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Good morning, I would like to know if there is a tweak, or better an other package that would let me have a continues vertical line in table IF it doesn't intersect any horizontal line. As I know booktabs wasn't designed for vertical lines. I'm using a lot of \cmidrule{a-b}, yet it leave a gap in the space where its not drawn. The code: \documentclass[a4paper, % svgnames, dvipsnames, % landscape, 9pt ]{article} %\usepackage{fontspec} \usepackage{ifthen} \usepackage[dvipsnames,table]{xcolor} % già presente in GRAPHICX?? \usepackage{graphicx} % Required for inserting images \usepackage{tikz} \usepackage{geometry}%[a4paper, total={27cm, 18cm}]{geometry} % invertiti per il fatto che è di LARGO \geometry{ %%impostiamo i margini personalizzati per il CV a4paper, left=6mm, right=6mm, top=4mm, bottom=4mm, } \usepackage{ragged2e} % toglie il rientro anglosassone di inizio paragrafo \usepackage{adjustbox} % \usepackage{lscape} \usepackage[small,compact]{titlesec} %% Small Compact => che fa?? \usepackage{amssymb} \usepackage{amsmath} \usepackage{mathtools} %\usepackage[printwatermark,%disablegeometry %]{xwatermark} %\usepackage{draftwatermark} %scive solo BOZZA, poche personalizzazioni => § XWATERMARK § %% Aggiunta Watermark in stampa \usepackage{xparse} %% Creare comandi %\usepackage{pgf} % \usepackage{tabulary} \usepackage{booktabs, tabularx} \usepackage{dcolumn} \usepackage[]{mdframed} \usepackage{multirow} \usepackage{multicol} \setlength{\columnsep}{9.5mm} \usepackage{makecell} \usepackage{pbox} \usepackage[most]{tcolorbox} \usepackage{footnote} \usepackage{tablefootnote} \usepackage[stable]{footmisc} %% Footnote nei titoletti \usepackage[narrower, %% Margine supplementare, ~ in linea con la tabella notessf %% Stile in Sans Serif ]{parnotes} \usepackage{enumerate} % in quest'ordine altrimenti non trova i vari parsep \usepackage{enumitem} \usepackage{array} % OPZ ma richiesto per LOGIX.pkg \usepackage{hyperref} %% Dopo tablefootnote o causa problemi %\usepackage{fdsymbol} % simbolini speciali % tolto per errore con "math$ definition" \usepackage{pifont} % permette di avere i simbolini del bridge % \usepackage{arev} % permette di avere i simbolini del bridge \usepackage{fontspec} \usepackage{anyfontsize} %\usepackage{fontawesome} \usepackage{fontawesome5} %\usepackage{MnSymbol} % tolto per errore con "math$ definition" % \usepackage[dvipsnames]{xcolor} % già presente in GRAPHICX?? %%%%%%%%%%%%%%%%%%%%%%%%%%% %%%% Math cursive bold \usepackage{mathptmx}% http://ctan.org/pkg/mathptmx \DeclareMathAlphabet{\mathbfit}{T1}{lmr}{b}{it} %\usepackage{unicode-math} %\setmathfont{rm} %%%%%%%%%%%%%%%%%%%%%%%%%%% %% Simboli per il bridge \def\picche{\textcolor{blue}{\ding{171}}$\,$} \def\cuori{\textcolor{Red}{\ding{170}}$\,$} \def\quadri{\textcolor{YellowOrange}{\ding{169}}$\,$} \def\fiori{\textcolor{OliveGreen}{\ding{168}}$\,$} \newcommand{\cParnote}[2][black]{% %% Numerino del PARNOTES colorato {\color{#1}\parnote{#2}}% } %% Comando per avere le licite del contratto. \newcommand\biddingBox[3][]{% \ifthenelse{\equal{#1}{}} %% Condizione %% True statement { \Biddingbox{\textbf{#2}$\,${\textbf{#3}}} } %% False statement { % \ifthenelse{\equal{#1}{Alert}}%% Condizione % %% True statement % { \BiddingboxAlert{\textbf{#2}$\,${\textbf{#3}}} % } % %% False statement % { % \Biddingbox{\textbf{#2}$\,${\textcolor{#3}{\scriptsize\faAsterisk$\!$}}} % } } } \NewDocumentCommand{\Livello}{ O{Fuchsia} }{ \textcolor{#1}{\scriptsize\faAsterisk$\!$} } \newtcbox{\Biddingbox}[1][white]{on line, arc=1.6pt, colback=white, colframe=black, % before upper={\rule[-3pt]{0pt}{10pt}}, boxrule=.55pt, %right skip=-3.35pt, left skip=-1.35pt, right skip=-.55ex, left skip=-.09ex, boxsep=0pt, left=1.49pt, right=1.49pt, top=1.25pt, bottom=1.25pt }%\hspace{-6em} \newtcbox{\BiddingboxAlert}[1][white]{on line, enhanced, nobeforeafter,%tcbox raise base, boxrule=0.55pt,%top=0mm,bottom=0mm, top=1.25pt, bottom=1.25pt, %left=1.49pt, right=1.49pt, %right=0mm, left=2.8mm, arc=1.6pt, right skip=-.95ex, left skip=-.39ex, boxsep=0pt,%before upper={\vphantom{dlg}}, colframe=blue,%coltext=green!25!black, %font=\bfseries, colback=white, overlay={\begin{tcbclipinterior} \fill[blue!95!OliveGreen!67!black] (frame.south west) rectangle node[text=white!82!black,font=\sffamily\bfseries\scriptsize,%rotate=90 ] {A} ([xshift=2.73mm]frame.north west);\end{tcbclipinterior} } } %% Visto \newcommand{\OKay}{\textcolor{ForestGreen}{\ding{52}}$\,$} %% Croce \newcommand{\NotOk}{\textcolor{red}{\ding{55}}$\,$} \begin{document} \thispagestyle{empty} % togliamo il numero di pagina \setmainfont{Arial} %\SetWatermarkText{BOZZA} %\SetWatermarkScale{1} %\DraftwatermarkOptions{stamp=true,color=red!35} %\newwatermark[allpages,color=red!35,angle=45,scale=7,xpos=0,ypos=0]{BOZZA} \begin{multicols*}{2} %\vspace{-2.3mm} \section*{Conta Punti Onore} %\vspace{-1.7mm} \begin{center} \fontsize{8pt}{9pt}\selectfont \setlength{\tabcolsep}{2.5pt} \begin{tabular}{l|l} \toprule Conta PO & Possibili aperture \\ \midrule $\bullet$ 6-10 PO& \biddingBox[]{2}{\quadri}, \biddingBox[]{2}{\cuori}, \biddingBox[]{2}{\picche} \\ $\bullet$ 12-19 PO & \biddingBox{1}{\Livello} (Livello 1)\\ % \hspace{2mm} $\smallblacktriangleright$ 15-17 PO & \SA{1} \\ \hspace{2mm} $\blacktriangleright$ 15-17 PO & \biddingBox[]{1}{SA} \\ $\bullet$ 20-21 PO & \biddingBox[]{2}{SA} \\ $\bullet$ 22-23 PO & \biddingBox[]{2}{\fiori}, \biddingBox[]{2}{\quadri}\\ \bottomrule \end{tabular} \end{center} %\vspace{-1.6mm} Il numero di prese è facilmente determinabile con il punteggio di linea, %\vspace{-1.63mm} \begin{center} % \scriptsize \fontsize{8pt}{9pt}\selectfont \setlength{\tabcolsep}{2.5pt} \begin{tabular}{r|c|c|c|c|c|c|c} \toprule % \emph{5$^{\circ}$} \picche / \cuori & \Picche{1} o \Cuori{1} \\ % \emph{4$^{\circ}$} \quadri & \Quadri{1} \\ % \emph{altro} & \Fiori{1}\\ PO & 20-21 & 22-23 & 24-25 & 26-28 & 29-32 & 33-34 & 35-37 \\ Prese& \textbf{7}& \textbf{8}& \textbf{9}& \textbf{10}& \textbf{11}& \textbf{12}& \textbf{13} \\ \midrule \multirow{2}{*}{\emph{\fontsize{7pt}{9pt}\selectfont \bfseries Manches}} & & & \multirow{2}{*}{\biddingBox[]{3}{SA}} & \biddingBox[]{4}{\picche}& \biddingBox[]{5}{\quadri} & \multirow{2}{*}{\bfseries SLAM} & \multirow{2}{*}{\bfseries G-slam} \\ & & & &\biddingBox[]{4}{\cuori} &\biddingBox[]{5}{\fiori} & & \\ \bottomrule \end{tabular} \end{center} \subsection{Steyman} \label{sec:Steyman} %\vspace{-2.3mm} Per invitare una ricerca ai nobili per una possibile \emph{Manche}. %\vspace{-3.2mm} \begin{center} \fontsize{8pt}{9pt}\selectfont \setlength{\tabcolsep}{2.5pt} \begin{tabular}{r|rl|rl|rl} \toprule Apertore & \multicolumn{2}{c|}{Appoggio} & \multicolumn{2}{c|}{Apertore} & \multicolumn{2}{c}{Compagno} \\ \midrule \multirow{8.5}{*}{\biddingBox{1}{SA}} & \multirow{8.5}{*}{\biddingBox{2}{\fiori} \cParnote[magenta]{Ora mai è diventata d'uso comune, e non si allerta più}} & \multirow{8.5}{*}{\makecell[l]{ 8+ PO \\con $\mathbfit{4}^{\circ}$\cuori\\ o \emph{$\mathbfit{4}^{\circ}$}\picche o\\ entramabi}} & \biddingBox{2}{\quadri} & \makecell[l]{ no \emph{$\mathbfit{4}^{\circ}$}\\ nobili} & \biddingBox{3}{SA} & \\ \cmidrule{4-7} & & & \biddingBox{2}{\cuori} & \makecell[l]{appoggio\\ \cuori \emph{$\mathbfit{4}^{\circ}$}} & \biddingBox{3}{SA} & \makecell[l]{\biddingBox{4}{\cuori} se ha \\appoggio \emph{$\mathbfit{5}^{\circ}$}} \\ \cmidrule{4-7} & & & \biddingBox{2}{\picche} & \makecell[l]{appoggio\\ \picche \emph{$\mathbfit{4}^{\circ}$}} & \biddingBox{3}{SA} & \makecell[l]{\biddingBox{4}{\picche} se ha \\appoggio \emph{$\mathbfit{5}^{\circ}$}} \\ \cmidrule{4-7} & & & \biddingBox{2}{SA} & \makecell[l]{entrambi \\Nobili \emph{$\mathbfit{4}^{\circ}$}} & \multicolumn{2}{c}{\makecell[l]{Nobile (\biddingBox{3}{\picche} / \biddingBox{3}{\cuori}) \\assente o debole}} \\ \bottomrule \end{tabular} \end{center} \renewcommand{\parnoteintercmd}{\\} %% Per averle una sotto l'latra il "a capo" ossia "\\" \renewcommand{\parnotevskip}{1pt} %% Per metterle più in alto \vspace{-3.1mm} %% Done to cram more explanation tables into the coloumn \parnotes %\vspace{-5.9mm} %%%%%%%%---------------------------------------------------- %% %% All the other Bidding convetions as well as the "Contre" explaination %% %%%%%%%%____________________________________________________ \end{multicols*} \end{document} Leaving this ghost like line. I like the booktabs for its horizontal readability, as it gives priority to horizontal lines vs vertical lines when enclosing cells, yet this gap annoys me.

