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I have a 2×2 groupplot (where the first plot should be replaced by a title "Supertitle") with titles in boxes. These "title boxes" should all have the same width, and boxes in the same row should have the same height. I achieved this using \vphantom{} because I didn't find a better method. How can I configure the settings such that the entire groupplot has a width of \textwidth? And a horizontal space between the columns like \tabcolsep (or something similar)? Is there a elegant way to do this by package keys? (resizebox etc. would certainly work, but that would be less elegant.) Ideally, it should stay a groupplot. PS: I'm using DIN A5 format here, but that shouldn't matter if the keys are set correctly. \documentclass[paper=a5]{scrartcl} \usepackage[margin=14mm, showframe]{geometry} \usepackage{pgfplots} \usepgfplotslibrary{groupplots} \pgfplotsset{compat=1.18} \begin{document} \section{Plots with Titles and Supertitle} \pgfmathsetlengthmacro\plotwidth{0.5*\textwidth-\the\arraycolsep} \begin{tikzpicture}[font=\footnotesize] \begin{groupplot}[ % Grouupplot settings ================== group style={ group size=2 by 2, % 2 columns, 2 rows vertical sep=25mm, horizontal sep=15mm, }, % Styles applied to all subplots ============== width=\plotwidth, height=30mm, % Title Styles ========================== title style={% at={(0,1)}, xshift=-3ex, align=left, anchor=south west, inner xsep=2pt, draw, fill=none, text width=0.925*\pgfkeysvalueof{/pgfplots/width}, },% ] % Title (Row 1, Col 1) \nextgroupplot[ % I don't know how to get this box to the same height without this trick: title={\vphantom{Plot 0} \\ \vphantom{000} \\ \vphantom{000}}, title style={name=super}, hide axis, ] \addplot[draw=none, samples={0}]{x}; % Plot 0 (Row 1, Col 2) \nextgroupplot[title={Title 0 \\ 000 \\ 000}] \addplot{x}; % Plot 1 (Row 2, Col 1) \nextgroupplot[title={Title 1 \\ 2-111 \\ 3-111 \\ 4-111}] \addplot{x^2}; % Plot 2 (Row 2, Col 2) \nextgroupplot[title={Title 2 \\ 2-222 \\ 3-222 \\ \vphantom{4-111}}] \addplot{x^3}; \end{groupplot} %% Supertitle \node[font=\bfseries\Large] at (super){Supertitle}; \node[anchor=north west, draw=none, align=left,] at (super.south west){ Some notes \\ below Supertitle}; \draw[cyan, very thick, |-|] (group c1r2.west) -- +(\plotwidth,0) node[midway, below, fill=yellow]{plotwidth =\plotwidth}; %% This gives a 'Overfull \hbox ' warning ================== \draw[red, thick, |-|, ] ([yshift=5mm]group c1r2.west) -- +(2*\plotwidth,0) node[midway, above, fill=yellow]{2*plotwidth =\plotwidth}; \end{tikzpicture} \end{document}

I'm probaby doing something stupid in this example and I don't know if anyone would ever do this; but should it be okay to set up the head in the lua code and still start the sections in ConTeXt code? If all of this brief example is coded in lua and run as a .cld file, it works. But if split it and run as .tex file, it errors concerning the command option line. If remove the command option line or remove the set up head from the lua code section and declare it in the ConTeXt section as \setuphead[section][command={\MySectionLua}] it works. Is there a way to write the command option line to permit the context.setuphead to remain in the lua code? Thank you. The error is: ! Control sequence expected instead of undefined tex error > tex error on line 16 in file ./junk.tex: { command = [[mber %s Title: %s",nbr,ttl) <argument> { command = [[\MySectionLua %s",nbr,ttl) ) ]] }, <macro> \luat_start_lua_code_indeed #1\stopluacode ->\directlua {#1 \beginlocalcontrol \endgroup \endlocalcontrol } <line 3.16> \stopluacode 6 protected = true, 7 actions = function(nbr, ttl) 8 context("Number %s Title: %s",nbr,ttl) 9 end, 10 } 11 12 context.setuphead( 13 { "section" }, 14 { command = [[\MySectionLua]] }, 15 ) 16 >> \stopluacode 17 18 \startTEXpage 19 \startsection[title={Title One}] 20 Paragraph 21 \stopsection 22 \stopTEXpage 23 You injected something that confused the parser, maybe by using some Lua call. mtx-context | fatal error: return code: 1 \startluacode interfaces.implement { name = "MySectionLua", public = true, arguments = "2 arguments", protected = true, actions = function(nbr, ttl) context("Number %s Title: %s",nbr,ttl) end, } context.setuphead( { "section" }, { command = [[\MySectionLua]] }, ) \stopluacode %\setuphead[section][command={\MySectionLua}] \startTEXpage \startsection[title={Title One}] Paragraph \stopsection \stopTEXpage

I know there are several relevant questions on TeX Stack Exchange about nicely highlighting matrix multiplication, and some of them have excellent answers. I apologize if my question is a duplicate. I have managed to highlight the various entries manually, but it requires quite a bit of work. Is there a way to automate this procedure? \documentclass{article} \usepackage{amsmath, amssymb} \usepackage{xcolor} \usepackage[margin=1.5cm]{geometry} \begin{document} \section*{Matrix Multiplication} We want to compute the product \(AB\) for \[ A = \begin{bmatrix} 3 & 1 & -1 \\ -1 & 0 & 4 \end{bmatrix}, \quad B = \begin{bmatrix} 2 & 1 & 3 \\ -1 & 3 & 4 \\ 0 & 2 & 5 \end{bmatrix}. \] We can illustrate the multiplication as follows, highlighting each row of \(A\) and each column of \(B\): \[ \begin{array}{c@{\hspace{2em}}c@{\hspace{1em}}c} & \begin{bmatrix} \color{blue}{2} & \color{orange}{1} & \color{purple}{3} \\ \color{blue}{-1} & \color{orange}{3} & \color{purple}{4} \\ \color{blue}{0} & \color{orange}{2} & \color{purple}{5} \end{bmatrix} & \\[1em] % \begin{bmatrix} \color{red}{3} & \color{red}{1} & \color{red}{-1} \\ \color{green}{-1} & \color{green}{0} & \color{green}{4} \end{bmatrix} & = & \begin{bmatrix} \underbrace{\color{red}{3}\cdot \color{blue}{2} + \color{red}{1}\cdot \color{blue}{-1} + \color{red}{-1}\cdot \color{blue}{0}}_{\color{black}{5}} & \underbrace{\color{red}{3}\cdot \color{orange}{1} + \color{red}{1}\cdot \color{orange}{3} + \color{red}{-1}\cdot \color{orange}{2}}_{\color{black}{4}} & \underbrace{\color{red}{3}\cdot \color{purple}{3} + \color{red}{1}\cdot \color{purple}{4} + \color{red}{-1}\cdot \color{purple}{5}}_{\color{black}{8}} \\[0.5em] % \underbrace{\color{green}{-1}\cdot \color{blue}{2} + \color{green}{0}\cdot \color{blue}{-1} + \color{green}{4}\cdot \color{blue}{0}}_{\color{black}{-2}} & \underbrace{\color{green}{-1}\cdot \color{orange}{1} + \color{green}{0}\cdot \color{orange}{3} + \color{green}{4}\cdot \color{orange}{2}}_{\color{black}{7}} & \underbrace{\color{green}{-1}\cdot \color{purple}{3} + \color{green}{0}\cdot \color{purple}{4} + \color{green}{4}\cdot \color{purple}{5}}_{\color{black}{17}} \end{bmatrix} \end{array} \] Thus, the final product is \[ AB = \begin{bmatrix} 5 & 4 & 8 \\ -2 & 7 & 17 \end{bmatrix}. \] \bigskip \textit{Note:} \(BA\) is not defined because \(B\) is \(3\times 3\) and \(A\) is \(2\times 3\); the number of columns of \(B\) (3) does not match the number of rows of \(A\) (2). In general, \(AB \neq BA\). \end{document}

My new keyboard writes ^ as ˆ, and overleaf doesn't recognize these the same way. Is there an alternative symbol in latex for writting powers and indexes or some way to make overleaf recognize ˆ as ^?

At the moment, I don't remember how to number the equations inside dcases , with the amsart class, without empheq, in order to assign a label to each one. \documentclass{amsart} \usepackage{mathtools} \begin{document} \begin{subequations} \begin{equation} \begin{dcases} 0 \le \frac{u+v}{2} \le 1 \\ 0 \le \frac{v-u}{2} \le 1 - \frac{u+v}{2} \end{dcases} \iff \begin{dcases} 0 \le u+v \le 2 \\ \label{Psojjn} 0 \le v-u \le 2 - (u+v) \end{dcases} \end{equation} \end{subequations} \end{document} Addendum: My desidered output.

