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diff --git a/Master/texmf-dist/doc/latex/unicode-math/um-doc-main.tex b/Master/texmf-dist/doc/latex/unicode-math/um-doc-main.tex new file mode 100644 index 00000000000..23d17472bb4 --- /dev/null +++ b/Master/texmf-dist/doc/latex/unicode-math/um-doc-main.tex @@ -0,0 +1,1207 @@ +%%^^A%% um-doc-main.tex -- part of UNICODE-MATH <wspr.io/unicode-math> + +\begin{abstract} +\noindent +This document describes the \pkg{unicode-math} package, which is +intended as an implementation of Unicode +maths for \LaTeX\ using the \XeTeX\ and Lua\TeX\ typesetting engines. +With this package, changing maths fonts is as easy as changing +text fonts --- and there are more and more maths fonts appearing now. +Maths input can also be simplified with Unicode since literal glyphs may be +entered instead of control sequences in your document source. + +The package provides support for both \XeTeX\ and Lua\TeX. The different +engines provide differing levels of support for Unicode maths. +Please let us know of any troubles. + +Alongside this documentation file, you should be able to find a minimal +example demonstrating the use of the package, +`\texttt{unimath-example.ltx}'. It also comes with a separate document, +`\texttt{unimath-symbols.pdf}', +containing a complete listing of mathematical symbols defined by +\pkg{unicode-math}, including comparisons between different fonts. + +Finally, while the STIX fonts may be used with this package, accessing +their alphabets in their `private user area' is not yet supported. +(Of these additional alphabets there is a separate caligraphic design +distinct to the script design already included.) +Better support for the STIX fonts is planned for an upcoming revision of the +package after any problems have been ironed out with the initial version. + +\end{abstract} + +\newpage +\tableofcontents + +\clearpage +\section{Introduction} + +This document describes the \pkg{unicode-math} package, which is an +\emph{experimental} implementation of a macro to Unicode glyph encoding for +mathematical characters. + +Users who desire to specify maths alphabets only (Greek and Latin letters, +and Arabic numerals) +may wish to use Andrew Moschou's \pkg{mathspec} package instead. +(\XeTeX-only at time of writing.) + +\section{Acknowledgements} + +Many thanks to: +Microsoft for developing the mathematics extension to OpenType as part of +Microsoft Office~2007; +Jonathan Kew for implementing Unicode math support in \XeTeX; +Taco Hoekwater for implementing Unicode math support in \LuaTeX; +Barbara Beeton for her prodigious effort compiling the definitive list of Unicode math +glyphs and their \LaTeX\ names (inventing them where necessary), and also +for her thoughtful replies to my sometimes incessant questions; +Philipp Stephani for extending the package to support \LuaTeX. +Ross Moore and Chris Rowley have provided moral and technical support +from the very early days with great insight into the issues we face trying +to extend and use \TeX\ in the future. +Apostolos Syropoulos, Joel Salomon, Khaled Hosny, and Mariusz Wodzicki +have been fantastic beta testers. + +\section{Getting started} + +Load \pkg{unicode-math} as a regular \LaTeX\ package. It should be loaded +after any other maths or font-related package in case it needs to overwrite +their definitions. Here's an example using the filename syntax to load the \TeX\ Gyre Pagella Math font: (this works for both \XeLaTeX\ and \LuaLaTeX) +\begin{Verbatim} +\usepackage{amsmath} % if desired +\usepackage{unicode-math} +\setmathfont{texgyrepagella-math.otf} +\end{Verbatim} + +Once the package is loaded, traditional TFM-based maths fonts are no longer supported; +you can only switch to a different OpenType maths font using the \cs{setmathfont} command. +If you do not load an OpenType maths font before |\begin{document}|, Latin Modern Math (see above) will be loaded automatically. + +\subsection{New commands} +\LaTeX, since the first version of \LaTeXe, changed the math group +selection from, say, |{\bf x}| to |\mathbf{x}|. It introduced commands +such as |\mathbf|, |\mathit|, |\mathsf|, |\mathtt| and |\mathcal|, +besides |\mathnormal|. This was not only done to maintain the analogy +with |\textbf|, |\textit| and so on, but with the precise purpose of +loading the needed math groups (or math families) on demand and not +allocating them if not required by the document. + +The introduction of \pkg{unicode-math} posed new problems. For +instance, there is a big difference between say |fit| as an operator +name in boldface type and the product of three boldface variables. +With legacy \TeX{} engines, |\mathbf{fit}| would use a ligature and +the same would happen with the input |\mathbf{f}\mathbf{i}\mathbf{t}|. +For the latter case, the user should probably use |\mathbf{f\/}|. + +However, there is another important point from a \emph{conceptual} +point of view. A boldface variable name should be printed using the +\emph{math font}, whereas a boldface operator name should be printed +using the \emph{text font}. OpenType math fonts make this distinction +feasible, because they contain several math alphabets. Of course a +boldface text~`x' will not differ much (or at all) from a boldface +math~`x', but this is not the point: they \emph{should} be considered +different, because the former is |U+0078| in Unicode, the latter is +|U+1D431|. + +It was clear that \emph{two} different commands are needed: one for using text boldface in math, +one for using math boldface. Only the document's author can know +whether one or the other is needed. The decision was to split off +the two meanings with a command like |\mathbf| for the boldface text font +in math and a command like |\symbf| (for the bold math font). + +The five new symbol font commands that behave in this way are: \cs{symup}, +\cs{symit}, \cs{symbf}, \cs{symsf}, and \cs{symit}. +These commands switch to single-letter mathematical symbols +(generally within the same OpenType font). + +The legacy \cs{math..} commands switch to text fonts that are set up to behave +correctly in mathematics, and should be used for multi-letter identifiers. These +could be denoted `text math alphabets'; further details are discussed +in \secref{mathselect}. Additional similar `text math alphabet' +commands can be defined using the \cs{setmathfontface} command +discussed in \secref{mathselect}. To control the behaviour of the +default text math alphabet commands to behave in a +backwards-compatible mode, see the package options described in +\secref{textmathlegacy}. + + +\begin{table}[t!] + \topcaption{New \pkg{unicode-math} commands which overlap with legacy + math commands. For new documents the \texttt{sym} versions are recommended.