This LuaLaTeX code tries to process key-value pairs from a Lua string. The Lua function parse_kv_pairs takes a string containing comma-separated key-value pairs, removes whitespace, and splits the string by commas. tex.print(key .. "\\par") can print keys properly, but tex.print(value) can't output raw Lua strings (e.g., "260", "174", ...) and produces a Missing $ inserted. error. How can I fix this error? \documentclass[12pt]{article} \usepackage{luacode} \begin{luacode*} function parse_kv_pairs(kv_string) local pairs = {} for pair in string.gmatch(kv_string:gsub("%s+", ""), "([^,]+)") do local key, value = pair:match("([^=]+)=(.+)") if key and value then tex.print(key .. "\\par") -- tex.print(value) end end end \end{luacode*} \NewDocumentCommand{\defvar}{m}{% \directlua{parse_kv_pairs("#1")}% } \begin{document} \defvar{ m = 260, n=174, lj=5.68, bb=0.2, lo=lj+bb, h=190, ta=30, tb=20, qj = math.atan(n/m) * 180 / 3.1416, co = round(m / (m^2 + n^2)^0.5, 3) } \end{document}

Suppose I have a paragraph, and the first line of it may or may not contain an inline picture or a big character with the height greater than that of normal characters. Something like this: Lorem ipsum dolor sit amet, {\huge X} consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum. I need a way to get the height of this first line with this character after the paragraph is already set. Something like a macro of the form \lastParagraphFirstLineHeight which would return the value. Is there way to do it in plain TeX, or, if not, maybe in LuaTeX?

I'm trying to set up tcolorbox blocks using minted engine. I want to use a font of my choice in those, not the default monospaced one (or tt or helvetica, per minted manual). Let's say I want 'Code New Roman'. In the following MWE the commented out style-setting line works, but requires of me knowing that (internal?) format. The line without \exfont works but sets the document's default font for tcolorbox blocks. If the line with \exfont is set last and so is actually used in listings, listings do not compile. At the same time, this tex fragment works in the main body of document. Is it possible to make the line with \exfont work? Or do that auto-adjustment to a specific font in some other way? \documentclass{article} \usepackage{fontspec} \usepackage[all]{tcolorbox} \newfontfamily\exfont{Code New Roman} \newtcblisting{exprog}{ listing only, listing engine=minted,. % minted options={ fontfamily={CodeNewRoman(0)} }, % minted expects that sort of string minted options={ fontfamily={\exfont\csname f@family\endcsname} }, % doesn't work minted options={ fontfamily={\csname f@family\endcsname} }, % works but sets the default font for tcolorbox blocks } \begin{document} {\exfont\csname f@family\endcsname} % works \begin{exprog} ts( n : integer ) : function: double; \end{exprog} \end{document}

Sometimes I see the accented è written in LaTeX sources as a command like this: \`e I've always wondered the reason. On my laptop (a modern machine), I can type è directly using the keyboard, and the document compiles without any issues. Is the use of "`e" due to a specific keyboard layout (for example on Mac), or is it just a historical LaTeX convention?

I heard verbatim fonts have extra characters for stuff you can type on a keyboard. How are they stored internally? Is it a secret? Is it hacked?

Problem I am encountering a problem which has already been raised in this site: Can't locate Algorithm/Diff.pm in @INC (you may need to install the Algorithm::Diff module) Can't locate Algorithm/Diff.pm in @INC (you may need to install the Algorithm::Diff module) - solution to earlier question does not work Namely when I try to run latexdiff old.tex new.tex > diff.tex I am getting the following exception: Can't locate Algorithm/Diff.pm in @INC (you may need to install the Algorithm::Diff module) (@INC entries checked: C:/Users/<user_name>/AppData/Local/Programs/MiKTeX/scripts/latexdiff/ /usr/lib/perl5/site_perl /usr/share/perl5/site_perl /usr/lib/perl5/vendor_perl /usr/share/perl5/vendor_perl /usr/lib/perl5/core_perl /usr/share/perl5/core_perl ) at C:/Users/<user_name>/AppData/Local/Programs/MiKTeX/scripts/latexdiff/latexdiff line 256. BEGIN failed--compilation aborted at C:/Users/<user_name>/AppData/Local/Programs/MiKTeX/scripts/latexdiff/latexdiff line 256. How can I fix this issue? Should I retry some of the below actions, but by modifying paths, etc.? Solutions tried No answers have been provided to the 2nd question. Re the first one, unfortunately the most upvoted answer does not work for me: when I try to run perl -MCPAN -e "install Algorithm::Diff" in bash, I am getting the following error: Can't locate CPAN/Author.pm in @INC (you may need to install the CPAN::Author module) (@INC entries checked: /usr/lib/perl5/site_perl /usr/share/perl5/site_perl /usr/lib/perl5/vendor_perl /usr/share/perl5/vendor_perl /usr/lib/perl5/core_perl /usr/share/perl5/core_perl ) at /usr/share/perl5/core_perl/CPAN.pm line 19. BEGIN failed--compilation aborted at /usr/share/perl5/core_perl/CPAN.pm line 19. Compilation failed in require. BEGIN failed--compilation aborted. The second answer also does not work either as pacman is not recognized. I have tried this answer which suggests adding environment variables PERL5LIB and PERLLIB but with no success. I have also found this other question but the indications given in the answers do not seem applicable to my case, or have not worked. Additional information When I run where perl in bash, I see the used installation comes from Git: $ where perl C:\Program Files\Git\usr\bin\perl.exe I actually see the following structure in the Git installation: Git\usr | |__bin\ | |__core_perl\ | |__vendor_perl\ | | ... | |__perl.exe | |__lib\ | |__perl5\ | |__core_perl\ | |__vendor_perl\ | |__share\ |__perl5\ |__core_perl\ |__vendor_perl\

Alphabetical list in my index is not sorted properly. Letters like č and š appear at the end, instead of after c and s. Now, I've tried solutions from previous similar posts, and they don't work. In fact, I copied an MWE from one of those solutions (for Slovenian) and my output is not the same - I'm still getting the wrong ordering, so I guess the problem is in the system. Below is my MWE \documentclass[croatian,12pt,oneside,notitlepage,a4paper]{book} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage[main=croatian]{babel} \usepackage{imakeidx} \makeindex[program=xindy, options=-L croatian -C utf8] \begin{document} avion\index{avion} cura\index{cura} čarapa\index{čarapa} dug\index{dug} džem\index{džem} nos\index{nos} nježan\index{nježan} šipak\index{šipak} slika\index{slika} žarulja\index{žarulja} zamak\index{zamak} \printindex \end{document}

Suppose we are working in the three-dimensional real vector space V. A cone is a subset C of V such that if an element v of V lies in C, then all of its nonnegative multiples also lie in C. I would like to draw, using TikZ, a cone that simulates infinitely many extremal rays, all accumulating toward a fixed one. A section of the cone should therefore look like a “polygon with infinitely many sides”. For example, the cone here Tikz: cones with a wide base is a circular one. I would like mine to be "polyhedral" away from the accumulation ray. How would you do that?