Is there a way to print the sidenote counter independently of the chapter? based on: Tex-sidenotes % !TEX TS-program=ConTeXt (LuaTeX) \setuppapersize[A4] \unprotect \def\caesarmarginwidth{142pt} \def\caesarmargindistance{10pt} % setup the side notes \setuplayout[topspace=40pt, header=0pt, headerdistance=0pt, height=270mm, footer=0pt, % backspace=42pt, leftmargin=0pt, width=425pt, rightmargindistance=\caesarmargindistance, rightmargin=\caesarmarginwidth] \setupmargindata [margintext] [location=outer, width=\caesarmarginwidth, align=flushleft, stack=continue, style={\tfx\setupinterlinespace[line=10pt]}] \usemodule[annotation] % setup the numbering of the side notes \define[2]\caesar_sidenote_command {\high{\rawnumber[sidenote]}% \margintext{#1.\,#2\vskip4pt}} \defineannotation [sidenote] [alternative=command, command=\caesar_sidenote_command, number=yes] \protect \starttext \chapter{My chapter} My first word \sidenote{Place here!}. \stoptext

How works \Xparindent in reledmac package? What does it depend on whether it is applied or not? I applied \Xparindent in a document, but the command only applied it in the last critical apparatus entry. Have other edition with indentation in apparatus, but in context of ledgroup, and it perfectly works. Usually use xe(la)tex, but even with lua(la)tex it doesn't apply it. This is not a strictly a "minimal" example, but is a page and it doesn't apply the indent. \documentclass[11pt,twoside]{article} \usepackage[noeledsec,noend,noledgroup,nopenalties,series={A,E},parapparatus]{reledmac} \usepackage{polyglossia} \usepackage[paperwidth=17.00cm,paperheight=25.00cm,top=1.40cm,inner=1.95cm,outer=1.65cm,bottom=2.50cm]{geometry} \setmainlanguage{spanish} \setlength{\parindent}{0.6cm} \fnpos{critical-familiar} \fnpos{{A}{familiar},{A}{critical},{E}{familiar}} \Xarrangement{paragraph} \arrangementX[A]{paragraph} \Xparindent \parindentX[E] \Xnumberonlyfirstinline \Xsymlinenum{\textbf{||}} \Xnotenumfont{\bfseries} \sloppy % \newcommand{\eg}{{\emph{\textbf{LB3}}}} \newcommand{\jm}{\emph{\textbf{82*JM}}} \newcommand{\rl}{\emph{\textbf{86*RL}}} \newcommand{\hh}{\emph{\textbf{HH1}}} \newcommand{\mn}{\emph{\textbf{MN19}}} \newcommand{\im}{\emph{\textbf{83*IM}}} % \begin{document} \beginnumbering \begin{center} \textbf{[I]}\footnoteA{\textbf{[\textsc{Incipit}]} Coplas que fiço don jorje manrriq\emph{ue} sobre la muerte del maestre de santiago don rrodrigo manrriq\emph{ue} su padre {\eg}; Dezir de don jorge manrriq\emph{ue} por la muerte de su padre {\jm}; De don jorge manrique por la muerte de su padre {\rl}; Coplas de do\emph{n} jorge ma\emph{n}riq\emph{ue} a la muerte del maestre don rrod\emph{rig}o ma\emph{n}riq\emph{ue} su padre {\hh}; Coplas que hizo do\emph{n} jorge manrriq\emph{ue} ala muerte del maestre de santiago do\emph{n} rodrigo manrique su padre {\im}.} \end{center} \pstart Recuerde\footnoteE{«Recuerde» no tiene la acepción de «traer a la memoria», sino la de «despertar» y, para ello, el \emph{Tesoro de la lengua castellana} de Covarrubias (1611) registra para el vocablo \emph{recordar} «despertar el que duerme, o boluer en acuerdo, del verbo recordor». Posteriormente se registró el significado «Metaphoricamente vale despertar al que está dormido» (\emph{Autoridades}, 2ª acepción).} el alma dormida,\\ avive el seso y despierte\\ contenplando\\ cómo se pasa la vida,\\ cómo se viene la muerte\\ tan callando;\par q\emph{uá}nd presto se va el plazer,\\ cómo después de acordado\\ da dolor,\\ cómo a nuestro paresçer\\ \edtext{q\emph{ua}lq\emph{uie}ra}{\Afootnote{qualqujer {\eg}}} tie\emph{n}po pasado \edtext{}{\Afootnote[nosep]{sapado \emph{err.} {\eg}}}\\ fue mejor.\par \pend \endnumbering \end{document}

I would like to align textsubscript and textsuperscript without math mode. \documentclass{article} \begin{document} text\textsubscript{1}\textsuperscript{1} \end{document}

I am writing a manuscript in revtex4-2, which is mostly in two-column format, but which has a (relatively meaty) section inside widetext. One quirk I've noticed, and which I would like to fix, is that one of the footnotes is inside that widetext, but it is being displayed in two-column mode, which looks rather ugly: How can this be fixed? I notice, in particular that the revtex4-1 guide says the following, \footnote in \widetext and table* environments improved. \footnotes in the \widetext or table* environments are now correctly placed and formatted. which would make one think that this was a problem in previous versions but should be fixed in RevTeX 4.1 and later. So what gives? Below is a minimal working example to produce the behaviour: \documentclass[% reprint, aps, pra, nofootinbib, ]{revtex4-2} \usepackage{lipsum} \begin{document} This is some two-column text. \lipsum[1-2] \begin{widetext} This is some one-column text, with a footnote.% \footnote{This is the footnote text, which is long enough to be just over one column wide.} \lipsum[1-8] \end{widetext} \end{document}

I would like to color equation and eqation number to different color. Every eqation should be blue, and every eqation number should be red. \documentclass{article} \usepackage{amsmath} \usepackage{lipsum} \usepackage{xcolor} \usepackage[colorlinks]{hyperref} \begin{document} \lipsum[1] \begin{equation} E = mc^2 \label{eq:emc} \end{equation} \begin{equation} F = ma \label{eq:fma} \end{equation} \eqref{eq:emc} \eqref{eq:fma} \lipsum[1] \end{document}

I have the following code, where there are equations inside the cases, at the cases hyperref is not working properly: 1a, 1b; 1 and 2 is OK. \documentclass{article} \usepackage{amsmath} \usepackage{cases} \usepackage{caption} \usepackage{float} \usepackage[colorlinks]{hyperref} \DeclareCaptionType{equ}[Equation][List of Equations] \begin{document} \listof{equ}{List of Equations} \begin{equ}[H] \begin{subnumcases}{f(x)=} 1 & \( x \geq 0 \) \label{eq:pos-sub} \\ 0 & \( x < 0 \) \label{eq:neg-sub} \end{subnumcases} \caption{Caption of the equation I} \label{eq:cases} \end{equ} \begin{equ}[H] \begin{equation} E = mc^{2} \end{equation} \caption{Caption of the equation II} \label{eq:emc} \end{equ} References: \ref{eq:cases}, \ref{eq:pos-sub}, \ref{eq:neg-sub}, \ref{eq:emc} \end{document}

First, apologies if this question has been asked before. I'm trying to create an image of a particular circular domain, but my limited TikZ knowledge has made this quite challenging. I've searched for similar examples online without success. Any guidance would be greatly appreciated!

I have two issues with the circumflex (hat{}) in the euler-math package/font. The first one is that for certain letters it seems to be not centered. \documentclass{article} \usepackage{euler-math} \setmainfont{TeX Gyre Pagella} \begin{document} \^T$\hat{T}$ % Very wide hat, not centered \setmathfont[range={"0302}, Scale=MatchUppercase]{TeX Gyre Pagella Math} \^T$\hat{T}$ % Small hat, still not centered \setmathfont{TeX Gyre Pagella Math} \^T$\hat{T}$ % Small hat, centered \end{document} This produces Additionally the circumflex is so wide, that it clashes with surrounding text: \documentclass{article} \usepackage{euler-math} \setmainfont{TeX Gyre Pagella} \begin{document} $|\hat{f}|$ % hat crashes into bar \end{document} Which produces: The later issue can be solved by simply using the circuflex from a different math font (as done in the first example) but the wrong centering remains. Could it be that something is off with the way the combining circumflex is implemented in the Euler-Math font?

I am referring to this Italian lecture notes by Prof. R. Tauraso, edited by a student/lecturer Massimiliano Pompegnani (link https://moodle2.units.it/pluginfile.php/767967/mod_resource/content/1/intdoppi.pdf) My question concerns which specific libraries are needed to draw in 3D (I’m not very familiar with 3D) what to me seems drawn in MetaPost and peraphs, for the their complexity, with IPE drawing https://ipe.otfried.org/ (?), WinFIG (?). From the axes arrows it appears to be MetaPost and also the fills. ecc. I’m not asking for any code but want to be informed. There are many 3D libraries for TikZ but I have never previously been interested in 3D. Are there any similar libraries that TikZ can use to reproduce Metapost drawings?