} + \tablabel{symvsmath} + \centering + \begin{tabular}[t]{ll} + \toprule + Command & Synonym \\ + \midrule + \cs{symnormal} & \cs{mathnormal} \\ + \cs{symliteral} & \\ + & \\ + & \\ + & \\ + \cs{symbb} & \cs{mathbb} \\ + \cs{symbbit} & \cs{mathbbit} \\ + \cs{symcal} & \cs{mathcal} \\ + \cs{symscr} & \cs{mathscr} \\ + \cs{symfrak} & \cs{mathfrak} \\ + \cs{symsfup} & \cs{mathsfup} \\ + \cs{symsfit} & \cs{mathsfit} \\ + \bottomrule + \end{tabular}\qquad + \begin{tabular}[t]{ll} + \toprule + Command & Synonym \\ + \midrule + & \\ + & \\ + \cs{symbfsf} & \cs{mathbfsf} \\ + \cs{symbfup} & \cs{mathbfup} \\ + \cs{symbfit} & \cs{mathbfit} \\ + & \\ + & \\ + \cs{symbfcal} & \cs{mathbfcal} \\ + \cs{symbfscr} & \cs{mathbfscr} \\ + \cs{symbffrak} & \cs{mathbffrak} \\ + \cs{symbfsfup} & \cs{mathbfsfup} \\ + \cs{symbfsfit} & \cs{mathbfsfit} \\ + \bottomrule + \end{tabular} +\end{table} + +In addition, \pkg{unicode-math} also provides a number of commands (such as +|\symcal|) to select specific `symbol alphabets' within the unicode +maths font, with usage, e.g., |$\symcal{G}$|${}\to\symcal{G}$. The +full listing is shown in \Tabref{symvsmath}. For backwards +compatibility, many of these are also defined with `familiar' synonyms +such as |\mathcal|. However, where possible the `sym' prefix +commands should be preferred, as certain synonyms may become +deprecated in time. The |\symliteral| command is described in +\secref{math-style}. + + +\subsection{Package options} +Package options may be set when the package as loaded or at any later +stage with the \cs{unimathsetup} command. Therefore, the following two +examples are equivalent: +\begin{Verbatim} +\usepackage[math-style=TeX]{unicode-math} +% OR +\usepackage{unicode-math} +\unimathsetup{math-style=TeX} +\end{Verbatim} +Note, however, that some package options affects how maths is initialised +and changing an option such as |math-style| will not take effect until a +new maths font is set up. + +Package options may \emph{also} be used when declaring new maths fonts, +passed via options to the \cs{setmathfont} command. +Therefore, the following two examples are equivalent: +\begin{Verbatim} +\unimathsetup{math-style=TeX} +\setmathfont{texgyrepagella-math.otf} +% OR +\setmathfont{texgyrepagella-math.otf}[math-style=TeX] +\end{Verbatim} + +A summary list of package options is shown in \tabref{pkgopt}. +See following sections for more information. + +\begin{table}\centering + \topcaption{Package options.} + \tablabel{pkgopt} + \begin{tabular}{lll} + \toprule + Option & Description & See\dots \\ + \midrule + |math-style| & Style of letters & \secref*{math-style} \\ + |bold-style| & Style of bold letters & \secref*{bold-style} \\ + |sans-style| & Style of sans serif letters & \secref*{sans-style} \\ + |nabla| & Style of the nabla symbol & \secref*{nabla} \\ + |partial| & Style of the partial symbol & \secref*{partial} \\ + |colon| & Behaviour of \cs{colon} & \secref*{colon} \\ + |slash-delimiter| & Glyph to use for `stretchy' slash & \secref*{slash-delimiter} \\ + \bottomrule + \end{tabular} +\end{table} + + +\section{Unicode maths font setup} + +In the ideal case, a single Unicode font will contain all maths glyphs we +need. The file |unicode-math-table.tex| (based on Barbara Beeton's \STIX\ table) +provides the mapping between Unicode +maths glyphs and macro names (all 3298 — or however many — of them!). A +single command +\codeline{\cmd\setmathfont\marg{font name}\oarg{font features}} +implements this for every every symbol and alphabetic variant. +That means |x| to $x$, |\xi| to $\xi$, |\leq| to $\leq$, etc., |\symscr{H}| +to $\symscr{H}$ and so on, all for Unicode glyphs within a single font. + +This package deals well with Unicode characters for maths +input. This includes using literal Greek letters in formulae, +resolving to upright or italic depending on preference. + +Font features specific to \pkg{unicode-math} are shown in \tabref{mathfontfeatures}. +Package options (see \tabref{pkgopt}) may also be used. +Other \pkg{fontspec} features are also valid. + +\begin{table}\centering + \topcaption{Maths font options.} + \tablabel{mathfontfeatures} + \begin{tabular}{lll} + \toprule + Option & Description & See\dots \\ + \midrule + |range| & Style of letters & \secref{range} \\ + |script-font| & Font to use for sub- and super-scripts & \secref{sscript} \\ + |script-features| & Font features for sub- and super-scripts & \secref{sscript} \\ + |sscript-font| & Font to use for nested sub- and super-scripts & \secref{sscript} \\ + |sscript-features| & Font features for nested sub- and super-scripts & \secref{sscript} \\ + \bottomrule + \end{tabular} +\end{table} + +\subsection{Using multiple fonts} +\seclabel{range} + +There will probably be few cases where a single Unicode maths font suffices +(simply due to glyph coverage). The \STIX\ font comes to mind as a +possible exception. It will therefore be necessary to delegate specific +Unicode ranges of glyphs to separate fonts: + \codeline{\cmd\setmathfont\marg{font name}|[range=|\meta{unicode range}|,|\meta{font features}|]|} +where \meta{unicode range} is a comma-separated list of Unicode slot numbers and ranges such as |{"27D0-"27EB,"27FF,"295B-"297F}|. +Note that \TeX's syntax for accessing the slot number of a character, such as |`\+|, will also work here. +Only numerical slots can be used in ranged declarations. + +You may also use the macro for accessing the glyph, such as |range=|\cs{int}, or whole collection of symbols with the same math type, such as |range=\mathopen|, or complete math styles such as |range=\symbb| (or just |range=bb|). + +\subsubsection{Control over alphabet ranges} + +As discussed earlier, Unicode mathematics consists of a number of `alphabet styles' within a single font. In \pkg{unicode-math}, these ranges are indicated with the following (hopefully self-explanatory) labels: +\begin{quote}\ttfamily +\ExplSyntaxOn +\clist_const:Nn \g__um_named_ranges_clist { +up , +it , +bb , +bbit , +scr , +cal , +bfcal , +frak , +tt , +sfup , +sfit , +bfup , +bfit , +bfscr , +bffrak, +bfsfup, +bfsfit, +} +\clist_use:Nn \g__um_named_ranges_clist {\,,\,~} +\ExplSyntaxOff +\end{quote} +Fonts can be selected (for predefined ranges only) using the following syntax, in which case all other maths font setup remains untouched: +\begin{itemize} +\item |[range=bb]| to use the font for `|bb|' letters only. +\item |[range=bfsfit/{greek,Greek}]| for Greek lowercase and uppercase only (also with |latin|, |Latin|, |num| as possible options for Latin lower-/upper-case and numbers, resp.). +\item |[range=up->sfup]| to map to different output styles. +\end{itemize} + +A common request is to load numerals only from a specific font. This can be +achieved with an option such as |range=up/{num}|. + +Note that `meta-styles' such as `|bf|' and `|sf|' are not included in the list above since they are context dependent. Use |[range=bfup]| and |[range=bfit]| to effect changes to the particular ranges selected by `|bf|' (and similarly for `|sf|'). + +If a particular math style is not defined in the font, we fall back onto the lower-base plane (i.e., `upright') glyphs. +Therefore, to