I'm trying to draw a pixelated (blocky) circle in TikZ where each filled 1×1 square corresponds exactly to an integer grid cell (think Minecraft blocks). Given a center and radius, I want a compact TikZ/PGF macro or clear algorithm that selects which unit squares to fill so the rasterized shape matches a standard discrete circle (midpoint/Bresenham or distance-threshold) while preserving octant symmetry and avoiding visual gaps or doubled squares on diagonals. What is a simple, robust method to compute the set of grid cells for a given (integer or real) radius, and how can that be implemented cleanly in TikZ? Short macro examples, notes on rounding/aliasing pitfalls, and advice on scaling to a fixed cell size would be especially useful. For a quick visual reference I compared expected output with a pixel-circle preview online (pixel-circle preview).

I am compiling my thesis using Latex, which eventually generates a PDF file. In addition to its textual content, I want to insert a graphical image (.png) as its cover page. This is what I am doing with the help of titlepic, pdfpages Latex packages. In my permeable: \usepackage{titlepic} \usepackage{pdfpages} In my document class: \begin{document} \includepdf[pages=1]{./figures/ThesisCover.png} \end{document} Now this brings the following Latex error: ! Undefined control sequence. l.31 \if@titlepage The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., \hobx'), type I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Can anybody shed a light on how to solve this problem ? Thanks