I am using various datatool-databases with sums of funding for different projects and years. My aim is to have a macro with which I can get the sum of either a type or a year. The problem with my approach is that I need to create a list of available databases first, which I can feed to \DTLsumforkeys. Neither \datatool_db_state:nnnn {requestedFunding-\pNumber} {\clist_put_right:Nn \l__project_list_requested_funds_clist {requestedFunding-\pNumber}} {}{} nor its non-expl3-command \DTLifdbexists {requestedFunding-\pNumber} {\clist_put_right:Nn \l__project_list_requested_funds_clist {requestedFunding-\pNumber}} {} is creating the proper list for \l__project_list_requested_funds_clist, which should be requestedFunding-A01,requestedFunding-A02,requestedFunding-B01. The list \l__project_list_requested_funds_clist is then meant to be used in the actual macro calculating the sums. \documentclass{scrartcl} \usepackage{datatool} \usepackage[ mode = match, propagate-math-font = true, reset-math-version = false, reset-text-family = false, reset-text-series = false, reset-text-shape = false, text-family-to-math = true, text-series-to-math = true, tight-spacing = true, group-minimum-digits = 4, group-separator = {,}, %table-format = 6, table-alignment-mode = format, table-auto-round = true, locale =UK, input-decimal-markers = {.}, output-decimal-marker = {.}, input-ignore={,}, parse-numbers = true ]{siunitx} \DTLnewdb{project} \DTLnewrow{project} \DTLnewdbentry{project}{number}{A01} \DTLnewrow{project} \DTLnewdbentry{project}{number}{A02} \DTLnewrow{project} \DTLnewdbentry{project}{number}{B01} \DTLnewrow{project} \DTLnewdbentry{project}{number}{Q01} \DTLnewdb{requestedFunding-A01} \DTLnewrow{requestedFunding-A01} \DTLnewdbentry{requestedFunding-A01}{type}{costs} \DTLnewdbentry{requestedFunding-A01}{sum-year1}{1000} \DTLnewdbentry{requestedFunding-A01}{sum-year2}{2000} \DTLnewrow{requestedFunding-A01} \DTLnewdbentry{requestedFunding-A01}{type}{staff} \DTLnewdbentry{requestedFunding-A01}{sum-year1}{1001} \DTLnewdbentry{requestedFunding-A01}{sum-year2}{2001} \DTLnewdb{requestedFunding-A02} \DTLnewrow{requestedFunding-A02} \DTLnewdbentry{requestedFunding-A02}{type}{costs} \DTLnewdbentry{requestedFunding-A02}{sum-year1}{1000} \DTLnewdbentry{requestedFunding-A02}{sum-year2}{2000} \DTLnewrow{requestedFunding-A02} \DTLnewdbentry{requestedFunding-A02}{type}{staff} \DTLnewdbentry{requestedFunding-A02}{sum-year1}{1001} \DTLnewdbentry{requestedFunding-A02}{sum-year2}{2001} \DTLnewdb{requestedFunding-B01} \DTLnewrow{requestedFunding-B01} \DTLnewdbentry{requestedFunding-B01}{type}{staff} \DTLnewdbentry{requestedFunding-B01}{sum-year1}{1001} \DTLnewdbentry{requestedFunding-B01}{sum-year2}{2001} % intentionally there is no entry for Q01 \begin{document} \DTLdisplaydb{project}\\ \DTLdisplaydb{requestedFunding-A01}\\ \DTLdisplaydb{requestedFunding-A02}\\ \DTLdisplaydb{requestedFunding-B01}\\ \ExplSyntaxOn \clist_new:N \l__project_list_requested_funds_clist \DTLforeach{project}{ \pNumber=number }{ % \DTLifdbexists {requestedFunding-\pNumber} % {\clist_put_right:Nn \l__project_list_requested_funds_clist % {requestedFunding-\pNumber}} % {} \datatool_db_state:nnnn {requestedFunding-\pNumber} {\clist_put_right:Nn \l__project_list_requested_funds_clist {requestedFunding-\pNumber}} {}{} } % Doublecheck: \clist_use:N \l__project_list_requested_funds_clist \NewDocumentCommand{\getSumOverviewFundsCurrent}{smm} { % #2: year % #3: type (staff, costs...) \str_if_eq:nnTF {#2}{all} { \DTLsumforkeys{% \clist_use:N \l__project_list_requested_funds_clist } {sum-year#3}% {\SumOverviewRequestedFunds} } {\DTLsumforkeys[\DTLiseq{\pType}{#3}][ \pType=type %{staff,costs,instrumentation,fellowships,globalfunds} ]{ \clist_use:N \l__project_list_requested_funds_clist } {sum-year#2} {\SumOverviewRequestedFunds}} \IfBooleanTF{#1} {\SumOverviewRequestedFunds} {\tablenum{\SumOverviewRequestedFunds}} } \ExplSyntaxOff \getSumOverviewFundsCurrent*{1}{staff} % expecting here: 3,003 \getSumOverviewFundsCurrent*{2}{staff} % expecting here: 6,003 \getSumOverviewFundsCurrent*{1}{costs} % expecting here: 2,000 \getSumOverviewFundsCurrent*{2}{costs} % expecting here: 4,000 \getSumOverviewFundsCurrent*{all}{staff} % expecting here: 9,009 \getSumOverviewFundsCurrent*{all}{costs} % expecting here: 6,000 \end{document}

While writing down the above expression on Overleaf, I encountered the problem of drawing the dashed line in between the Left Hand Side and the Right Hand Side expressions. Do help me in writing it exactly that way. (I had written it in my own unique way, but without the dashed line, and would be intrigued to know if such a function existed.) My code & Output: \documentclass{article} \usepackage{amsmath} \begin{document} ARCTAN TERMS: \[\boxed{\sqrt{2}\zeta_1+1 \to \infty \implies \tan^{-1}(\sqrt{2}\zeta_1+1)\rightarrow \dfrac{\pi}{2}}\text{ and } \boxed{\sqrt{2}\zeta_1+1 \rightarrow -\infty \implies \tan^{-1}(\sqrt{2}\zeta_1+1)\to \dfrac{-\pi}{2}}\] \[\boxed{\sqrt{2}\zeta_1-1 \to \infty \implies \tan^{-1}(\sqrt{2}\zeta_1-1)\rightarrow \dfrac{\pi}{2}}\text{ and } \boxed{\sqrt{2}\zeta_1-1 \rightarrow -\infty \implies \tan^{-1}(\sqrt{2}\zeta_1-1)\to \dfrac{-\pi}{2}}\] Hence, \[\text{ Arctan terms evaluates to } \frac{\sqrt{2}}{4}\left(\frac{\pi}{2}+\frac{\pi}{2}-\left(\frac{-\pi}{2}-\frac{\pi}{2}\right)\right)=\frac{\pi}{\sqrt2}\] \end{document} Output:

I am facing an unusual issue. My book contains over 11,000 lines of code, and I need to generate a list of figures that includes subfigures. The standard method for doing this does not work in the full document. However, when I tried to reproduce the problem in a minimal working example using only essential packages, it works correctly. This suggests that something in the preamble—which is 669 lines long—is interfering with the process. Could you please help identify the cause? Below is the complete code with the full preamble. \documentclass[a4paper]{book} \usepackage[tmargin=2in, bmargin=2in, lmargin=1.5in, rmargin=1.5in]{geometry} \usepackage{amssymb,amsthm,amsmath,amsfonts} \usepackage{emptypage} %\usepackage{showframe} %\usepackage{microtype} \usepackage{centernot} \usepackage{nccmath} \usepackage{stmaryrd} \usepackage{mathrsfs} \usepackage[inline]{enumitem} \usepackage{mathtools} \usepackage{blkarray} %\usepackage{etoolbox} \usepackage{thmtools} \usepackage{upgreek} \usepackage{multicol} \usepackage{xcolor} \usepackage{xifthen} \usepackage{graphicx} \usepackage{float} \usepackage[mathscr]{eucal} \usepackage[skins,breakable]{tcolorbox} \usepackage[nottoc,notlot,notlof]{tocbibind} \usepackage[page]{appendix} \let\plainappendixpage\appendixpage \makeatletter \renewcommand{\appendixpage}{% \begingroup \let\ps@plain\ps@empty \plainappendixpage \endgroup} \makeatother \allowdisplaybreaks[4] %\usepackage[font=footnotesize]{idxlayout} % Tag with dots \makeatletter \let\mytagform@=\tagform@ \renewcommand{\eqref}[1]{\textup{\mytagform@{\ref{#1}}}} \newtagform{dots}{$ \cdots $(}{)} \makeatother \usetagform{dots} % %============================================================ % % %==================================================================================================== %Index % \usepackage{imakeidx} \indexsetup{othercode=\footnotesize} \makeindex[columns=2, intoc=true, options=-s index_style.mst, columnseprule] \providecommand{\indexalso}[2]{% \index{#1!zzzzz@\emph{\alsoname} {#2}}} %==================================================================================================== % %==================================================================================================== % Revised slanted fraction \newcommand{\altfrac}[2]{\ifmmode\def\tmp{$}\else\def\tmp{}\fi\mbox{% {\raisebox{.24\ht\strutbox}{\tmp#1\tmp}}% \kern-2.2pt\scalebox{1.6}[1.5]{/}\kern-1.8pt% {\tmp#2\tmp}}} %==================================================================================================== % %Tikz sets % %==================================================================================================== \usepackage[edges]{forest} \usetikzlibrary{arrows.meta} \usepackage{wrapfig} \usepackage{pgfplots} %\pgfplotsset{compat=1.18} \usetikzlibrary{decorations.pathreplacing, calligraphy} \usetikzlibrary{decorations.markings} \usetikzlibrary{patterns} \usetikzlibrary{cd} \usetikzlibrary{hobby} \tikzset{mynode/.style={fill=white,text=black,font=\footnotesize}} \tikzset{mynode1/.style={fill=white,text=black,font=\footnotesize}} \tikzset{font=\footnotesize, line cap=round, line join=round} \usetikzlibrary{calc} \newcommand{\arcThroughThreePoints}[4][]{ \coordinate (middle1) at ($(#2)!.5!(#3)$); \coordinate (middle2) at ($(#3)!.5!(#4)$); \coordinate (aux1) at ($(middle1)!1!90:(#3)$); \coordinate (aux2) at ($(middle2)!1!90:(#4)$); \coordinate (center) at ($(intersection of middle1--aux1 and middle2--aux2)$); \draw[#1] let \p1=($(#2)-(center)$), \p2=($(#4)-(center)$), \n0={veclen(\p1)}, % Radius \n1={atan2(\y1,\x1)}, % angles \n2={atan2(\y2,\x2)}, \n3={\n2>\n1?\n2:\n2+360} in (#2) arc(\n1:\n3:\n0); } \makeatletter \tikzset{ reuse path/.code={\pgfsyssoftpath@setcurrentpath{#1}} } \tikzset{even odd clip/.code={\pgfseteorule}, protect/.code={ \clip[overlay,even odd clip,reuse path=#1] (current bounding box.south west) rectangle (current bounding box.north east) %(-16383.99999pt,-16383.99999pt) rectangle (16383.99999pt,16383.99999pt) ; }} \makeatother \usetikzlibrary{3d,perspective} \usepgfplotslibrary{fillbetween} \pgfmathsetmacro\sprayRadius{.1pt} \pgfmathsetmacro\sprayPeriod{.2cm} \pgfdeclarepatternformonly{spray}{\pgfpoint{-\sprayRadius}{-\sprayRadius}}{\pgfpoint{1cm + \sprayRadius}{1cm + \sprayRadius}}{\pgfpoint{\sprayPeriod}{\sprayPeriod}}{ \foreach \x/\y in {2/53,6/52,11/48,23/49,20/47,32/46,41/47,47/51,56/52,46/44,4/43,16/42,33/41,41/37,49/35,55/31,37/35,44/30,28/37,24/36,17/37,7/38,0/31,8/29,18/31,28/30,37/28,30/27,46/24,51/21,24/23,12/24,4/21,18/19,12/16,31/21,38/18,26/16,46/16,56/12,52/10,45/8,51/4,37/12,35/7,24/9,14/9,2/12,8/6,15/4,27/0,34/1,40/1} { \pgfpathcircle{\pgfpoint{(\x + random()) / 57 * \sprayPeriod}{\sprayPeriod - (\y + random()) / 55 * \sprayPeriod}}{\sprayRadius} } \pgfusepath{fill} } %\usepackage{tkz-euclide} %\usetkzobj{all} %==================================================================================================== %Figures % \usepackage{caption} \usepackage[list=true, labelformat=simple, labelsep=colon,lofdepth=2]{subcaption} \renewcommand{\thesubfigure}{\thefigure\,(\alph{subfigure})} \makeatletter \renewcommand\p@subfigure{} \makeatother %\usepackage[symbol]{footmisc} %\usepackage{tabularx,ragged2e} %\newcounter{rownum} %\newcolumntype{C}{>{\Centering\arraybackslash}X} %\newcolumntype{N}{>{\refstepcounter{rownum}\therownum}l} %==================================================================================================== % Customising Proof env % \makeatletter \renewenvironment{proof}[1][\proofname]{\par % \vspace{-\topsep}% remove the space after the theorem \pushQED{\qed}% \normalfont \topsep0pt \partopsep0pt % no space before \trivlist \item[\hskip\labelsep \scshape #1\@addpunct{:}]\ignorespaces }{% \popQED\endtrivlist\@endpefalse \addvspace{2ex} % some space after } \makeatother %==================================================================================================== %==================================================================================================== %\usepackage[backend=biber,style=apa,]{biblatex} % %\addbibresource{Mybib.bib} \bibliographystyle{acm} %==================================================================================================== \graphicspath{ {/Users/AaRBiTt/OneDrive/Documents/Salesian College/Class Notes/Topology of Metric Spaces/Figures/} } %==================================================================================================== % Chapter title format % \setcounter{secnumdepth}{3} \usepackage{titlesec} \definecolor{gray75}{gray}{0.75} \newcommand{\hsp}{\hspace{20pt}} \titleformat{\chapter}[hang]{\filleft\Huge\bfseries}{\thechapter\hsp\textcolor{gray75}{$\mid$}\hsp}{0pt}{\Huge\bfseries} \titlespacing*{\chapter}{0pt}{0pt}{3in} \titleformat{\subsubsection}{\bfseries}{\thesubsubsection}{1em}{\bfseries} \renewcommand{\thesubsubsection}{\bfseries{\ensuremath{\bullet}}} %==================================================================================================== %==================================================================================================== % Section symbol in TOC and in text % \usepackage{tocloft} \renewcommand\cftsecpresnum{\S} \titleformat{\section}{\normalfont\Large\bfseries}{\S\thesection}{1em}{} %==================================================================================================== %==================================================================================================== % Header-Footer % \usepackage[english]{babel} \usepackage{fancyhdr} \pagestyle{fancy} \fancyhf{} \fancyhead[RO]{\rightmark} \fancyhead[LE]{\leftmark} \fancyfoot[C]{\thepage} \renewcommand{\chaptermark}[1]{\markboth{Chapter \MakeUppercase{\thechapter.\ #1}}{}} \renewcommand{\sectionmark}[1]{\markright{\S\thesection.\ #1}} %==================================================================================================== %==================================================================================================== % footnote symbols % \usepackage[symbol]{footmisc} \renewcommand{\thefootnote}{\fnsymbol{footnote}} % 1 asterisk * 2 dagger † 3 double dagger ‡ % 4 section symbol § 5 paragraph ¶ 6 parallel lines ‖ % 7 two asterisks ** 8 two daggers †† 9 two double daggers ‡‡ %==================================================================================================== % % %==================================================================================================== %Exercises % \newlist{exlist}{enumerate}{3} \setlist[exlist,1]{left=0pt, label=\thechapter.\arabic*., ref= \thechapter.\arabic*, before={% \section*{\hfill Exercises -- \thesection \hfill} \markright{Exercises -- \thesection} \addcontentsline{toc}{subsection}{Exercises -- \thesection}} } \setlist[exlist,2]{left=0pt, label=(\alph*), ref= \theexlisti\,(\alph*) } \setlist[exlist,3]{left=0pt,nosep, label=(\textit{\roman*}), ref= \theexlistii(\textit{\roman*}) } % %==================================================================================================== % Cross-references % \usepackage{varioref} \usepackage{hyperref} \hypersetup { colorlinks=true, %set true if you want colored links linktoc=all, %set to all if you want both sections and subsections linked linkcolor=black, %choose some color if you want links to stand out citecolor=black, urlcolor=black } \usepackage{cleveref} % be sure to load 'cleveref' AFTER 'hyperref' \crefname{subfigure}{Figure}{Figures} \crefname{thm}{Theorem}{Theorems} \crefname{axiom}{Axiom}{Axioms} \crefname{prop}{Proposition}{Propositions} \crefname{lem}{Lemma}{Lemmas} \crefname{defn}{Definition}{Definitions} \crefname{cor}{Corollary}{Corollaries} \crefname{figure}{Figure}{Figures} \crefname{chapter}{Appendix}{Appendices} \crefname{subsection}{Subsection}{Subsections} \crefname{subsubsection}{Subsubsection}{Subsubsections} \newlist{examplenum}{enumerate}{1} \setlist[examplenum]{label=\thedefn.\arabic*., left=0pt, ref=\thedefn.\arabic*, itemsep=1.5ex} \crefname{examplenumi}{Example}{Examples} \newlist{miscnum}{enumerate}{1} \setlist[miscnum]{label=\thechapter.\arabic*., font=\bfseries, ref=\thechapter.\arabic*, itemsep=1.5ex} \crefname{miscnumi}{Miscellaneous result}{Miscellaneous results} \newlist{thmnum}{enumerate}{2} \setlist[thmnum,1]{left=0pt, label=\roman*), ref=\thethm.(\textit{\roman*}), itemsep=0pt, topsep=0pt} \setlist[thmnum,2]{left=0pt, label=\alph*), font=\itshape, ref=\thethm.(\textit{\roman*})(\textit{\alph*}), itemsep=0pt, topsep=0pt} \crefname{thmnumi}{Theorem}{Theorems} \crefname{thmnumii}{Theorem}{Theorems} \newlist{propnum}{enumerate}{1} \setlist[propnum]{label=\roman*), ref=\thethm.