use an \ascii-encoded fractur font, for example, write +\begin{Verbatim} + \setmathfont{SomeFracturFont}[range=frak] +\end{Verbatim} +and because the math plane fractur glyphs will be missing, \pkg{unicode-math} will know to use the \ascii\ ones instead. +If necessary this behaviour can be forced with |[range=frak->up]|, since the `|up|' range corresponds to \ascii\ letters. + +%If you wanted to swap the maths symbols with sans serif forms, it would be possible to write |[range={up->sfup,it->sfit}]|. +%Note, however, that at present Unicode does not encode glyphs for sans serif Greek (\tabref{mathalphabets}). + +Users of the impressive Minion Math fonts (commercial) may use remapping to access the bold glyphs using: +\begin{Verbatim} + \setmathfont{MinionMath-Regular.otf} + \setmathfont{MinionMath-Bold.otf}[range={bfup->up,bfit->it}] +\end{Verbatim} +To set up the complete range of optical sizes for these fonts, a font declaration such as the following may be used: (adjust may be desired according to the font size of the document) +\begin{Verbatim} +\setmathfont{Minion Math}[ + SizeFeatures = { + {Size = -6.01, Font = MinionMath-Tiny}, + {Size = 6.01-8.41, Font = MinionMath-Capt}, + {Size = 8.41-13.01, Font = MinionMath-Regular}, + {Size = 13.01-19.91, Font = MinionMath-Subh}, + {Size = 19.91-, Font = MinionMath-Disp} + }] + +\setmathfont{Minion Math}[range = {bfup->up,bfit->it}, + SizeFeatures = { + {Size = -6.01, Font = MinionMath-BoldTiny}, + {Size = 6.01-8.41, Font = MinionMath-BoldCapt}, + {Size = 8.41-13.01, Font = MinionMath-Bold}, + {Size = 13.01-19.91, Font = MinionMath-BoldSubh}, + {Size = 19.91-, Font = MinionMath-BoldDisp} + }] +\end{Verbatim} + + +\subsection{Script and scriptscript fonts/features} +\seclabel{sscript} + +Cambria Math uses OpenType font features to activate smaller optical sizes +for scriptsize and scriptscriptsize symbols (the $B$ and $C$, respectively, +in $A_{B_C}$). +Other typefaces (such as Minion Math) may use entirely separate font files. + +The features |script-font| and |sscript-font| allow alternate fonts to be +selected for the script and scriptscript sizes, and |script-features| and +|sscript-features| to apply different OpenType features to them. + +By default |script-features| is defined as |Style=MathScript| and |sscript-features| is |Style=MathScriptScript|. +These correspond to the two levels of OpenType's |ssty| feature tag. +If the |(s)script-features| options are specified manually, you must +additionally specify the |Style| options as above. + + +\subsection{Maths `versions'} + +\LaTeX\ uses a concept known as `maths versions' to switch math fonts +mid-document. +This is useful because it is more efficient than loading a complete maths +font from scratch every time---especially with thousands of glyphs in the case of Unicode maths! +The canonical example for maths versions is to select a `bold' maths font +which might be suitable for section headings, say. +(Not everyone agrees with this typesetting choice, though; be careful.) + +To select a new maths font in a particular version, use the syntax + \codeline{\cmd\setmathfont\marg{font name}|[version=|\meta{version name}|,|\meta{font features}|]|} +and to switch between maths versions mid-document use the standard \LaTeX\ command +\cmd\mathversion\marg{version name}. + +Note there are currently open issues regarding the interaction between the |version| +and the |range| features, so please proceed with caution. + +\subsection{Legacy maths `alphabet' commands} +\seclabel{mathselect} + +\LaTeX\ traditionally uses \cs{DeclareMathAlphabet} and \cs{SetMathAlphabet} to define document commands such as \cs{mathit}, \cs{mathbf}, and so on. +While these commands can still be used, \pkg{unicode-math} defines a wrapper command to assist with the creation of new such maths alphabet commands. +This command is known as \cs{setmathface} in symmetry with \pkg{fontspec}'s \cs{newfontface} command; it takes syntax: +\begin{quote} + \cmd\setmathfontface\meta{command}\marg{font name}|[|\meta{font features}|]| + + \makebox[0pt][l]{\cmd\setmathfontface\meta{command}\marg{font name}|[||version=|\meta{version name}|,|\meta{font features}|]|} +\end{quote} +For example, if you want to define a new legacy maths alphabet font \cs{mathittt}: +\begin{verbatim} + \setmathfontface\mathittt{texgyrecursor-italic.otf} + ... + $\mathittt{foo} = \mathittt{a} + \mathittt{b}$ +\end{verbatim} + + +\subsubsection{Default `text math' fonts} + +The five `text math' fonts, discussed above, are: \cs{mathrm}, \cs{mathbf}, \cs{mathit}, \cs{mathsf}, and \cs{mathtt}. +These commands are also defined with their original definition under synonyms \cs{mathtextrm}, \cs{mathtextbf}, and so on. +(These definitions hold regardless of package option, in case you need to be sure.) + +When selecting document fonts using \pkg{fontspec} commands such as \cs{setmainfont}, \pkg{unicode-math} inserts some additional code into \pkg{fontspec} that keeps the current default fonts `in sync' with their corresponding \cs{mathrm} commands, etc. + +For example, in standard \LaTeX, \cs{mathsf} doesn't change even if the main document font is changed using |\renewcommand\sfdefault{...}|. With \pkg{unicode-math} loaded, after writing |\setsansfont{Helvetica}|, \cs{mathsf} will now be set in Helvetica. + +If the \cs{mathsf} font is set explicitly at any time in the preamble, this `auto-following' does not occur. The legacy math font switches can be defined either with commands defined by \pkg{fontspec} (|\setmathrm|, |\setmathsf|, etc.) or using the more general |\setmathfontface\mathsf| interface defined by \pkg{unicode-math}. + + +\subsubsection{Replacing `text math' fonts by symbols} +\seclabel{textmathlegacy} + +For certain types of documents that use legacy input syntax, it may be preferable to have |\mathbf| behave as if it were |\symbf| en masse (et cetera respectively). +A series of package options (\tabref{legacyfontswitch}) are provided to facilitate switching the definition of \cs{mathXYZ} for the five legacy text math font definitions. + +For example, if in a particular document |\mathbf| is used only for choosing symbols of vectors and matrices, a dedicated symbol font (|\symbf|) will produce better spacing and will better match the main math font. +In that case loading |unicode-math| with the |mathbf=sym| will achieve the desired result. + +\begin{table} + \centering + \topcaption{Maths text font configuration options. Note that \cs{mathup} and \cs{mathrm} are aliases of each other and cannot be configured separately.