$\xi =e^{2*\pi/pi }$ , proof that is only two quadratic extention to $\Bbb Q $ that contained in $Q(\xi_p)$
Unique quadratic subfield of $\mathbb{Q}(\zeta_p)$ is $\mathbb{Q}(\sqrt{p})$ if $p \equiv 1$ $(4)$, and $\mathbb{Q}(\sqrt{-p})$ if $p \equiv 3$ $(4)$
Why is it called an “Indian file”? Why can't variable names start with numbers? I was working with a new C++ developer a while back when he asked the question: "Why can't variable names start with numbers?"  I couldn't come up with an answer except that some numbers can have text in them (123456L, 123456U) and that wouldn't be possible if the compilers were thinking everything with some amount of alpha characters was a variable name.  Was that the right answer?  Are there any more reasons?  string 2BeOrNot2Be = "that is the question"; // Why won't this compile? Basically, I want the header fonts to use a different (smaller) font size than the size I set using \documentclass. What should be the option I'd be using ?  \documentclass[12pt]{article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage[margin=1in, headsep=10pt]{geometry} \usepackage{fancyhdr} \pagestyle{fancy}  \fancyhead[L]{Personal Statement} % What other option should I use to get a custom font size ? How can I add a Login link to the "Main navigation" menu?  When a user clicks on the link, it should take them to the /user/login page. Once they login, the link should change to say "Logout" instead of "Login".  Is there any way to add such a link? Does Python SciPy need BLAS? Reversing Drop Bars If I need to sit more upright on an old Fuji road bike, can I turn the drop handlebars upright and reversed so that they come up and then point to the rear?  I haven't seen anything on the net from anyone who has done that. Shape of a string/chain/cable/rope/wire? The height of a string in a gravitational field in 2-dimensions is bounded by $h(x_0)=h(x_l)=0$ (nails in the wall)  and also $\int_0^l ds= l$. ($h(0)=h(l)=0$, if you take $h$ as a function of arc length) .  What shape does it take?  My try so far: minimise potential energy of the whole string,  $$J(x,h, \dot{h})=\int_0^l gh(x) \rho \frac{ds}{l}=\frac{g \rho }{l}\int_0^l h(x) \sqrt{1+\dot{h}^2} dx$$  With the constraint  $$\int_0^l \sqrt{1+\dot{h}^2} dx- l=0$$ If it helps, it's evident that $\dot{h}(\frac{l}{2})=0$.  Generally, this kind of equation is a case of a constrained variational problem, meaning that the integrand in  $$\int_0^l \frac{g \rho }{l}h(x) \sqrt{1+\dot{h}^2} +\lambda(\int_0^l \sqrt{1+\dot{h}^2} dx- l)dx$$  Must satisfy the Euler Lagrange equation. The constraint must also be satisfied.  But, in truth, by this point I am clueless. $\lambda$ is worked through $\nabla J  = \lambda \nabla(\int_0^l \sqrt{1+\dot{h}^2} dx- l)$. I have tried this , but get nonsensical answers.  Is this method the best? If so, in what ways am I going about it wrongly thusfar? Consider a common proof of the uncountability of $(0,1]$, as presented  for example:  We assume that the reals can be arranged in a sequence $x_k$, represent every number in $x_k$ by its nonterminating decimal expansion, use the diagonal argument to create a sequence of decimal digits that differs from the nonterminating decimal expansion of each number in $x_k$ and then claim that this sequence of digits so generated must be the decimal expansion of some number not in $x_k$.  My problem is with this last step. Could it not be the case that the new sequence of digits is just the terminating decimal expansion of some number already in $x_k$?  Would it not be more correct to use the sequence $x_k$ to generate a sequence of all (both terminating and non-terminating) decimal expansion of all numbers in $[0,1)$ and then apply the diagonal argument? QGIS corrupting shapefiles? I'm hoping someone out there might be able to help or suggest some tests to try and resolve some very odd QGIS behaviour of late...  Our core GIS team of 4 users has been testing v2.10 prior to roll-out for the remainder of the organization.  In the past couple of weeks we have had some very odd shapefile corruption things happening and are yet to isolate or identify a potential cause...  These have included:   Editing one line (using the scissor tool to split into two records) and having the resulting records attributes completely replaced by attributes from another geometry no-where near the edited row (spatially or in the attribute dbf) Line geometries completely disappear while their attributes get associated with an unrelated geometry  Line geometry get partially deleted and replaced with a vertice in infinity (line visually extends beyond the dataset and no matter how far zoomed out you never see the end)   The above is happening in a polyline layer, that we did discover has some multi-line geometries..? Perhaps this is impacting... but never saw this issue with v2.8 and the same layer. The layer has undergone MANY save-as's in the past week and many verify geometry checks as we thought invalid geometry may have been the cause...  