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diff --git a/Master/texmf-dist/doc/optex/optex-math.tex b/Master/texmf-dist/doc/optex/optex-math.tex new file mode 100644 index 00000000000..789dd5a1877 --- /dev/null +++ b/Master/texmf-dist/doc/optex/optex-math.tex @@ -0,0 +1,1662 @@ +%% This is part of the OpTeX project, see http://petr.olsak.net/optex + +% Run optex optex-math (two times) to generate this document +% or look at PDF here: http://petr.olsak.net/ftp/olsak/optex/optex-math.pdf + +\fontfam[lmfonts] + +\font\ttlib=[LiberationMono-Regular] +\def\ttspec{\let\_ttfont=\ttlib} + +\report + +\def\new #1 {\mnote{\Red$\blacktriangleleft$\,\sans\setfontsize{at9pt}\rm#1}} +\fixmnotes\right +\enquotes +\verbchar` +\catcode`\<=13 +\def<#1>{$\langle\hbox{\it#1\/}\rangle$} +\everyintt={\catcode`\<=13 } +\def\ss#1{$\vrule height3pt#1\vrule height3pt$} + +\addto\_secfont\Blue \addto\_seccfont\Blue +\_def\_printsec#1{\_par + \_abovetitle{\_penalty-400}\_bigskip + {{\_secfont \_noindent \_raggedright \llap{\_printrefnum[@\_quad]}#1}\_nbpar}\_insertmark{#1}% + \_nobreak \_belowtitle{\_medskip}% + \_firstnoindent +} +\_def\_printsecc#1{\_par + \_abovetitle{\_penalty-200}\_medskip + {{\_seccfont \_noindent \_raggedright \llap{\_printrefnum[@\_quad]}#1}\_nbpar}% + \_nobreak \_belowtitle{\_medskip}% + \_firstnoindent +} + +\def\i #1 {\ii .#1 \iis .#1 {{\code{\\#1}}}} +\def\x`{\bgroup\_setverb\xx} +\bgroup \lccode\string`\.=\string`\` \lowercase{\egroup \def\xx #1#2.{\i #2 \egroup `#1#2.}} + + +\hyperlinks\Green\Green + +\insertoutline{MATH} +\outlines{0} + + + +\tit Typesetting Math with \OpTeX/ + +\hfill Version 03, January 2021 + +\author Petr Olšák + + +This document is a brief summary of typesetting math. It describes \TeX/, +Plain \TeX/ and \OpTeX/ features concerned to math. The first two types of +features are documented in \TeX/book in chapters 16, 17, and 18, but it is +summarized here in short again in order to give a complete guide about math +typesetting for \OpTeX/ users. + +\new {} +The \OpTeX/ features which differs from standard \TeX/ or Plain \TeX/ are +documented with the red triangle at the margin (like in this paragraph). +Reader can simply distinguish between \"standard" features (given by +\TeX/ or Plain \TeX/) and new \OpTeX/ features. + +There are more types of extensions: e\TeX, lua\TeX/, Unicode math and +\OpTeX/ macros. The appropriate label (e\TeX, Lua\TeX/, Unicode, \OpTeX/) +is appended to the red triangle to inform you about the extension type. +Nevertheless, \OpTeX/ user doesn't have to worry about it, all extensions +are available if Unicode Math font is loaded (e.g., by the command +`\fonfam[lmfonts]`). See section 1.3.3 in \OpTeX/ documentation about +loading Unicode math fonts. + +{\iindent=2em +\bigskip +\maketoc } +\vfil\break + +\sec Basics structure of math formulas + +\secc General rules and terminology + +The \ii in-line/math in-line math (in the paragraph) is created by `$<math list>$`. The +\ii display/math display math (a standalone line between paragraphs) is created by `$$<math list>$$`. +More than one line can be here if an appropriate macro is used. In-line math is +processed in a \TeX/ group in \ii in-line/math/mode {\em in-line math mode}. The display math is +processed in a \TeX/ group in \ii display/math/mode {\em display math mode}. Spaces are +ignored in math modes, so `$x+y$` and `$x + y$` gives the same result: $x+y$. + +The \ii math/list <math list> is a sequence of \ii math/atom,atom {\em math atoms} and +\ii other/material {\em other material}. +The math atoms are \ii single/math/object {\em single math objects} or +\ii composed/math/atom composed math atoms. + +\begitems \hfuzz=.6pt +* The single math object is a single character to be printed in math mode + like `x`, `+`, `\int`. +* The math atom is constructed in general by `{<math list 1>}^{<math list 2>}_{<math list 3>}`. + It consists from \ii nucleus {\em nucleus} <math list 1>, \ii exponent exponent <math list 2> + and \ii subscript subscript <math list 3>. Each part of the atom should be empty. + If <math list 2> or <math list 3> is empty, we need not to write brackets and + the prefix `^` or `_`. + If the <math list 1> or <math list 2> or <math list 3> + consist only from a single math object then we need not use brackets. + For example + `x^2` is a math atom with `x` in the nucleus, `2` in the exponent, and with empty subscript. + Or `a_{i,j}` is a math atom with `a` in the nucleus, empty exponent, and `i,j` in the subscript.% + \fnote{In \OpTeX/, the character `_` can be interpreted as a part of + the control sequence name, not as the subscript constructor. But in common cases, + constructions of math atoms are interpreted exactly as in plain \TeX. See sections + 2.2.2 and 2.14 of \OpTeX/ documentation for more details. If you want to + be sure that `_` is just a subscript constructor in \OpTeX/ then you can set \code{\\catcode`\\_=8} + but after this, you cannot use control sequences with `_` character.