How to draw this graph in LaTeX I would like help drawing a specific graph in LaTeX
Materials for learning TikZ I feel intimidated in learning TikZ. I was wondering if there are some nice materials (or just your replies) at different level:   for providing big picture, which is important to beginners to not lose direction during learning. for comprehensive reference.   Examples are important, but only examples are not always clear for understanding the big picture and organization.
How do I prevent widow/orphan lines? How do I prevent a line from appearing by itself:  Orphan: at the bottom of the page, or Widow: at the top of the page? Should we host our own nameservers? This is a  about whether to outsource DNS resolution for ones own domains   I currently have my ISP providing DNS for my domain, but they impose limitations on adding records. Therefore, I am thinking about running my own DNS.  Do you prefer to host your own DNS, or is it better to have your ISP do this?  Are there alternatives which I can look into? What is the recommended CIDR when creating VPC on AWS? I have been creating AWS VPCs and I am wondering if there is a recommended CIDR value when creating VPCs. What are the factors that I must consider when choosing a CIDR and does the CIDR value affect the performance of the network? Most useful additions in KOMA-Script? (Background: I'm a beginner who will mostly use LaTeX for university articles and reports, but no math. Also, as I reside in Canada, the German typography conventions, which I understand KOMA-Script supports better than LaTeX, are less relevant).  I've read that the KOMA-Script package has a lot of improvements for the default document classes. Yet the 's length, about 250 pages, is somewhat daunting. I plan to read the chapters I'm interested in anyway but it'd be useful to have some pointers about low hanging fruits. I searched the site and  answers say KOMA-Script adds improvements but do not delve into details.  I'll ask this as a community wiki topic and, since the audience of this site is international, feel free to mention German typography if KOMA-Script is better there. When to use "do" in phrases which are not questions? How to find historical stock price for a de-listed or defunct company? With services like Google Finance or Yahoo Finance it is very convenient to find the historical stock price metric of a listed company, but if the company is not listed, I can't find the data.  For example, I want to see the price metrics for Macromedia, which had been listed in 1993 on NASDAQ (MACR), then acquired by Adobe in 2005. How could I find its historical price metrics? What is the value of $1^i$? What is the value of $1^i$? $\,$ 3D arrows with TikZ Asymptote does give 3D arrows when drawing three dimensional figures (they even have shade!). Could we fake it with TikZ? Here's an example, manually written, with just one arrow worked:  \documentclass{scrartcl} \usepackage{tikz} \usetikzlibrary{arrows.meta} \begin{document} \begin{tikzpicture}[-&gt;,scale=2]   \draw[&gt;={Triangle[width=3pt,length=5pt]}] (0,0,0) -- (1,0,0);   \draw[&gt;={Triangle[width=3pt,length=5pt]}] (0,0,0) -- (0,1,0);   \draw[&gt;={Circle[sep=-.9pt,width=3.08pt,length=2pt]Triangle[width=3pt,length=5pt]}] (0,0,0) -- (0,0,1); \end{tikzpicture} \end{document}     But that's (wrongly) manually calculated by trial and error (apart from the fact that it's not perfect, seeing how the other two axis —x and y— are oriented, it should have certain slant). It would be nice to have an interface like the other arrows  &gt;={3D[length=⟨real length⟩,width=⟨real width of the base⟩]}   Which would then calculate from those values (and, of course, also taking into account x=⟨x vect⟩,y=⟨y vect⟩,z=⟨z vect⟩)  Circle[sep=⟨value⟩,width=⟨value⟩,length=⟨value⟩,slant=⟨value⟩] Triangle[width=⟨value⟩,length=⟨value⟩] % And I'm not sure if `slant=⟨value⟩`                                        % is necessary in this Triangle case   Example  Using the code from the answer (thanks to Symbol1), for instance, this code (taking the idea from another question, link in the comments)  \begin{tikzpicture}[x={(0cm,1cm)},                     y={({cos(30)*1cm},{sin(30)*-1cm})},                     z={({cos(20)*1cm},{sin(20)*1cm})},                     thick,                     scale=3]   \pgfmathsetmacro{\ax}{.4}   \pgfmathsetmacro{\ay}{.6}   \pgfmathsetmacro{\az}{-.6}   \pgfmathsetmacro{\bx}{.4}   \pgfmathsetmacro{\by}{-.7}   \pgfmathsetmacro{\bz}{-.8}   \draw[densely dotted,thin] (\ax,\ay,\az) -- (\ax,0,\az);   \draw[densely dotted,thin] (\ax,\ay,\az) -- (0,\ay,\az);   \draw[densely dotted,thin] (\ax,0,0) -- (\ax,0,\az) -- (0,0,\az);   \draw[densely dotted,thin] (0,0,\az) -- (0,\ay,\az) -- (0,\ay,0);   \draw[densely dotted,thin] (\bx,\by,\bz) -- (\bx,0,\bz);   \draw[densely dotted,thin] (\bx,\by,\bz) -- (0,\by,\bz);   \draw[densely dotted,thin] (\bx,0,0) -- (\bx,0,\bz) -- (0,0,\bz);   \draw[densely dotted,thin] (0,0,\bz) -- (0,\by,\bz) -- (0,\by,0);   \draw[-{Cone3}] (0,0,0) -- (1,0,0) node[right] {$x$};   \draw[-{Cone3}] (0,0,0) -- (0,1,0) node[above right] {$y$};   \draw[-{Cone3}] (0,0,0) -- (0,0,1) node[below right] {$z$};   \draw[-{Cone3}] (0,0,0) -- (0,0,-1) node[above left] {$-z$};   \draw[thin] (0,0,0) -- (0,-.9,0);   \draw[-{Cone3}] (0,0,0) -- (\ax,\ay,\az) node[below left] {source};   \draw[-{Cone3}] (0,0,0) -- (\bx,\by,\bz) node[above right] {sim}; \end{tikzpicture}   gives this figure Iterating each character in a string using Python How to interpret this yum dependency error? I'm trying to install XRDP and I'm hitting the following:  [root@box ~]# yum -y install xrdp Loaded plugins: fastestmirror, langpacks Loading mirror speeds from cached hostfile  * base: centos.serverspace.co.uk  * epel: mirrors.coreix.net  * extras: mirror.sov.uk.goscomb.net  * updates: mirror.sov.uk.goscomb.net Resolving Dependencies --&gt; Running transaction check ---&gt; Package xrdp.x86_64 1:0.9.10-1.el7 will be installed --&gt; Processing Dependency: xrdp-selinux = 1:0.9.10-1.el7 for package: 1:xrdp-0.9.10-1.el7.x86_64 --&gt; Processing Dependency: xorgxrdp for package: 1:xrdp-0.9.10-1.el7.x86_64 --&gt; Running transaction check ---&gt; Package xorgxrdp.x86_64 0:0.2.10-4.el7 will be installed --&gt; Processing Dependency: xorg-x11-server-Xorg(x86-64) = 1.20.4 for package: xorgxrdp-0.2.10-4.el7.x86_64 ---&gt; Package xrdp-selinux.x86_64 1:0.9.10-1.el7 will be installed --&gt; Finished Dependency Resolution Error: Package: xorgxrdp-0.2.10-4.el7.x86_64 (epel)            Requires: xorg-x11-server-Xorg(x86-64) = 1.20.4            Installed: xorg-x11-server-Xorg-1.20.1-5.6.el7_6.x86_64 (@updates)                xorg-x11-server-Xorg(x86-64) = 1.20.1-5.6.el7_6            Available: xorg-x11-server-Xorg-1.20.1-3.el7.x86_64 (base)                xorg-x11-server-Xorg(x86-64) = 1.20.1-3.el7            Available: xorg-x11-server-Xorg-1.20.1-5.el7.x86_64 (updates)                xorg-x11-server-Xorg(x86-64) = 1.20.1-5.el7            Available: xorg-x11-server-Xorg-1.20.1-5.1.el7.x86_64 (updates)                xorg-x11-server-Xorg(x86-64) = 1.20.1-5.1.el7            Available: xorg-x11-server-Xorg-1.20.1-5.2.el7_6.x86_64 (updates)                xorg-x11-server-Xorg(x86-64) = 1.20.1-5.2.el7_6            Available: xorg-x11-server-Xorg-1.20.1-5.3.el7_6.x86_64 (updates)                xorg-x11-server-Xorg(x86-64) = 1.20.1-5.3.el7_6  You could try using --skip-broken to work around the problem  You could try running: rpm -Va --nofiles --nodigest   Now, I get that it's missing a dependency, however, it appears to be saying it requires xorg-x11-server-Xorg version 1.20.4.   It then continues to say version 1.20.1-5.6.el7_6 is installed.  From where I'm sitting, 4 is in the range 1-5 so I'm unclear what the issue is. They all seem to be for the right architecture.  