} + \tablabel{legacyfontswitch} + \begin{tabular}{lll} + \toprule + Defaults (from `text' font) & From `maths symbols' \\ + \midrule + |mathrm=text| & |mathrm=sym | \\ + |mathup=text|\rlap{$^\ast$} & |mathup=sym|{}\rlap{$^\ast$} \\ + |mathit=text| & |mathit=sym | \\ + |mathsf=text| & |mathsf=sym | \\ + |mathbf=text| & |mathbf=sym | \\ + |mathtt=text| & |mathtt=sym | \\ + \bottomrule + \end{tabular} +\end{table} + + +\subsubsection{Operator font} + +\LaTeX\ defines an internal command \cs{operator@font} for typesetting elements such as |\sin| and |\cos|. +This font is selected from the legacy |operators| NFSS `MathAlphabet', which is no longer relevant in the context of \pkg{unicode-math}. +By default, the \cs{operator@font} command is defined to switch to the \cs{mathrm} font. +You may now change these using the command: +\begin{Verbatim} +\setoperatorfont\mathit +\end{Verbatim} +Or, to select a \pkg{unicode-math} range: +\begin{Verbatim} +\setoperatorfont\symscr +\end{Verbatim} +\setoperatorfont\symscr +For example, after the latter above, |$\sin x$| will produce `$\sin x$'. + +\mathversion{normal} +\setoperatorfont\mathrm + + +\section{Maths input} + +\XeTeX's Unicode support allows maths input through two methods. Like +classical \TeX, macros such as \cmd\alpha, \cmd\sum, \cmd\pm, \cmd\leq, and +so on, provide verbose access to the entire repertoire of characters defined +by Unicode. The literal characters themselves may be used instead, for more +readable input files. + +\subsection{Math `style'} +\seclabel{math-style} + +Classically, \TeX\ uses italic lowercase Greek letters and \emph{upright} +uppercase Greek letters for variables in mathematics. This is contrary to +the \textsc{iso} standards of using italic forms for both upper- and lowercase. +Furthermore, in various historical contexts, often associated with French typesetting, it was common to use upright uppercase \emph{Latin} letters as well as upright +upper- and lowercase Greek, but italic lowercase latin. Finally, it is not unknown to use upright letters +for all characters, as seen in the Euler fonts. + +The \pkg{unicode-math} package accommodates these possibilities with the +option \opt{math-style} that takes one of four (case sensitive) arguments: +\opt{TeX}, \opt{ISO}, \opt{french}, or \opt{upright}.\footnote{Interface inspired by Walter Schmidt's \pkg{lucimatx} package.} +The \opt{math-style} options' effects are shown in brief in \tabref{math-style}. + +The philosophy behind the interface to the mathematical symbols +lies in \LaTeX's attempt of separating content and formatting. Because input +source text may come from a variety of places, the upright and +`mathematical' italic Latin and Greek alphabets are \emph{unified} from the +point of view of having a specified meaning in the source text. That is, to +get a mathematical ‘$x$’, either the \ascii\ (`keyboard') letter |x| may +be typed, or the actual Unicode character may be used. Similarly for Greek +letters. The upright or italic forms are then chosen based on the +|math-style| package option. + +If glyphs are desired that do not map as per the package option (for +example, an upright `g' is desired but typing |$g$| yields `$g$'), +\emph{markup} is required to specify this; to follow from the example: +|\symup{g}|. +Maths style commands such as \cmd\symup\ are detailed later. + +For compatibility and consistency, however, upright and italic Greek letters +can be `forced` using \verb|up| or \verb|it| prefixes before their names. +For example, \cs{Gamma} will give an upright or italic Gamma depending on the +\opt{math-style}, but \cs{upGamma} and \cs{itGamma} will always give upright +or italic Gammas, respectively. + +\paragraph{`Literal' interface} +Some may not like this convention of normalising their input. +For them, an upright |x| is an upright `x' and that's that. +(This will be the case when obtaining source text from copy/pasting PDF or +Microsoft Word documents, for example.) +For these users, the |literal| option to |math-style| will effect this behaviour. +The \cs{symliteral}\marg{syms} command can also be used, regardless of package setting, to force the style to match the literal input characters. +This is a `mirror' to \cs{symnormal}\marg{syms} (also alias \cs{mathnormal}) which `resets' the character mapping in its argument to that originally set up through package options. + + +\begin{table} + \centering + \topcaption{Effects of the \opt{math-style} package option.} + \tablabel{math-style} + \begin{tabular}{@{}>{\ttfamily}lcc@{}} + \toprule + & \multicolumn{2}{c}{Example} \\ + \cmidrule(l){2-3} + \rmfamily Package option & Latin & Greek \\ + \midrule + math-style=ISO & $(a,z,B,X)$ & $\symit{(\alpha,\beta,\Gamma,\Xi)}$ \\ + math-style=TeX & $(a,z,B,X)$ & $(\symit\alpha,\symit\beta,\symup\Gamma,\symup\Xi)$ \\ + math-style=french & $(a,z,\symup B,\symup X)$ & $(\symup\alpha,\symup\beta,\symup\Gamma,\symup\Xi)$ \\ + math-style=upright & $(\symup a,\symup z,\symup B,\symup X)$ & $(\symup\alpha,\symup\beta,\symup\Gamma,\symup\Xi)$ \\ + \bottomrule + \end{tabular} +\end{table} + +\paragraph{`Full-width' letters} +Unicode contains `full-width' versions of ASCII from \unichar{FF01}. +The numerals and latin letters in this range are defined by \pkg{unicode-math} +to map to their standard ASCII counterparts, which are then controlled by the relevant \opt{math-style} setting. +Other full-width symbols are not currently included but can be if there is sufficient need or desire. + +\subsection{Bold style} +\seclabel{bold-style} + +Similar as in the previous section, ISO standards differ somewhat to \TeX's +conventions (and classical typesetting) for `boldness' in mathematics. In +the past, it has been customary to use bold \emph{upright} letters to denote +things like vectors and matrices. For example, \( \symbfup{M} = +(\mitM_x,\mitM_y,\mitM_z) \). Presumably, this was due to the relatively +scarcity of bold italic fonts in the pre-digital typesetting era. +It has been suggested by some that \emph{italic} bold symbols should be used nowadays instead, but this practise is certainly not widespread. + +Bold Greek letters have simply been bold variant glyphs of their regular +weight, as in \( \mbfitxi = (\mitxi_\mitr,\mitxi_\mitphi,\mitxi_\mittheta) +\). +Confusingly, the syntax in \LaTeX\ traditionally has been different for obtaining `normal' bold symbols in Latin and Greek: \cmd\mathbf\ in the former (`$\symbfup{M}$'), and \cmd\bm\ (or +\cmd\boldsymbol, deprecated) in the latter (`$\mbfitxi$'). + +In \pkg{unicode-math}, the \cmd\symbf\ command works directly with both +Greek and Latin maths characters and depending on package option +either switches to upright for Latin letters (|bold-style=TeX|) as well or +keeps them italic (|bold-style=ISO|). +To match the package options for non-bold characters, with option +|bold-style=upright| all bold characters are upright, and +|bold-style=literal| does not change the upright/italic shape of the letter. +The \opt{bold-style} options' effects are shown in brief in \tabref{bold-style}. + +Upright and italic bold mathematical letters input as direct Unicode +characters are normalised with the same rules. For example, with +|bold-style=TeX|, a literal bold italic latin character will be typeset +upright. + +Note that \opt{bold-style} is independent of \opt{math-style}, although if +the former is not specified then matching defaults are chosen based on the +latter. + +\begin{table} + \centering + \topcaption{Effects of the \opt{bold-style} package option.