} + The constructors for exponent `^` and subscript `_` can be used in arbitrary order + after the nucleus, for example, `z_1^{x+y}` is the same math atom as + `z^{x+y}_1`. The single math objects not followed by `^` nor `_` are + considered as math atoms with this object in the nucleus and with empty + exponent and subscript (this is a very common case). + \TeX/ assigns the \ii class {\em class} for each math atom, see section~\ref[class]. +* Other material can be \TeX/ box or glue (space) or `\kern` or `\vrule` etc. +\enditems + +Example: The `Z = \int``_\Omega x^{2y} + z\, dx` generates +$Z = \int_\Omega x^{2y} + z\, dx$ and it is <math list> which consists from: + +\begitems +* `Z` is math atom with empty exponent and subscript, class: Ord, +* `=` is math atom with empty exponent and subscript, class: Rel, +* `\int``_\Omega` is math atom with empty exponent and with subscript `\Omega`, class: Op, +* `x^{2y}` is math atom with exponent `2y` and empty subscript, class: Ord, + \begitems \let\_bullet=\circ + * `2` is math atom with empty exponent and subscript, class: Ord, + * `y` is math atom with empty exponent and subscript, class: Ord, + \enditems +* `+` is math atom with empty exponent and subscript, class: Bin, +* `z` is math atom with empty exponent and subscript, class: Ord, +* `\,` is another material, the glue (space) in this case, +* `d` is math atom with empty exponent and subscript, class: Ord, +* `x` is math atom with empty exponent and subscript, class: Ord. +\enditems + +\secc[class] Classes of math atoms + +\TeX/ assigns \ii class {\em a class} for each math atom.\fnote +{Using terminology of \TeX/book, each single math object has its {\em class} but the + math atom has its {\em kind} derived from this class. I use only one word + for both meanings in this document.} +This data type is used when +\TeX/ decides about \ii horizontal/spacing horizontal spaces between atoms in the output. (Note +that spaces in the input are ignored.) For example, +`$xy$` prints two atoms without space between them but `$x+y$` is printed with +small spaces around the `+` binary operator. Compare: $xy$ and $x+y$. + +The class is assigned depending on the nucleus of the atom. If the nucleus is +not a single math object, i.e. it is constructed by `{<math list>}` with braces +then the atom has its class Ord. If the nucleus is a single math object constructed +without braces then the class of the atom depends on this single math +object. Each single math object must be declared in \TeX/ with its default +class. The following table lists the classes with typical examples. +The full set of all math objects used in math typesetting +is listed in section~\ref[objects] with their default classes. + +\bigskip +\noindent\hfil\table{llll}{ + & \ii class Class & Meaning & Example \crl + 0 & \iid Ord & ordinary object & variables, digits, $x, {\bbchar R}, \Gamma, 0, 1$ \cr + 1 & \iid Op & big opertator & $\sum, \int, \bigcup$ \cr + 2 & \iid Bin & binary operator & $+, \times, -, \pm, \cup$ \cr + 3 & \iid Rel & reations & $=, \ne, \leq, \supseteq, \succsim$ \cr + 4 & \iid Open & opening bracket & $\{, (, [, \langle$ \cr + 5 & \iid Close & closing bracket & $\}, ), ], \rangle$ \cr + 6 & \iid Punct & punctuation & comma \cr + & \iid Inner & left-right & \code{\\left...\\right} outputs, see section~\ref[delims] +} +\bigskip + +There are \ii horizontal/spacing,spacing three space types used +by the algorithm for horizontal spacing in the math formulas. + +\begitems +* \ii thin/space Thin space: \x`\thinmuskip` primitive register, `\,` macro. Used around Op atoms. +* \ii medium/space Medium space: \x`\medmuskip` primitive register, `\>` macro. Used around Bin atoms. +* \ii thick/space Thick space: \x`\thickmusip` primitive register, `\;` macro. Used around Rel atoms. +\enditems + +\puttext 7.8cm -3.7cm {\rotbox{90}{Left atom}} +\puttext 11.5cm -.5cm {Right atom} +\puttext 8.2cm -4.4cm {\typosize[9/11] +\thistable{\def\_enspace{ }}% +\table {l|8c|} { + \omit & Ord & Op & Bin & Rel & Open & Close & Punct & \omit \hfil Inner \crlp{2-9} + Ord & 0 & 1 & 2 & 3 & 0 & 0 & 0 & 1 \cr + Op & 1 & 1 & & 3 & 0 & 0 & 0 & 1 \cr + Bin & 2 & 2 & & & 2 & & & 2 \cr + Rel & 3 & 3 & & 0 & 3 & 0 & 0 & 3 \cr + Open & 0 & 0 & & 0 & 0 & 0 & 0 & 0 \cr + Close & 0 & 1 & 2 & 3 & 0 & 0 & 0 & 1 \cr + Punct & 1 & 1 & & 1 & 1 & 1 & 1 & 1 \cr + Inner & 1 & 1 & 2 & 3 & 1 & 0 & 1 & 1 \crlp{2-9} +}} + +\hangindent=-8.7cm \hangafter=0 +Ord atoms are printed without spaces between them. The spaces are not +cumulated, so the rule about spaces mentioned above is only a rough idea. +The exact rule for horizontal spaces is given for each pairs of atoms +in the table here. The symbol 0 means no space, 1 thin space, 2 medium space, +and 3 means thick space. + +\hangindent=-8.7cm \hangafter-2 +The Bin atom is automatically transformed to the +Ord atom if no atom precedes or if Op, Bin, Rel, Open, or Punct atom +precedes. And it is transformed to the Ord atom if Rel, Close or Punct atom +follows. This corresponds to the empty cells in the table. +Why such behavior? Compare \"\hbox{$0-3$}" and \"$-3$". The Bin atom in +the second case behaves like Ord atom because it is \ii unary/minus {\em unary minus}. +There is no space between the unary minus and the following object. + +All medium spaces and thick spaces and some thin spaces from this table are +omitted if the <math list> is processed in +\ii script/style,scriptscript/style script or scriptscript styles +(smaller size). See section~\ref[styles] about math styles. + +You can overwrite the default class derived from the nucleus of the atom by +\TeX/ primitives \x`\mathord`, \x`\mathop`, \x`\mathbin`, \x`\mathrel`, \x`\mathopen`, +\x`\mathclose`, \x`\mathpunct` and \x`\mathinner`. They can precede a nucleus of +the atom and they set the class of the atom. +For example, `x \mathrel+ y` behaves like `x = y` from a spacing point of view but + +is printed. Another example: `\mathop{\rm lim} z` creates the atom `lim` in +roman font of class Op. So, the thin space is inserted between lim and $z$. + +There are more special kinds of math atoms: fractions, math accents, +radicals. They are constructed in a special way (see next sections) but they behave +like Ord atom in the horizontal spacing algorithm. + +\secc[styles] Math styles + +When a formula (or a sub-formula) is processed by \TeX/ then one from four +\ii math/style,display/style,text/style,script/style,scriptscript/style +styles is active: display style ($D$), text style ($T$), script style ($S$) or +scriptscript style ($SS$). + +\ii T/style,D/style,S/style,SS/style The $T$ style is started in in-line math mode `$...