How to list all user-defined variables with current values?
Is there an equivalent of MATLAB's Workspace window in Mathematica?
No field properly between $\mathbb Q$ and $E$ iff $G(K/\mathbb Q) \cong A_4$ or $S_4$ Why was mixing declarations and code forbidden up until C99? Correctly typesetting a tilde How do I set the tilde (~) character correctly in LaTeX?  There’s a  on Stack Overflow, with a lot of answers. But dare I say it? They all suck:   \textasciitilde is too high, \texttildelow is too low. $\sim$ can be tweaked to look more or less acceptable: {\raise.17ex\hbox{$\scriptstyle\sim$}} – but even that is a hack and uses the wrong symbol.   The point is – the tilde character is definitely an existing glyph in any font I am tempted to use. How can I just access and typeset that character, please? Without resorting to some other, similar-looking glyph that first needs to be nudged into place using a cunning combination of font size and raised boxes?  There must be a possibility to access that glyph directly from the font definition.  To demonstrate, look at this screenshot which attempts simply to display a C++ destructor of a type T (~T):    Compare this with the symbol we get in the browser: ~ – that’s what I want. Too many SE sites causes confusion have already been created through .  have already completed their beta stage and are waiting for launch.  are in public beta stage.  are in commitment phase in   proposals are listed in   Now it is really confusing to find a suitable site to ask a question. As an example - I host a blog using . Now I have a question about this hosting. I want to post it in a . Where will I post? I have 2 options available now.     Are developers trying anything to solve this confusing matter? How to allow Page Up in GNU Screen? I use Vim to edit text files on Linux. Commonly I connect to remote Linux machines using PuTTY from Windows.  I use GNU Screen commonly as well.  When using Vim inside Screen I am unable to use the Page Up key because Screen interprets it as a command to start copy mode.    I would like to use Page Up for its regular up-paging functionality.  How can I configure Screen to do this? This question is also open on EL&amp;U:   Considering the amount of controversy it aroused, I believe it's past "Learners'" level.    An edit was suggested to my sentence.     There was were an orange, some grapes, two apples and a small pile of cherries on the plate.   In my native language plurality of the verb always follows plurality of the first element on the list. There were an orange,... sounds awkward to me, no matter what follows up. My simple solution was reordering:     There were some grapes, an orange, two apples and a small pile of cherries on the plate.   But that's not the first time I faced this situation and I'd like to know what the rules of grammar say about that — was my editor overzealous or am I trying to copy rules of my language that don't apply in English? With variable length instructions how does the computer know the length of the instruction being fetched? Why doesn't the command "ls | file" work? I've been studying about the command line and learned that | (pipeline) is meant to redirect the output from a command to the input of another one. So why does the command ls | file doesn't work?  file input is one of more filenames, like file filename1 filename2  ls output is a list of directories and files on a folder, so I thought ls | file was supposed to show the file type of every file on a folder.  When I use it however, the output is:      Usage: file [-bcEhikLlNnprsvz0] [--apple] [--mime-encoding] [--mime-type]         [-e testname] [-F separator] [-f namefile] [-m magicfiles] file ...     file -C [-m magicfiles]     file [--help]   As there was some error with the usage of the file command Is there a general formula for solving 4th degree equations (quartic)? There is a general formula for solving quadratic equations, namely the Quadratic Formula:  $$ x = \frac{ -b \pm \sqrt{ b^2 - 4ac } }{ 2a } $$  For third degree equations of the form $ax^3+bx^2+cx+d=0$, there is a set of three equations: one for each root. Is there a general formula for solving equations of the following form? $$ ax^4 + bx^3 + cx^2 + dx + e = 0 $$ How about for higher degrees? If not, why not? How is the notation $X\sim N(\mu,\sigma^2)$ read? Is it $X$ follows a normal distribution? Or $X$ is a normal distribution? Or perhaps $X$ is approximately normal..  What if there are several variables that follow (or whatever the words is) the same distribution? How is it written? Find the ratio of $\frac{\int_{0}^{1} \left(1-x^{50}\right)^{100} dx}{\int_{0}^{1} \left(1-x^{50}\right)^{101} dx}$ $$I_1=\int_{0}^{1} \left(1-x^{50}\right)^{100} dx$$ and $$I_2=\int_{0}^{1} \left(1-x^{50}\right)^{101} dx$$ Then find $\frac{I_1}{I_2}$  I tried by subtracting $I_1$ and $I_2$   $$I_1-I_2=\int_{0}^{1}\left(1-x^{50}\right)^{100}\left(1-(1-x^{50}\right))dx$$ so  $$I_1-I_2=\int_{0}^{1} \left(1-x^{50}\right)^{100} x^{50} dx$$ Now using Integration by Parts we get  $$I_1-I_2= \left(1-x^{50}\right)^{100} \times \frac{x^{51}}{51}\bigg|_{0}^{1} -\int_{0}^{1} 100 \left(1-x^{50}\right)^{99} \times -50 x^{49} \times \frac{x^{51}}{51} dx$$  So $$I_1-I_2=\frac{5050}{51} \times \int_{0}^{1}\left(1-x^{50}\right)^{99} x^{100} dx$$  Now $x^{100}=\left(1-x^{50}\right)^2-(1-x^{50}-x^{50})$ so  $$\frac{51}{5050}(I_1-I_2)=\int_{0}^{1} \left(1-x^{50}\right)^{99} \times \left(\left(1-x^{50}\right)^2-(1-x^{50})+x^{50}\right)dx=I_2-I_1+\int_{0}^{1} \left(1-x^{50}\right)^{99} x^{50} dx$$  Need a hint to proceed further. For which $f,g \in k[t]$, $k[f,g]$ is integrally closed? Let $f,g \in k[t]$, $k$ is a field of characteristic zero, $\deg(f)=n \geq 2$, $\deg(g)=m \geq 2$.     