} + \tablabel{bold-style} + \begin{tabular}{@{}>{\ttfamily}lcc@{}} + \toprule + & \multicolumn{2}{c}{Example} \\ + \cmidrule(l){2-3} + \rmfamily Package option & Latin & Greek \\ + \midrule + bold-style=ISO & $(\symbfit a, \symbfit z, \symbfit B, \symbfit X)$ & $(\symbfit\alpha, \symbfit\beta, \symbfit\Gamma, \symbfit\Xi)$ \\ + bold-style=TeX & $(\symbfup a,\symbfup z,\symbfup B,\symbfup X)$ & $(\symbfit\alpha, \symbfit\beta,\symbfup \Gamma,\symbfup \Xi)$ \\ + bold-style=upright & $(\symbfup a,\symbfup z,\symbfup B,\symbfup X)$ & $(\symbfup \alpha,\symbfup \beta,\symbfup \Gamma,\symbfup \Xi)$ \\ + \bottomrule + \end{tabular} +\end{table} + + +\subsection{Sans serif style} +\seclabel{sans-style} + +Unicode contains upright and italic, medium and bold mathematical style characters. +These may be explicitly selected with the \cs{symsfup}, \cs{symsfit}, \cs{symbfsfup}, and \cs{symbfsfit} +commands discussed in \secref{all-math-alphabets}. + +How should the generic \cs{symsf} behave? Unlike bold, sans serif is used much more sparingly +in mathematics. I've seen recommendations to typeset tensors in sans serif italic +or sans serif italic bold (e.g., examples in the \pkg{isomath} and \pkg{mattens} packages). +But \LaTeX's \cs{mathsf} is \textsl{upright} sans serif. + +Therefore, the package options |[sans-style=upright]| and |[sans-style=italic]| control the behaviour of \cs{symsf}. +The |upright| style sets up the command to use upright sans serif, including Greek; +the |italic| style switches to using italic in both Latin and Greek. +In other words, this option simply changes the meaning of \cs{symsf} to either \cs{symsfup} or \cs{symsfit}, respectively. +Please let me know if more granular control is necessary here. + +There is also a |[sans-style=literal]| setting, set automatically with |[math-style=literal]|, which retains the uprightness of the input characters used when selecting the sans serif output. + +\subsubsection{What about bold sans serif?} + +While you might want your bold upright and your sans serif italic, I don't believe you'd also want your bold sans serif upright (etc.). +Therefore, bold sans serif follows from the setting for sans serif; it is completely independent of the setting for bold. + +In other words, \cs{symbfsf} is either \cs{symbfsfup} or \cs{symbfsfit} based on |[sans-style=upright]| or |[sans-style=italic]|, respectively. And \texttt{[sans-style = literal]} causes \cs{symbfsf} to retain the same italic or upright shape as the input, and turns it bold sans serif. + +N.B.: there is no medium-weight sans serif Greek range in Unicode. +Therefore, |\symsf{\alpha}| does not make sense (it produces `$\symsf{\alpha}$'), while |\symbfsf{\alpha}| gives `$\symbfsfup{\alpha}$' or `$\symbfsfit{\alpha}$' according to the |sans-style|. + +\subsection{All (the rest) of the mathematical styles} +\seclabel{all-math-alphabets} + +Unicode contains separate codepoints for most if not all variations of style +shape one may wish to use in mathematical notation. The complete list is shown +in \tabref{mathalphabets}. Some of these have been covered in the previous sections. + +The math font switching commands do not nest; therefore if you want +sans serif bold, you must write |\symbfsf{...}| rather than |\symbf{\symsf{...}}|. +This may change in the future. + +\begin{table} +\caption{Mathematical styles defined in Unicode. Black dots indicate an style exists in the font specified; blue dots indicate shapes that should always be taken from the upright font even in the italic style. See main text for description of \cs{mathbbit}.} +\tablabel{mathalphabets} +\centering +\def\Y{\textbullet} +\def\M{\textcolor[rgb]{0.5,0.5,1}{\textbullet}} +\begin{tabular}{@{} lll l ccc @{}} +\toprule +\multicolumn{3}{c}{Font} & & \multicolumn{3}{c}{Alphabet} \\ +\cmidrule(r){1-3} +\cmidrule(l){5-7} +Style & Shape & Series & Switch & Latin & Greek & Numerals \\ +\midrule +Serif & Upright & Normal & \cs{symup} & \Y & \Y & \Y \\ + & & Bold & \cs{symbfup} & \Y & \Y & \Y \\ + & Italic & Normal & \cs{symit} & \Y & \Y & \M \\ + & & Bold & \cs{symbfit} & \Y & \Y & \M \\ +Sans serif & Upright & Normal & \cs{symsfup} & \Y & & \Y \\ + & Italic & Normal & \cs{symsfit} & \Y & & \M \\ + & Upright & Bold & \cs{symbfsfup} & \Y & \Y & \Y \\ + & Italic & Bold & \cs{symbfsfit} & \Y & \Y & \M \\ +Typewriter & Upright & Normal & \cs{symtt} & \Y & & \Y \\ +Double-struck & Upright & Normal & \cs{symbb} & \Y & & \Y \\ + & Italic & Normal & \cs{symbbit} & \Y & & \\ +Script & Upright & Normal & \cs{symscr} & \Y & & \\ + & & Bold & \cs{symbfscr} & \Y & & \\ +Fraktur & Upright & Normal & \cs{symfrak} & \Y & & \\ + & & Bold & \cs{symbffrac} & \Y & & \\ +\bottomrule +\end{tabular} +\end{table} + +\subsubsection{Scope of the functionality of the \cs{sym..} commands} + +The \cs{sym..} commands are designed to affect only the follow sets of input letters: numerals ($0$--$9$), Latin ($a$--$z$, $A$--$Z$), Greek ($\alpha$--$\omega$, $\Alpha$--$\Omega$,), and the \cs{partial} and \cs{nabla} symbols ($\partial$, $\nabla$). +These are the only symbols for which Unicode defines separate codepoints with varying mathematical style. + +There is currently no scope for including other symbols in the \cs{sym..} commands, such as writing |\symbf{\int}| for a bold integral symbol. +Therefore the commands provided by \pkg{unicode-math} should not be compared to those provided by the \pkg{bm} package. + +\subsubsection{Double-struck} + +The double-struck style (also known as `blackboard bold') consists of +upright Latin letters $\{\symbb{a}$--$\symbb{z}$,$\symbb{A}$$\symbb{Z}\}$, +numerals $\symbb{0}$--$\symbb{9}$, summation symbol $\symbb\sum$, and four +Greek letters only: $\{\symbb{\gamma\pi\Gamma\Pi}\}$. + +While |\symbb{\sum}| does produce a double-struck summation symbol, +its limits aren't properly aligned. Therefore, +either the literal character or the control sequence \cs{Bbbsum} are +recommended instead. + +There are also five Latin \emph{italic} double-struck letters: $\symbbit{Ddeij}$. +These can be accessed (if not with their literal characters or control sequences) +with the \cs{mathbbit} style switch, but note that only those five letters +will give the expected output. + +\subsubsection{Caligraphic vs.