$` and the $D$ +style is started in display math mode `$$...$$`. The first level of exponents or +subscripts is processed in $S$ style and the second and more levels of +exponents or indexes are processed in $SS$ style. +There are special rules for math styles when fractions are constructed, see +section~\ref[frac]. + +The $D$ and $T$ styles use basic \ii font/size font size, $S$ uses smaller font size (typically +70~\%) and $SS$ style uses more smaller font size (typically 50~\%). Next +levels of \"more smaller fonts" are not used due to classical typographic rules. + +The \ii nucleus nucleus of \iid Op atoms (big operators, $\sum$, $\int$, etc.) have typically bigger versions +of the character shape for $D$ style than for $T$ style. +So, there are four sizes for such math +objects: one size for each math style. All other math objects (with non Op +class) are printed only in three sizes: The sizes for $T$ and $D$ styles are equal. + +The \iid Op atom puts its \iid exponent and \iid subscript above and below the nucleus in $D$ +style but right to the nucleus in other styles: +$$ + `\sum``_{i=1}^\infty` \quad \hbox{gives}\quad \sum_{i=1}^\infty \hbox{ in $D$ style and} + \quad \textstyle \sum_{i=1}^\infty \hbox{ in $T$ style}. +$$ +This default behavior of the Op atom +can be modified by placing \x`\limits` or \x`\nolimits` or +\x`\displaylimits` \TeX/ primitive just after its nucleus before the constructors +of exponent and/or index. The `\nolimits` puts exponent and subscript right +to the nucleus (regardless of the current style) and `\limits` puts these +objects above and below the nucleus (regardless of the current style). There +can be more such primitives in a queue (due to a macro expansion, for +instance). Then the last primitive in the queue wins. +If the last primitive is \x`\displaylimits` then +the default behavior is processed regardless there are \x`\limits` or \x`\nolimits` +before it. +$$ + `\sum\nolimits``_{i=1}^\infty` \quad \hbox{gives}\quad \sum\nolimits_{i=1}^\infty + \hbox{ in $D$ style and}\quad \textstyle\sum\nolimits_{i=1}^\infty + \hbox{ in $T$ style}. +$$ +Atoms of all other classes have their exponents and/or subscripts only right +to their nucleus without any exception. + +The primitives \x`\displaystyle`, \x`\textstyle`, \x`\scriptstyle` and +\x`\scriptscriptstyle` set the given style regardless the default rules. For +example, you can create a formula in in-line math mode and in $D$ style by +`$\displaystyle <fomula>$` or a formula in display mode and $T$ style can be printed +by `$$\textstyle <fomrula>$$`. + +If a subformula is placed below something (below a line from root symbol, +below a fraction line), then the processed style $D, T, S$ or $SS$ is +\ii cramped/style {\em cramped}. +The exponents are positioned slightly lower than in +\ii non-cramped/style non-cramped style. The selectors `\displaystyle`\,\dots +`\scriptscriptstyle` mentioned above select non-cramped style. The +non-cramped style is selected when math mode starts too. +\new \OpTeX/ +You can select a cramped style by the macro \x`\cramped` at the start of the +math formula or after the math-style selectors: `\scriptstyle\cramped` for +example. + +Several macros need to know what math style is currently processed (for +example they need to draw something in an appropriate size). But it +not possible simply due to the syntax of fractions (section~\ref[frac]). +This syntax requires to process all math lists in two steps: the first step +expands all macros and creates structured data of processed math list. The +second step reads the output of the first step, switches between math +styles and creates definitive output. So, macros (working in the first step) +cannot know the current math +style because it is set only in the second step. \TeX/ supports the primitive +\x`\matchchioce``{<D>}{<T>}{<S>}{<SS>}` which prepares four math lists in the +first step and only one of these four lists are used in the second step. We +can put different macros into each of the four parameters of `\mathchoice`. +Plain \TeX/ supports the macro \x`\mathpalette` which gives a more comfortable +interface of \x`\mathchoice` to the macro programmer. +The cramped/non-cramped variants of the current style are kept when `\mathchioce` +is used. + +\new \OpTeX/ +We describe another interface for creating macros depending on the current +style. You can use \x`\mathstyles``{<math list>}`. It +behaves like `{<math list>}`, moreover, you can use the following commands inside such +<math list>: +\begitems +* The macro \x`\currstyle`. It expands to + `\displaystyle`, `\textstyle`, + `\scriptstyle` or `\scriptscriptstyle` depending on the current math style + when the `\mathstyles` was opened. +* The \x`\dobystyle``{<D>}{<T>}{<S>}{<SS>}` is expandable macro. It expands its + parameter `<D>`, `<T>`, `<S>` or `<SS>` depending on the current math style + when `\mathstyles` was opened. +* The value of the \x`\stylenum` register is 0, 1, 2 or 3 + depending on the current math style when `\mathstyles` was opened. +\enditems +% +Example of usage of \x`\mathstyles`: +\def\mysymbol{\mathbin\mathstyles + {\kern1pt\vrule height\mysymbolA width\mysymbolA\kern1pt}} +\def\mysymbolA{\dobystyle{5pt}{5pt}{3.5pt}{2.5pt}} +\begtt +\def\mysymbol{\mathbin\mathstyles + {\kern1pt\vrule height\mysymbolA width\mysymbolA\kern1pt}} +\def\mysymbolA{\dobystyle{5pt}{5pt}{3.5pt}{2.5pt}} +Test: $a\mysymbol b_{c \mysymbol d}$ or $a\mysymbol b\over c$. +\endtt +This example gives Test: $a\mysymbol b_{c \mysymbol d}$ or $a\mysymbol b\over c$. + +The \x`\mathstyles` macro mentioned above uses \TeX/ primitive \x`\mathchoice`, so it +creates four