I was inspired by some of the illustrations in https://math.stackexchange.com/a/46222. I wanted to try graphing implicit surfaces myself, and came across the method of marching cubes. See https://paulbourke.net/geometry/polygonise/. I collaborated with AI to produce the following code. If you are opposed to AI, this is your fair chance to recognize this fact and not participate in answering this question. It is extremely slow for many subdivisions, and unfortunately, I need many subdivisions to even remotely approach the desired graphic. The desired graphic is something like this: I would very much like for my attempt to be almost isomorphic (same shape) to the original picture. I cut out a large portion of occlusion code to get this to run in my lifetime. I hope to use far less triangles, and for it to adapt to regions of high and low density if possible. One idea I had was to take an initial coarse subdivision set, then up the samples in regions where the surface was not found up to a maximum depth. Then we could only sample highly where it is needed. This is just speculation though, and sounds very difficult to achieve. Obviously the desired technology exists currently, because of the desired picture's existence. MWE: \documentclass[tikz,border=3mm]{standalone} \usepackage{luacode} \begin{document} % Run LuaTeX code to generate the triangles \begin{luacode*} -- Parameters local nx, ny, nz = 80, 80, 80 -- grid resolution local x0, y0, z0 = -1, -1, -1 local x1, y1, z1 = 1, 1, 1 local isovalue = 0.0 local dx = (x1-x0)/nx local dy = (y1-y0)/ny local dz = (z1-z0)/nz -- Scalar function local function f(u, v, w) return (2.92*(u-1)*u*u*(u+1) + 1.7*v*v)^2 * ((v*v - 0.88)^2) + (2.92*(v-1)*v*v*(v+1) + 1.7*w*w)^2 * ((w*w - 0.88)^2) + (2.92*(w-1)*w*w*(w+1) + 1.7*u*u)^2 * ((u*u - 0.88)^2) - 0.02 end -- On-demand vertex value local function vertex_value(i,j,k) return f(x0 + i*dx, y0 + j*dy, z0 + k*dz) end -- Edge bisection local function edge_root(p0,p1,v0,v1,tol) local a,b = 0,1 local fa,fb = v0,v1 for iter=1,20 do local m = 0.5*(a+b) local pm = { x = p0.x + m*(p1.x-p0.x), y = p0.y + m*(p1.y-p0.y), z = p0.z + m*(p1.z-p0.z) } local fm = f(pm.x, pm.y, pm.z) if math.abs(fm)<tol then return pm end if fa*fm<=0 then b,fb = m,fm else a,fa = m,fm end end return {x=p0.x+0.5*(p1.x-p0.x), y=p0.y+0.5*(p1.y-p0.y), z=p0.z+0.5*(p1.z-p0.z)} end -- Minimal demo marching cubes table -- https://paulbourke.net/geometry/polygonise/ local raw_table = {{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 1, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {1, 8, 3, 9, 8, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 8, 3, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {9, 2, 10, 0, 2, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {2, 8, 3, 2, 10, 8, 10, 9, 8, -1, -1, -1, -1, -1, -1, -1}, {3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 11, 2, 8, 11, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {1, 9, 0, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {1, 11, 2, 1, 9, 11, 9, 8, 11, -1, -1, -1, -1, -1, -1, -1}, {3, 10, 1, 11, 10, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 10, 1, 0, 8, 10, 8, 11, 10, -1, -1, -1, -1, -1, -1, -1}, {3, 9, 0, 3, 11, 9, 11, 10, 9, -1, -1, -1, -1, -1, -1, -1}, {9, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {4, 3, 0, 7, 3, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 1, 9, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {4, 1, 9, 4, 7, 1, 7, 3, 1, -1, -1, -1, -1, -1, -1, -1}, {1, 2, 10, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {3, 4, 7, 3, 0, 4, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1}, {9, 2, 10, 9, 0, 2, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1}, {2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4, -1, -1, -1, -1}, {8, 4, 7, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {11, 4, 7, 11, 2, 4, 2, 0, 4, -1, -1, -1, -1, -1, -1, -1}, {9, 0, 1, 8, 4, 7, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1}, {4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1, -1, -1, -1, -1}, {3, 10, 1, 3, 11, 10, 7, 8, 4, -1, -1, -1, -1, -1, -1, -1}, {1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4, -1, -1, -1, -1}, {4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3, -1, -1, -1, -1}, {4, 7, 11, 4, 11, 9, 9, 11, 10, -1, -1, -1, -1, -1, -1, -1}, {9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {9, 5, 4, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 5, 4, 1, 5, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {8, 5, 4, 8, 3, 5, 3, 1, 5, -1, -1, -1, -1, -1, -1, -1}, {1, 2, 10, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {3, 0, 8, 1, 2, 10, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1}, {5, 2, 10, 5, 4, 2, 4, 0, 2, -1, -1, -1, -1, -1, -1, -1}, {2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8, -1, -1, -1, -1}, {9, 5, 4, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 11, 2, 0, 8, 11, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1}, {0, 5, 4, 0, 1, 5, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1}, {2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5, -1, -1, -1, -1}, {10, 3, 11, 10, 1, 3, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1}, {4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10, -1, -1, -1, -1}, {5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3, -1, -1, -1, -1}, {5, 4, 8, 5, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1}, {9, 7, 8, 5, 7, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {9, 3, 0, 9, 5, 3, 5, 7, 3, -1, -1, -1, -1, -1, -1, -1}, {0, 7, 8, 0, 1, 7, 1, 5, 7, -1, -1, -1, -1, -1, -1, -1}, {1, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {9, 7, 8, 9, 5, 7, 10, 1, 2, -1, -1, -1, -1, -1, -1, -1}, {10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3, -1, -1, -1, -1}, {8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2, -1, -1, -1, -1}, {2, 10, 5, 2, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1}, {7, 9, 5, 7, 8, 9, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1}, {9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11, -1, -1, -1, -1}, {2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7, -1, -1, -1, -1}, {11, 2, 1, 11, 1, 7, 7, 1, 5, -1, -1, -1, -1, -1, -1, -1}, {9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11, -1, -1, -1, -1}, {5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0, -1}, {11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0, -1}, {11, 10, 5, 7, 11, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 8, 3, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {9, 0, 1, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {1, 8, 3, 1, 9, 8, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1}, {1, 6, 5, 2, 6, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {1, 6, 5, 1, 2, 6, 3, 0, 8, -1, -1, -1, -1, -1, -1, -1}, {9, 6, 5, 9, 0, 6, 0, 2, 6, -1, -1, -1, -1, -1, -1, -1}, {5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8, -1, -1, -1, -1}, {2, 3, 11, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {11, 0, 8, 11, 2, 0, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1}, {0, 1, 9, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1}, {5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11, -1, -1, -1, -1}, {6, 3, 11, 6, 5, 3, 5, 1, 3, -1, -1, -1, -1, -1, -1, -1}, {0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6, -1, -1, -1, -1}, {3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9, -1, -1, -1, -1}, {6, 5, 9, 6, 9, 11, 11, 9, 8, -1, -1, -1, -1, -1, -1, -1}, {5, 10, 6, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {4, 3, 0, 4, 7, 3, 6, 5, 10, -1, -1, -1, -1, -1, -1, -1}, {1, 9, 0, 5, 10, 6, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1}, {10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4, -1, -1, -1, -1}, {6, 1, 2, 6, 5, 1, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1}, {1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7, -1, -1, -1, -1}, {8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6, -1, -1, -1, -1}, {7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9, -1}, {3, 11, 2, 7, 8, 4, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1}, {5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11, -1, -1, -1, -1}, {0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1}, {9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6, -1}, {8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6, -1, -1, -1, -1}, {5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11, -1}, {0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7, -1}, {6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9, -1, -1, -1, -1}, {10, 4, 9, 6, 4, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {4, 10, 6, 4, 9, 10, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1}, {10, 0, 1, 10, 6, 0, 6, 4, 0, -1, -1, -1, -1, -1, -1, -1}, {8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10, -1, -1, -1, -1}, {1, 4, 9, 1, 2, 4, 2, 6, 4, -1, -1, -1, -1, -1, -1, -1}, {3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4, -1, -1, -1, -1}, {0, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {8, 3, 2, 8, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1}, {10, 4, 9, 10, 6, 4, 11, 2, 3, -1, -1, -1, -1, -1, -1, -1}, {0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6, -1, -1, -1, -1}, {3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10, -1, -1, -1, -1}, {6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1, -1}, {9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3, -1, -1, -1, -1}, {8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1, -1}, {3, 11, 6, 3, 6, 0, 0, 6, 4, -1, -1, -1, -1, -1, -1, -1}, {6, 4, 8, 11, 6, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {7, 10, 6, 7, 8, 10, 8, 9, 10, -1, -1, -1, -1, -1, -1, -1}, {0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10, -1, -1, -1, -1}, {10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0, -1, -1, -1, -1}, {10, 6, 7, 10, 7, 1, 1, 7, 3, -1, -1, -1, -1, -1, -1, -1}, {1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7, -1, -1, -1, -1}, {2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9, -1}, {7, 8, 0, 7, 0, 6, 6, 0, 2, -1, -1, -1, -1, -1, -1, -1}, {7, 3, 2, 6, 7, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7, -1, -1, -1, -1}, {2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7, -1}, {1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11, -1}, {11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1, -1, -1, -1, -1}, {8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6, -1}, {0, 9, 1, 11, 6, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0, -1, -1, -1, -1}, {7, 11, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {3, 0, 8, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 1, 9, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {8, 1, 9, 8, 3, 1, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1}, {10, 1, 2, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {1, 2, 10, 3, 0, 8, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1}, {2, 9, 0, 2, 10, 9, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1}, {6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8, -1, -1, -1, -1}, {7, 2, 3, 6, 2, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {7, 0, 8, 7, 6, 0, 6, 2, 0, -1, -1, -1, -1, -1, -1, -1}, {2, 7, 6, 2, 3, 7, 0, 1, 9, -1, -1, -1, -1, -1, -1, -1}, {1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6, -1, -1, -1, -1}, {10, 7, 6, 10, 1, 7, 1, 3, 7, -1, -1, -1, -1, -1, -1, -1}, {10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8, -1, -1, -1, -1}, {0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7, -1, -1, -1, -1}, {7, 6, 10, 7, 10, 8, 8, 10, 9, -1, -1, -1, -1, -1, -1, -1}, {6, 8, 4, 11, 8, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {3, 6, 11, 3, 0, 6, 0, 4, 6, -1, -1, -1, -1, -1, -1, -1}, {8, 6, 11, 8, 4, 6, 9, 0, 1, -1, -1, -1, -1, -1, -1, -1}, {9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6, -1, -1, -1, -1}, {6, 8, 4, 6, 11, 8, 2, 10, 1, -1, -1, -1, -1, -1, -1, -1}, {1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6, -1, -1, -1, -1}, {4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9, -1, -1, -1, -1}, {10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3, -1}, {8, 2, 3, 8, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1}, {0, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {1, 9, 0, 2, 3, 4, 2, 4, 6, 4, 3, 8, -1, -1, -1, -1}, {1, 9, 4, 1, 4, 2, 2, 4, 6, -1, -1, -1, -1, -1, -1, -1}, {8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1, -1, -1, -1, -1}, {10, 1, 0, 10, 0, 6, 6, 0, 4, -1, -1, -1, -1, -1, -1, -1}, {4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3, -1}, {10, 9, 4, 6, 10, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {4, 9, 5, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 8, 3, 4, 9, 5, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1}, {5, 0, 1, 5, 4, 0, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1}, {11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5, -1, -1, -1, -1}, {9, 5, 4, 10, 1, 2, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1}, {6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5, -1, -1, -1, -1}, {7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2, -1, -1, -1, -1}, {3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6, -1}, {7, 2, 3, 7, 6, 2, 5, 4, 9, -1, -1, -1, -1, -1, -1, -1}, {9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7, -1, -1, -1, -1}, {3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0, -1, -1, -1, -1}, {6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8, -1}, {9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7, -1, -1, -1, -1}, {1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4, -1}, {4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10, -1}, {7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10, -1, -1, -1, -1}, {6, 9, 5, 6, 11, 9, 11, 8, 9, -1, -1, -1, -1, -1, -1, -1}, {3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5, -1, -1, -1, -1}, {0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11, -1, -1, -1, -1}, {6, 11, 3, 6, 3, 5, 5, 3, 1, -1, -1, -1, -1, -1, -1, -1}, {1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6, -1, -1, -1, -1}, {0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10, -1}, {11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5, -1}, {6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3, -1, -1, -1, -1}, {5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2, -1, -1, -1, -1}, {9, 5, 6, 9, 6, 0, 0, 6, 2, -1, -1, -1, -1, -1, -1, -1}, {1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8, -1}, {1, 5, 6, 2, 1, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6, -1}, {10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0, -1, -1, -1, -1}, {0, 3, 8, 5, 6, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {10, 5, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {11, 5, 10, 7, 5, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {11, 5, 10, 11, 7, 5, 8, 3, 0, -1, -1, -1, -1, -1, -1, -1}, {5, 11, 7, 5, 10, 11, 1, 9, 0, -1, -1, -1, -1, -1, -1, -1}, {10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1, -1, -1, -1, -1}, {11, 1, 2, 11, 7, 1, 7, 5, 1, -1, -1, -1, -1, -1, -1, -1}, {0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11, -1, -1, -1, -1}, {9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7, -1, -1, -1, -1}, {7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2, -1}, {2, 5, 10, 2, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1}, {8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5, -1, -1, -1, -1}, {9, 0, 1, 5, 10, 3, 5, 3, 7, 3, 10, 2, -1, -1, -1, -1}, {9, 8, 2, 9, 2, 1, 8, 7, 2, 10, 2, 5, 7, 5, 2, -1}, {1, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 8, 7, 0, 7, 1, 1, 7, 5, -1, -1, -1, -1, -1, -1, -1}, {9, 0, 3, 9, 3, 5, 5, 3, 7, -1, -1, -1, -1, -1, -1, -1}, {9, 8, 7, 5, 9, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {5, 8, 4, 5, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1}, {5, 0, 4, 5, 11, 0, 5, 10, 11, 11, 3, 0, -1, -1, -1, -1}, {0, 1, 9, 8, 4, 10, 8, 10, 11, 10, 4, 5, -1, -1, -1, -1}, {10, 11, 4, 10, 4, 5, 11, 3, 4, 9, 4, 1, 3, 1, 4, -1}, {2, 5, 1, 2, 8, 5, 2, 11, 8, 4, 5, 8, -1, -1, -1, -1}, {0, 4, 11, 0, 11, 3, 4, 5, 11, 2, 11, 1, 5, 1, 11, -1}, {0, 2, 5, 0, 5, 9, 2, 11, 5, 4, 5, 8, 11, 8, 5, -1}, {9, 4, 5, 2, 11, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {2, 5, 10, 3, 5, 2, 3, 4, 5, 3, 8, 4, -1, -1, -1, -1}, {5, 10, 2, 5, 2, 4, 4, 2, 0, -1, -1, -1, -1, -1, -1, -1}, {3, 10, 2, 3, 5, 10, 3, 8, 5, 4, 5, 8, 0, 1, 9, -1}, {5, 10, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2, -1, -1, -1, -1}, {8, 4, 5, 8, 5, 3, 3, 5, 1, -1, -1, -1, -1, -1, -1, -1}, {0, 4, 5, 1, 0, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {8, 4, 5, 8, 5, 3, 9, 0, 5, 0, 3, 5, -1, -1, -1, -1}, {9, 4, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {4, 11, 7, 4, 9, 11, 9, 10, 11, -1, -1, -1, -1, -1, -1, -1}, {0, 8, 3, 4, 9, 7, 9, 11, 7, 9, 10, 11, -1, -1, -1, -1}, {1, 10, 11, 1, 11, 4, 1, 4, 0, 7, 4, 11, -1, -1, -1, -1}, {3, 1, 4, 3, 4, 8, 1, 10, 4, 7, 4, 11, 10, 11, 4, -1}, {4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2, -1, -1, -1, -1}, {9, 7, 4, 9, 11, 7, 9, 1, 11, 2, 11, 1, 0, 8, 3, -1}, {11, 7, 4, 11, 4, 2, 2, 4, 0, -1, -1, -1, -1, -1, -1, -1}, {11, 7, 4, 11, 4, 2, 8, 3, 4, 3, 2, 4, -1, -1, -1, -1}, {2, 9, 10, 2, 7, 9, 2, 3, 7, 7, 4, 9, -1, -1, -1, -1}, {9, 10, 7, 9, 7, 4, 10, 2, 7, 8, 7, 0, 2, 0, 7, -1}, {3, 7, 10, 3, 10, 2, 7, 4, 10, 1, 10, 0, 4, 0, 10, -1}, {1, 10, 2, 8, 7, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {4, 9, 1, 4, 1, 7, 7, 1, 3, -1, -1, -1, -1, -1, -1, -1}, {4, 9, 1, 4, 1, 7, 0, 8, 1, 8, 7, 1, -1, -1, -1, -1}, {4, 0, 3, 7, 4, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {4, 8, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {9, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {3, 0, 9, 3, 9, 11, 11, 9, 10, -1, -1, -1, -1, -1, -1, -1}, {0, 1, 10, 0, 10, 8, 8, 10, 11, -1, -1, -1, -1, -1, -1, -1}, {3, 1, 10, 11, 3, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {1, 2, 11, 1, 11, 9, 9, 11, 8, -1, -1, -1, -1, -1, -1, -1}, {3, 0, 9, 3, 9, 11, 1, 2, 9, 2, 11, 9, -1, -1, -1, -1}, {0, 2, 11, 8, 0, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {3, 2, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {2, 3, 8, 2, 8, 10, 10, 8, 9, -1, -1, -1, -1, -1, -1, -1}, {9, 10, 2, 0, 9, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {2, 3, 8, 2, 8, 10, 0, 1, 8, 1, 10, 8, -1, -1, -1, -1}, {1, 10, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {1, 3, 8, 9, 1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 9, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 3, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}} -- Convert raw_table to marching_cubes_table (list of triangles per config) local triTable = {} for idx, entry in ipairs(raw_table) do local triangles = {} local i = 1 while entry[i] ~= -1 do if entry[i+2] ~= -1 then table.insert(triangles, {entry[i], entry[i+1], entry[i+2]}) i = i + 3 else break end end triTable[idx] = triangles -- 1-based end -- Edge to corners mapping (1-based) local edge_to_corners = { {1,2},{2,3},{3,4},{4,1}, {5,6},{6,7},{7,8},{8,5}, {1,5},{2,6},{3,7},{4,8} } -- Corner offsets and edges local cornerOffsets = {{0,0,0},{1,0,0},{1,1,0},{0,1,0},{0,0,1},{1,0,1},{1,1,1},{0,1,1}} local edgeIndex = {{1,2},{2,3},{3,4},{4,1},{5,6},{6,7},{7,8},{8,5},{1,5},{2,6},{3,7},{4,8}} -- Preallocated triangle points local pts = {{},{},{}} -- Open output file local f = io.open("triangles.tex","w") f:write([[ \documentclass[tikz,border=3mm]{standalone} \begin{document} \begin{tikzpicture} ]]) -- Main loop for i=0,nx-1 do for j=0,ny-1 do for k=0,nz-1 do -- corner values on-demand local cubeVals = {} for ci=1,8 do local ox,oy,oz = cornerOffsets[ci][1], cornerOffsets[ci][2], cornerOffsets[ci][3] cubeVals[ci] = vertex_value(i+ox,j+oy,k+oz) end -- cube index local cubeIndex = 0 for ci=1,8 do if cubeVals[ci]<isovalue then cubeIndex = cubeIndex + 2^(ci-1) end end if cubeIndex ~=1 and cubeIndex ~=256 then local x = x0 + i*dx local y = y0 + j*dy local z = z0 + k*dz -- corner positions local p = {} for ci=1,8 do p[ci] = {x=x+cornerOffsets[ci][1]*dx, y=y+cornerOffsets[ci][2]*dy, z=z+cornerOffsets[ci][3]*dz} end -- triangles -- triangles for _, tri in ipairs(triTable[cubeIndex+1] or {}) do for ei=1,3 do local e = tri[ei] local c1,c2 = edgeIndex[e+1][1], edgeIndex[e+1][2] local v1,v2 = cubeVals[c1], cubeVals[c2] local pos = edge_root(p[c1],p[c2],v1,v2,1e-6) pts[ei].x = pos.x pts[ei].y = pos.y pts[ei].z = pos.z -- <--- THIS LINE IS MISSING end f:write(string.format([[\draw[fill=blue!20,draw=blue!60,line join = round, ultra thin] (%.5f,%.5f,%.5f) -- (%.5f,%.5f,%.5f) -- (%.5f,%.5f,%.5f) -- cycle; ]], pts[1].x, pts[1].y, pts[1].z, pts[2].x, pts[2].y, pts[2].z, pts[3].x, pts[3].y, pts[3].z)) end end end end end f:write([[\end{tikzpicture}\end{document}]]) f:close() \end{luacode*} \end{document}