(\textit{\roman*}), itemsep=0pt, topsep=0pt} \crefname{propnumi}{Proposition}{Propositions} \crefname{exlisti}{Exercise}{Exercises} \crefname{exlistii}{Exercise}{Exercises} \crefname{exlistiii}{Exercise}{Exercises} % %==================================================================================================== \newcounter{cases} \newcounter{subcases}[cases] \renewenvironment{cases} {% \setcounter{cases}{0}% \setcounter{subcases}{0}% \def\case {% \par\noindent \refstepcounter{cases}% \textbf{Case \thecases:} }% \def\subcase {% \par\noindent \refstepcounter{subcases}% \textit{Subcase (\thesubcases):} }% } {% \par } \renewcommand*\thecases{\arabic{cases}} \renewcommand*\thesubcases{\roman{subcases}} \newcounter{steps} \newenvironment{steps} {% \setcounter{steps}{0}% \def\step {% \par\noindent \refstepcounter{steps}% \textbf{Step \thesteps:} }% } {% \par } \renewcommand*\thesteps{\arabic{steps}} \newcommand{\myhref}[3][black]{\hyperref{#2}{\color{#1}{#3}}} \makeatletter \let\save@mathaccent\mathaccent \newcommand*\if@single[3]{% \setbox0\hbox{${\mathaccent"0362{#1}}^H$}% \setbox2\hbox{${\mathaccent"0362{\kern0pt#1}}^H$}% \ifdim\ht0=\ht2 #3\else #2\fi } %The bar will be moved to the right by a half of \macc@kerna, which is computed by amsmath: \newcommand*\rel@kern[1]{\kern#1\dimexpr\macc@kerna} %If there's a superscript following the bar, then no negative kern may follow the bar; %an additional {} makes sure that the superscript is high enough in this case: \newcommand*\widebar[1]{\@ifnextchar^{{\wide@bar{#1}{0}}}{\wide@bar{#1}{1}}} %Use a separate algorithm for single symbols: \newcommand*\wide@bar[2]{\if@single{#1}{\wide@bar@{#1}{#2}{1}}{\wide@bar@{#1}{#2}{2}}} \newcommand*\wide@bar@[3]{% \begingroup \def\mathaccent##1##2{% %Enable nesting of accents: \let\mathaccent\save@mathaccent %If there's more than a single symbol, use the first character instead (see below): \if#32 \let\macc@nucleus\first@char \fi %Determine the italic correction: \setbox\z@\hbox{$\macc@style{\macc@nucleus}_{}$}% \setbox\tw@\hbox{$\macc@style{\macc@nucleus}{}_{}$}% \dimen@\wd\tw@ \advance\dimen@-\wd\z@ %Now \dimen@ is the italic correction of the symbol. \divide\dimen@ 3 \@tempdima\wd\tw@ \advance\@tempdima-\scriptspace %Now \@tempdima is the width of the symbol. \divide\@tempdima 10 \advance\dimen@-\@tempdima %Now \dimen@ = (italic correction / 3) - (Breite / 10) \ifdim\dimen@>\z@ \dimen@0pt\fi %The bar will be shortened in the case \dimen@<0 ! \rel@kern{0.6}\kern-\dimen@ \if#31 \overline{\rel@kern{-0.6}\kern\dimen@\macc@nucleus\rel@kern{0.4}\kern\dimen@}% \advance\dimen@0.4\dimexpr\macc@kerna %Place the combined final kern (-\dimen@) if it is >0 or if a superscript follows: \let\final@kern#2% \ifdim\dimen@<\z@ \let\final@kern1\fi \if\final@kern1 \kern-\dimen@\fi \else \overline{\rel@kern{-0.6}\kern\dimen@#1}% \fi }% \macc@depth\@ne \let\math@bgroup\@empty \let\math@egroup\macc@set@skewchar \mathsurround\z@ \frozen@everymath{\mathgroup\macc@group\relax}% \macc@set@skewchar\relax \let\mathaccentV\macc@nested@a %The following initialises \macc@kerna and calls \mathaccent: \if#31 \macc@nested@a\relax111{#1}% \else %If the argument consists of more than one symbol, and if the first token is %a letter, use that letter for the computations: \def\gobble@till@marker##1\endmarker{}% \futurelet\first@char\gobble@till@marker#1\endmarker \ifcat\noexpand\first@char A\else \def\first@char{}% \fi \macc@nested@a\relax111{\first@char}% \fi \endgroup } \makeatother \renewcommand{\a}{\alpha} \renewcommand{\b}{\beta} \newcommand{\g}{\gamma} %\newcommand{\G}{\Gamma} \renewcommand{\d}{\delta} \newcommand{\e}{\epsilon} \renewcommand{\t}{\tau} \renewcommand{\th}{{\theta}} \renewcommand{\l}{\lambda} \renewcommand{\r}{\rho} \renewcommand{\L}{\Lambda} \renewcommand{\k}{\kappa} \newcommand{\W}{\Omega} \newcommand{\w}{\omega} \newcommand{\s}{\sigma} \newcommand{\ph}{\varphi} \renewcommand{\u}{\mathbf{u}} \newcommand{\x}{\mathbf{x}} \newcommand{\y}{\mathbf{y}} \newcommand{\z}{\mathbf{z}} \let\emptyset\varnothing \let\subsetneq\varsubsetneq \let\subsetneqq\varsubsetneq \let\setminus\smallsetminus \newcommand{\wrt}{w.r.t.\ } \newcommand{\B}{\mathscr{B}} \newcommand{\D}{\mathscr{D}} \newcommand{\K}{\mathbb{K}} \newcommand{\R}{\mathbb{R}} \newcommand{\N}{\mathbb{N}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\C}{\mathbb{C}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\bb}[1]{\mathbb{#1}} \newcommand{\G}{\mathscr{G}} \newcommand{\ts}{\textstyle} \newcommand{\ds}{\displaystyle} \newcommand{\func}[3]{#1\mathpunct{:}#2\to#3} \newcommand{\dfn}{\coloneqq} \newcommand{\inv}[1]{{#1}^{-1}} \newcommand{\bd}[1]{\partial #1} \newcommand{\comb}[2]{\begin{psmallmatrix}{#1}\\{#2}\end{psmallmatrix}} \newcommand{\rest}[2]{#1\bigr|_{#2}} \renewcommand{\bf}[1]{\mathbf{#1}} \renewcommand{\thefootnote}{\fnsymbol{footnote}} \newcommand{\dldx}[2]{\frac{\partial #1}{\partial #2}} \renewcommand{\qedsymbol}{$\blacksquare$} \renewcommand{\P}{\mathscr{P}} \let\bar\widebar \let\limsup\varlimsup \let\liminf\varliminf \newcommand{\X}{\tilde{X}} \newcommand{\td}{\tilde{d}} \newcommand{\tx}{\tilde{x}} \newcommand{\ty}{\tilde{y}} \newcommand{\tz}{\tilde{z}} \newcommand{\symmdiff}{\mathbin{\triangle}} \newcommand{\dotp}{\mathbin{\cdot}} \newcommand{\comp}{\mathbin{\circ}} \def\centerarc[#1](#2)(#3:#4:#5)% Syntax: [draw options] (center) (initial angle:final angle:radius) { \draw[#1] ($(#2)+({#5*cos(#3)},{#5*sin(#3)})$) arc (#3:#4:#5) } \newcommand*{\dt}[1][t]{\,\mathrm{d}#1} \DeclareMathOperator{\image}{Im} \DeclareMathOperator{\rank}{rank} \DeclareMathOperator{\nullity}{\mathrm{N}} \DeclareMathOperator{\sgn}{sgn} \DeclareMathOperator{\interior}{int} \DeclareMathOperator{\exterior}{ext} \DeclareMathOperator{\diam}{diam} \DeclareMathOperator{\trace}{tr} \DeclareMathOperator{\diag}{diag} \DeclareMathOperator{\adj}{adj} \DeclareMathOperator{\lip}{Lip} \DeclareMathOperator{\ls}{span} \let\hom\relax \DeclareMathOperator{\hom}{Hom} \DeclarePairedDelimiter\abs{\lvert}{\rvert} \DeclarePairedDelimiter\norm{\lVert}{\rVert} \DeclarePairedDelimiter\mat{\llbracket}{\rrbracket} \def\upint{\mathchoice% {\mkern13mu\overline{\vphantom{\intop}\mkern7mu}\mkern-20mu}% {\mkern7mu\overline{\vphantom{\intop}\mkern7mu}\mkern-14mu}% {\mkern7mu\overline{\vphantom{\intop}\mkern7mu}\mkern-14mu}% {\mkern7mu\overline{\vphantom{\intop}\mkern7mu}\mkern-14mu}% \int} \def\lowint{\mkern3mu\underline{\vphantom{\intop}\mkern7mu}\mkern-10mu\int} %\delimitershortfall-1sp %\newcommand{\abs}[1]{\left\lvert #1 \right\rvert} %\newcommand{\norm}[1]{\left\lVert #1 \right\rVert} \newcommand{\ip}[2]{\left\langle #1,#2 \right\rangle} %\newcommand{\mat}[1]{\left\llbracket #1 \right\rrbracket} \renewcommand{\tilde}[1]{\widetilde{#1}} \renewcommand{\Bar}[1]{\widebar{#1}} \newcommand{\scr}[1]{\mathscr{#1}} \newcommand{\ssubset}{\subset\joinrel\subset} \catcode`@=11 \def\underarrow#1{\mathop{\vtop{\m@th\ialign{##\crcr $\hfil\displaystyle{#1}\hfil$% \crcr\noalign{\kern3pt\nointerlineskip} \hfil$\uparrow$\hfil\crcr\noalign{\kern3pt}}}}\limits} \catcode`@=12 \newtheoremstyle{mythmstyle}{3ex}{1ex}{\itshape}{}{\bfseries}{:}{.5em}{} \theoremstyle{mythmstyle} \newtheorem{thm}{Theorem}[chapter] \newtheoremstyle{mycorstyle}{3ex}{1ex}{\itshape}{}{\scshape}{:}{.5em}{} \theoremstyle{mycorstyle} \newtheorem{cor}{Corollary}[thm] \newtheoremstyle{mydefnstyle}{3ex}{2ex}{}{}{\bfseries}{:}{.5em}{} \theoremstyle{mydefnstyle} \newtheorem{defn}[thm]{Definition} \newtheorem{axiom}[thm]{Axiom} \newtheorem*{misc}{Miscellaneous results} \newtheorem{exmp}{Example}[defn] \newtheorem*{exmps}{Examples} \newtheorem*{conseq}{Consequences} \newtheorem*{motivation}{Motivation} \newtheorem*{rem}{Remark} \newtheorem*{rems}{Remarks} \newtheorem*{properties}{Properties} \newenvironment{Rems} { \begin{rems}\ \vspace{-1ex} \begin{enumerate}[label=(\alph*)] } { \end{enumerate} \end{rems} } %==================================================================================================== % Continued Examples % \makeatletter \newcommand*{\my@start@example}[2] {% \begin{exmps}#1 \mbox{}\par\nobreak\vskip -0.5ex\@nobreaktrue \begin{examplenum}[#2] } \newenvironment{Exmps}[1][] {% \ifstrequal{#1}{start} {\my@start@example{}{series=resumable-series}}% {\ifstrequal{#1}{continued} {\my@start@example{[continued]}{resume=resumable-series}} {\my@start@example{}{}}} } { \end{examplenum}% \end{exmps} } \makeatother % %==================================================================================================== %==================================================================================================== % Continued Misc % \newcounter{miscex}[chapter] \setcounter{miscex}{0} \newenvironment{Misc}[1][] {% \ifthenelse{\isempty{#1}}{\begin{misc}}{\begin{misc}[#1]} \mbox{}\par\nobreak\vspace*{-1ex}% \begin{miscnum} \setcounter{miscnumi}{\value{miscex}} } { \setcounter{miscex}{\value{miscnumi}} \end{miscnum} \end{misc} } % %==================================================================================================== \newenvironment{Conseqs} { \begin{conseq}\ \vspace{-1ex} \begin{itemize} } { \end{itemize} \end{conseq} } %\newlength\myremark %\settowidth\myremark{\textsc{Remark}. } % %\newlength\myclaim %\settowidth\myclaim{\textsc{Claim}. } \def\blankpage{% \clearpage% \thispagestyle{empty}% \addtocounter{page}{-1}% \null% \clearpage} \newtheoremstyle{mylemstyle}{3ex}{1ex}{\itshape}{}{\scshape}{:}{.5em}{} \theoremstyle{mylemstyle} \newtheorem{lem}[thm]{Lemma} \newtheorem{conj}[thm]{Conjecture} \newtheorem{prop}[thm]{Proposition} \newtheoremstyle{loosestyle}{1ex}{1ex}{}{}{\scshape}{:}{.5em}{} \theoremstyle{loosestyle} \newtheorem*{notation}{Notation} \newtheorem*{rec}{Recall} \newtheorem*{note}{Note} \newtheoremstyle{myclaimstyle}{1ex}{0.5ex}{\itshape}{}{\scshape}{:}{.5em}{} \theoremstyle{myclaimstyle} \newtheorem*{claim}{Claim} \newlength\myclaim \settowidth\myclaim{\textit{Claim}: } \newtheoremstyle{myprfclaimstyle}{0ex}{1ex}{}{}{\itshape}{:}{0.5em}{} \theoremstyle{myprfclaimstyle} \newtheorem*{prfclaim}{Proof of claim} \theoremstyle{remark} %\newtheorem*{prf}{Proof} \newtheorem*{qn}{Question} \newtheorem*{ans}{Answer} %\newcommand*{prfname}{Proof} %\newenvironment{prf}[1][\prfname]{\begin{proof}[#1]\renewcommand*{\qedsymbol}{$ \square $}}{\end{proof}} %\declaretheorem[name=Proof,qed={\lower-0.3ex\hbox{$\square$}}]{prf} \newtheorem*{prfx}{Proof} \newenvironment{prf} {\pushQED{\qed}\renewcommand{\qedsymbol}{$\square$}\prfx} {\popQED\endprfx} \title{Metric Spaces} \author{Subhajit Paul} \parindent 0em \parskip 1ex % %======================================================================================================== %Styles for enumerate % %Definitions: [label=(\alph*), noitemsep, topsep=0pt] %Theorems: [label=(\roman*), ref=\thethm.\theenumii, noitemsep, topsep=0pt] %Proofs: [label=(\roman*)] %======================================================================================================== % \begin{document} \listoffigures \begin{figure} \centering \begin{subfigure}{0.49\linewidth} \includegraphics[width=\linewidth]{example-image-a} \caption{Sub figure 1} \end{subfigure} \hfill \begin{subfigure}{0.49\linewidth} \includegraphics[width=\linewidth]{example-image-a} \caption{Sub figure 2} \end{subfigure} \caption{To display subfigures} \end{figure} \end{document} Below is the portion of the code that controls the standard behaviour used throughout the book. This is the exact style in which subfigures are included in the main document, sometimes with the obvious replacement of \includegraphics by a tikzpicture environment. \documentclass{article} \usepackage{graphicx} \usepackage{caption} \usepackage[list=true, labelformat=simple, labelsep=colon,lofdepth=2]{subcaption} \renewcommand{\thesubfigure}{\thefigure\,(\alph{subfigure})} \makeatletter \renewcommand\p@subfigure{} \makeatother \begin{document} \listoffigures \begin{figure} \centering \begin{subfigure}{0.49\linewidth} \includegraphics[width=\linewidth]{example-image-a} \caption{Sub figure 1} \end{subfigure} \hfill \begin{subfigure}{0.49\linewidth} \includegraphics[width=\linewidth]{example-image-a} \caption{Sub figure 2} \end{subfigure} \caption{To display subfigures} \end{figure} \end{document} EDIT: After investigating further, following the suggestions in the comments, I have traced the issue primarily to two packages, as shown in the code below. At this point, my question becomes: how can I display subfigures in \listoffigures while keeping these packages in use? \documentclass{article} \usepackage{graphicx} \usepackage{caption} \usepackage[list=true, labelformat=simple, labelsep=colon,lofdepth=2]{subcaption} \renewcommand{\thesubfigure}{\thefigure\,(\alph{subfigure})} \makeatletter \renewcommand\p@subfigure{} \makeatother \setcounter{secnumdepth}{3} \usepackage{titlesec} \newcommand{\hsp}{\hspace{20pt}} \titleformat{\chapter}[hang]{\filleft\Huge\bfseries}{\thechapter\hsp{$\mid$}\hsp}{0pt}{\Huge\bfseries} \titlespacing*{\chapter}{0pt}{0pt}{3in} \titleformat{\subsubsection}{\bfseries}{\thesubsubsection}{1em}{\bfseries} \renewcommand{\thesubsubsection}{\bfseries{\ensuremath{\bullet}}} %==================================================================================================== %==================================================================================================== % Section symbol in TOC and in text % \usepackage{tocloft} \renewcommand\cftsecpresnum{\S} \titleformat{\section}{\normalfont\Large\bfseries}{\thesection}{1em}{} \begin{document} \listoffigures \begin{figure} \centering \begin{subfigure}{0.49\linewidth} \includegraphics[width=\linewidth]{example-image-a} \caption{Sub figure 1} \end{subfigure} \hfill \begin{subfigure}{0.49\linewidth} \includegraphics[width=\linewidth]{example-image-a} \caption{Sub figure 2} \end{subfigure} \caption{To display subfigures} \end{figure} \end{document}