\ Script variants} + +The Unicode maths encoding contains a style for `Script' letters, +and while by default \cs{mathcal} and \cs{mathscr} +are synonyms, there are some situations when a +separate `Caligraphic' style is needed as well. + +If a font contains alternate glyphs for a separat caligraphic style, +they can be selected explicitly as shown below. +This feature is currently only supported by the XITS~Math font, where +the caligraphic letters are accessed with the same glyph slots as the +script letters but with the first stylistic set feature (|ss01|) applied. +\begin{verbatim} + \setmathfont{xits-math.otf}[range={cal,bfcal},StylisticSet=1] +\end{verbatim} +An example is shown below. +\begin{quote} +\setmathfont{xits-math.otf}[range=scr] +\setmathfont{xits-math.otf}[range=cal,StylisticSet=1] +The Script style (\cs{mathscr}) in XITS Math is: $\symscr{ABCXYZ}$\par +The Caligraphic style (\cs{mathcal}) in XITS Math is: $\symcal{ABCXYZ}$ +\end{quote} + + +\subsection{Miscellanea} + +\subsubsection{Nabla} +\seclabel{nabla} + + The symbol $\nabla$ comes in the six forms shown in \tabref{nabla}. + We want an individual option to specify whether we want upright or italic + nabla by default (when either upright or italic nabla is used in the + source). \TeX\ classically uses an upright nabla, and \textsc{iso} + standards agree with this convention. + The package options |nabla=upright| (default) and + |nabla=italic| switch between the two choices, and |nabla=literal| respects + the shape of the input character. +|nabla=literal| is activated automatically after |math-style=literal|. + +These settings are then inherited through \cmd\symbf; \cmd\symit\ and \cmd\symup\ can be used to force the shape of the nabla one way or the other. + + +\begin{table} + \begin{minipage}[b]{0.49\textwidth} + \centering + \topcaption{The various forms of nabla.} + \tablabel{nabla} + \let \tmpshow\empty + \begin{tabular}{@{}llc@{}} + \toprule + \multicolumn{2}{@{}l}{Description} & Glyph \\ + \cmidrule(r){1-2}\cmidrule(l){3-3} + Upright & Serif & $\symup\nabla$ \\ + & Bold serif & $\symbfup\nabla$ \\ + & Bold sans & $\symbfsfup\nabla$ \\ + \cmidrule(lr){1-2}\cmidrule(lr){3-3} + Italic & Serif & $\symit\nabla$ \\ + & Bold serif & $\symbfit\nabla$ \\ + & Bold sans & $\symbfsfit\nabla$ \\ + \bottomrule + \end{tabular} + \end{minipage}\hfill + \begin{minipage}[b]{0.49\textwidth} + \centering + \topcaption{The partial differential.} + \tablabel{partial} + \begin{tabular}{@{}llc@{}} + \toprule + \multicolumn{2}{@{}l}{Description} & Glyph \\ + \cmidrule(r){1-2}\cmidrule(l){3-3} + Regular & Upright & $\symup\partial$ \\ + & Italic & $\symit\partial$ \\ + Bold & Upright & $\symbfup\partial$ \\ + & Italic & $\symbfit\partial$ \\ + Sans bold & Upright & $\symbfsfup\partial$ \\ + & Italic & $\symbfsfit\partial$ \\ + \bottomrule + \end{tabular} + \end{minipage} +\end{table} + + +\subsubsection{Partial} +\seclabel{partial} + +The same logic as for nabla applies to the symbols \unichar{2202} partial differential and \unichar{1D715} math italic partial differential. +However, in practice these symbols are often designed identically in an italic style. + +If the font you are using supports it, use the |partial=upright| or |partial=italic| (default) package options to specify +which one you would like, or |partial=literal| to have the same character +used in the output as was used for the input. +|partial=literal| is activated following |math-style=literal|. + +See \tabref{partial} for the variations on the partial differential symbol. + + +\subsubsection{Primes} + +Primes ($x'$) may be input in several ways. You may use any combination +the \ascii\ straight quote (\texttt{\char`\'}) or the Unicode prime \unichar{2032} +($'$); when multiple primes occur next to each other, they chain +together to form double, triple, or quadruple primes if the font contains +pre-drawn glyphs. The individual prime glyphs are accessed, as usual, +with the \cs{prime} command, and the double-, triple-, and quadruple-prime +glyphs are available with \cs{dprime}, \cs{trprime}, and \cs{qprime}, +respectively. + +If the font does not contain the pre-drawn glyphs or more than four primes +are used, the single prime glyph is used multiple times with a negative +kern to get the spacing right. There is no user interface to adjust this +negative kern yet (because I haven't decided what it should look like); +if you need to, write something like this: +\begin{Verbatim} +\ExplSyntaxOn +\muskip_gset:Nn \g_@@_primekern_muskip { -\thinmuskip/2 } +\ExplySyntaxOff +\end{Verbatim} +Backwards or reverse primes behave in exactly the same way; use the \ascii\ +back tick (\texttt{\char`\`}) or the Unicode reverse prime \unichar{2035} +({\umfont\char"2035}). +The command to access the backprime is \cs{backprime}, and +multiple backwards primes can accessed with \cs{backdprime}, +\cs{backtrprime}, and \cs{backqprime}. + +In all cases above, no error checking is performed if you attempt to +access a multi-prime glyph in a font that doesn't contain one. For this +reason, it may be safer to write |x''''| instead of |x\qprime| +in general. + +If you ever need to enter the straight quote |'| or the backtick |`| in +maths mode, these glyphs can be accessed with \cs{mathstraightquote} and +\cs{mathbacktick}. + +\subsubsection{Unicode subscripts and superscripts} + +You may, if you wish, use Unicode subscripts and superscripts in your +source document. For basic expressions, the use of these characters +can make the input more readable. +Adjacent sub- or super-scripts will be concatenated into a single +expression. + +The range of subscripts and superscripts supported by this package +are shown in \figref{superscripts,subscripts}. Please request more if +you think it is appropriate. + +\begin{figure}\centering +\fbox{\fontspec{CharisSILR.ttf}\Large +A +^^^^2070 ^^^^00b9 ^^^^00b2 ^^^^00b3 ^^^^2074 ^^^^2075 ^^^^2076 ^^^^2077 +^^^^2078 ^^^^2079 ^^^^207a ^^^^207b ^^^^207c ^^^^207d ^^^^207e ^^^^2071 +^^^^207f ^^^^207f ^^^^02b0 ^^^^02b2 ^^^^02b3 ^^^^02b7 ^^^^02b8 +Z} +\caption{ + The Unicode superscripts supported as input characters. + These are the literal glyphs from Charis SIL, + not the output seen when used for maths input. + The `A' and `Z' are to provide context for the size and + location of the superscript glyphs. +} +\figlabel{superscripts} +\end{figure} + +\begin{figure}\centering +\fbox{\fontspec{CharisSILR.ttf}\Large +A +^^^^2080 ^^^^2081 ^^^^2082 ^^^^2083 ^^^^2084 ^^^^2085 ^^^^2086 ^^^^2087 +^^^^2088 ^^^^2089 ^^^^208a ^^^^208b ^^^^208c ^^^^208d ^^^^208e ^^^^2090 +^^^^2091 ^^^^1d62 ^^^^2092 ^^^^1d63 ^^^^1d64 ^^^^1d65 ^^^^2093 ^^^^1d66 +^^^^1d67 ^^^^1d68 ^^^^1d69 ^^^^1d6a +Z} +\caption{ + The Unicode subscripts supported as input characters. + See note from \figref{superscripts}. +} +\figlabel{subscripts} +\end{figure} + +\subsubsection{Colon} +\seclabel{colon} + +The colon is one of the few confusing characters of Unicode maths. +In \TeX, \texttt{:} is defined as a colon with relation spacing: `$a:b$'. +While \cs{colon} is defined as a colon with punctuation spacing: `$a\colon b$'. + +In Unicode, \unichar{003A} {colon} is defined as a punctuation symbol, +while \unichar{2236} {ratio} is the colon-like symbol used in mathematics to denote +ratios and other things. + +This breaks the usual straightforward mapping from control sequence to Unicode input character +to (the same) Unicode glyph. + +To preserve input compatibility, we remap the \ascii\ input character `\texttt{:}' to \unichar{2236}. +Typing a literal \unichar{2236} char will result in the same output. +If \pkg{amsmath} is loaded, then the definition of \cs{colon} is inherited from there +(it looks like a punctuation colon with additional space around it). +Otherwise, \cs{colon} is made to output a colon with \cs{mathpunct} spacing. + +The package option |colon=literal| forces \ascii\ input `|:|' to be printed as \cs{mathcolon} instead. + + +\subsubsection{Slashes and backslashes} +\seclabel{slash-delimiter} + +There are several slash-like symbols defined in Unicode. The complete list is shown in \tabref{slashes}. + +\begin{table}\centering +\caption{Slashes and backslashes.