I have a list of numbers from 1 to 12. I want to print the numbers 3,6,9 and 12 in purple, the others in blue. With my code: \documentclass{standalone} \usepackage{tikz,ifthen} \begin{document} \begin{tikzpicture} \foreach \i in {1,...,12}{ \ifthenelse {\i/3=int(\i/3)} {\draw[purple] (.75*\i,0) node () {\i};}{\draw[blue] (.75*\i,0) node () {\i};} } \end{tikzpicture} \end{document} I have errors and all numbers in blue. Why?

What is the meaning of Package tagpdf Warning: Destination 'section*.2' has no related structure. (tagpdf) /Ref not updated. It appears to be caused by: \DocumentMetadata{lang=en-US,tagging=on,pdfversion=2.0,pdfstandard=a-4f,pdfstandard=UA-2} \documentclass[a4paper,12pt,USenglish]{book} \usepackage{fontspec} \usepackage{hyperref} \usepackage{unicode-math} \usepackage[toc, acronym]{glossaries} \newacronym{pdf}{PDF}{Portable Document Format} \makeglossaries \begin{document} \gls{pdf} \tableofcontents \printglossaries% \end{document} I compiled with lualatex and then once makeglossaries and again lualatex. Then the problem occurs in xxx.toc: \contentsline {chapter}{Acronyms}{5}{section*.2}% Here is the mysterious anonymous section. Now my question: how to avoid the warning from tagpdf? How to make latex write something different into the toc and what??

Every now and then I need a refresher on LaTeX logic. In the example below I expected either an error or at least a different result — certainly not the value 2, which is the behavior I would have expected only if the increment function were protected. Could someone please clarify what’s going on? \documentclass{article} \ExplSyntaxOn \int_new:N \g__erw_counter_int \cs_new:Npn \__erw_bad_increment: { \int_gincr:N \g__erw_counter_int } \cs_new_protected:Npn \__erw_good_increment: { \int_gincr:N \g__erw_counter_int } \ExplSyntaxOff \begin{document} \ExplSyntaxOn \int_gset:Nn \g__erw_counter_int { 0 } \tl_set:Nx \l_tmpa_tl { \__erw_bad_increment: } \tl_set:Nx \l_tmpb_tl { \__erw_good_increment: } \tl_use:N\l_tmpa_tl \tl_use:N\l_tmpa_tl Value:~\int_use:N\g__erw_counter_int % Outputs Value:2 \ExplSyntaxOff \end{document}

I am getting the following error message: (biblatex-ext-tabular) 'bibtabular' undefined. See the biblatex-ext-tabular package documentation for explanation. Type H for immediate help. ... l.146 \referencepage Please supply a suitable definition with \defbibtabular. See the documentation for more details. biblatex-ext-tabular defines defbibtabular as follows: % user-level command for defining tabular bibliography format \newrobustcmd*{\defbibtabular}[4]{% \long\csdef{extblxtab@env@#1}{#2}% \long\csdef{extblxtab@endenv@#1}{#3}% \long\csdef{extblxtab@tabrow@format@#1}{#4}} The definition in the STY file that I'm using, I didn't create this, it's beyond my capability, defines \defbibtabular as follows: \defbibtabular{bibtabular} {\setlength{\LTpre}{0pt}% \setlength{\LTpost}{0pt}% \begin{longtable}{% @{} |C{1in} |L{5.1in}| @{}} \hline \cellcolor{deepBlue} {\bfseries\color{white} Reference} & \cellcolor{deepBlue} {\bfseries\color{white} Document Title} \\ \hline \endfirsthead \hline \cellcolor{deepBlue} {\bfseries\color{white} Reference} & \cellcolor{deepBlue} {\bfseries\color{white} Document Title} \\ \hline \endhead \end{longtable}} {\printtext[labelnumberwidth]{% \plainlang{\printfield{labelnumber}}} & \plainlang{\printfield{title}}\\\hline} I am using OverLeaf and so I can't type H for help as that appears for local use. I am not experienced enough yet to understand what the definition parameters, such as extblxtab@env@#1, might be in error generating \defbibtabular{bibtabular} and so would like to know how I would manually parse it such that I can figure out what I need to do to fix it?

