New hardware support install error
Hardware Enablement Stack (HWE) out of support
Prove that a polynomial is irreducible or the field contains a $p$th root An exercise from Lang:  Let $k$ be a field. Let $n$ be a nonnegative integer. Consider the polynomial $x^{p^n}-a \in k[x]$. Assume that $\text{char}(k) = p &gt; 0$. Prove that either the polynomial $x^{p^n}-a$ is irreducible over the field $k$ or there exists a $b\in k$ such that $a = b^p$.  How to prove this statement? I am a little bit confused with this statement. Probability that two random numbers are coprime is $\frac{6}{\pi^2}$ This is a really natural question for which I know a stunning solution. So I admit I have a solution, however I would like to see if anybody will come up with something different. The question is     What is the probability that two numbers randomly chosen are coprime?   More formally, calculate the limit as $n\to\infty$ of the probability that two randomly chosen numbers, both less than $n$ are coprime. How do I call legacy PHP files? I am unable to call PHP files inside the Drupal directory. My task is maintaining staff's old pages on the new platform. With pages written on clear HTML, there is no problem: I place files in a folder I created (domain.org/sites/default/files/share/staff_folder).  In sites/default/files/.htaccess I added DirectoryIndex share and now the link to the domain.org/sites/default/files/share/staff_folder/index.html can be used. When I import pages written in PHP, e.g. calling domain.org/sites/default/files/share/staff2_folder/index.php, I get a 403 error:     Forbidden      You don't have permission to access /sites/default/files/share/staff2_folder/index.php on this server.   While /sites/default/files/share/staff2_folder/index.html still works. I recently received this rather amusing message while reviewing a user's first post:  Congratulations! This was only a test, designed to make sure you were paying attention. This post has already been removed, but thanks for taking time to leave feedback for the author.   What is the purpose of this test? How does the audit work? What happens if I fail? Why was the system expecting me to negatively review a good post, or positively review a bad post? A review is obviously an audit. Should I report it? Do review audits count toward the Reviewer badge? Do robo-reviewers dream of electric sheep? So our 6-month-old boy still doesn't sleep through the night. He still wakes up at least once and wants to eat.  He takes 3 naps during the day, ranging from 30 minutes to 1.5 (sometimes 2) hours.  We usually put him down for the night at least 2 hours after his latest nap, but we haven't been able to get him down to 2 naps per day because he gets pretty cranky during the evenings. Depending on the duration and times of his naps, his bedtime ranges between 10 and midnight.  We have started feeding him a small amount (2 tablespoons dry) of rice cereal after his morning and evening naps in the hopes that he'll have a fuller stomach through the night, but he still wakes up hungry after sleeping between 3 and 6 hours. I can handle the 6 hours, since that means I get 6 hours of pretty much uninterrupted sleep, but it's usually more like 3-4.  Any suggestions? Given a filesystem path, is there a shorter way to extract the filename without its extension? Let $f:[0,\infty)\rightarrow [0,\infty) $ be a continuous strictly increasing function and $g=f^{-1}$. Let $a,b&gt;0$ and $a\neq b$. Then how $\displaystyle\int_{0}^af(x)dx+\int_0^bg(y)dy\geq ab.$ Any hint will be appreciated. How to get exact camera view? Radius of Convergence when using Series[] Someone who gives unsolicited explanations in a condescending way Can we continue to show the "Take a tour" banner after a user has created an account? When you view a Stack Exchange site without being logged in, you see a friendly banner, prompting you to take a tour and understand the features of the site:    This links off to a high quality resource that can help new users understand how the site works. However, the moment a user signs up to the site, this banner disappears from immediate view and hides itself as a link under the help menu.  My proposal is to continue showing this banner until one of the following conditions are met;   The user gets the "Informed" badge The user reaches a set amount of reputation (250 or 500 should be sufficient) The user chooses to hide the banner   This should increase the exposure of the tour to new users, who are the people who need the tour, rather than hiding it the moment a user signs up. I am having trouble loading csv files into layers using QgsVectorLayer().  I know this looks like a repeat, but I have carefully read     and    but still cannot get it work.  An example of my data file, test.csv:  Index,y,x 0,37.7646618,-122.4960858 1,37.777494,-122.416311 2,37.717707,-122.3997056 3,37.732284,-122.498118 4,37.749998,-122.392333   My code:  import os import urllib  import pathlib from qgis.core import QgsVectorLayer  local_path = 'C:\dev\FCMS_conflation\data\TMC_nodes.csv' node_layer = 'test'  abspath = os.path.abspath(local_path) params = {'delimiter': ',',           'decimalPoint': '.',           'xField': longitude,           'yField': latitude}  uri = "%s?