math lists and only one is used. It may take more +computer time in special cases. +\new Lua\TeX/ +Lua\TeX/ supports the \x`\mathstyle` primitive +(no \"`s`" at the end of this control sequence) which +expands to values 0 to 7 depending on the current style: +$D, D', T, T', S, S', SS, SS'$ +(where $X'$ means cramped variant of the style). This primitive does +not use `\mathchoice` but it simply ignores the fraction syntax, so +`$a\mysymbol b\over c$` cannot work if `\mysymbol` is defined using the `\mathstyle` +primitive. See section 7.3.1 of Lua\TeX/ documentation for more information. + + +\secc[frac] Fractions + +The \iid fraction can be constructed by `{<numerator>`\x`\over``<denominator>}`. If the +fraction is only a single object in the whole math mode (between dollars), +you need not use the outer braces, so you can write `$1\over2$` to get $1\over2$. + +The \ii numerator,denominator <numerator> and <denominator> are printed in \"smaller" math style than +current math style. More exactly the following schema is used. +$D$: $T\over T$., $T$: $S\over S$, $S$: $SS\over SS$, $SS$: $SS\over SS$. +For example +$$ + `{a+b \over c}` \quad \hbox{is printed as } + {a+b\over c} \hbox{ in $D$ style and as } + \textstyle {a+b\over c} \hbox{ in $T$ style}. +$$ + +The \LaTeX/ macro \x`\frac``{<numerator>}{<denominator>}` is not supported in +Plain \TeX/ nor in \OpTeX/ but you can define such macro if you want. + +The syntax with \x`\over` is more preferred because it is more human-readable +notation. You can write the fraction in the same manner as you can read it. +You can compare: `$1\over2$` (one over two) with `$\frac12$` (frac twelve). + +Besides the `\over` primitive, there are analogical \TeX/ primitives which +create \"generalized" fractions. The result is similar to `{<above>\over <below>}` +but there is something extra: + +\begitems +* `{<above>`\x`\atop``<below>}` does `{<above>\over<below>}` but + without the fractional rule. +* `{<above>`\x`\above``<dimen><below>}` creates fractional rule with <dimen> thickness. +* `{<above>`\x`\overwithdelims``<delim-l><delim-r><below>}` adds the <delim-l> left to + the fraction and the <delim-r> right to the fraction. +* `{<above>`\x`\atopwithdelims``<delim-l><delim-r><below>}` is analogical to + `\overwithdelims` but without fractional rule. +* `{<above>`\x`\abovewithdelims``<delim-l><delim-r><dimen><below>}` behaves as + `\overwithdelims` but the fractional rule has <dimen> thickness. +\enditems +% +The `\...withdelims` variants read <delim-l> and <delim-r>, they must be +declared as {\em math delimiter} in \TeX. They are vertically scalable +math objects, typically brackets. See section~\ref[delims] for more +information about math delimiters. Example: +$$ + `{n \atopwithdelims() k}`\quad \hbox{ creates } + {n \choose k} \hbox{ in $D$ style and } + \textstyle {n \choose k} \hbox{ in $T$ style}. +$$ +The \x`\choose` macro is defined by `\def\choose{\atopwithdelims()}`, so the +user can write `{n\choose k}` in order to get binomial coefficients. + + +\secc[delims] Vertically scalable objects: math delimiters + +The vertically scalable objects are called \ii delimiters {\em delimiters}. For example, +all types of brackets are declared as delimiters. +This means that you can use a bracket in arbitrary +vertical size.\fnote{ +This is not exactly true, because traditional typography says that they +cannot be scaled continuously but by visible steps. This means that there is +a sequence of increasing brackets in the font, the reader must see a difference +between every two sizes of brackets.} + +The following objects are declared as delimiters (i.e.\ vertically scalable): + +\bigskip +{\tt \adef!{\bslash} +\table{l 14c}{ + \rm source: & ( & ) & [ & ] & \code{\\\{} & \code{\\\}} & / + & !backslash & !langle & !rangle + & | & \code{\\|} & \cr + \rm output: &$($&$)$&$[$&$]$& $\{$ & $\}$ & $/$ + & $\backslash$ & $\langle$ & $\rangle$ + & $|$ & $\|$ +} +\medskip +\table{l 14c}{ + \rm source: & !lfloor & !rfloor & !lceil & !rceil \cr + \rm output: & $\lfloor$ & $\rfloor$ & $\lceil$ & $\rceil$ +} +\medskip +\table{l 14c}{ + \rm source: & !uparrow & !Uparrow & !dowarrow & !Downarrow + & !updownarrow & !Updownarrow \cr + \rm output: & $\uparrow$ & $\Uparrow$ & $\downarrow$ & $\Downarrow$ + & $\updownarrow$ & $\Updownarrow$ +}} +\bigskip +\noindent \new Unicode +If you can produce the characters $\langle$, $\rangle$,\fnote + {Do not confuse $\string<, >$ and $\langle, \rangle$. The first pair are Rel atoms + with meaning \"less than" or \"greater than", but the second pair are special + types of brackets. They are not directly available at computer keyboards without + using a keyboard macro.} +$\lfloor$, $\rfloor$, ... $\updownarrow$, $\Updownarrow$ +directly in your text editor then you can use these Unicode characters in your source instead of control +sequences `\langle`, `\rangle`, `\lfloor`, `\rfloor` ... `\updownarrow`, `\Updownarrow`. +For many users (including me), there is more simple to type `\lfloor` than to find +how to create the $\lfloor$ character in my text editor. Note that there exist +text editors (Emacs, for example) +enabling you to type `\lfloor` and this control sequence is immediately +converted to the $\lfloor$ Unicode character. +Your source text looks pretty and you can use classical \TeX/ sequences. + +\new Unicode +There are more \ii delimiters delimiters, but it heavily depends on loaded Unicode Math +font. For example, this document is printed in `latinmodern-math` font and +there are six more delimiters `\lBrack`~$\lBrack$, `\rBrack`~$\rBrack$, +`\lAngle` $\lAngle$, `\rAngle` $\rAngle$, `\lgroup` $\lgroup$, `\rgroup` $\rgroup$. +See section~\ref[objects] for table of all Unicode symbols for math typesetting. + +Arbitrary tall formula can be surrounded by a pair of delimiters using +\x`\left` and \x`\right` \TeX/ primitives: `\left<delim> <formula> \right<delim>`. +The delimiters are scaled to the height and depth of the <formula> +and vertically centered to the {\em math axis}.