How can I translate or add words that seems not to be part of core strings?
How do I translate strings in Twig templates?
Let $n$ be a nonnegative integer, and $k$ a positive integer. Could someone explain to me why the identity $$ \sum_{i=0}^n\binom{i+k-1}{k-1}=\binom{n+k}{k} $$ holds? Tikz and ctable incompatibility, gives error when printing When I print a report I get an error:     An error exists on this page. Acrobat may not display the page   correctly. Please contact the person who created the PDF document to correct the problem   After a lot of debugging, I've found that this MWE reproduces the problem. I've tried it on three different computers with the same error.   \documentclass{standalone}           \usepackage{tikz} \usepackage{ctable} \begin{document} \begin{tikzpicture} \filldraw[opacity=.5] (0,0) rectangle (1,1); \end{tikzpicture} \end{document}   When loading the ctable package, the image is changed (the opacity disappears), so it seems the error comes from some incompatibility between ctable and opacity in tikz. The error only appears when trying to print though, acrobat before attempting to print. (Printing either to a pdf file or to a real printer)  I have the following versions of tikz and ctable:      tikz.sty    2013/12/13 v3.0.0   ctable.sty    2014/04/25 v1.29   How can I fix this?    EDIT: I found the warning Transparency disabled: incompatible with tikz package from ctable so I guess this incompatibility can explain the error in the first MWE.  However, I continued digging and found that the spy library seem to be incompatible with ctable as well.   Here's an MWE that generates the same error when printing (either to a pdf file or to a real printer):   \documentclass{standalone}           \usepackage{tikz} \usetikzlibrary{spy} \usepackage{ctable} \begin{document} \begin{tikzpicture}[spy using outlines={size=2cm,connect spies}] \begin{scope} \spy on (-3,.25) in node at (2,0); \end{scope} \end{tikzpicture} \end{document}   There seem to be a serious problem with using tikz + ctable, can it be fixed? C# "internal" access modifier when doing unit testing I'm new to unit testing and I'm trying to figure out if I should start using more of internal access modifier. I know that if we use internal and set the assembly variable InternalsVisibleTo, we can test functions that we don't want to declare public from the testing project. This makes me think that I should just always use internal because at least each project (should?) have its own testing project. Can you guys tell me why I shouldn't do this? When should I use private? How do I display PHP code in HTML? How to handle WndProc messages in WPF? In Windows Forms, I'd just override WndProc, and start handling messages as they came in.  Can someone show me an example of how to achieve the same thing in WPF? Why did Terence Tao write Proposition 2.1.11 about mathematical induction in "Analysis I"? Is there a technical reason to use > (<) instead of != when incrementing by 1 in a 'for' loop? Let $A$ be a real square matrix en let $I$ be the identity matrix with the same size. Let $n&gt;0$ be the smallest natural number for which there exist  $a_0,a_1,...a_{n-1} \in {R}$ such that $A^n+a_{n-1}A^{n-1}+....+a_1A+a_0I=O$.  Show that A is invertible if and only if $a_0\neq0 $.  So i need to proof    $A$ invertible $\rightarrow$$a_0 \neq 0$ $a_0 \neq0 \rightarrow$ $A$ invertible    I don't really know where to start with 1, and with 2 I tried to prove it with a contradiction but I don't think it's right either. Determinant of a special $n\times n$ matrix How to change the voltage polarity in an inverting amplifier? I want to implement a simple circuit which can map -10V  +10V voltage range to 0V 5V voltage range. Thus I'm planning to use two op-Amps, one for the slope and the other for the offset. So basically I'm planning to use an inverting amplifier and a summing amplifier consecutively.  But Inverting amplifiers multiplies the input voltage with a minus sign. I need a positive slope. How can I overcome this?  Also Could you gibe me any ideas for a cheap op-Amp models for this purpose? Make Windows 7 ignore WiFi when ethernet is available When I dock my Windows 7 laptop, I want it to prefer the wired ethernet connection over WiFi.  This is a pretty straightforward thing to do on my Mac - I just reorder my network preferences, and it "does the right thing." I just can't figure out how to achieve the same thing on my Win7 laptop.  So, when I'm docked, it connects to WiFi, and then fails to connect to servers on the local wired network. How do I fix this? Let $A ∈ M_{m\times n}(\mathbb{Q})$ and $B ∈ \mathbb{Q}^m$. Suppose that the system of linear equations $AX = B$ has a solution in $\mathbb{R}^n$. Does it necessarily have a solution in $\mathbb{Q}^n$?  Where do I start?    I feel I can use this to :  $$x_i=\frac{1}{a'_{ii}}\left(b'_i - \sum_{j=i+1}^{k} a'_{ij} x_j \right).