If $(x-a)^2|f(x)$, then $(x-a)|f'(x)$ and if $(x-a)|f(x)$ and $(x-a)|f'(x)$, then $(x-a)^2|f(x)$
How to prove that r is a double root if and only if it is a root of a polynomial and of its derivative.
Can regular expressions be used to match nested patterns? I wanted to send a single email to different users. I save an email to drafts and send the email to a user and it goes to the sent box instead of staying in the drafts box. Is there a way I can send an email repeatedly from the drafts box? We have a new application that requires glibc 2.4 (from gcc 4.1). The machine we have runs on has gcc 3.4.6.   We can not upgrade, and the application must be run on this machine.    We installed gcc 4.1, however, when it comes to compile time it is using all the includes, etc, from 3.4.6.    How do we get around this?  Any suggestions on using 4.1 for just this application? I installed Blender from official Ubuntu repository but its version is always behind the version available from the official Blender website.  I'm aware that I can launch the program within the downloaded folder, but i want to replace the install version with a new version downloaded from the website?   It must be present in the unity launcher.  I'm also aware of the available PPA's that are available, however I just want to install Blender manually.  Thanks in advance What special characters must be escaped in regular expressions? I am tired of always trying to guess, if I should escape special characters like '()[]{}|' etc. when using many implementations of regexps.  It is different with, for example, Python, sed, grep, awk, Perl, rename, Apache, find and so on. Is there any rule set which tells when I should, and when I should not, escape special characters? Does it depend on the regexp type, like PCRE, POSIX or extended regexps? When is the message "Have you considered accepting an answer or starting a bounty for this question?" displayed? Using a keyboard shortcut to paste text What's the single-word for "left or right handed"? 'Male'/'female' is to 'gender' as 'left-handed'/'right-handed 'is to...?  Is there a word to describe this? For example, if I ask a guy     What's your ____?   It should mean I'm asking whether he's left or right-handed.  Another example could be     Our designs are not biased  against your ____.   Basically, I'm looking for something that means the state of being left- or right-handed which could be used analogously as gender.  EDIT: Sorry for the delay in the edit, but I was tied up. There are some points I'd like to clarify:   I'm not looking for a way to paraphrase my questions. I'm looking for a single word. I know people normally ask something along the lines of "Are you left-handed or not?" People also ask "Are you afraid of the dark?" instead of "Are you scotophobiac?". The word for it,  still exists, right? It has been pointed out that I should go with Our designs are not biased against left-handed people as that is what I mean. But that is not necessarily what I mean.    For example, let's say there is a washbasin with the tap on the right. Clearly, it's biased against lefties. Sometimes, you come across a washbasin with a tap on the left. (The logic being: you use your left hand to turn the tap as your right one's dirty). But, your right hand might not always be dirty, in which case, it's biased against righties.  A washbasin with the tap on the center is, then, handedness-blind or chirality-blind, if you will. (I foresee that some would dwell on Our designs are symmetrical. Please don't.)  I'm looking for a term that would be applicable here, as well as in the 1st example.  My favorite so far is chirality, suggested by Dan Bron in a comment (with 25 upvotes!) But, I'm reluctant to use it because there's no hard proof it's used in that sense  If we are talking about male-female, gender works perfectly. What's your gender? and Our designs aren't biased against your gender. , both work perfectly here.  Sorry for the late edit again. If the consensus is that I rollback, I will. Let me know in the comments. Are there 'stack' sites for Mac or Windows? I try to create a common extent for rasters in QGIS 2.99. Here is my script:  import processing  processing.runalg("script:unifyextentandresolution",                   "/qgis_data/rasters/Image2.tif;                   /qgis_data/rasters/Image1.tif",                  -9999,"/qgis_data/rasters",True)   However, processing.runalg is being used for QGIS 2.99. I need it for QGIS 2.99 Drupal site moved from development to live - IE won't load stylesheets anymore Before you ask ... I have looked everywhere for a solution, even drupal.org but nothing so far seems to work.  I developed a Drupal site (custom child theme for Zen) and on the development server everything looks fine in all browsers.  