\fnote +{Math axis is a horizontal line passing through the center of symbols $+$ + and $-$. All vertically scalable objects are vertically centered with + respect to this axis.} +Example: +$$ + `+ \left\{ \sum_{i=1}^\infty x_i \right)` \quad \hbox{ gives } + + \left\{ \sum_{i=1}^\infty x_i \right). +$$ +The pair `\left<delim> <formula> \right<delim>` creates the formula in a +\TeX/ group. Such group can be nested with another groups. +Each `\left` must have its `\right` counterpart at the same group level. +If you don't want to create visible delimiter, use dot instead <delim>. +Example: +$$ + `\left. \int``_0^t e^{x^2}\,dx\, \right|_{t=42}` \quad \hbox{ gives } + \left. \int_0^t e^{x^2} \,dx\, \right|_{t=42} +$$ + +\new e\TeX/ +You can use \x`\middle``<delim>` inside the <formula> which is surrounded by +`\left...\right`. Then the given <delim> is scaled to the same size like +their `\left` and `\right` counterparts. + +When a delimiter is used without `\left` nor `\right` prefix, then it is the +Open, Close, Ord or Bin atom by its natural meaning: +$(, [, \{, \ldots, \lfloor, \lceil$ are Open atoms, +$], ], \}, \ldots, \rfloor, \rceil$ are Close atoms, +$/, \backslash, |, \|$ are Ord atoms and +$\uparrow, \Uparrow, \ldots, \Updownarrow$ are Bin atoms. You can overwrite +this default setting, for example `\mathclose(`. If delimiters are used with +`\left` and `\right` prefixes then `\left<delim>` behaves like Open atom, +`\right<delim>` behaves like Close atom and the math list +`\left<delim><formula>\right<delim>` is encapsulated as a single Inner atom. +The `\middle<delim>` behaves like Open atom at its left side and like Close +atom at its right side. + +The sequence of increasing delimiters can be printed by the following +macros: +$$ + `(` \to (,\quad \x`\big``(` \to \big(,\quad \x`\Big``(` \to \Big(,\quad + \x`\bigg``(` \to \bigg(, \quad \x`\Bigg``(` \to \Bigg(. +$$ +The `\Bigg<delim>` is not the maximal size of the bracket. Try +`\left(\vbox to5cm{}\right.`, for example. You can see that the font +\"cheats" from certain sizes, because there are not all infinity number of +sizes of brackets drawn in the font, of course. + +The `\big<delim>` creates Ord atom. We need to create Open atom +for opening bracket and Close atom for closing bracket more often. +Then we can use macros +\x`\bigl``<delim>`, +\x`\Bigl``<delim>`, +\x`\biggl``<delim>`, +\x`\Biggl``<delim>` for creating Open atoms and +\x`\bigr``<delim>`, +\x`\Bigr``<delim>`, +\x`\biggr``<delim>`, +\x`\Biggr``<delim>` for creating Close atoms. Unfortunately, the source is not +too attractive when more sizes of brackets are used, but typographic +traditions say that we have to distinguish brackets by the size in math +mode if they are in equal types: +$$ + `\Bigl( f\bigl( 2(x+y) + z\bigr) \Bigr)'` \quad \hbox{gives } + \Bigl(f\bigl(2(x+y)+z\bigr)\Bigr)'. +$$ + +\secc Horizontally scalable objects: math accents + +Arbitrary wide formula can be covered by \ii math/accent,accent {\em scalable math accent}. +Example: +$$ + \x`\overrightarrow`` {a+b+c+d+e+f}` \quad \hbox{gives } \overrightarrow {a+b+c+d+e+f}. +$$ +The usage is: control sequence of selected math accent followed by `{<math list>}`. + +Standard scalable math accents are: +\x`\overline` $\overline{abc}$, +\x`\overbrace` $\overbrace{abc}$, +\x`\overrightarrow` $\overrightarrow{abc}$, +\x`\overleftarrow`~$\overleftarrow{abc}$, +\x`\underline` $\underline{abc}$, +\x`\underbrace` $\underbrace{abc}$. + +An Op atom is created. The exponents and subscripts are centered above +and below the nucleus of this atom (regardless of the current style). Example: +$$ + `\overbrace {b\cdot b\cdot b \cdots b}^{k\times}` \quad \hbox{gives } + \overbrace {b\cdot b\cdot b \cdots b}^{k\times} +$$ +There are scalable accents with a limited maximum width: +\x`\widehat` $\widehat{abc}$ and \x`\widetilde` $\widetilde{abc}$. If the +formula is wider than the font can cover then the widest variant from the +font is used and it is horizontally centered. + +\new Unicode +There are more scalable accents in Unicode math fonts: +\x`\overparen` $\overparen{abc}$, \x`\underparen` $\underparen{abc}$, +\x`\overbracket` $\overbracket{abc}$, \x`\underbracket` $\underbracket{abc}$, +\x`\overleftrightarrow` $\overleftrightarrow{abc}$, +\x`\overleftharpoon` $\overleftharpoon{abc}$, +\x`\overrightharpoon` $\overrightharpoon{abc}$, + + +\secc Fixed math accents + +Fixed \ii math/accent,accent math accents can be applied to single math object or to the `{<math list>}`. +The accent is centered (with respect of slanting axis) and the result is a +nucleus of Ord +atom. For example `\dot x` gives $\dot x$. The list of fixed math accents +follows: \x`\acute`` x` $\acute x$, \x`\bar`` x` $\bar x$, +\x`\breve`` x` $\breve x$, \x`\check`` x` $\check x$, +\x`\dot`` x` $\dot x$, \x`\ddot`` x` $\ddot x$, +\x`\grave`` x` $\grave x$, \x`\hat`` x` $\hat x$, +\x`\vec`` x` $\vec x$, \x`\tilde`` x` $\tilde x$. + +\new Unicode +The additional fixed accents depends on used Unicode math font. The +`latinmodern-math` supports: +\x`\ovhook`` x` $\ovhook x$, \x`\ocirc`` x` $\ocirc x$, +\x`\leftharpoonaccent`` x` $\leftharpoonaccent x$, \x`\rightharpoonaccent`` x` $\rightharpoonaccent x$, +\x`\dddot`` x` $\dddot x$, \x`\ddddot`` x` $\ddddot x$, +\x`\widebridgeabove`` x` $\widebridgeabove x$, \x`\asteraccent`` x` $\asteraccent x$. + +There exist one special math accent `'` (single quote, ASCII 39) +which can be appended after a symbol like this: `f'` +and it creates $f'$ (typical meaning is the +derivation of the given function). You can put more such accents, for +example `g'''` gives $g'''$. + +\secc Roots + +There is a macro \x`\sqrt``{<math list>}` to create \ii square/root square root. For example: +$$ + `\sqrt{\sqrt{\sqrt{x+1}+1}+1}` \quad \hbox{gives } + \sqrt{\sqrt{\sqrt{x+1}+1}+1} +$$ +The \ii root $n$-th root is created by the macro \x`\root`` <n>\of{<math list>}`. For +example `\root k+1\of x` gives $\root k+1\of x$. + +\secc Math alphabets + +Letters \ii math/alphabet $a\dots z$, $A\dots Z$ and $\alpha$\dots$\omega$ are printed in italic +in math mode. This follows the traditional typographic rule. +All other math symbols, digits, and uppercase Greek letters must be +upright.