} +\tablabel{slashes} +\begin{tabular}{@{}cl@{}cl@{}} +\toprule +Slot & Name & Glyph & Command \\ +\midrule +\unichar{002F} & \textsc{solidus} & \umfont \char"002F & \cs{slash} \\ +\unichar{2044} & \textsc{fraction slash} & \umfont \char"2044 & \cs{fracslash} \\ +\unichar{2215} & \textsc{division slash} & \umfont \char"2215 & \cs{divslash} \\ +\unichar{29F8} & \textsc{big solidus} & \umfont \char"29F8 & \cs{xsol} \\ +\midrule +\unichar{005C} & \textsc{reverse solidus} & \umfont \char"005C & \cs{backslash} \\ +\unichar{2216} & \textsc{set minus} & \umfont \char"2216 & \cs{smallsetminus} \\ +\unichar{29F5} & \textsc{reverse solidus operator}& \umfont \char"29F5 & \cs{setminus} \\ +\unichar{29F9} & \textsc{big reverse solidus} & \umfont \char"29F9 & \cs{xbsol} \\ +\bottomrule +\end{tabular} +\end{table} + +In regular \LaTeX\ we can write \cs{left}\cs{slash}\dots\cs{right}\cs{backslash} +and so on and obtain extensible delimiter-like symbols. Not all of the Unicode slashes +are suitable for this (and do not have the font support to do it). + +\paragraph{Slash} + +Of \unichar{2044} {fraction slash}, TR25 says that it is: +\begin{quote} +\dots used to build up simple fractions in running text\dots +however parsers of mathematical texts should be prepared to handle fraction slash +when it is received from other sources. +\end{quote} + +\unichar{2215} {division slash} should be used when division is represented +without a built-up fraction; $\pi\approx22/7$, for example. + +\unichar{29F8} {big solidus} is a `big operator' (like $\sum$). + +\paragraph{Backslash} + +The \unichar{005C} {reverse solidus} character \cs{backslash} is used for denoting +double cosets: $A\backslash B$. (So I'm led to believe.) +It may be used as a `stretchy' delimiter if supported by the font. + +MathML uses \unichar{2216} {set minus} like this: $A\smallsetminus B$.\footnote{\S4.4.5.11 \url{http://www.w3.org/TR/MathML3/}} +The \LaTeX\ command name \cs{smallsetminus} is used for backwards compatibility. + +Presumably, \unichar{29F5} {reverse solidus operator} is intended to +be used in a similar way, but it could also (perhaps?) be used to +represent `inverse division': $\pi\approx7\mathbin{\backslash}22$.^^A +\footnote{This is valid syntax in the Octave and Matlab programming languages, +in which it means matrix inverse pre-multiplication. I.e., $A\mathbin{\backslash} B\equiv A^{-1}B$.} +The \LaTeX\ name for this character is \cs{setminus}. + +Finally, \unichar{29F9} {big reverse solidus} is a `big operator' (like $\sum$). + +\paragraph{How to use all of these things} + +Unfortunately, font support for the above characters/glyphs is rather inconsistent. +In Cambria Math, the only slash that grows (say when writing +\[ +\left.\left[\begin{array}{cc} a & b \\ c & d\end{array}\right]\middle\slash + \left[\begin{array}{cc} 1 & 1 \\ 1 & 0\end{array}\right] \right.\quad ) +\] +is the \textsc{fraction slash}, which we just established above is +sort of only supposed to be used in text. + +Of the above characters, the following are allowed to be used after +\cs{left}, \cs{middle}, and \cs{right}: +\begin{itemize} +\item \cs{fracslash}; +\item \cs{slash}; and, +\item \cs{backslash} (the only reverse slash). +\end{itemize} + +However, we assume that there is only \emph{one} stretchy slash +in the font; this is assumed by default to be \unichar{002F} {solidus}. +Writing \cs{left/} or \cs{left}\cs{slash} or \cs{left}\cs{fracslash} +will all result in the same stretchy delimiter being used. + +The delimiter used can be changed with the |slash-delimiter| package option. +Allowed values are |ascii|, |frac|, and |div|, corresponding to the respective +Unicode slots. + +For example: as mentioned above, Cambria Math's stretchy slash is +\unichar{2044} {fraction slash}. When using Cambria Math, then +\pkg{unicode-math} should be loaded with the |slash-delimiter=frac| option. +(This should be a font option rather than a package option, but +it will change soon.) + +\subsubsection{Behaviour of hyphens in mathematics} +\seclabel{hyphen} + +Unicode defines the following related characters: +\begin{itemize} +\item \unichar{0002D}{hyphen-minus} +\item \unichar{02212}{minus sign} +\item \unichar{02010}{hyphen} (\cs{mathhyphen}) +\end{itemize} +The first two of these characters in the input will all behave as the binary operator +`minus sign'. +The third is defined by \pkg{unicode-math} as a `math letter' for constructions +like \verb|$R‐\text{Mod}$| ($R‐\text{Mod}$). +If more control is needed surrounding these symbols, additional options can be added to the package; +please get in touch if this is the case for you. + + +\subsubsection{Growing and non-growing accents} +\seclabel{growing-accents} + +There are a few accents for which \TeX\ has both non-growing and growing +versions. Among these are \cs{hat} and \cs{tilde}; the corresponding growing +versions are called \cs{widehat} and \cs{widetilde}, respectively. + +Older versions of \XeTeX\ and \LuaTeX\ did not support this distinction, +however, and \emph{all} accents there were growing automatically. (I.e., +\cs{hat} and \cs{widehat} are equivalent.) As of \LuaTeX\ v0.65 and \XeTeX\ +v0.9998, these wide/non-wide commands will again behave in their expected +manner. + + +\subsubsection{Negations and the \cs{not} command} +\seclabel{negations} + +The \cs{not} command in classic \LaTeXe\ was a mathematical slash modifying glyph that allowed for `negating` maths symbols where pre-built glyphs were not available. While Unicode encodes a slot for this modifying slash, it is only well-supported in \LuaTeX\ and not in \XeTeX. + +To provide more flexibility, the \pkg{unicode-math} package defines \cs{not} to search for a predefined `negated' definitions for its argument and use that if available. This method can be used for fine-tuning in cases where spacing needs to be adjusted. + +A `negated definition` is any symbol command prefixed by either \verb|n| or \verb|not|. For example, \pkg{unicode-math} by default defines both \cs{leftarrow} ($\leftarrow$) and \cs{nleftarrow} ($\nleftarrow$). + +To define custom negated definitions for either symbols (e.g., \verb|\not=|) or commands (e.g., \verb|\not\equal|), use