I am trying to move away from Overleaf and compile my things locally. I set up VS Code on my Mac with Latex Workshop as the extension and things have worked well for a while. Something changed recently, and my bibliographies stopped compiling, and I've been trying to figure out how to reset things so that it works again. After uninstalling Latex Workshop and re-installing it, and deleting all settings.json files I can find, I am still struggling to have my bibliographies compile. If I hit Command + S (or LaTeX Workshop: Build with recipe: pdflatex -> bibtex -> pdflatex * 2) on the minimal working example \documentclass{article} \usepackage{csquotes} \usepackage[backend=biber,style=numeric]{biblatex} \usepackage{biblatex} \addbibresource{bibliography.bib} \title{Test} \author{Me} \date{February 2026} \begin{document} \maketitle \section{Introduction} This is a \cite{bob} \printbibliography \end{document} And a bibliography.bib file of @misc{bob, author = {Bob}, month = {2}, publisher = {Bob}, title = {Bob}, year = {2026} } I get a Recipe terminated with error'. The full output is below when I run latexmk -pdf test`, what is going on? Should I completely uninstall VS code to reset my system? (I'd rather not need to reset all the other things I have set up with VS code for e.g. Python). Is there something obvious I'm missing? Things compile fine when I never flirt with a bibliography, but the moment I put a bibliography anywhere the whole thing falls apar. Thank you so much. Rc files read: NONE Latexmk: This is Latexmk, John Collins, 27 Dec. 2024. Version 4.86a. No existing .aux file, so I'll make a simple one, and require run of *latex. Latexmk: applying rule 'pdflatex'... Rule 'pdflatex': Reasons for rerun Category 'other': Rerun of 'pdflatex' forced or previously required: Reason or flag: 'Initial setup' ------------ Run number 1 of rule 'pdflatex' ------------ ------------ Running 'pdflatex -recorder "test.tex"' ------------ This is pdfTeX, Version 3.141592653-2.6-1.40.27 (TeX Live 2025) (preloaded format=pdflatex) restricted \write18 enabled. entering extended mode (./test.tex LaTeX2e <2024-11-01> patch level 2 L3 programming layer <2025-01-18> (/usr/local/texlive/2025/texmf-dist/tex/latex/base/article.cls Document Class: article 2024/06/29 v1.4n Standard LaTeX document class (/usr/local/texlive/2025/texmf-dist/tex/latex/base/size10.clo)) (/usr/local/texlive/2025/texmf-dist/tex/latex/csquotes/csquotes.sty (/usr/local/texlive/2025/texmf-dist/tex/latex/etoolbox/etoolbox.sty) (/usr/local/texlive/2025/texmf-dist/tex/latex/graphics/keyval.sty) (/usr/local/texlive/2025/texmf-dist/tex/latex/csquotes/csquotes.def) (/usr/local/texlive/2025/texmf-dist/tex/latex/csquotes/csquotes.cfg)) (/usr/local/texlive/2025/texmf-dist/tex/latex/biblatex/biblatex.sty (/usr/local/texlive/2025/texmf-dist/tex/generic/pdftexcmds/pdftexcmds.sty (/usr/local/texlive/2025/texmf-dist/tex/generic/infwarerr/infwarerr.sty) (/usr/local/texlive/2025/texmf-dist/tex/generic/iftex/iftex.sty) (/usr/local/texlive/2025/texmf-dist/tex/generic/ltxcmds/ltxcmds.sty)) (/usr/local/texlive/2025/texmf-dist/tex/latex/kvoptions/kvoptions.sty (/usr/local/texlive/2025/texmf-dist/tex/latex/kvsetkeys/kvsetkeys.sty)) (/usr/local/texlive/2025/texmf-dist/tex/latex/logreq/logreq.sty (/usr/local/texlive/2025/texmf-dist/tex/latex/logreq/logreq.def)) (/usr/local/texlive/2025/texmf-dist/tex/latex/base/ifthen.sty) (/usr/local/texlive/2025/texmf-dist/tex/latex/url/url.sty) (/usr/local/texlive/2025/texmf-dist/tex/latex/biblatex/blx-dm.def) (/usr/local/texlive/2025/texmf-dist/tex/latex/biblatex/blx-compat.def) (/usr/local/texlive/2025/texmf-dist/tex/latex/biblatex/biblatex.def) (/usr/local/texlive/2025/texmf-dist/tex/latex/biblatex/bbx/numeric.bbx (/usr/local/texlive/2025/texmf-dist/tex/latex/biblatex/bbx/standard.bbx)) (/usr/local/texlive/2025/texmf-dist/tex/latex/biblatex/cbx/numeric.cbx) (/usr/local/texlive/2025/texmf-dist/tex/latex/biblatex/biblatex.cfg) (/usr/local/texlive/2025/texmf-dist/tex/latex/l3kernel/expl3.sty (/usr/local/texlive/2025/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def)) (/usr/local/texlive/2025/texmf-dist/tex/latex/biblatex/blx-case-expl3.sty (/usr/local/texlive/2025/texmf-dist/tex/latex/l3packages/xparse/xparse.sty))) (./test.aux) (/usr/local/texlive/2025/texmf-dist/tex/latex/biblatex/lbx/english.lbx) No file test.bbl. LaTeX Warning: Citation 'bob' on page 1 undefined on input line 18. LaTeX Warning: Empty bibliography on input line 21. [1{/usr/local/texlive/2025/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] (./test.aux) LaTeX Warning: There were undefined references. Package biblatex Warning: Please (re)run Biber on the file: (biblatex) test (biblatex) and rerun LaTeX afterwards. )</usr/local/texlive/2025/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx10.pfb ></usr/local/texlive/2025/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb> </usr/local/texlive/2025/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb></ usr/local/texlive/2025/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb></us r/local/texlive/2025/texmf-dist/fonts/type1/public/amsfonts/cm/cmr17.pfb> Output written on test.pdf (1 page, 49319 bytes). Transcript written on test.log. Latexmk: Getting log file 'test.log' Latexmk: Examining 'test.fls' Latexmk: Examining 'test.log' Latexmk: Missing bbl file 'test.bbl' in following: No file test.bbl. Latexmk: Log file says output to 'test.pdf' Latexmk: Bibliography file(s) from .bcf file: bibliography.bib Latexmk: applying rule 'biber test'... Rule 'biber test': Reasons for rerun Category 'other': Rerun of 'biber test' forced or previously required: Reason or flag: 'Initial set up of rule' ------------ Run number 1 of rule 'biber test' ------------ ------------ Running 'biber "test.bcf"' ------------ INFO - This is Biber 2.20 INFO - Logfile is 'test.blg' INFO - Reading 'test.bcf' INFO - Found 1 citekeys in bib section 0 INFO - Processing section 0 INFO - Looking for bibtex file 'bibliography.bib' for section 0 INFO - LaTeX decoding ... INFO - Found BibTeX data source 'bibliography.bib' Latexmk: Found biber source file(s) [bibliography.bib, test.bcf] Latexmk: Error return from 'biber test' I will add to its source list, anything cached from analysis of bcf file. Latexmk: Summary of warnings from last run of *latex: Latex failed to resolve 1 citation(s) Latexmk: ====Undefined refs and citations with line #s in .tex file: Citation 'bob' on page 1 undefined on input line 18 Latexmk: Errors, so I did not complete making targets Collected error summary (may duplicate other messages): biber test: Command for 'biber test' gave return code 2 Latexmk: Sometimes, the -f option can be used to get latexmk to try to force complete processing. But normally, you will need to correct the file(s) that caused the error, and then rerun latexmk. In some cases, it is best to clean out generated files before rerunning latexmk after you've corrected the files. The test.blg file is [0] Config.pm:308> INFO - This is Biber 2.20 [0] Config.pm:311> INFO - Logfile is 'test.blg' [65] biber-darwin:340> INFO - === Tue Feb 10, 2026, 14:49:52 [81] Biber.pm:420> INFO - Reading 'test.bcf' [153] Biber.pm:994> INFO - Found 1 citekeys in bib section 0 [165] Biber.pm:4463> INFO - Processing section 0 [175] Biber.pm:4654> INFO - Looking for bibtex file 'bibliography.bib' for section 0 [176] bibtex.pm:1713> INFO - LaTeX decoding ... [179] bibtex.pm:1519> INFO - Found BibTeX data source 'bibliography.bib' but the test.bbl file is empty

