What is the ideal class group?
Motivation behind the definition of ideal class group
PHP Session data not being saved I have one of those "I swear I didn't touch the server" situations. I honestly didn't touch any of the php scripts. The problem I am having is that php data is not being saved across different pages or page refreshes. I know a new session is being created correctly because I can set a session variable (e.g. $_SESSION['foo'] = "foo" and print it back out on the same page just fine. But when I try to use that same variable on another page it is not set! Is there any php functions or information I can use on my hosts server to see what is going on?  Here is an example script that does not work on my hosts' server as of right now:  &lt;?php session_start(); if(isset($_SESSION['views']))     $_SESSION['views'] = $_SESSION['views']+ 1; else     $_SESSION['views'] = 1;  echo "views = ". $_SESSION['views']; echo '&lt;p&gt;&lt;a href="page1.php"&gt;Refresh&lt;/a&gt;&lt;/p&gt;'; ?&gt;   The 'views' variable never gets incremented after doing a page refresh. I'm thinking this is a  problem on their side, but I wanted to make sure I'm not a complete idiot first.  Here is the phpinfo() for my hosts' server (PHP Version 4.4.7): Why do you add +1 in counting test questions? Simple series convergence/divergence: $\sum_{k=1}^{\infty}\frac{2^{k}k!}{k^{k}}$ How can I reliably and accurately identify the passive voice in writing or speech? How can I reliably and accurately identify the passive voice in writing or speech? I'm not interested in advice about whether or not to use it yet... I just want to know for sure what it is, so that I don't look as stupid as . I've seen papers (e.g., in Science) where the first two authors are listed in non-alphabetical order, and yet there are asterisks behind their names to say that they contributed equally.   It seems strange to me, because if the two authors are in alphabetical order, then it could be that the first author contributed more or the two contributed equally, and this can be made clear with asterisks in the paper if it's the latter case. When they're in non-alphabetical order, however, if someone only sees the author list without seeing the paper, he/she will likely assume that the first author contributed most.  So my question is: Are there particular reasons why people do that? (This  is related, but I don't think the answers there get to my question.) I would like a brief explanation of the following command line:  grep -i 'abc' content 2&gt;/dev/null Regex match entire words only Calculating the determinant gives $(a^2+b^2+c^2+d^2)^2$? I need to calculate the following determinant in order to prove the following equality:  $$\det\begin{pmatrix} a &amp; b &amp; c &amp; d \\ -b &amp; a &amp; -d &amp; c \\ -c &amp; d &amp; a &amp; -b \\ -d &amp; -c &amp; b &amp; a \end{pmatrix} = (a^2+b^2+c^2+d^2)^2.$$  I tried using Gauss-algorithm to get an easier matrix, but I'm not sure if I did it correctly.  Calling the $4$ lines $I$, $II$, $III$ and $IV$, I did:  (1) $II \cdot a$  (2) $III \cdot a$  (3) $IV \cdot a$  After this I did:  (4) $II' + I \cdot b$  (5) $III' + I \cdot c$  (6) $IV' + I \cdot d$  So finally I got the following matrix:  $$\begin{pmatrix} a &amp; b &amp; c &amp; d \\ 0 &amp; a^2+b^2 &amp; bc-ad &amp; ac+bd \\ 0 &amp; ad+bc &amp; a^2+c^2 &amp; cd-ab \\ 0 &amp; bd-ac &amp; ab-cd &amp; a^2+d^2 \end{pmatrix}.$$  I thought this would make the determinant a bit easier, unfortunately I must have done something wrong. Is multiplication with single lines allowed as I have done it?  Thank you very much. Unexpected AdjacencyMatrix output How to deal with "java.lang.OutOfMemoryError: Java heap space" error? How do I install GNOME Shell extensions?  Is it possible to update, remove and manage the extensions? How to modify the system default background image I am about to ship a new 10.04 installed system to a customer. This is the 1st system that we are shipping with our preinstalled software and an additional hardware test platform, so I thought it would be a nice idea to have the desktop wallpaper include our company's logo.  What I want to do is just to add the logo to the default background image. the questions are:   Where are the set of backgrounds stored? What are the rules for creating a custom background from scratch? If I create a background from scratch, how do I add it to the system's background set (i.e., not just save it in the user's Pictures directory - I want it to be available to all future users of the machine)? $\int_0^{\infty } \frac{\log (x)}{e^x+1} \, dx = -\frac{1}{2} \log ^2(2)$ How to show? What is the limit of cabin baggage on Wizz Air flights? What's the weight limit on Wizz Air, for cabin baggage?    I can't find anything about the weight on their website. I know that for Ryanair is 10kg, and EasyJet say they don't have a limit for weight. Java generics type erasure: when and what happens? I read about Java's type erasure .  When does type erasure occur? At compile time or runtime? When the class is loaded? When the class is instantiated?  A lot of sites (including the official tutorial mentioned above) say type erasure occurs at compile time. If the type information is completely removed at compile time, how does the JDK check type compatibility when a method using generics is invoked with no type information or wrong type information?  Consider the following example: Say class A has a method, empty(Box&lt;?&nbsp;extends&nbsp;Number&gt;&nbsp;b). We compile A.java and get the class file A.class.  public class A {     public static void empty(Box&lt;? extends Number&gt; b) {} }     public class Box&lt;T&gt; {}   Now we create another class B which invokes the method empty with a non-parameterized argument (raw type): empty(new Box()). If we compile B.java with A.class in the classpath, javac is smart enough to raise a warning. So A.class has some type information stored in it.  public class B {     public static void invoke() {         // java: unchecked method invocation:         //  method empty in class A is applied to given types         //  required: Box&lt;? extends java.lang.Number&gt;         //  found:    Box         // java: unchecked conversion         //  required: Box&lt;? extends java.lang.Number&gt;         //  found:    Box         A.empty(new Box());     } }   My guess would be that type erasure occurs when the class is loaded, but it is just a guess. So when does it happen? The number of (non-equal) forests on the vertex set V = {1, 2, ...,n} that contains exactly 2 connected components is given by The number of (non-equal) forests on the vertex set V = {1, 2, ...,n} that contains exactly 2 connected components is given by $\sum_{k=1}^{n-1} {n-1 \choose k-1} k^{k-2} (n-k)^{n-k-2}$.  I am unsure how to approach this question. Could someone guide me through the proof? If G is a spanning tree and it is disconnected then I know it is a spanning forest. Also, I know by Cayley's thm that there are $n^{n-2}$ nonequal tree on a vertex set V = {1, 2, ...,n} which is where i'm assuming the $k^{k-2}$ comes from but I do not understand where the rest of it is coming from. Cap colour in IPL If a player is the highest run scorer and at the same time is the highest wicket taker in IPL, which colour cap would he wear? From the command line is it possible to open a package installer window (not install the application).  I understand I could run the application using sudo installer -pkg ..... -target ....... Instead i would like to open the package in a similar way to if I double clicked the package within the Finder. Texture packing algorithm What is a good texture packing algorithm?  Technically,  is , so a heuristic is what I'm really after. I'm not sure if this is possible architecturally, but when judging whether to set a bounty and how much it should be, it would be nice to see the impact based on our previous questions. If you're not visiting the site throughout the day, there is no way to tell how effective that bounty might be--particularly for increasing traffic. There is a similar question with adding and removing tags that increase the visibility in the right places, and the effect on views that may have.