\fnote +{French typographic convention says that uppercase Greek letters have to be + in italic too. Use `\_itGreek` declaration in this case.} +These rules are independent of the current variant of surrounding text font. + +If we want to use the letters or digits +in another than this default shape, then we can use +\ii math/alphabet/selector {\em math alphabet selectors}: +\x`\mit`, \x`\rm`, \x`\it`, \x`\bf`, \x`\cal`. +\new \OpTeX/ +\OpTeX/ supports more such selectors \x`\script`, \x`\frak`, \x`\bbchar`, \x`\bi`, see +section 1.3.3 in the \OpTeX/ documentation. The math selectors have local +validity in the group. + +The control sequences \x`\rm`, \x`\it`, \x`\bf`, and \x`\bi` act as variant selectors +of fonts in non-math mode (text mode) and they act +as math alphabet selectors in math mode. This \"overlaying" concept +is given by Plain \TeX/. Example: math operators lim, sin, cos, +log, etc.\ must be printed unslanted. We are using `\lim`, `\sin`, `\cos`, +`\log` etc.\ in math mode in order to comply with this typographic convention. For +example `\sin` is defined as: +\begtt +\def\sin {\mathop{\rm sin}\nolimits} +\endtt +The `\rm` is used here as math alphabet selector, no variant selector of +text fonts. + +The list of all predefined `\rm`-like math operators follows: \x`\arccos`, +\x`\arcsin`, \x`\arctan`, \x`\arg`, \x`\cos`, \x`\cosh`, \x`\cot`, \x`\coth`, \x`\deg`. +\x`\det`, \x`\dim`, \x`\exp`, \x`\gcd`, \x`\hom`, \x`\inf`, \x`\ker`, \x`\lg`, \x`\lim`, +\x`\liminf`, \x`\limsup`, \x`\ln`, \x`\log`, \x`\max`, \x`\min`, \x`\Pr`, \x`\scs`, \x`\sin`, +\x`\sinh`, \x`\sup`, \x`\tan`, \x`\tanh`, You can define another such operator +analogically. + +\new Unicode +Unicode font can include the following math alphabets: +\begtt \typosize[9/11] +\_rmvariables % upright letters A-Z, a-z +\_bfvariables % bold letters A-Z, a-z +\_itvariables % italic letters A-Z, a-z +\_bivariables % bold italic letters A-Z, a-z +\_calvariables % calligraphic letters A-Z, a-z +\_bcalvariables % calligraphic letters A-Z, a-z +\_frakvariables % fraktur A-Z, a-z +\_bfrakvariables % bold fraktur A-Z, a-z +\_sansvaraibales % sans serif letters A-Z, a-z +\_bsansvaraibales % bold sans serif letters A-Z, a-z +\_isansvaraibales % slanted sans serif letters A-Z, a-z +\_bisansvaraibales % bold slanted sans serif letters A-Z, a-z +\_ttvariables % monospace, typewriter letters A-Z, a-z +\_bbvariables % double struck A-Z, a-z +\_rmdigits % upright digits 0..9 +\_bfdigits % bold digits 0..9 +\_sansdigits % sans serif digits 0..9 +\_bsansdigits % bold sans serif digits 0..9 +\_ttdigits % monospace typewriter digits 0..9 +\_bbdigits % double-struck digits 0..9 +\_rmgreek % upright Greek letters \alpha-\omega +\_itgreek % slanted Greek letters \alpha-\omega +\_bfgreek % bold Greek letters \alpha-\omega +\_bigreek % bold italic Greek letters \alpha-\omega +\_bsansgreek % bold sans serif Greek letters \alpha-\omega +\_bisansgreek % bold slanted snas serif Greek letters \alpha-\omega +\_itGreek % slanted Greek letters \Alpha-\Omega +\_bfGreek % bold Greek letters \Alpha-\Omega +\_biGreek % bold italic Greek letters \Alpha-\Omega +\_bsansGreek % bold sans serif Greek letters \Alpha-\Omega +\_bisansGreek % bold slanted snas serif Greek letters \Alpha-\Omega +\endtt +% +Not all Unicode math fonts include all math alphabets listed here. Typically, +the lowercase letters of calligraphic shape and all letters of +bold calligraphic shape are missing. + +\new \OpTeX/ +\OpTeX/ defines internal math alphabet selectors as mentioned in the +previous listing of math alphabets and sets as default: +\begtt \typosize[10/12] +\_itvariables \_rmdigits \_itgreek \_rmGreek +\endtt +% +Moreover, it defines the alphabet selectors at user level (see section 1.3.3 +of the \OpTeX/ manual). For example +\begtt \typosize[10/12] +\def\rm {\_tryload\_tenrm \_inmath{\_rmavariables \_rmdigits}} +\endtt +% +The first part +\new \OpTeX/ +`\_tryload\_tenrm` is applicable for text fonts and the +`\_inmath` part is processed only in math mode and sets the math alphabets. +You can see the file `unimath-codes.opm` where all user-level selectors are +defined. You can redefine them. For example, \OpTeX/ defines `\bf` as a math +alphabet selector that selects sans serif bold in math. This is the common +notation for vectors, tensors, and matrices. If you dislike this, then you can define: +\begtt \typosize[10/12] +\def\bf {\_tryloadbf\_tenbf \_inmath{\_bfvariables\_bfdigits\_bfgreek\_bfGreek}} +\endtt + + +\secc[objects] List of single math objects + +\new Unicode +All \ii single/math/object single math objects are listed in the `unimath-table.opm` or +`unicode-math-table.tex` file. You can +look into this file. The codes, \TeX/ sequences, classes, and comments +for all possible math codes are here. Maybe, your Unicode math font which is loaded +does not support all these codes. +\new \OpTeX/ +You can try all codes of the currently loaded font by +\begtt +\input print-unimath.opm +\endtt +The `unimath-table` is printed with characters available