Clarification regarding hint given for showing $p(x)$ is irreducible over $\mathbb{Q}(\sqrt{-2})$.
Irreducibility of $p(x)=x^4-4x^2+8x+2$ over $\mathbb{Q}(\sqrt{-2})$- Dummit Foote Abstract algebra $9.4.10$
Why is it OK to jump into the scope of an object of scalar type w/o an initializer? Icon for pinned tabs in Safari? It would be nice to  for .  As it is, SE kind of stands out (in a not cool way): Series with denominator that is square of product of consecutive numbers Evaluate $\sum_{k=1}^{\infty} \frac{1}{k^2(k+1)^2}$.   I've tried to use a telescoping approach, but it doesn't seem to work. It doesn't also seem to converge to a "pretty" value as well. options for [for /f "usebackq" %%f in (`find "" path`) do] sentence in batch I symplified my problem: @echo off set res=  for /f &quot;usebackq&quot; %%f in (`find &quot;a&quot; list.txt`) do set res=%%f echo %res%  pause&gt;nul and that things.txt file in the code is like:  list.txt file in the code is: apple pitch pear melon mango  As you expect, the result of this code is mango  because the line 'mango' is located below the line 'apple' and 'pear' But the result I want is apple  or pear  Specifically, I want to put each of the other values above mango such as apple and pear into the variable res using option keys provided. is there any way to do that? Escape a string for a sed replace pattern In my bash script I have an external (received from user) string, which I should use in sed pattern.  REPLACE="&lt;funny characters here&gt;" sed "s/KEYWORD/$REPLACE/g"   How can I escape the $REPLACE string so it would be safely accepted by sed as a literal replacement?  NOTE: The KEYWORD is a dumb substring with no matches etc. It is not supplied by user. Was "book" to "beek" as "foot" is to "feet"? "Foot" is a curious word in English because it is pluralized in an unusual way; the "oo" in the word is changed to "ee".  Did this once use to be a standard way of pluralizing things in English (or a language that contributed to English), which would mean that the plural of "book" was "beek" instead of "books"?  Or, is "feet" just a one-off? How to get RGB values from UIColor? I'm creating a color object using the following code.  curView.backgroundColor = [[UIColor alloc] initWithHue:229 saturation:40 brightness:75 alpha:1];   How can I retrieve RGB values from the created color object? A map is continuous if and only if for every set, the image of closure is contained in the closure of image How do I move Steam games to a new computer without re-downloading them? I often see "replace with" and "replace by" used interchangeably, but this doesn't sound right to me:     I replaced that component by this one.   I would use "with" in such a sentence. "By" only seems reasonable in passive, although "with" sounds like it would there work too:     That component was replaced by this one.   That component was replaced with this one.   In my native language, the equivalent of "replace by" can only be used in passive, and even then it's a bit weird unless a person is the object replacing something – perhaps this affects my judgment?  Web searches haven't come up with anything conclusive; the results are contradictory and speculative at best.  Are "replace with" and "replace by" interchangeable in active context? What about passive? Are there stylistic reasons to prefer one over the other? Does this double sum $\sum_{m=0}^\infty \sum_{n=0}^\infty \frac{m+n+mn}{2^m(2^m+2^n)}$ converge? I'm granted a one-entry Schengen visa and now I can't go. Will having an unused visa in my travel passport have any consequences like future visas refusal? Do I need to do anything special? Number of possible marriage arrangements if Marriage Condition is satisfied Suppose I have a set of $n$ boys and each subset of $1\leqslant k \leqslant n$ boys knows at least $k$ girls then this means that the set of boys $B$ satisfies the marriage condition.  I am doing an exercise from a Graph Theory book and it says we can show by induction on $n$ that the number of possible marriage arrangements is $\geqslant t!$ if every individual boy knows at least $t \leqslant n$ girls or there are $\geqslant t!/(t-n)!$ possible marriages if each individual boy knows at least $t&gt;n$ girls.   I am struggling to see how the induction hypothesis can be implemented to prove the $n+1$ case. When you swap from the $n$ to $n+1$ case the conditions change and I can't see the link between them.  Would anyone be able to point me in the right direction? What is the right ffmpeg output format for a v4l2-loopback device? Following the guide in  I did:  $ sudo modprobe v4l2loopback $ ffmpeg -f x11grab -r 15 -s 1280x720 -i :0.0+0,0 -vcodec rawvideo -pix_fmt yuv420p -threads 0 -f v4l2 /dev/video0   The device /dev/video0 shows up as expected but the ffmpeg command fails with following output:  $ ffmpeg -f x11grab -r 15 -s 1280x720 -i :0.0+0,0 -vcodec rawvideo -pix_fmt yuv420p -threads 0 -f v4l2 /dev/video0 ffmpeg version 4.0 Copyright (c) 2000-2018 the FFmpeg developers ... [x11grab @ 0x559767794cc0] Stream #0: not enough frames to estimate rate; consider increasing probesize .... [v4l2 @ 0x55976779e6c0] ioctl(VIDIOC_G_FMT): Invalid argument Could not write header for output file #0 (incorrect codec parameters ?): Invalid argument Error initializing output stream 0:0 --  Conversion failed!   I already tried to follow the suggestions below the answer to no avail. I noticed that v4l2 is listed as demux only in ffmpeg -formats. Does that mean I can't use it for output to /dev/video0? If so, what should I use instead? I tried h264 but that crashes after ~1000 frames with following error message:  $ ffmpeg -f x11grab -r 15 -s 1280x720 -i :0.0+0,0 -vcodec rawvideo -pix_fmt yuv420p -threads 0 -f h264 /dev/video0 ffmpeg version 4.0 Copyright (c) 2000-2018 the FFmpeg developers ... [x11grab @ 0x55da61e29cc0] Stream #0: not enough frames to estimate rate; consider increasing probesize ... File '/dev/video0' already exists. Overwrite ? [y/N] y .... Error writing trailer of /dev/video0: Invalid argument .... Conversion failed! msiexec is command prompt software that installs an  program. But I have found that you can install an MSI file from the command line by just typing in the name of the MSI file on the command line.  But in order to uninstall the MSI file, it seems you have to call the msiexec program and give it a /x or /uninstall.  How can I uninstall an MSI from the command line without using the msiexec routine? How to find files between two dates using "find"? how to extend a basis Let $\alpha(t)$ be a regular curve. Suppose there is a point $a$ in $R^3$ such that $\alpha(t)-a$ is orthogonal to $T(t)$ for all t. Prove that $\alpha(t)$ lies on a sphere.  So, I let $\alpha(t)=(x(t), y(t),z(t))$ and $a=(a,b,c)$.  Since, $\alpha(t)-a$ is orthogonal to $T(t)$,  $&lt;\alpha(t)-a,T(t)&gt;=0$.  But I don't know how to solve this.. Does anyone have a simple work-flow for drawing cross sections of earth features in QGIS?   My thing is that QGIS is being used to present the plan view, but we have a little interest in some elevations as well. All the data is one set and is simply an elevation value in the attribute table, I don't want to have to move all that to CAD.  One logical workaround is to present the z value as the y.  I am a dunce in paper space in CAD, and would be more comfortable with the QGIS Composer. How to set a default query timeout with JPA and Hibernate?