%s" %(pathlib.Path(abspath).as_uri(), urllib.unquote(urllib.urlencode(params)))  layer = QgsVectorLayer(uri, node_layer, "delimitedtext")   The formatted URI looks like:  [] uri &gt;&gt;&gt; 'file:///C:/dev/FCMS_conflation/data/TMC_nodes.csv?decimalPoint=.&amp;delimiter=,&amp;xField=longitude&amp;yField=latitude'   I have tried many variations of the parameters, including the crs and type. But no matter what I try, I cannot create a valid layer.  [] layer.isValid() &gt;&gt;&gt; False   I have verified that I can add the file using the QGIS gui. I even tried using the uri provided by layer.metadata from within the Python plugin.   I am using QGIS 2.10.1 on Windows 7 64-bit machine. Finding the closure of some subsets of the ordered square I need to find the closure of these sets on the ordered square: $$A = \{(1/n)\times 0 | n\in \mathbb{Z}_+\}$$ $$B = \{(1-1/n)\times \frac{1}{2}| n\in \mathbb{Z}_+\}$$ $$C = \{x\times 0 | 0&lt;x&lt;1\}$$ $$D = \{x\times \frac{1}{2}| 0&lt;x&lt;1\}$$ $$E = \{\frac{1}{2}\times y | 0&lt;y&lt;1\}$$ I know that the closure is just the set itself united with its limit points. For $A$, the set of limit points, I imagine, are $\{&lt;1,0&gt;\}$, that is, the $x$ coordinate is $1$ and the $y$ is $0$. But  is says the reverse. What am I getting wrong? Following the same reasoning, $B' = \{&lt;1,\frac{1}{2}&gt;\}$ $C' = \{&lt;0,0&gt;,&lt;0,1&gt;\}$ What am I doing wrong? Low Quality review queue erroneously showing "Close" instead of "Recommended Close"? I was in the Low Quality Review queue, and the following review confused me:    It's showing eight "Close votes", which should be more than enough to close a question.  I checked the question's , and it wasn't somehow closed, then re-opened in the middle of the review.  So I then checked on each of the users, and noticed that the majority of them are under 3000 reputation, meaning they can only "Recommend Close".    However, all reviews are simply showing as "Close", which is extremely confusing.  Is this a bug, or possibly an undocumented change related to ?    Another recent example: Projecting a point onto a convex set decreases its distance from each point of that set For a convex set $K$, $x\in \mathbb{R}^d$ and $y=\Pi_K(x) $ (the projection of $x$ onto $K$), we want to show that for any $z\in K$ it holds that: $\|x-z\| \ge \|y-z\|$.  $$ $$  I'm not sure if the following proof is valid:  $$ y=\Pi_K(x) = \arg \min_{y\in K} ||y-x||  \Rightarrow \forall z\in K \langle y-x,y-z\rangle =0 $$ $$ ||y-x||^2_2+||y-z||^2_2=||x-z||^2_2  \quad (Pythagoras)$$  $$ \Rightarrow ||y-z||^2_2 \le ||x-z||^2_2 $$ $$ \Rightarrow||y-z|| \le ||x-z|| $$ So I integrate the holomorphic function $\frac{e^{iz} -1}{iz}$ over the half disk in the upper half plane, let me name it $\Gamma$. By using Cauchy's theorem, it equals 0.  $$0 = \int_{\Gamma} \frac{e^{iz} -1}{iz} = \int_{0}^{\pi}(e^{iRe^{i\theta}}-1)d\theta + \int_{-R}^{R} \frac{e^{it}-1}{it}dt$$  ($Re^{[0, \pi]}$ and $t: [-R, R]$ being the respective parametrizations.)  By splitting the left integral in two, I get $\int_{0}^{\pi} e^{iRe^{i\theta}}d\theta \rightarrow 0$ by dominated convergence, and $\int_{0}^{\pi} -1d\theta = -\pi$. By making $R \rightarrow \infty$, I'm left with  $$\pi = \int_{-\infty}^{\infty} \frac{e^{it} - 1}{it}dt = \int_{-\infty}^{\infty}\frac{\sin t}{t}dt + \int_{-\infty}^{\infty}\frac{\cos t -1}{it}dt.$$  How do I get rid of the integral on the right? I welcome all feedback. Show $\,p\mid 9^q -1 \implies q\mid p-1$ for odd primes $p$ and $q$ If $p$ and $q$ are odd primes show that $$p|(9^q -1) \implies q|(p-1).$$ ....  I am having difficulty to prove this.  Yes that was the question I have misunderstood between 9 and q!!! How to remove enamel from wire? What's the difference between Kage Bunshin no Jutsu and Tajuu Kage Bunshin no Jutsu? While the Kage Bunshin no Jutsu seems to be taught, the Tajuu Kage Bunshin no Jutsu is sealed, so nobody can learn the jutsu. Does that mean that there's a difference between these jutsus, aside from the number of Kage Bunshin created?   Or, why was the Tajuu Kage Bunshin no Jutsu sealed away? If there's no other difference, everybody could use this without reading the sealed scroll. How would Voldemort restore himself from a horcrux? If Voldemort's body dies, what process would he use to restore himself from a horcrux? His plans seem sloppy for the pains he had taken. For example, why create horcruxes from pieces of jewellery when they dont have the agency to seek out a new body by themselves?  He needed Quirrel, a person with unlikely ambitions to seek him out to gain an useful body. When that body was gone, he needed Barty Crouch, someone with questionable agency (he could be imprisoned) to transport Harry and draw his blood.  Nagini and the diary seems the only horcruxes with agency, the others are mostly inert.  What plans were ever taken to restore Voldemort from his horcruxes?