Is 1-5 a version string in and of itself as opposed to a range, or -if not- what am I missing?  Solution: Thanks to , here's a workaround:     Having the same issue, I installed manually archived xorgxrdp   yum -y install https://archive.fedoraproject.org/pub/archive/epel/7/x86_64/Packages/x/xorgxrdp-0.2.9-1.el7.x86_64.rpm   then   yum -y install xrdp and it works This is a question that arose in the comments here:   I normally hide footnotes from the TOC by doing this:  \section[title]{title\footnote{This is a footnote.}}.   This works in a lot of document classes (memoir, article, ...), but not in all of them. amsbook, for example, uses the optional argument only for the running heads so the footnote mark still ends up in the TOC. So what is the 'universal solution'? Let $p$ be a prime number, and let $\mathbb{F}_p$ be the field with $p$ elements. How many elements of $\mathbb{F}_p$ have cube roots in $\mathbb{F}_p$?   I had this question on an exam and after reviewing I am still not sure. Any help would be appreciated. I installed Opera 12.16 from a .deb for reasons. Just assume that I need this specific browser of this specific version and that there’s no alternative.  However, that deb depends on packages (such as the gstreamer0.10 series) which are not in my distribution anymore (Debian testing). This makes apt fail on every operation except apt remove opera with dependency errors:  # apt install cli-common Reading package lists... Done Building dependency tree        Reading state information... Done You might want to run 'apt --fix-broken install' to correct these. The following packages have unmet dependencies:  opera : Depends: gstreamer0.10-plugins-good but it is not installable          Recommends: flashplugin-nonfree but it is not going to be installed E: Unmet dependencies. Try 'apt --fix-broken install' with no packages (or specify a solution).   apt --fix-broken install will just propose to remove opera:  # apt --fix-broken install Reading package lists... Done Building dependency tree        Reading state information... Done Correcting dependencies... Done The following packages will be REMOVED:   opera 0 upgraded, 0 newly installed, 1 to remove and 92 not upgraded. 1 not fully installed or removed. After this operation, 46.6 MB disk space will be freed. Do you want to continue? [Y/n]   Currently, my workaround is to install Opera when I need it, and remove it as soon as anything else needs to be done with apt. This is annoying.  Any suggestions? Ideally, I’d like to make apt ignore the dependencies of opera forever, since it works well-enough for my purposes. Creating triangle commutative diagram with tikz-cd I've just started using TikZ and need to create a simple triangle commutative diagram like this one.    The closest I've been able to get is this.   How do I get the h arrow to go from A2 to A3? Everything I've tried just causes errors.  Here's my current code:  \begin{tikzcd}[column sep=small] A \arrow{r}{i}  \arrow{rd}{g}    &amp; A3 \arrow{d}{h} \\     &amp; A2 \end{tikzcd} Iterate a list as pair (current, next) in Python I would like to . Apparently this is possible as of Minecraft 1.4.2, so how do I do it? How can I model the mechanics of an army battlefield scene? TL;DR;  I want to model a strategic battlefield fight for my players to command and participate. I'm seeking advice on how to model it mechanically so that it is exciting for the players.  Background  The final scene of Act II of my campaign is envisioned to be a big battle between the army of the Big Bad and the allied forces gathered by my players. The full set of Act II runs with the players gaining the allegiance of the different factions to support them on the fight.  