sorry [input stack size=5000].   However, when I remove hyperref package it compiles successfully. I traced it back and found that \maketitle causes the error but don't know how to fix it. Is there any way to use hyperref in my setup.   Code:       %!TEX TS-program = xelatex     \documentclass[journal,transmag,]{IEEEtran}      \usepackage[hyphens]{url}     \usepackage{hyperref}      \usepackage{xunicode}      \usepackage{fontspec}      \usepackage{polyglossia}     \setmainlanguage{english}     \setotherlanguage{arabic}     \newfontfamily\arabicfont[Script = Arabic]{Amiri} % Replace 'Simplified Arabic' with a font from your system       \begin{document}     \title{A Very Nice Title}      \author{\IEEEauthorblockN{             John Doe\IEEEauthorrefmark{1}}%,~\IEEEmembership{Member,~IEEE}         \IEEEauthorblockA{\IEEEauthorrefmark{1}My address}         % &lt;-this % stops an unwanted space         \thanks{Manuscript received mm dd, 20xx; revised mm dd, 20xx.               }     }      % The paper headers     \markboth{headers...}%     {Shell \MakeLowercase{\textit{et al.}}: Bare Demo of IEEEtran.cls for IEEE Transactions on Magnetics Journals}      \IEEEtitleabstractindextext{%         \begin{abstract}My Abstract.\end{abstract}          % Note that keywords are not normally used for peerreview papers.         \begin{IEEEkeywords}             Key 1, Key 2     \end{IEEEkeywords}}      \maketitle       \IEEEdisplaynontitleabstractindextext     % \IEEEdisplaynontitleabstractindextext has no effect when using     \IEEEpeerreviewmaketitle       \section{Introduction}     English Text      \begin{Arabic}      السَلَامُ عَلَيكُمْ     \end{Arabic}       \end{document} Repeat command n times? Is it possible to define a command, which repeats the following command n-times? Call it for example \Repeat, then   \Repeat[4] \command{...}    should be equivalent to   \command{...} \command{...} \command{...} \command{...} Suspected adware infection of Mac So I had  closed within eight minutes of asking.  Is this a little fast? Not only do I object to the reason it was closed (not a real question, come on I'm asking for decent books!), but it was closed insanely fast. Should there be a grace period for questions (diamond mods exempt if so) before they can be voted on to be closed? "Dark L" is "L" at the end of the word or after a vowel sound. Example: ball, pull.  "Light L" is "L" at the beginning or before a vowel sound. Example: light, love.  There are 4 explanations of how to pronounce "dark L":   1st explanation: the tongue tip must contact the ridge right behind the upper teeth. 2nd explanation: before the tongue tip must contact the ridge right behind the upper teeth, you must curl the tongue and make sound like /r/ before make the /l/ as in the 1st explanation. 3rd explanation: just put the tongue between upper and lower teeth is enough to make the dark L 4th explanation: the tongue tip must contact the ridge right behind the upper teeth &amp; the back of the tongue raises up (a British teacher teaches that).   see this vid:  and  for more info  So what is the correct way to make the "dark L"? Getting attributes of Enum's value Clearly this is an edge case and I probably shouldn't have even tried awarding the bounty to a deleted answer, but why is the bounty award button even available?  It's not a bug since someone added in the notification seen in the final image.  But that sure seems like a roundabout way to let the user know that they can't award a bounty to a deleted answer.  The second step is particularly strange since the system really ought to know that the warning is pointless: no bounty can be awarded.  My suggestion is to rip-off the  and let bounties be awarded without the warning.  Then remove the single click button from deleted answers. How do I connect to a WPA wifi network using the command line? So basically, I'd like to use iwconfig to connect to my wifi network when I'm not inside X. But I just don't see a way to do it in the man page. Any idea? I've been learning about Galois theory recently on my own, and I've been trying to solve tests from my university. Even though I understand all the theorems, I  seem to be having some trouble with the technical stuff. A specific example would be how to find the Galois group of a given polynomial. I know some tricks, and I manage to solve some of those questions, but some not.  