I have the following snippet \documentclass{article} \usepackage{tabularx} \usepackage{rotating} \usepackage{multirow} \newcolumntype{C}{>{\centering\arraybackslash}X} \newcolumntype{V}{>{\centering\arraybackslash}m{1.5cm}} \newcommand{\verttext}[1]{\rotatebox{90}{\parbox{3cm}{\centering\textbf{#1}}}} \renewcommand{\arraystretch}{1.5} \begin{document} \begin{table}[h] \centering \begin{tabularx}{\textwidth}{V | V | C | C |} \multicolumn{2}{c}{} & \multicolumn{2}{c}{Ausmass des Interesses am Unternehmen} \\ \cline{3-4} \multicolumn{1}{c}{} & \multicolumn{1}{c|}{} & Gering & Hoch \\ \cline{2-4} \multirow{2}{*}{\verttext{Ausmass der Macht}} & \verttext{Hoch} & Zufrieden stellen & Key Players \\ \cline{2-4} & \verttext{Gering} & minimal betreuen & informieren \\ \cline{2-4} \end{tabularx} \end{table} \end{document} which looks like this: as you can see, the "Ausmass der Macht" isnt centered (its two cell high) and shouldn't be wrapped. The two cells (Hoch + Gering) are high enough so the text shouldn't be wrapped. I already found a kinda similar question here: Vertical Text using multirow in the Table though I have no clue how to resolve that issue. Thanks in advance 🙂

For some reason, when using \mathfrak{}, everything works up until using \boldsymbol{}, after which it gives me an error saying, "Use of \reserved@a doesn't match its definition". Here is an example: \documentclass{article} \usepackage{graphicx} \usepackage{lmodern} \usepackage[dvipsnames]{xcolor} \usepackage[T1]{fontenc} \usepackage{amsthm, amsmath, amssymb, amsfonts, mathrsfs} \usepackage[fixamsmath]{mathtools} \usepackage[cal=cm, scr=rsfs, frak=euler, bb=ams]{mathalpha} \usepackage{tikz} \usetikzlibrary{shapes.geometric,positioning} \newtheorem{theorem}{Theorem}[subsection] \begin{document} $\mathfrak{X}$ $\boldsymbol{\gamma}$ $\mathfrak{X}$ \end{document} This gives the following with the error occurring at the second \mathfrak{X}. Is it an issue with any of the packages/libraries I am using? Is my preamble overloaded with them?

Do people creatively use math mode for things other than math? If so, when and why?

In a previous question (i.e., How to align the visual bottom of a large quotation mark with the cap height of the text?) I was looking for a solution for how to properly align a quotation mark. As cfr also suggests in one of his comments, using TikZ seems more appropriate. To this end, I would like to replicate the following quotation mark in TikZ (i.e., a single one will do; see image below). I managed to get somewhat close, but not quite there: \documentclass[12pt]{article} \usepackage[T1]{fontenc} \usepackage[p, osf, swashQ]{cochineal} \usepackage{tikz} \begin{document} % Model. {\fontsize{1000}{0}\selectfont\textcolor{lightgray}{`'}} % Implementation. \begin{tikzpicture}[baseline=0pt, scale=10] % Grid. \draw[help lines, color=lightgray, step=0.1] (-1, -1.2) grid (0.2, 0); % Zoom. \draw[red] (0, 0) -- (0, -1) -- (-1, -1) -- (-1, 0) -- cycle; % Coordinates. \fill[blue] (0, 0) circle (0.2pt) node[above] {$(0, 0)$}; \fill[blue] (0, -1) circle (0.2pt) node[below] {$(0, -1)$}; \fill[blue] (-1, 0) circle (0.2pt) node[above] {$(-1, 0)$}; \fill[blue] (-1, -1) circle (0.2pt) node[below] {$(-1, -1)$}; % Junction points. \fill[red] (0, 0) circle (0.1pt); \fill[red] (-0.4, -1) circle (0.1pt) node[below] {$(-0.4, -1)$}; \fill[red] (-0.5, -0.9) circle (0.1pt) node[left] {$(-0.5, -0.9)$}; \fill[red] (-0.2, -0.5) circle (0.1pt) node[left] {$(-0.2, -0.5)$}; % The curve with new control points \draw[thick, color=blue] % Start. (0, 0) % Curved back. .. controls (0.4, -0.43) and (-0.38, -1) .. % (-0.4, -1) % The tip. .. controls (-0.4, -1) and (-0.5, -0.95) .. % (-0.5, -0.9) % The curved inner. .. controls (-0.4, -0.9) and (-0.1, -0.5) .. % (-0.2, -0.5) % The bulge. .. controls (-0.6, -0.15) and (-0.2, 0.05) .. % End. cycle; \end{tikzpicture} \end{document} Based on the attempt above, I obtained the following shape below. However, some of the "control points" are not properly "rounded," e.g., (-0.2, -0.5) or (-0.4, -1). I'd appreciate any ideas.

I'm still really a noob with fonts in LaTeX. I'm looking for a better font display than the one used in the code below. What other nice font codes should I try on line marked with a comment, to get better results in the epigraphs? This is for an adventure novel (no maths here), and I'm looking for something a bit poetic, lyrical, without fancy hard to read curvy fonts, but still something elegant for an epic novel. Here's a MWE to play with: \documentclass[11pt,twoside]{report} \usepackage[T1]{fontenc} \usepackage[tt=false]{libertinus} \usepackage[french]{babel} \usepackage[stretch=50]{microtype} \usepackage[letterpaper,left=1.25in,right=1in,top=0.5in,bottom=0.5in,includeheadfoot,headheight=15pt]{geometry} \usepackage{epigraph} \renewcommand{\textflush}{flushleft} \setlength{\epigraphrule}{0pt} \newcommand*{\styling}{\usefont{T1}{qzc}{m}{it}\selectfont} % ANOTHER FONT TO BE USED HERE! \newcommand{\epig}[2]{\epigraphhead[70]{\epigraph{\styling{#1}}{\styling{#2}}}} \begin{document} \chapter{Nice chapter title} \epig{ Some nice epic epigraph, To be written here, Some words to shows up the style. }{} Blabla bla blabla bla. \end{document} Here's a preview of what this MWE code is doing: The question here is how should I edit the MWE code to use other fonts just for the epigraphs, without touching the main text font (libertinus)?

Experience Latex users The following code is the template I am using for my notes. Since the top margin of Chapter 1 is a lot greater than I thought and this pushes the last bullet point (circle in pink) to the next page. Reducing the set chapter title of titlesec margin would solve this problem. Could you please give me some tips on this? Thank you. \documentclass[12pt]{book} \usepackage[margin=0.5in]{geometry} % % Packages \usepackage[utf8]{inputenc} \usepackage{amsmath, amssymb, amsfonts} % math symbols \usepackage{geometry} \usepackage{graphicx} % figures \usepackage{tikz} % drawings \usepackage{hyperref} % clickable links \usepackage{fancyhdr} % headers/footers \usepackage{titlesec} % formatting chapter titles % Page layout % \usepackage{pgfplots} \usepackage{mathtools} \usepackage{cancel} \usepackage{pgfplots} \usepackage{array} \usepackage{amsmath} \newtheorem{theorem}{THEOREM} \newtheorem{proof}{PROOF} \usepackage{tikz} \usepackage{amssymb} \usetikzlibrary{patterns} \usepackage{bigints} \usepackage{color} \usepackage{tcolorbox} \usepackage{cancel} \usepackage{soul} \usepackage{multirow} \usepackage{dcolumn} \usepackage{graphicx} % Required for \includegraphics %\usepackage{background} %\usepackage{fullpage, lipsum, tikz} %\usepackage{eso-pic} % % Headers and footers \pagestyle{fancy} \fancyhf{} \fancyhead[LE,RO]{\thepage} \fancyhead[LO]{\rightmark} \fancyhead[RE]{\leftmark} % \titlespacing{\chapter}{0pt}{-128pt}{1cm}% <-- CHANGE DONE HERE!! \begin{document} % % Title \begin{titlepage} \centering \vspace*{3cm} {\Huge\bfseries TITLE}\\[1cm] %{\Large Covering Five Core Topics}\\[2cm] \vfill {\Large ME}\\ %{\Large \today} \end{titlepage} \tableofcontents \newpage %\voffset -2.0cm % \chapter{Natural Numbers} \textbf{01 DIVISORS AND MULTIPLES}\\ \\ \textbf{QUOTIENTS AND REMAINDERS}\\ \\ Let $A$, $B$, $Q$, and $R$ be whole numbers\\[0.15cm] When dividing $A$ by $B$, let the quotient be $Q$ and the remainder be $R$.\\[0.15cm] Then\\ \\ $A = B \times Q + R$, where $0 \le R < B$.\\ \\ If $R = 0$, then $A$ is said to be divisible by $B$.\\ \\\\ \textbf{DIVISORS AND MULTIPLES}\\ \\ If $A$ is divisible by $B$, that is, if $A = B \times Q$, then $A$ is a multiple of $B$, and $B$ is a divisor of $A$.\\ \\ For example, $24$ is divisible by $6$.\\[0.15cm] Since $24 = 6 \times 4$, $24$ is a multiple of $6$ and $6$ is a divisor of $24$.\\ \\ Note that $0$ is a multiple of every non-zero whole number.\\[0.15cm] This is because, for any non-zero whole number $K$, we have\\ \\ $0 = K \times 0$.\\ \\ In other words, every non-zero whole number is a divisor of $0$.\\ \\\\ \textbf{TESTS FOR MULTIPLES}\\ \\ $\bullet$ A number is a multiple of $4$ if its last two digits are a multiple of $4$.\\ \\ $\bullet$ A number is a multiple of $8$ if its last three digits are a multiple of $8$.\\ \\ $\bullet$ A number is a multiple of $9$ if the sum of its digits is a multiple of $9$.\\ \\ $\bullet$ A number is a multiple of $3$ if the sum of its digits is a multiple of $3$.\\ \\ % \newpage \voffset 0cm \text{}\\ \\ $\bullet$ A number is a multiple of $11$ if the difference between the sum of its digits in odd positions and the sum\\[0.15cm] \hspace*{4mm}of its digits in even positions is $0$ or a multiple of $11$.\\ \\\\ \textbf{02 POWERS AND PRIME NUMBERS}\\ \\ \textbf{POWERS}\\ \\ A power is a notation used to show repeated multiplication of a number or variable. \end{document}