I have created a class for typesetting articles submitted to a scientific journal. Authirs will compile their papers through pdflatex. However, in production, the typesetting is done with LuaLatex due to specific typographical reasons (fonts, etc.). I am using unicode-math to load the font (in this case Cambria Math), and I am looking for a way to switch the subscripts (by default typeset in italic) to a default upright. I have gone throguh the different options, but I have not been able to specify the upright only for subscripts. The math-style option can make "everything" upright, as well as the range may help me to switching some sets (latin, greek) in upright, but then this will apply also to non-subscript variables. The sript-font option allows me to specify a different font or colour, so we are very near: however, I am not able to understand if I can specify some script-features that may help in getting subscripts in upright by default. In the end, the goal shoould be to reverse the normal behavior "latex" behavior, and have subscript normally in upright, and by user choice in italic. Is there a way to achieve this? As a note: I have seen the discussion in the past, and for instance here a solution has been provided for latex. I was curious about a unicode-math solution, given I can change (almost) any aspect of mathematical typesetting with it. Thanks Federico

In the following example, I get a fatal error on the second compilation round once I uncomment the line \Xarrangement[]{paragraph}, thus generating a critical footnote in which a linebreak occurs. As is, the example compiles successfully. Also if I load the font without HarfBuzz. \documentclass{memoir} \usepackage{fontspec} \newfontfamily\devfont{Shobhika}[Script=Devanagari, Renderer=HarfBuzz] \input{loadhyph-sa.tex} \usepackage{reledmac} %\Xarrangement[]{paragraph} \begin{document} \devfont \beginnumbering \pstart इत्थम्, \edtext{पूर्वोक्तप्रकारेण}{\Bfootnote{पूर्वोक्तप्रकारेण .}}, \edtext{विश्रुतस्य}{\Bfootnote{विश्रुतस्य .}} प्रख्या[७]तस्य विद्याधरस्य \edtext{सम्बन्धिनीः}{\Bfootnote{सम्बन्धिनीः .}}, \pend \endnumbering \end{document} The error is as follows: ! error: (linebreak): invalid node with type whatsit and subtype 16 found in d iscretionary ! ==> Fatal error occurred, no output PDF file produced! This is kind of a follow-up to the following question. I am aiming at an edition where I do not type Devanāgarī directly but use babel's IAST transform, but as the behaviour can be reproduced without babel I entered the Devanāgarī directly for this example.

I have an issue in typing the above equation in LaTeX, where the two rows of the cases environment are so close that they almost touch. Help me do it in a clean way. Code: \[ \boxed{ \displaystyle\int\limits_{0}^{\pi/2}\sin^{n}{x}dx= \displaystyle\int\limits_{0}^{\pi/2}\cos^{n}{x}dx= \begin{cases} \dfrac{n-1}{n}\cdot\dfrac{n-3}{n-2}\cdots \dfrac45 \cdot\dfrac23 \text{ if $n$ is odd}\\ \dfrac{n-1}{n}\cdot\dfrac{n-3}{n-2}\cdots \dfrac34 \cdot\dfrac12\cdot \dfrac{\pi}{2}\text{ if $n$ is even} } \]

I am trying to express the roots of a quadratic equation `t^2-3t-7=0' in radical form. I tried \documentclass[12pt]{article} \usepackage{polexpr} \usepackage{xint} \begin{document} \poldef f(t) = t^2-3t-7; \xintdefvar a = (f(2)-2*f(1)+f(0))/2; \xintdefvar c = f(0); \xintdefvar b = reduce(f(1)-a-c); \xintdefvar delta = b^2 - 4*a*c; \xintdefvar t1=reduce((-b+sqrt(delta))/2/a); \xintdefvar t2=reduce((-b-sqrt(delta))/2/a); \[\xinteval{t1}, \quad \xinteval{t2}\] \[t=\frac{1}{2} \left(3-\sqrt{37}\right)\lor t=\frac{1}{2} \left(3+\sqrt{37}\right).\] \end{document} I got How can I get?