$$    Here is a thought that just crossed my mind, but I'm not sure if this is legal:  Suppose $Y\in \{\mathbb{R}\setminus \mathbb{Q}\}^n$ and $Y'\in\mathbb{Q}^n$ are solutions to $AX=B$. Then $AY=AY'=B$, or $A(Y-Y')=A(Y+(-Y'))=0$, but  addition between $\{\mathbb{R}\setminus \mathbb{Q}\}^n$ and $\mathbb{Q}^n$ is . . . I unplugged my USB stick from Ubuntu 16.04 without the save remove option, but exfat should be fine doing so. No read write was happening, the partition does not use journaling. What I end up with is an unmountable USB stick with checksum error.   What tools are there to recover the partition table or at least the data on the USB stick? What I am doing now is scanning via parted. Has anyone experienced the same problem with exfat and recovery options? Unfortunately parted probably won't detect the partition because .  I also tried to use Partition Wizard on Windows but it failed to detect anything, just showing unallocated space. How do I proceed? are there helpful tools under Windows or Ubuntu?    I also tried to use gpart -v /dev/sdb but it failed to detect anything. On OS X there is a tool called fsck_exfat, is there any on Windows?  update The disk is preinstalled with Parted Magic. After quick search no partition shows up. Expandably change letter case and use inside \csname, without a package I want to change the letter-case of a single character argument, and use that changed letter inside a \csname.  And I want to do it without an additional package.  For example, I want to pass a macro the letter {S}, and have it execute the macro \csname macros\endcsname, or pass it the letter {T}, and have it execute the macro \csname macrot\endcsname.    In my MWE, I show three approaches:   I didn't expect \lowercase to work, since I recall reading that it is not truly expanded until the last possible moment.  Surprisingly, it goes into an \edef okay, but it must not be truly expanded, because it breaks the \csname. I also formulated an approach where I used \numexpr to add 32 to the ASCII code of the argument and perform a \char upon that result.  Like \lowercase, it gives the appearance of being expandable, but it also fails inside the \csname. I finally achieve success with the stringstrings package.  Having written the package, I know the conversion was not pretty... essentially, it is an exhaustive 26-fold check of the form \if #1Aa\else\if #1Bb\else\if #1Cc\else...\fi\fi\fi, which has the virtue that it can be expandably placed into an \edef, and so it works.   There has to be a better way.  The MWE works only because I use the inefficiently calculated \tmp from METHOD 3 inside the \csname.  If I use \tmp from either of the two earlier methods, it breaks.  \documentclass{article} \usepackage{stringstrings} \def\macros{Expandably converted an S to a s} \def\macrot{Expandably converted a T to a t} \newcommand\convert[1]{%   %MAKE THE ARGUMENT LOWER CASE   1) LOWERCASE\\   \edef\tmp{\lowercase{#1}}% PRETENDS TO EXPAND, BUT FAILS IN \csname   Here is the ``expanded'' conversion: \tmp\\   % OR   2) ASCII CONVERSION\\   \edef\tmp{\expandafter\char\numexpr`#1+32\relax}% PRETENDS TO EXPAND, BUT FAILS IN \csname   Here is the ``expanded'' conversion: \tmp\\   % OR   3) STRINGSTRINGS PACKAGE\\   \caselower[q]{#1}\def\tmp{\thestring}% WORKS BUT USES A PACKAGE   Here is the ``expanded'' conversion: \tmp\\   %   Now use it in a csname: \csname macro\tmp\endcsname% } \begin{document} \convert{S}\par \convert{T} \end{document}       SUMMARY OF ANSWERS:  I have added egreg's code snippets into this MWE to produce a document (and not just terminal output), showing the methods put forth to this point:  \documentclass{article}  %%%%%%%%%%%%%%%%%%%%%%%%%%%% L3 APPROACH  \usepackage{expl3}  \ExplSyntaxOn \cs_set_eq:NN \Xexplower \tl_expandable_lowercase:n \ExplSyntaxOff  %%%%%%%%%%%%%%%%%%%%%%%%%%%% EGREG'S LESS HACKY SOLUTION  \def\explowerchar#1{%   \ifcase\numexpr`#1-`A\relax    a\or b\or c\or d\or e\or f\or g\or h\or i\or j\or k\or l\or m\or    n\or o\or p\or q\or r\or s\or t\or u\or v\or w\or x\or y\or z\else    #1\fi }  \def\explower#1{%   \doexplowerchar#1\relax }  \def\doexplowerchar#1{%   \ifx#1\relax   \else     \explowerchar{#1}\expandafter\doexplowerchar   \fi }  %%%%%%%%%%%%%%%%%%%%%%%%%%%% STEVE'S HACKY PACKAGE APPROACH  \usepackage{stringstrings}  %%%%%%%%%%%%%%%%%%%%%%%%%%%%  \def\macros{Expandably converted an S to a s} \def\macrot{Expandably converted a T to a t}  \begin{document}  \textbf{Steve's hacky approach}  \caselower[q]{S}\csname macro\thestring\endcsname\par \caselower[q]{T}\csname macro\thestring\endcsname  \textbf{egreg's less hacky approach}  \edef\lcstring{\explowerchar{S}}\csname macro\lcstring\endcsname\par \edef\lcstring{\explower{T}}\csname macro\lcstring\endcsname  \textbf{L3 approach}  \edef\lcstring{\Xexplower{S}}\csname macro\lcstring\endcsname\par \edef\lcstring{\Xexplower{T}}\csname macro\lcstring\endcsname  \end{document} How to deal with bibliography items containing long URLs? How to test if a string is basically an integer in quotes using Ruby What changes after peer review but prior to final submission are acceptable for a conference paper? what is the relationship between the dynamical casimir effect and virtual particles? find $\sum_{k=2}^{\infty}\frac{1}{k^2-1}$ Does measurement, quantum in particular, always increase the total entropy?