This is related with another question about tagging floating lstlisting environment. The example file is the following: \DocumentMetadata{lang=en-US,tagging=on} \documentclass{article} \usepackage{unicode-math} \usepackage{listings} \title{listings always problems} \author{E. Lister} \date{\today} \begin{document} \maketitle some text \begin{lstlisting}[language=tex, basicstyle=\small] \RequirePackage[l2tabu, orthodox]{nag} % optional \documentclass{...} \begin{document} ... \end{document} \end{lstlisting} \end{document} The result is as follows: Package tagpdf Warning: Parent-Child 'pdf:StructTreeRoot' --> 'pdf2:Part'. (tagpdf) Relation is not allowed! on line 27 (tagpdf) struct 1, StructTreeRoot --> struct 24, text-unit Package tagpdf Warning: Parent-Child 'pdf:StructTreeRoot' --> 'pdf2:P'. (tagpdf) Relation is not allowed! on line 27 (tagpdf) struct 24, text-unit --> struct 25, text Package tagpdf Warning: Parent-Child 'pdf:StructTreeRoot' --> 'pdf2:P'. (tagpdf) Relation is not allowed! on line 27 (tagpdf) struct 24, text-unit --> struct 26, text Package tagpdf Warning: Parent-Child 'pdf:StructTreeRoot' --> 'pdf2:Part'. (tagpdf) Relation is not allowed! on line 27 (tagpdf) struct 1, StructTreeRoot --> struct 28, text-unit Package tagpdf Warning: Parent-Child 'pdf:StructTreeRoot' --> 'pdf2:P'. (tagpdf) Relation is not allowed! on line 27 (tagpdf) struct 28, text-unit --> struct 29, text [2]<<latex-list-css.html>><<latex-align-css.html>> (./test2.aux) ! Package tagpdf Error: The number of automatic begin (10) and end (11) (tagpdf) text-unit para hooks differ! For immediate help type H <return>. ... l.27 \end{document} ? so does not even compile any more.. What happened?? Note that Understanding and avoiding tagpdf warning caused by floating lstlisting environment is a solution if lstlisting is floating. The solution is to insert after loading listings \usepackage{unicode-math} \usepackage{listings} \ExplSyntaxOn % Internal variable, temporary work-around! \prop_gput:Nnn\g__tag_float_sect_prop{lstlisting-struct}{\tag_get:n{current_Sect}} \ExplSyntaxOff Then the result is better but not good at all: al/texlive/2025/texmf-var/fonts/map/pdftex/updmap/pdftex.map}]<<latex-list-css. html>><<latex-align-css.html>> (./test2.aux) ! Package tagpdf Error: The number of automatic begin (8) and end (9) (tagpdf) text-unit para hooks differ! For immediate help type H <return>. ... l.33 \end{document} I would also like to know the meaning of the errors.

I'm trying to put multiple numbered equations into one line to save space. One way to do this is to put the equations inside a tabularx table. However, when I try to put an equation environment inside a tabularx the vertical alignment is off: \documentclass{article} \usepackage{tabularx,amsmath} \begin{document} \begin{equation*} \begin{tabularx}{\textwidth}{m{0.4\textwidth}m{0.4\textwidth}} \begin{equation} \begin{pmatrix}1\\2\\3\end{pmatrix} \end{equation} & \begin{equation} x \end{equation} \end{tabularx} \end{equation*} \end{document} produces As you can see, the vertical alignment between the two labels (1) and (2) is slightly off. I've not been able to figure out what latex aligns in this case, it seems erratic to me. Changing the column type from m to p or b didn't fix the problem.

As a continuation of TikZ word search diagram here is the problem I'm facing. I did what Explorer suggested and it worked fine except that my rounded rectangles look like sausages or like Hieroglyphic cartouches because at their narrow ends they have lines on the secondary axis: Here is the code: \documentclass{article} \usepackage[cmyk]{xcolor} \definecolor{myPB}{cmyk}{0.85,0.75,0,0} \definecolor{myLB}{cmyk}{0.1,0.06,0,0} \usepackage{tikz} \usetikzlibrary{matrix,backgrounds} \newlength{\mydrawlinewidth} \setlength{\mydrawlinewidth}{1pt} \NewDocumentCommand{\markA}{ O{red} m m }{% \draw[rounded corners=6mm,opacity=.5, line width=2pt,myPB,fill=myLB] ([xshift=5pt,yshift=-5pt]yannis-#2.north west) rectangle ([xshift=-5pt,yshift=5pt]yannis-#3.south east); } \NewDocumentCommand{\markB}{ O{red} m m }{% \draw[rounded corners=6mm,opacity=.5,line width=2pt,myPB,fill=myLB] ([yshift=2pt]yannis-#2.north) -- ([xshift=2pt]yannis-#3.east) -- ([yshift=-2pt]yannis-#3.south) -- ([xshift=-2pt]yannis-#2.west) -- cycle; } \NewDocumentCommand{\markC}{ O{red} m m }{% \draw[rounded corners=6mm,opacity=.5,line width=2pt,myPB,fill=myLB] ([xshift=2pt]yannis-#2.east) -- ([yshift=-2pt]yannis-#3.south) -- ([xshift=-2pt]yannis-#3.west) -- ([yshift=2pt]yannis-#2.north) -- cycle; } \begin{document} \begin{tikzpicture} \matrix (yannis) [% matrix of nodes,% column sep=0mm,% row sep=0mm, nodes={ % draw, rectangle,anchor=center, line width=0.5pt, inner sep=2pt,outer sep=0pt, %font=\bfseries\huge, minimum size=1.1cm, } ] { S & G & A & Q & Q & T & C & E & F & R & E & P & Y & W & R \\ W & L & Q & E & L & B & A & R & A & P & M & O & C & E & L \\ Y & I & T & S & X & E & L & I & Y & A & H & U & W & R & A \\ B & K & E & E & Y & C & W & L & J & T & M & A & K & B & F \\ J & E & R & I & O & R & T & M & K & E & R & L & Q & E & T \\ P & N & P & L & S & B & R & W & H & D & U & U & E & H & E \\ E & E & R & R & E & W & V & S & S & M & L & N & K & E & R \\ H & S & E & E & H & T & A & P & H & Y & S & I & C & A & L \\ S & S & T & D & S & H & E & U & Q & V & L & V & R & Z & I \\ O & R & N & N & I & F & L & L & A & S & N & E & E & K & F \\ M & T & I & U & N & L & G & E & P & H & U & R & A & S & E \\ W & K & O & Q & U & P & U & H & A & M & G & S & T & M & I \\ A & F & A & R & P & J & M & S & L & R & O & E & E & H & C \\ B & X & H & C & A & I & H & S & A & M & S & C & D & F & G \\ I & P & R & O & P & H & E & T & S & N & S & I & F & X & Q \\ }; \begin{scope}[on background layer] \markA{1-6}{1-12} \markA{1-14}{6-14} \markC{1-15}{7-9} \markA{2-2}{9-2} \markA{2-4}{2-13} \markA{3-3}{11-3} \markA{3-4}{11-4} \markA{3-6}{3-12} \markA{3-15}{11-15} \markC{4-11}{9-6} \markA{6-5}{13-5} \markA{6-12}{13-12} \markA{7-1}{11-1} \markB{7-5}{14-12} \markA{8-8}{8-15} \markA{8-13}{14-13} \markB{10-7}{15-12} \markB{11-2}{15-6} \markA{14-3}{14-10} \markA{15-2}{15-9} \end{scope} \end{tikzpicture} \end{document} How can I fix this? @mickep I replaced the snippets by a complete minimal example.