For example, one of the tests asks to find the Galois group of $x^{4}-4x+2$.  I can see that it is irreducible over $\mathbb Q$ (Eisenstein), but I have no clue as to how to find its Galois group over $\mathbb Q$. Can someone tell me how to do this? General techniques concerning this sort of problems are also welcome :).  Thanks! According to Hubble's Law, how can the expansion of the Universe be accelerating? Scientists today think the expansion of the universe is accelerating.   According to Hubble's law, objects further away are moving faster than objects closer to us. The further away an object is, the further back in time we are seeing, so in the past objects moved faster (is this sentence correct?).  So because objects moved faster before than they do now, surely that's deceleration not acceleration?  my textbook says "if Scientists today think the rate of expansion of the Universe were decreasing then distant objects should appear different to Hubble's Law predictions: universe is accelerating. More distant objects would seem to be receding faster (since expansion was faster in the past)" I'm doing some web scraping and sites frequently use HTML entities to represent non ascii characters. Does Python have a utility that takes a string with HTML entities and returns a unicode type?  For example:  I get back:  &amp;#x01ce;   which represents an "ǎ" with a tone mark.  In binary, this is represented as the 16 bit 01ce.  I want to convert the html entity into the value  u'\u01ce' I am reading a paper and have questions about the details of the procedure described. I have read other papers by the same team but they don't explain too much about that procedure anyway. I think it might be common, but my supervisor doesn't know it too.  I am stuck and I want to get out of it. As a student working on my master thesis, can I email the contact author for the manuscript cold out, or should I ask someone to contact him for me? I would ask my supervisor but I don't want it to imply that I'm avoid taking initiatives when I could do it on my own. What is the VC dimension of a decision tree? What is the  of a decision tree with k splits in two dimensions? Let us say the model is CART and the only allowed splits are parallel to the axes.  So for one split we can  and then for any labeling of the points we could get perfect prediction (i.e.: shattered points)  But what about 2 splits, or any general k? class C {   T a; public:   C(T a): a(a) {;} };   Is it legal? for $f\in L^1[0,2\pi]$ define $$\hat{f}(n)=\int_{0}^{2\pi} f(t)e^{-int} dt$$ for $n\in\mathbb{Z}$, $X$ is a closed linear subspace of $L^1[0,2\pi]$ such that $\sum_{n} |\hat{f}(n)|&lt;\infty$ for each $f\in X$, we need to show that there is $M&lt;\infty$ such that  $\sum_{n} |\hat{f}(n)|\le M\int_{0}^{2\pi}|f(t)|dt$ for each $f\in X$  please tell me how to solve this one, I have no clue. What is the probability that the selected function maps prime numbers to prime numbers? Let $X = \{1, 2, 3, . . . , 25\}$. If a student selects a function randomly from the set of all functions from $X$ onto $X$, then what is the probability that the selected function maps prime numbers to prime numbers ? No idea how to proceed, please guide. Identifying a thin, black, worm-like creature with a hammer-shaped head I came across the creature shown in the photo below yesterday evening while walking the dogs. At first, I thought it was an earthworm, but a flashlight revealed it to be something I had never seen before.    It is approximately 12 inches (300 mm) in length and about 1/3 of an inch (10 mm) in diameter at its maximum. It is pitch black and very shiny—like piano black. It moves very slowly, using a snake-like motion. It had a very strange head, like a hammerhead shark.  I live in Durban, South Africa, if that helps to narrow down the possibilities.  Can anyone help in identifying this creature? How much hard disk space should be needed for Xbox 360? I want to get a 360 and don't know wether to get the bigger (250GB), newer, more expensive Elite, or get one of the older, smaller (120GB), last gen ones. I know the arcade is going to be too small to save anything useful  How much hard disk space is recommend? What else is stored besides games? Jutifying: irrational + rational = irrational