May I ask a couple questions about this example that is finally at least working. (I apologize for deleting this question a couple times, today, while struggling through some syntax items.) In order to get to the values of #1 and #2 passed automatically in the command option of \setuphead, I had to define a separate command \InterMediate as an intermediate step to get the values of these two variables plus the user variables ct and pw rather than invoking \MySectionLua directly. Is there a more direct method of getting from the command to \MySectionLua? Related to Item 1, regardless of whether or not the intermediate command is required, how can setuphead be declared in luacode. I tried numerous attempts such as below and they all either fail, are ignored,or arae treated as text only. That is, the command option. context.setuphead( {"section"}, { conversion="Romannumerals", sectionstopper=".", command={context.command{InterMediate}}, distance="0mm", }) In the example, I have to try different values of pw until the second column of that table looks correct. Is there a way to determine the width of the widest line in the title, such that it can be used to set the width of the paragraph column? I've been reading a bit about nodes but, at this point, the title hasn't been written; so, can its dimensions be queried? For example, if I needed to do this in the HTML DOM, I would build the DOM node in JavaScript, set it's style classes, add its content, and then add it to the DOM off-screen or under the visible content; and then query its geometry to use to set it before adding it to its correct location in the DOM. Can the ConTeXt table be written to a buffer and queried somehow before it is written? Thank you. \startluacode interfaces.implement { name = "MySectionLua", public = true, arguments = { "string", "string", "string", "string" }, actions = function (nbr,ttl,ct,pw) local prop if ct == "l" then prop = "|l|l|" elseif ct == "p" then prop = "|l|p(" .. pw .. ")|" end context.startplacetable({location="middle,none"}) context.starttabulate({prop},{frame="on",align="middle",unit="0mm"}) context.NC() context(nbr) context.VL() context(ttl) context.NC() context.NR() context.stoptabulate() context.stopplacetable() end, } \stopluacode \define[2]\InterMediate{\MySectionLua{#1}{#2}{\structureuservariable{ct}}{\structureuservariable{pw}}} \setuphead[section][ conversion=Romannumerals, sectionstopper={.}, command={\InterMediate}, distance=0mm, ] \starttext \startsection[title={A centered multi-line\\Title One}][ct={p},pw={50mm}] A paragraph \ldots \stopsection \stoptext

How can I make the included image larger than the surrounding \fbox{\includegraphics{img.png}}? I need to include an image with a transparent background that "spills" into adjacent cells of a (tabular) table -- I don't need the fbox finally.

I'm annotating a fraction with TikZ arrows pointing to specific parts. The blue arrow works fine, but the red curved arrow is bisecting the "3" in the denominator instead of arcing over it. Current behavior: The red arrow cuts straight through the middle of "3" Desired behavior: The red arrow should arc upward and over the "3" with clear space. I initially tried adjusting the out angle from 160° to 120° to make it launch upward, but this still results in the arrow bisecting the number. How do I increase the arc height to make the curve clear the "3" completely as shown in the 2nd image? Note: I'm still learning TikZ best practices. If you spot any obvious improvements to the code structure, please mention them. MWE \usepackage{mathtools} \usetikzlibrary{calc, arrows.meta} \definecolor{textBlue}{RGB}{50, 50, 255} \definecolor{deepRed}{RGB}{200, 40, 40} \begin{document} \begin{tikzpicture} % Math fraction \node (fraction) at (0,0) { \scalebox{1.8}{% $\displaystyle \frac{2x^3 - 5x^2 - x + 3}{x + 3}$ } }; % Blue annotation (works fine) \node[ellipse, draw=textBlue, dashed, minimum width=0.3cm, minimum height=0.6cm, xshift=-0.4cm, yshift=0.4cm] (blueCircle) at ($(fraction.south) + (-0.65, 0.28)$) {}; \node[draw=textBlue, text=textBlue, align=center, anchor=north] (blueLabel) at ($(blueCircle.south) + (0, -0.6)$) {coefficient\\must be 1}; \draw[textBlue, ->, >=latex] (blueLabel.north) -- (blueCircle.south); % Red annotation (PROBLEM: arrow bisects the "3") \node[circle, draw=deepRed, dashed, minimum size=0.2cm, xshift=-0.2cm, yshift=0.3cm] (redCircle) at ($(fraction.south) + (-0.2, 0.55)$) {}; \node[draw=deepRed, text=deepRed, align=left, anchor=west] (redLabel) at ($(fraction.south) + (0.8, 0.3)$) {exponent\\must be 1}; % This arrow bisects "3" - how to make it arc higher? \draw[deepRed, ->, >=latex] (redLabel.west) to[out=120, in=0] (redCircle.east); \end{tikzpicture} \end{document}``` [1]: https://i.sstatic.net/zirlpD5n.png [2]: https://i.sstatic.net/BOIovYSz.png

Outgoing from the question Dropping separator at line break in an inline list I want to achieve some more things: Line breaks should (if possible) only be placed between items The list should have a left and right margin (maybe it is easier to not use an inline list?) The list should be centered There should be no vspace inserted above or below the list Note that \textperiodcentered is a separator, not a label (aka. bullet point) The list should be startet at a new line and end with a line break (Done, but I guess (2.) solves this automatically. MWE: \documentclass[a4paper]{article} \usepackage{showframe} \newcommand{\middot}{~\textperiodcentered~} \usepackage{enumitem} \newlist{skills}{itemize*}{1} \setlist[skills]{label={}, afterlabel={}, leftmargin=2cm, rightmargin=2cm, before={\newline}, after={\newline}, itemjoin=\discretionary{}{}{\hbox{\middot}}} %TODO leftmargin and rightmargin have no effect \setlength{\parindent}{0pt} \begin{document} Text before \begin{skills} \item This \item list \item should \item only \item break \item between \item items \item and not inside a longer item \item Also \item this \item list \item should \item be \item centered \item and \item indented \end{skills} text after \vspace{2cm} The desired output is: Text before (no vspace before the list) \vspace{-3mm} \begin{center} This\hbox{\middot}list\hbox{\middot}should\hbox{\middot}only\hbox{\middot}break\hbox{\middot}between \hbox{\middot}items and not inside a longer item\hbox{\middot}Also\hbox{\middot}this\hbox{\middot}list\hbox{\middot}should\hbox{\middot}be centered\hbox{\middot}and\hbox{\middot}indented \end{center} \vspace{-3mm} text after (no vspace after the list) \end{document}

I have a groupplot where I want to use the legend as the title in the \nextgroupplots. And then I have a "Supertitel" that I would like to put in place of the first groupplot. How do I set it such that the text, like the small box, is aligned to the top edge? \documentclass[margin=5pt, varwidth]{standalone} \usepackage{pgfplots} \pgfplotsset{compat=1.18} \usepgfplotslibrary{groupplots} \usetikzlibrary{patterns} \begin{document} \begin{tikzpicture}[font=\footnotesize, mypattern/.style={% postaction={pattern=north east lines}, },% ] \begin{groupplot}[ group style={% group size=2 by 3, vertical sep=15mm, },% height=30mm,width=55mm, group/every plot/.style={%% ybar=0pt, bar width=1, bar shift=0pt, xmin=-0.5,% to see the bar at x=0 correctly ymin=0, xtick=data, },%% end of group/every plot/.style %% every axis plot/.style={ fill=lightgray, area legend,% legend as title 1/2 }, legend style={% legend as title 2/2 at={(0,1)}, yshift=6pt, anchor=south west, draw=none, fill=none, inner sep=0pt, cells={anchor=north, align=left},% PROBLEM HERE ..... },% ] \nextgroupplot[hide axis=true, title={Supertitle}, title style={at={(0.5,0.5)}, anchor=center, yshift=-6pt,% kill pgfplots's default draw=none, font=\bfseries\Large} ] \addplot[draw=none, fill=none]{x};% to avoid warning; don't know how to make this else \nextgroupplot[] \addplot[samples at={0,...,8}, forget plot]{x}; \addplot[mypattern, samples at={3,...,6}]{x}; \addlegendentry{plot 0: \\ plot good, \\ legend bad :(} \end{groupplot} \end{tikzpicture} \end{document}

Consider the following example, in which I wish to define a command that draws a bold dot over a symbol (ideally, the first optional argument adjusts horizontal position, and the second adjusts vertical position). However, I cannot seem to get \raisebox work: no matter what length value I put in, the dot always remains at the current position. May I ask where have I done wrong, and how to fix it? \documentclass{article} \usepackage{mathtools} \begin{document} \NewDocumentCommand \dotted { O{0mu} O{-.1em} m } { \smash{\overset{\raisebox{#2}{\scalebox{.5}{$\mspace{#1}\bullet$}}}{#3}} } \( \dotted[5mu]{M} \) \end{document}

I'm translating Kazakh problems for the Art of Problem Solving forum, and I faced an obstacle with this problem: It translates like: Aigerim and Batyrkhan play the following game. There is a board of size $2\times2024$ (2 rows and 2024 columns). They take turns, with Aigerim moving first. On her move, Aigerim places a horizontal domino on the board $\boxed{\phantom{a}}\boxed{\phantom{a}}$, covering exactly two squares. On his move, Batyrkhan places a vertical domino on the board $\begin{aligned} \fbox{\rule{0pt}{1.2em}\hspace{1.2em}}[0em] \fbox{\rule{0pt}{1.2em}\hspace{1.2em}} \end{aligned}$, also covering exactly two squares. A player who cannot make a move loses. (Dominoes may be placed only on empty squares.) Who wins if both players play optimally? and I don't know how to do the vertical domino without separation between the squares. AoPS doesn't support features like tikzpicture, so I need to come up with a different method.

I have the following code, I would like to number the subcases with 1a, 1b, so not just one big case with (1). \documentclass{article} \usepackage{amsmath} \begin{document} \begin{equation} f(x) = \begin{cases} x^2& x \ge 0,\\ -x & x < 0. \end{cases} \end{equation} \end{document}