when facing the text in latex: Receiver class org.springframework.cloud.netflix.ribbon.RibbonLoadBalancerClient does not define or inherit an implementation of the resolved method 'abstract org.springframework.cloud.client.ServiceInstance choose(java.lang.String, org.springframework.cloud.client.loadbalancer.Request)' of interface org.springframework.cloud.client.loadbalancer.ServiceInstanceChooser it could not wrap properly, so I tried to put the text with \url like this: \url{Receiver class org.springframework.cloud.netflix.ribbon.RibbonLoadBalancerClient does not define or inherit an implementation of the resolved method 'abstract org.springframework.cloud.client.ServiceInstance choose(java.lang.String, org.springframework.cloud.client.loadbalancer.Request)' of interface org.springframework.cloud.client.loadbalancer.ServiceInstanceChooser} but the space was moved automatically. is it possible to keep the space? this is the full reproduce demo: \documentclass{article} \usepackage{xurl} \usepackage{hyperref} \usepackage{path} \begin{document} hello world!12\url{Receiver class org.springframework.cloud.netflix.ribbon.RibbonLoadBalancerClient does not define or inherit an implementation of the resolved method 'abstract org.springframework.cloud.client.ServiceInstance choose(java.lang.String, org.springframework.cloud.client.loadbalancer.Request)' of interface org.springframework.cloud.client.loadbalancer.ServiceInstanceChooser} \end{document} this is the result has no space: I also tried to use \href command, still did not work.

I sometimes want to put the content of a float on a page by itself and control the alignment in the usual type area. To do this, I use a minipage that has exactly the size \textwidth x \textheight. However, depending on the content (and the packages loaded), I get Float too large warnings. In the following example, both figures contain only a minipage with some text in them, the second one additionally has a footnote. For the first one I get a warning about the float being too large by 1.94397pt, for the second one by 2.85002pt. If I remove \usepackage[T1]{fontenc}, the first warning goes away, but the second stays. If I switch to LuaLaTeX, the first warning is back, this time about 2.06pt. Why does the minipage not perfectly fit the type area and how can I fix this? Why does it even depend on the minipage's content? I would have thought the whole point of a fixed-height minipage is that the height is, well, fixed. \documentclass{article} \usepackage[T1]{fontenc} \usepackage{lipsum} \begin{document} Hello World! \begin{figure}[p] \begin{minipage}[b][\textheight]{\textwidth} \lipsum[1] \end{minipage} \end{figure} \begin{figure}[p] \begin{minipage}[b][\textheight]{\textwidth} \lipsum[1]\footnote{test} \end{minipage} \end{figure} \end{document}

I need to put diagonal arrows under an equation (the red ones in the picture). I tried using \swarrow \qquad \searrow, but they are not positioned where I need them. I would prefer not to use tikzmark. Is there another way to achieve this? Thanks for your help. \documentclass[11pt,a4paper]{article} \usepackage[utf8]{inputenc} \usepackage[czech]{babel} \usepackage[T1]{fontenc} \usepackage{pgfplots} \usepackage{multicol,array,tabularx,xcolor,enumitem} \usepackage{amsmath,amsfonts,amssymb,mathrsfs} \pagestyle{empty} % % % % \definecolor{modra}{cmyk}{1,0,0,0} %%%%DEFINCIE%%%%%BARVY \definecolor{cerna}{cmyk}{0,0,0,1} \definecolor{bila}{cmyk}{0,0,0,0} % %\color{modra} % \begin{document} \begin{align*} S & = \rho \cdot \dfrac{a + b +c}{2} & S & = \dfrac{a \cdot b}{2} \\ \rho \cdot \dfrac{a + b +c}{2} & = \dfrac{a \cdot b}{2} \qquad | \cdot 2 & & \\ 18 (a +b+ c ) & = a \cdot b & a & = b \\ 18 (a + a + c ) & = a \cdot a & c^2 & = a^2 + b^2 \\ 18 (2a + c ) & = a^2 & c^2 & = a^2 + a^2 = 2a^2 \\ 36 a + 18 c & = a^2 & c & = \sqrt{2a^2} = a \sqrt{2} \\ 36 a + 18 a \sqrt{2} & = a^2 & & \\ a^2 - 36 a - 18 a \sqrt{2} & = 0 & & \\ a \left( a - 36 - 18 \sqrt{2} \right) & = 0 & & \\ \Large \swarrow \qquad \searrow \end{align*} % % \end{document}

My previous question's actual case is as below: In this YouTube link, it introduced a following nested integral question: Or the simpler the SAME one: The most important patterns, here, is described as below, the Recursive Formula: Now I have the following code: \documentclass[border=5pt]{standalone} \usepackage{amsmath} \usepackage{fourier} \usepackage{cmupint} \usepackage{fixdif} \parindent=0pt % \DeclareMathOperator{\myint}{\int\nolimits} \DeclareRobustCommand{\myint}{\int\nolimits} \newcommand{\basicint}{\myint_0^1xdx} \newcommand{\basicintt}{\myint_{\basicint}^{\basicint}xdx} % https://tex.stackexchange.com/a/5192/322482 \makeatletter \newcommand{\raisemath}[1]{\mathpalette{\raisem@th{#1}}} \newcommand{\raisem@th}[3]{\raisebox{#1}{$#2#3$}} \makeatother \newcommand{\originintunit}{% \displaystyle\myint_{ \textstyle\myint^{0}_{\basicintt} }^{ \textstyle\myint_{1}^{\basicintt} } }% \newcommand{\intunit}[2]{% \myint_{ \myint^{0}_{\myint_{#1}^{\basicint}xdx} }^{ \myint_{1}^{\myint_{\basicint}^{#2}xdx} } } \ExplSyntaxOn % \cs_generate_variant:Nn \tl_use:N {V} \tl_new:N \l_explorer_base_tl \tl_new:N \l_explorer_tmp_tl \tl_new:N \l_explorer_script_tl \tl_new:N \g_explorer_tmp_tl \cs_new_protected:Npn \typeset_integral_recursive:Nn #1#2 { % #1:tl to store % #2:depth \group_begin: \tl_set_eq:NN \l_explorer_tmp_tl #1 \int_compare:nNnTF { #2 } = { 1 } { \tl_put_right:Ne \l_explorer_tmp_tl { \intunit{\basicint}{\basicint} } } { \tl_clear:N \l_explorer_script_tl \typeset_integral_recursive:Nn \l_explorer_script_tl { \int_eval:n { #2 - 1 } } \tl_put_right:Ne \l_explorer_tmp_tl { \intunit{\l_explorer_script_tl}{\l_explorer_script_tl} } } \tl_put_right:Nn \l_explorer_tmp_tl { xdx } \tl_gset_eq:NN \g_explorer_tmp_tl \l_explorer_tmp_tl \group_end: \tl_set_eq:NN #1 \g_explorer_tmp_tl } % \typeset_integral_recursive:Nn \l_explorer_base_tl { 4 } \NewDocumentCommand{\explorerint}{ m }{ \begingroup \typeset_integral_recursive:Nn \l_explorer_base_tl { #1 } $\l_explorer_base_tl$ \endgroup } \ExplSyntaxOff \begin{document} \explorerint{3} \end{document} But it gives the following, with no tweak of the location of subscript and superscript. I don't think in this case, l3coffin could handle better than just recursion with l3tl, but it's not easy for me, now, to tweak the sub/superscript's position, and the \int's scale, to make the final result looks more like an \int "tower". Any suggestions or perspectives would be welcome! And IMO, this question, deserved my bounty😀. I would start one in three days.

Is there a way in TikZ or Lua to make a short function which converts letters to their corresponding alphabetical position (and vice versa)? The only way I can think of it so string check each letter, but that sounds too computationally expensive. M(non)WE: \documentclass[tikz,border=1cm]{standalone} \newcommand{\letterpos}[1]{ \pgfmathparse{#1 == a} \ifnum\pgfmathresult=1 1 \fi \pgfmathparse{#1 == ab} \ifnum\pgfmathresult=1 2 \fi \pgfmathparse{#1 == c} \ifnum\pgfmathresult=1 3 \fi \pgfmathparse{#1 == d} \ifnum\pgfmathresult=1 4 \fi \pgfmathparse{#1 == e} \ifnum\pgfmathresult=1 5 \fi } \begin{document} \begin{tikzpicture} \foreach \letter in {a,b,...,e} { \node at (\letterpos{\letter},0) {\letter}; } \end{tikzpicture} \end{document}