In another separate layer yesterday, to a separate user (me) i created a layer with approx 30 polygons... adding, deleting some and doing some 'avoid intersection' to remove overlaps. Layer looks fine in qgis, saved and also a save-as to a completely new file but when i load into ArcGIS online (and later is ArcMap as a test) some of the overlaps and deleted objects are still there. Close and reopen qgis,  reopen the file and they are definitely not.  The project was created in v2.8 that i was editing in (but had been saved in 2.10).  Does anyone have any ideas/suggestions.  We do still have 2.8 installed as well as 2.10? We have never encountered issues like this when testing other new qgis versions while still running old ones? Trying to manually sign android package with jarsigner.exe and install with adb.exe This question attempts to collect a community-maintained list of quality books on the  programming language, targeted at various skill levels.  C is a complex programming language that is difficult to pick up on-the-go by reading online tutorials. A comprehensive book is often the best way to learn the language, and finding a good book is the first step. It is important to avoid badly-written books, and even more importantly, books that contain serious technical errors.  Please suggest edits to the accepted answer to add quality books, with an approximate skill level and a short blurb/description about each book. (Note that the question is locked, so no new answers will be accepted. A single answer is being maintained with the list)  Feel free to debate book choices, quality, headings, summaries, skill levels, and anything else you see that is wrong. Books that are deemed satisfactory by the C community here will stick around on the list; the rest will be regularly removed.  For books that have reviews by the Association of C and C++ Users (ACCU), a link to those reviews should be added along with the book.  See also:   Other C-related resources in the   A similar list for :      This question was discussed on  as part of the .The consensus was to keep it undeleted and actively maintained. I'm confused. Running Fedora Linux, lscpu yields:  Architecture:            i686 CPU op-mode(s):          32-bit, 64-bit ...   But when I try to install a 64-bit program (Chrome) I get error like:     Package /....x86_64.rpm has incompatible architecture x86_64. Valid architectures are ['i686', 'i586', 'i486', i386']   I'm less interested in being able to install Chrome and more interested in why lscpu says that my CPU can run in 64-bit mode; clearly this can't mean I can run 64-bit programs. Can anyone clarify? Let $S = \{ax + by: x,y \in \mathbb{Z}\}$  and let $e &gt; 0$ be the smallest element in $S$. Prove that $e \mid a$, and hence prove that $e = \gcd(a,b)$  I'm afraid I can't provide much of my initial working here because I'm at a loss of how to start.  I suppose that to show $e\mid a$ I would have to show that $eg = a$ for some $g \in \mathbb{Z}$. But I have no idea how I would do this. Fiction novel or movie about sentient dinosaurs Sponsor Gallery, Page, or Something Like That? Blocking web sites with Windows Firewall Is it possible to use Windows Firewall to block specific web sites for all browsers? Want to set a guest session password for login. How do you do this after skipping it at OS install? Why avoid increment ("++") and decrement ("--") operators in JavaScript? Number of automorphisms of a direct product of two cyclic $p$-groups Is there an alternative to string.Replace that is case-insensitive? I need to search a string and replace all occurrences of %FirstName% and %PolicyAmount% with a value pulled from a database. The problem is the capitalization of FirstName varies. That prevents me from using the String.Replace() method. I've seen web pages on the subject that suggest  Regex.Replace(strInput, strToken, strReplaceWith, RegexOptions.IgnoreCase);   However for some reason when I try and replace %PolicyAmount% with $0, the replacement never takes place. I assume that it has something to do with the dollar sign being a reserved character in regex.   Is there another method I can use that doesn't involve sanitizing the input to deal with regex special characters?