in the loaded font. +\new \OpTeX/ +If the character is unsupported by the font then the slot is empty and only +\TeX/ sequence and the class of the code is printed in the table. +For example, this document loads `latimodern-math.otf` font. +And the result from `\input print-unimath.opm` looks like the following ten +pages. + +Unsupported characters can be replaced by characters from other Unicode math +font, see +\ulink[http://petr.olsak.net/optex/optex-tricks.html\#addumathfont]{OpTeX trick 0030} +or section~\ref[newfam]. + + +\label[listA]\wlabel{} + +\bigskip +\input print-unimath.opm +\bigskip + +\label[listB]\wlabel{} + +It isn't very comfortable to find something in the previous table +if you know the shape. You can try the online web tool \ii Detexify +\ulink[https://detexify.kirelabs.org/classify.html]{Detexify}. +You can draw the symbol here and the suggestion of \TeX/ sequence is +printed. + +\def\g#1{{\tt\string#1}~$#1$} + +The generic \TeX/ sequences for the Greek letters \ii Greek/letters can be used: +\g\alpha, \g\beta, \g\gamma, \g\delta, \g\varepsilon, \g\zeta, \g\eta, +\g\theta, \g\iota, \g\kappa, \g\lambda, \g\mu, \g\nu, \g\xi, +\g\omicron, \g\pi, \g\rho, \g\varsigma, \g\sigma, \g\tau, \g\upsilon, +\g\varphi, \g\chi, \g\psi, \g\omega, \g\vardelta, \g\epsilon, \g\vartheta, +\g\varkappa, \g\phi, \g\varrho, \g\varpi\ +and +\g\Alpha, \g\Beta, \g\Gamma, \g\Delta, \g\Epsilon, \g\Zeta, \g\Eta, \g\Theta, +\g\Iota, \g\Kappa, \g\Lambda, \g\Mu, \g\Nu, \g\Xi, \g\Omicron, \g\Pi, \g\Rho, +\g\Sigma, \g\Tau, \g\Upsilon, \g\Phi, \g\Chi, \g\Psi, \g\Omega. + +\new \OpTeX/ +The variant of Greek letters in the output +(upright, italic, bold, bold sans serif, etc.) +written by the sequences `\alpha`, `\beta` etc. depends on the math alphabet +selected by `\_itgreek`, `\_rmgreek`, etc. selectors. The user-level +selectors `\bf` and `\bi` set `\_bsansgreek` and `\_bisansgreek`, so +`{\bi\delta}` produces $\bi\delta$. + +\new Unicode +All characters available in the math font can be accessed by \TeX/ control +sequence or by directly using the Unicode character in the document source. +Example: +\begtt \adef/{} +$$ + \sum/_{k=0}^\infty e^{(\alpha+i\beta/_k)} = + e^\alpha \sum/_{k=0}^\infty e^{i\beta/_k} = + e^\alpha \sum/_{k=0}^\infty (\cos\beta/_k + i\sin\beta/_k). +$$ +\endtt +or +\begtt \ttspec +$$ + ∑_{k=0}^∞ e^{(α + iβ_k)} = e^α ∑_{k=0}^∞ e^{iβ_k} + = e^α ∑_{k=0}^∞ (\cos β_k + i\sin β_k). +$$ +\endtt +both gives the same result: +$$ + ∑_{k=0}^∞ e^{(α + iβ_k)} = e^α ∑_{k=0}^∞ e^{iβ_k} + = e^α ∑_{k=0}^∞ (\cos β_k + i\sin β_k). +$$ +\medskip + + +\sec Other specialities + +\secc The `\not` prefix + +You can apply \x`\not` before a following math object. +The slash $/$ is overprinted such math object, for example +`$a \not= b$` gives $a \not= b$. + +\new \OpTeX/ +If there exists a direct Unicode character for the negation of a relation symbol +(for example `\ne` creates $\ne$ directly as a character U+2260) +then `\not<char>` expands to appropriate Unicode character. +For example `\not=` expands to `\ne` or `\not\in` expands to `\notin`. +If such character does not exist then +the centered $/$ is overprinted over the next character. + + +\secc The `\buildrel` macro: text over the relation + +The macro \x`\buildrel`` <text>\over <relation>` creates a new atom Rel with the +<relation> and with the smaller <text> above this <relation>. Example: +`$M \buildrel\rm def\over= X\cup Y$` gives $M\buildrel\rm def\over= X\cup Y$. + + +\secc Spaces + +Spaces between atoms are created automatically as were mentioned in +section~\ref[class]. But sometimes you have to help \TeX/ to create +appropriate space. You can use following macros: + +\begitems +* `\,` is \ii thin/space {\em thin space} used around Op atoms, after comma, etc.: \ss\,, +* `\!` is \ii negative/thin/space negative thin space, +* `\>` is \ii medium/space {\em medium space} used around Bin atoms: \ss\>, +* `\;` is \ii thick/space {\em thick space} used around Rel atoms: \ss\;, +* \x`\quad` is \ii em/space {\em em space}: \ss\quad, +* \x`\qquad` is \ii double/em/space {\em double em space}: \ss\qquad. +\enditems +% +Of course, you can use \ii direct/space {\em direct space} {\visiblesp`\ `} which is \TeX/ primitive +and gives interword space: \ss\ \ +or you can use \x`\hskip`` <value>` to put arbitrary space. + +The space size of `\,`, `\!` resp. `\>`, resp. `\;` is given by +`\thinmuskip`, resp. `\medmuskip`, resp. `\thickmuskip` values. You can see +in the `plain.tex` file that these default values differ very little in their basic +size but there is no stretchability/shrinkability in the `\,` space, there is small +stretchability in the `\>` space, and more stretchability in the `\;` space. + +The registers \x`\thinmuskip`, \x`\medmuskip`, and \x`\thickmuskip` store so-called +\ii mu/values {\em mu values} given by math unit `mu`. It is 1/18 em and this unit depends +on the current font size used in the math formula ($S$ or $SS$ styles use +smaller font size, the `mu` unit is smaller here). You can use \x`\muskip` +instead `\hskip` or \x`\mukern` instead `\kern` if you want to use this +special mu unit. It is allowed only in math mode. + +The \x`\quad` and \x`\qquad` spaces have fixed width and they can be used in text +mode too. (\OpTeX/ allows to use `\,` in text mode too). +Use `\quad` or `\qquad` if you want to separate more formulas created in +single math mode. Examples of typical usage of spaces: + +\begtt \adef/{} \typosize[10/12] +$$ \alpha\,(x+y), \qquad \int/_a^b \!\! f(x)\,{\rm d}x, \qquad \Gamma/_{\!i}. $$ +\endtt +$$ \alpha\,(x+y), \qquad \int_a^b \!\! f(x)\,{\rm d}x, \qquad \Gamma_{\!i}. $$ + + +\secc Texts in math mode + +If you write `$Hello world!$` (i.e.\ Hello world in math mode), then you get +$Hello world!