the \cs{NewNotCommand}\marg{symbol or cmd}\marg{definition} command. Its usage is as follows: +\begin{verbatim} +\NewNegationCommand {=} {\neq} +\NewNegationCommand {\equal} {\neq} +\end{verbatim} +If the command has already been defined, an error will result and \verb|\RenewNegationCommand| can be used to overwrite the original definition. + + +\subsubsection{Pre-drawn fraction characters} + +Pre-drawn fractions \unichar{00BC}--\unichar{00BE}, \unichar{2150}--\unichar{215E} +are not suitable for use in mathematics output. However, they can be useful +as input characters to abbreviate common fractions. +\begin{center} +\fontspec{DejaVuSerif.ttf} ^^A available in TeX Live 2012 if not earlier +¼ ½ ¾ ↉ ⅐ ⅑ ⅒ ⅓ ⅔ ⅕ ⅖ ⅗ ⅘ ⅙ ⅚ ⅛ ⅜ ⅝ ⅞ +\end{center} +For example, instead of writing `|\tfrac12 x|', you may consider it more readable to have +`|½x|' in the source instead. + +If the \cs{tfrac} command exists (i.e., if \pkg{amsmath} is loaded or +you have specially defined \cs{tfrac} for this purpose), it will be used +to typeset the fractions. If not, regular \cs{frac} will be used. The command +to use (\cs{tfrac} or \cs{frac}) can be forced either way with the package +option |active-frac=small| or |active-frac=normalsize|, respectively. + +\subsubsection{Circles} + +Unicode defines a large number of different types of circles for a variety +of mathematical purposes. There are thirteen alone just considering the +all white and all black ones, shown in \tabref{circles}. + +\LaTeX\ defines considerably fewer: \cs{circ} and \cs{bigcirc} for white; +\cs{bullet} for black. This package maps those commands to \cs{vysmwhtcircle}, +\cs{mdlgwhtcircle}, and \cs{smblkcircle}, respectively. + +\begin{table}\centering +\def\showchar#1#2#3{ \textsc{u}+{\small\ttfamily #1} & \texttt{\string#3} & \umfont \char"#1 \\} +\begin{tabular}{@{}llc@{}} +\toprule +Slot & Command & Glyph \\ +\midrule +\showchar{00B7}{centerdot}{\cdotp} +\showchar{22C5}{small middle dot}{\cdot} +\showchar{2219}{bullet operator}{\vysmblkcircle} +\showchar{2022}{round bullet, filled}{\smblkcircle} +\showchar{2981}{z notation spot}{\mdsmblkcircle} +\showchar{26AB}{medium black circle}{\mdblkcircle} +\showchar{25CF}{circle, filled}{\mdlgblkcircle} +\showchar{2B24}{black large circle}{\lgblkcircle} +\bottomrule +\end{tabular} +\def\showchar#1#2#3{ \umfont \char"#1 & \texttt{\string#3} & \textsc{u}+{\small\ttfamily #1} \\} +\begin{tabular}{@{}cll@{}} +\toprule +Glyph & Command & Slot \\ +\midrule +\\ +\\ +\showchar{2218}{composite function (small circle)}{\vysmwhtcircle} +\showchar{25E6}{white bullet}{\smwhtcircle} +\showchar{26AC}{medium small white circle}{\mdsmwhtcircle} +\showchar{26AA}{medium white circle}{\mdwhtcircle} +\showchar{25CB}{large circle}{\mdlgwhtcircle} +\showchar{25EF}{large circle}{\lgwhtcircle} +\bottomrule +\end{tabular} +\caption{Filled and hollow Unicode circles.} +\tablabel{circles} +\end{table} + +\subsubsection{Triangles} + +While there aren't as many different sizes of triangle as there are circle, +there's some important distinctions to make between a few similar characters. See \tabref{uptriangles} for the full summary. + +These triangles all have different intended meanings. Note for backwards +compatibility with \TeX, \unichar{25B3} has \emph{two} different mappings +in \pkg{unicode-math}. \cs{bigtriangleup} is intended as a binary operator +whereas \cs{triangle} is intended to be used as a letter-like symbol. + +But you're better off if you're using the latter form to indicate an +increment to use the glyph intended for this purpose, \unichar{2206}: $\increment x$. + +Finally, given that $\triangle$ and $\increment$ are provided for you +already, it is better off to only use upright Greek Delta $\Delta$ if you're +actually using it as a symbolic entity such as a variable on its own. + +\begin{table}\centering +\begin{tabular}{@{}llcl@{}} +\toprule +Slot & Command & Glyph & Class \\ +\midrule +\unichar{25B5} & \cs{vartriangle} & \umfont \char"25B5 & binary \\ +\unichar{25B3} & \cs{bigtriangleup} & \umfont \char"25B3 & binary \\ +\unichar{25B3} & \cs{triangle} & \umfont \char"25B3 & ordinary \\ +\unichar{2206} & \cs{increment} & \umfont \char"2206 & ordinary \\ +\unichar{0394} & \cs{mathup}\cs{Delta} & \umfont \char"0394 & ordinary \\ +\bottomrule +\end{tabular} +\caption{Different upwards pointing triangles.} +\tablabel{uptriangles} +\end{table} + +\iffalse +\subsubsection{Normalising some input characters} + +I believe +all variant forms should be used as legal input that is normalised to +a consistent output glyph, because we want to be fault-tolerant in the input. +Here are the duplicates: +\begin{quote}\obeylines +\unichar {251} {latin small letter alpha} +\unichar {25B} {latin small letter epsilon} +\unichar {263} {latin small letter gamma} +\unichar {269} {latin small letter iota} +\unichar {278} {latin small letter phi} +\unichar {28A} {latin small letter upsilon} +\unichar {190} {latin capital letter epsilon} +\unichar {194} {latin capital letter gamma} +\unichar {196} {latin capital letter iota} +\unichar {1B1} {latin capital letter upsilon} +\end{quote} + +(Not yet implemented.) +\fi + +\section{Advanced} + +\subsection{Warning messages} + +This package can produce a number of informational messages to try and inform the user when something might be going wrong due to package conflicts or something else. +As an experimental feature, these can be turn off on an individual basis with the package option |warnings-off| which takes a comma-separated list of warnings to suppress. +A warning will give you its name when printed on the console output; e.g., +\begin{Verbatim} + * unicode-math warning: "mathtools-colon" + * + * ... <warning message> ... +\end{Verbatim} +This warning could be suppressed by loading the package as follows: +\begin{Verbatim} + \usepackage[warnings-off={mathtools-colon}]{unicode-math} +\end{Verbatim} + +\subsection{Programmer's interface} + +(Tentative and under construction.) +If you are writing some code that needs to know the current +maths style (\cs{mathbf}, \cs{mathit}, etc.), you can query the +variable \cs{l_@@_mathstyle_tl}. It will contain the maths style +without the leading `math' string; for example, +|\symbf { \show \l_@@_mathstyle_tl }| +will produce `bf'. + +\endinput + +% /© +% +% ------------------------------------------------ +% The UNICODE-MATH package <wspr.io/unicode-math> +% ------------------------------------------------ +% This package is free software and may be redistributed and/or modified under +% the conditions of the LaTeX Project Public License, version 1.3c or higher +% (your choice): <http://www.latex-project.org/lppl/>. +% ------------------------------------------------ +% Copyright 2006-2018 Will Robertson, LPPL "maintainer" +% Copyright 2010-2017 Philipp Stephani +% Copyright 2011-2017 Joseph Wright +% Copyright 2012-2015 Khaled Hosny +% ------------------------------------------------ +% +% ©/ |