How to work with very large number like 100 digits or so?
Handling very large numbers in Python
Remove border from IFrame How would I remove the border from an iframe embedded in my web app? An example of the iframe is:  &lt;iframe src="myURL" width="300" height="300"&gt;Browser not compatible.&lt;/iframe&gt;   I would like the transition from the content on my page to the contents of the iframe to be seamless, assuming the background colors are consistent. The target browser is IE6 only and unfortunately solutions for others will not help. How do you force constructor signatures and static methods? Is there a way of forcing a (child) class to have constructors with particular signatures or particular static methods in C# or Java?  You can't obviously use interfaces for this, and I know that it will have a limited usage. One instance in which I do find it useful is when you want to enforce some design guideline, for example:  Exceptions They should all have the four canonical constructors, but there is no way to enforce it. You have to rely on a tool like FxCop (C# case) to catch these.  Operators There is no contract that specifies that two classes can be summed (with operator+ in C#)  Is there any design pattern to work around this limitation? What construct could be added to the language to overcome this limitation in future versions of C# or Java? In the Wikipedia article on positive definite matrices they claim that if $M$ is positive definite, then the determinant of $M$ is bounded by the product of its diagonal entries. How might we show this?  Ideas: The sum of the diagonal entries of $M$ is the trace, which is also the sum of the eigenvalues. The product of the eigenvalues is the determinant. All the diagonal entries of $A$ must be real and strictly positive. Also we have $|m_{ij}|\leq \sqrt{m_{ii}m_{jj}}\leq \frac{m_{ii}+m_{jj}}{2}$. So far nothing is working...  We might try to write the Gram matrix $m_{ij} = \langle v_i, v_j \rangle$, and then $\prod_i m_{ii} = \prod_i \|v_i\|^2$. Now we'd need to show that the determinant, which is a polynomial in the entries of $v_i$, is less than $\prod_i \|v_i\|^2$ somehow. I have been trying to install ubuntu (I tried 12.04LTS, 12.10, 12.10-secure-remix) using the wubi installer on Windows 8 and all the three times ran into the same problem showing some cannot find /ubuntu/winboot/wubildr when I tried to start ubuntu.  I tried to change the boot settings from UEFI to Legacy and then my laptop restarted and showed that "No operating System Found".  I then tried to install Ubuntu using a cd and after a lot of effort and using boot repair,etc. I landed into a new trouble. When I select UEFI on, the laptop loads Windows and windows too does not detect ubuntu. When I select Legacy mode, it starts ubuntu, shows me an option to start windows 8 but gives an error showing windows failed to load.  So in legacy mode, i am able to use only ubuntu and in UEFI mode, I am able to use only Win8. Please explain any process of starting windows in legacy mode (which I tried without any success) or starting ubuntu in UEFI mode. Font characters displayed as squares in Ubuntu 18.04 Recently, on my Ubuntu 18.04 I have noticed that at least on gnome-calculator and chromium browser the fonts are displayed as squares. I have followed instructions  and , the calculator is fixed, but the problem on chromium still exists when I open a dialog to search for a file.  Not sure if this happens on other applications as well, I haven't checked all my apps, but File managers nemo and nautilus are working fine.  Also, before few months ago, I have included some windows fonts for my libre office shown . I used the copy (cp) method, not the link (ln -s). But, was working fine until yesterday. Haven't done any major change or update, at least on my Linux partition (dual boot). But, I don't think that this has anything to do with that.  Any idea how can I fix this issue?  . Are there any rulesets or laws for Q or Q continuum? Anything, that would prevent them from doing... anything? Or at least limit them from doing something really bad?  In "" episode Q explains to  that they can do, have, get, become anything they want or appear anywhere they want, with just a snap of fingers. If that is true and if there are absolutely no borders or limits, they can't pass, then how can universe work in general? Or, how did it manage to exist so far?  I mean -- any Q could wipe out Borg, entire human population or even entire universe... with just a snap of fingers. What could prevent Q from doing that? How to calculate the following sum: How may one calculate  $$\lim_{n\to\infty} \ \left(\left(\sum_{k=1}^{n} \frac{1}{3k-1}\right) - \frac{\ln n}{3}\right) \ ?$$ Redirect automatically when selecting an item from a select drop-down list This page does it the way I want it to:   But I want to find a better way using jQuery, can anyone point me to a good script that uses jQuery to accomplish this? Excel 2010 on multi monitor screen Field that is a subfield of own of its subfields Let $K$ and $L$ be fields. We have homomorphisms $f: K \to L$ and $g: L \to K$. Are $K$ and $L$ necessarily isomorphic? Use of "though" versus "however" Consider the sentence      E-books are on the rise, but they haven't suppressed paper books though.    