Is it possible to characterize all such $f$ and $g$ for which $k[f,g]$ is integrally closed in its field of fractions $k(f,g)$?   I do not mind to further assume that $k(f,g)=k(t)$ (but I do not want to assume that $k[f,g]=k[t]$, which makes my question trivial).  Thank you very much!  Edit: (i)  is relevant.  (ii) If also $k(f,g)=k(t)$, then being integrally closed is equivalent to $k[f,g]=k[t]$. Indeed: (a) If $k[f,g]=k[t]$ then $k[f,g]$ is integrally closed (since $k[t]$ is). (b) If $k[f,g]$ is integrally closed then, in particular, since $t \in k(t)=k(f,g)$ (= the field of fractions of $k[f,g]$) and obviously $t$ is integral over $k[f,g]$ (for example, $t$ is a root of $f(T)-f \in k[f,g][T]$) hence $t \in k[f,g]$, so $k[f,g]=k[t]$.  For example: $f(t)=t^2+1$, $g(t)=t^3-4t$. We have, $t= \frac{t(t^2-4)}{t^2+1-5}=\frac{g}{f-5}$, so $k(f,g)=k(t)$. By Abhyankar-Moh-Suzuki theorem, $k[f,g] \neq k[t]$, so $k[f,g]$ is not integrally closed. Similarly, for every $f,g$ such that $k(f,g)=k(t)$ and one of the degrees does not divides the other, then $k[f,g]$ is not integrally closed.  (iii) If also $k(f,g)=k(t)$ and $k$ is algebraically closed, then being integrally closed is equivalent to $H(t)=(f(t),g(t))$ is injective and $H'(t)=(f'(t),g'(t)) \neq (0,0)$ for every $t \in k$. Indeed, $k[f,g]=k[t]$ is equivalent to the new conditions (it is important that $k$ is algebraically closed!!).  Edit: What if we replace $k$ by an integral domain $D$ (which is a $k$-algebra)? See also  question. How do I get the UTC time of "midnight" for a given timezone? The best I can come up with for now is this monstrosity:  &gt;&gt;&gt; datetime.utcnow() \ ...   .replace(tzinfo=pytz.UTC) \ ...   .astimezone(pytz.timezone("Australia/Melbourne")) \ ...   .replace(hour=0,minute=0,second=0,microsecond=0) \ ...   .astimezone(pytz.UTC) \ ...   .replace(tzinfo=None) datetime.datetime(2008, 12, 16, 13, 0)   I.e., in English, get the current time (in UTC), convert it to some other timezone, set the time to midnight, then convert back to UTC.  I'm not just using now() or localtime() as that would use the server's timezone, not the user's timezone.  I can't help feeling I'm missing something, any ideas? If $x^{2}-x\in Z(R)$ for all $x\in R$, then $R$ is commutative. If $x^{2}-x\in Z(R)$ for all $x\in R$, then $R$ is commutative.  I need to proof this theorem and I have something like this below. However, I do not know how to continue this proof.   $(x+y)^{2}-(x+y)=x^{2}+xy+yx+y^{2}-x-y=(x^{2}-x)+(y^{2}-y)+xy+yx\in Z(R)$  so $xy+yx\in Z(R)$ Sponsor Gallery, Page, or Something Like That? Looking for a powershell script that can pull a file from a set of PC's and FTP I'm looking to write a script (preferably powershell) that will essentially copy a file from a bunch of PC's and FTP it to a server.   So the structure of the environment is that we have a file on multiple PC's (around 50 or so) that need to placed on a server. Sometimes one of the PC's may be turned off so the script would first need to ensure the PC is up and running (maybe a ping result), then it would need to go into a directory on that PC, pull a file off of it, rename the file, place into a source directory, then remove the file. Naming convention doesn't matter, but date/time stamp would be easiest. Ideally, it would be best to first move all the files to a source directory to save on FTP bandwidth, but since the files will be named the same, the files must be renamed during the move process. Move not copy because the directory needs to be empty so the file can be re-created the next day. So once moved to the source directory, now all the files need to be FTP'd to a server for processing.   After all of this, we need to know which PC's on the list did not respond so we can manually retrieve the file so the script should output a file (txt is fine) that will show which PC's were offline.   Everything is one domain and script will be run from an server with admin creds.   Thank you! Why was Dumbledore worried by the cut in Harry's arm? What part of speech is “there” when used in “There is (blah blah)”? What part of speech is there in the sentence “There is a book on the table?”  Also, while typing it out, another question pops up vis-à-vis punctuation. In my complete first sentence above, I ended it with a question mark since my main sentence is a question. The quote is not a question, but it looks like it because of the question mark. Is this the right way to punctuate? Android cancel Toast when exiting the app and when toast is being shown Firstly, I apologise if my thinking is completely incorrect - I am by no means a physicist (yet!), I have included layman illustrations to hopefully assist in explaining my thinking.  I am imagining the big bang to be, for lack of a better word, an explosion, thus the universe to be progressively expanding:    Therefore, to me it seems logical to suggest that there is an edge.  If this is the case, then is it reasonable to suggest that explosion + edge = 'bright edge'? Where light projects in all directions at the edge, not just outwards into the 'nothingness'.     So, this brings me to my question: why, when someone looks deeply enough 'at the edge' do they see an absence of light?   Again, apologies if I'm jumping to irrational conclusions &amp; am way off.