Now, in terms of that final scene, I'm struggling to decide how to DM the fight. In games and movies the action is made epic by having cinematic scenes of the fight happening with cuts to our heroes doing their amazing things, be it just plowing through dozens of enemies in quick succession or fighting the big ugly overpowered monster that is otherwise cause havoc among the army. I want that feeling  The set up will involve an army of several thousand enemies agains the different forces gathered by my players. Depending on what they've done during the second act, they'll have more or less support with a minimum number of regiments belonging to several faction (i.e. the silver guard of Wizardwight).  Intended way of DMing the scenario.  What I've come up with is to have the players be military leaders. Draw the map of the battlefield and have them manage the battlefield strategically and tactically, distributing the units and, somehow, enabling a dice based mechanism to evaluate how well each unit is doing. This will transform the tabletop into something similar to Warhammer Fantasy. They can choose to join a particular place of the battlefield to help either together or separately.  I have absolutely no idea on how to model this mechanically (as far as I know D&amp;D 5e does not cover this kind of fights).  Question:  What are good ways to mechanically model this kind of strategic army combat? Should I switch to a different system just for this scene or can I model this with D&amp;D 5e?  Notes on level: At this point I expect my players to range between level 9-12 and for the party to be between 3 and 4 players (this is not a limitation of the campaign, more like the players I'm running the campaign with). Basically I want  \mint{python}|'banana'|   to produce straight single quotes, rather than the curly ones it normally produces (in pdflatex). Converse of Schur's Lemma in finite dimensional vector spaces I am trying to prove (or disprove) the converse of Schur's Lemma in finite dimensional vector spaces. I am not sure if it holds in this case, but I have tried to apply the idea that proves it in representation theory (see for example Theorem 4.3  that uses Maschke's theorem or in questions  and ).  The converse of Schur's Lemma in finite dimensional vector spaces is:     Let $V$ be a finite dimensional vector space over the complex numbers. Let $S$ be a set of endomorphisms of $V$ and assume that every endomorphism $A$ of $V$ such that $$AB=BA\text{ for all }B\in S$$ is of the form $\lambda I, \ \lambda\in\mathbb{C}$. Then $V$ is a simple $S$-space.   (*an endomorphism of $V$ is a linear operator from $V$ to $V$  *$V$ is a simple $S$-space if the only $S$-invariant subspaces of $V$ are $V$ itself and the zero subspace)  What I've tried so far:  Assume to the contrary that $V$ is not a simple $S-$space. Then, there exists a subspace $W$ of $V$ such that $W\not =\{0\}$, $W\not= V$ and $W$ is $S$-invariant. Let $W'=V\setminus W$. Then, since $V$ is finite, we can easily prove that $V=W\oplus W'$ (this is my attempt to translate Maschke's theorem in vector spaces). Consequently, for every $v\in V$, there exists unique $w\in W$ and $w'\in W'$, such that $v=w+w'$. Define the projection $P:V\rightarrow V$ by $Pv=w$ for every $v\in V$.   What is left to prove is that $PB=BP$ for all $B\in S$. Then $P$ is clearly not a scalar and thus we have the contradiction we are looking for.  There is a difficulty in showing that $PB=BP$ for all $B\in S$, because $W'$ might be $S$-invariant or not. More precisely:   Let $v\in V=W\oplus W'$ and $v\not =0_V$.  If $v\in W$ then $Bv\in W$ because $W$ is $S$-invariant, therefore: $PBv=Bv$ and $BPv=Bv$.  If $v\in W'$ then $Pv=0$, hence $BPv=B\cdot 0=0$, and  (i) if $Bv\in W'$ then $PBv=0$.  (ii) if $Bv\in W$ then $PBv=Bv$ and this is where the problem occurs.  Any hints, ideas or counterexamples would be very helpful. How do I add CSS files? Here is an example of my *.info file.      Why the page cannot load the CSS that I add myself?