I did a test migration to another server before the launch. This move went well and everything looks fine in all browsers.  Then I moved the site to its live server where everything looks fine in all browsers except Internet Explorer which is not loading the stylesheets.  I know Drupal is known for generating many stylesheets and Internet Explorer will not load them if there are more than 31 (I believe) of them, but I did set the "Aggregate and compress CSS files" feature and clear the cache. This did not seem to help.  Could the answer be in one of the two following things?   The development site and backup site are both with one hosting provider. The live site is with a different hosting provider. The development site and backup site are in subfolders of two different portfolio sites ... ie www.portfoliosite.com/Newsite. The live site is a subdomain of the parent site ... ie www.newsite.parentsite.com.   I have run out of ideas so if anyone has a possible solution or direction to look, please let me know. Thanks Newton's Law of Graviation: Why $G$ and not e.g. $\dfrac{1}{4\pi G_0}$? Logical or operator not behaving as expected This is fairly easy.  If I go to https://webserver.com/someurl?a=b, will the someurl?a=b part be protected, or just the contents of the site? Does a photon exert a gravitational pull? I know a photon has zero rest mass, but it does have plenty of energy. Since energy and mass are equivalent does this mean that a photon (or more practically, a light beam) exerts a gravitational pull on other objects? If so, does it depend on the frequency of the photon? How to shift EXIF date/time created by time in days, hours, minutes? I have two camera bodies, I was shooting while on vacation, when I downloaded the photos to lightroom, one body was set to the correct date/time, the other was off by 722 days, 4 hours, 32 minutes.  Is there a tool available that can help me fix the date/time so that they appear in sequence while browsing my lightroom library?  I'd like for them to be as close to the right time.     I was able to adjust created year, month, date, but it doesn't appear lightroom will allow me to adjust increments (only hour increments).  Many thanks if you can help me in this task! I'm trying to boot Canonical's Azure 16.04 .vhd file in a VirtualBox VM and it hangs at "non blocking pool is initialized".  It works in Hyper-V, so it may only be a bug in virtual box (5.0.20). Downcasting in Java Upcasting is allowed in Java, however downcasting gives a compile error.   The compile error can be removed by adding a cast but would anyway break at the runtime.   In this case why Java allows downcasting if it cannot be executed at the runtime? Is there any practical use for this concept?   public class demo {   public static void main(String a[]) {       B b = (B) new A(); // compiles with the cast,                           // but runtime exception - java.lang.ClassCastException   } }  class A {   public void draw() {     System.out.println("1");   }    public void draw1() {     System.out.println("2");   } }  class B extends A {   public void draw() {     System.out.println("3");   }   public void draw2() {     System.out.println("4");   } } Is there a constraint that restricts my generic method to numeric types? Can anyone tell me if there is a way with generics to limit a generic type argument T to only:   Int16 Int32 Int64 UInt16 UInt32 UInt64   I'm aware of the where keyword, but can't find an interface for only these types,  Something like:  static bool IntegerFunction&lt;T&gt;(T value) where T : INumeric Polynomial divisibility is unchanged by coeff. field extension I would like to verify the validity of the following line of thought:  Let $K \subset E$ be a field extension. Let $K[x]$ be the polynomial ring over $x$ and denote $K(x)$ its field of quotients (the rational functions over $K$).  Now assume $f(x)=g(x)h(x)$ with $f(x),g(x) \in K[x]$ and $h(x) \in E[x]$ and all $f$, $g$, $h$ are different than zero. Then $\frac{f(x)}{g(x)} = h(x)$ in $E(x)$. So $h(x) \in K(x)$. But $h(x)$ is a polynomial, so $h(x) \in K[x]$.  Is there any other simpler argument than that?  Added:  Let me be more specific. Let $x^p - a \in K[x]$, with $p$ being prime and $char(K)=p$. Let $b$ be the unique root of $x^p - a$ in its splitting field $K(b)$. Then $x^p - a=(x-b)^p \in K(b)[x].$ Let $m_b(x) \in K[x]$ be the minimal polynomial of $b$ over $K$. Then $m_b(x)$ divides $(x-b)^p$ and so $m_b(x)=(x-b)^l$ and $l$ is the smallest positive integer for which $(x-b)^l \in K[x]$. Let $p = lq+r$ where $0 \ge &lt;l$. Then $x^p-a=(m_b(x))^q (x-b)^r$. Can i conclude that $(x-b)^r \in K[x]$ and so $r=0$ by the minimality of $l$?  Thanks.