This usage seems to be quite common, but when I learned English  I was taught to use "however" where I now read "though". My questions on this use of "though" are:     Is this a new trend? Is it restricted to American English? Is "though"  considered more colloquial than "however" ?    And on a syntactic level: Do you put a comma before "though"? How to change folders color? How do i change the folders colors? i am using this icon theme   and there are several folders. like black, gray, purple, orange(which is the default), yellow, green, red, blue, brown and lightblue  How can i use any of them? for example have a blue folder called "family" in images and another right beside that have a purple folder called "others".  Basically why have he created all those folders with different colors? Proof of linear independence of $e^{at}$ Given $\left\{ a_{i}\right\} _{i=0}^{n}\subset\mathbb{R}$ which are distinct, show that $\left\{ e^{a_{i}t}\right\} \subset C^{0}\left(\mathbb{R},\mathbb{R}\right)$,  form a linearly independent set of functions.   Any tips on how to go about this proof. I tried a working from the definition of an exponential and combining sums but that didn't seem to get me anywhere. I saw a tip on the internet that said write it in the form  $\mu_{1}e^{a_{1}t}+\dots+\mu_{n}e^{a_{n}t}=0$ to try to show $\mu_{1}=\dots=\mu_{n}=0$ considering each term of the left hand side must be positive, but I can't get my head around that because while I understand $e^{x}&gt;0\forall x\in\mathbb{R}$ I cannot see why $\mu_{i}$ must be positive in any case. I have thought about differentiating but that doesn't seem to help. The question did originally ask for a "rigourous" proof but I'll take any hints right now and the provided the solution of 'is obvious' is most unhelpful to me.  Any input would be fantastic. Thank you. How to change the list of file types which Safari will open immediately after download? I would like to change Safari Safe List of type files which open immediately after download. Any ideas how? I am trying to solve the following exercise.      Assume that $m$ and $n$ are co-prime positive integers, and that $k$ is a field. Prove that the ideal generated by $x^{m} - {y^n}$ is a prime ideal in $k[x,y]$.   I tried the following approach : Consider the ring homomorphism ${\varphi}:k[x,y]\rightarrow{k[t]}$ defined by $\varphi(x) = t^n$, and $\varphi(y) = t^m$, and extend $\varphi$ to $k[x,y]$ to ensure that it is a ring homomorphism. Then the ideal $(x^m - y^n)$ is clearly contained in the kernel of $\varphi$. It remains to prove the reverse set inclusion. i.e. to prove that this ideal is exactly equal to the kernel of $\varphi$. I don't know how to go about this! Why is the top bar not changed on Stack Exchange, Area 51 and Ask Ubuntu? I have recently published my first research paper and have already received a request to review a manuscript. The journal's impact factor is low, but it is open access, and the paper's topic is relevant to my field of study. What factors should I keep in mind when deciding whether to accept or decline the request to review? What level of expertise is typically expected from a good-quality review? Debugging with command-line parameters in Visual Studio I'm developing a C++ command-line application in Visual Studio and need to debug it with command-line arguments. At the moment I just run the generated EXE file with the arguments I need (like this program.exe -file.txt) , but this way I can't debug. Is there somewhere I can specify the arguments for debugging? Nodejs Nginx error: (13: Permission denied) while connecting to upstream I'm trying to run multiple Nodejs applications on Nginx server running on CentOS 7. I noticed that when I run a Nodejs app on some ports I get an 502 Bad Gateway error in the browser so I checked the error logs:  [notice] 12806#0: signal process started [crit] 12807#0: *13 connect() to 127.0.0.1:7777 failed (13: Permission denied) while connecting to upstream, client: **.**.99.58, server: myapp.com, request: "GET / HTTP/1.1", upstream: "http://127.0.0.1:7777/", host: "myapp.com" [crit] 12807#0: *13 connect() to [::1]:7777 failed (13: Permission denied) while connecting to upstream, client: **.**.99.58, server: myapp.com, request: "GET / HTTP/1.1", upstream: "http://[::1]:7777/", host: "myapp.com"   when I change the app to listen to 8008 for example everything is working fine. I checked permissions and if the process is running as root and everything seems ok. I played with the timeouts as well but no result. Can anyone help? Taking notes, I was going to write this:     therefore p′ is a shortest path.   But the topic is APSP which stands for "all pairs shortest paths" so I decided to just write SP instead and...  Is it written with a like this     therefore p′ is a SP   or with an like this (because in my head I would "read" the S)     therefore p′ is an SP