$. It is interpreted as the product of variables $H$, and $e$, and +$l^2$, and $o$, etc., followed by the symbol ! used for factorial. +The non-ASCII letters (with accents) don't work at all because they are +never used as symbols for variables. Spaces are ignored. + +If you want to write a short text in the math mode, then you can use +`\hbox{<text>}`. The \x`\hbox` primitive initializes text mode regardless of +the \"outer mode". Example: + +\begtt \adef/{} \typosize[10/12] +$$ \sum/_{n=0}^\infty (-1)^n a_n \hbox{ converges, if $a_n\searrow 0$.} $$ +\endtt +$$ \sum_{n=0}^\infty (-1)^n a_n \hbox{ converges, if $a_n\searrow 0$.} $$ +% +Note the space before the word \"converges". The space before `\hbox` is +irrelevant. Second notice: the example shows the text mode inside math mode +and the in-line math mode inside this text mode. The same result can be +produced by: + +\begtt \adef/{} \typosize[10/12] +$$ \sum/_{n=0}^\infty (-1)^n a_n \hbox{ converges, if } a_n\searrow 0. $$ +\endtt +% +The difference can be visible if the formula $a_n\searrow 0$ includes a +fraction, for example ${1\over2}a_n\searrow 0$. The first example prints the +fraction in the text style and the second example prints it in the display style. + +The disadvantage of `\hbox` is that it starts in the text mode independently +of the current style, but we want to use smaller font in $S$ or $SS$ styles. +\new \OpTeX/ +You can use \x`\mathbox``{<text>}` in such situations. This macro behaves like +`\hbox` but the text is appropriately smaller in $S$ and $SS$ styles. +Example: +$$ + `{\mathbox{cena}\over\mathbox{výkon}}` \quad \hbox{gives } + {\mathbox{cena}\over\mathbox{výkon}} \hbox{ in $D$ style and } + \textstyle {\mathbox{cena}\over\mathbox{výkon}} \hbox{ in $T$ style.} +$$ +Note that $\mathbox{cena}\over\mathbox{výkon}$ means $\rm price\over performance$ +and you can write `$\rm price\over performance$` when you are using only +words without spaces and accented letters. But phrases with spaces or accented letters +should be printed in text mode using `\hbox` or `\mathbox`. + +\secc `\vcenter` + +The \x`\vcenter` primitive behaves like `\vbox`, but it can be used only in +math mode and its result is vertically centered to the math axis. +For example, matrices, are created by tables in `\vcenter`. + +All big objects in math formula are centered on the math axis and the baseline is +ignored. In the following example, we create a new big math operator by +`\vcenter`: +\begtt +$$ + \def\myop#1{\mathop{\vcenter{\frame{\vbox to2em{\vss\hbox{ $#1$ }\vss}}}}} + F(x) = \myop{x(i)}_{i=1}^\infty +$$ +\endtt +\vskip-2em +$$ + \def\myop#1{\mathop{\vcenter{\frame{\vbox to2em{\vss\hbox{ $#1$ }\vss}}}}} + F(x) = \myop{x(i)}_{i=1}^\infty +$$ + + +\secc Three dots + +You can write `$1,2,\dots,n$` to get $1,2,\dots,n$. The \x`\dots` macro puts +thin space between dots and after the last dot, so the five object: comma, +dots, comma are exactly equidistant. + +Typographic conventions say that you have to use the repeating symbol +before and after three dots (comma in the previous example) and the three dots +should be at baseline if the repeating symbol is at baseline. Or they should be +at the math axis if the repeating symbol is at the math axis. We have to use \x`\cdots` instead +`\dots` in the second case. Example: +$$ + `a_1, a_2, \dots, a_n, \quad a_1 + a_2 + \cdots + a_n` \qquad + a_1, a_2, \dots, a_n, \quad a_1 + a_2 + \cdots + a_n +$$ +\vskip-.7em +There are \x`\vdots` $\vdots$, \x`\ddots` $\ddots$ and \x`\adots` $\adots$ which +can be used in matrices. + +\new Unicode +Three dots like the output of the `\dots` macro are present as a single +character in fonts too. This character is called ellipsis. Font designers +typically suggest this character with smaller spaces between dots than we +need in math mode. So the rule about equidistant \"comma, three dots, comma" +is not met when this character is used. You can try `$1,2,\unicodeellipsis, n$` +and `$1+2+\unicodecdots + n$`. You get $1,2,\unicodeellipsis, n$ and +$1+2+\unicodecdots + n$. If you feel that this is better, then you can set: +`\let\dots=\unicodeellipsis \let\cdots=\unicodecdots`. + +The Unicode fonts includes compact variants `\unicodevdots` $\unicodevdots$, +`\unicodeddots` $\unicodeddots$ and `\unicodeadots` $\unicodeadots$ too. + + +\secc Phantoms and `\smash` + +The \x`\phantom``{<math list>}` macro creates an invisible subformula equal to +the formula generated by <math list>. It has its size, so it can +interfere with surrounding visible subformulas. This macro is very useful for +aligning with special requirements. Examples are shown in +sections~\ref[matrix] and~\ref[elines]. + +The \x`\vphantom``{<math list>}` has only its vertical size (i.e.\ its height +and depth), the width is zero. The \x`\hphantom``{<math list>}` has only its +width. + +The \x`\smash``{<math list>}` is the opposite of `\vphantom`. It creates visible +subformula but it has only its width. Its height and depth are zero. + +The result of these macros is the nucleus of an Ord atom. You can use `\mathop`, +`\mathbin`, etc. primitives to change this class. For example +`$a\mathrel{\phantom{=}}b$` creates the same formula as $a=b$ with the same +distance from $a$ to $b$ but without the equal sign: +$a\mathrel{\phantom{=}}b$. + +These macros work in the text mode too. Then their argument is +the <horizontal list>. + + +\sec Structured objects + +\secc[matrix] Matrices + +The macro \x`\matrix``{<data>}` creates a vertically centered table of items. +The <data> includes <items> separated by `&` and rows are separated by +`\cr`. The number of columns and rows are unlimited. Columns are printed centered +and separated by the `\quad` space. The vertically scalable +brackets around the table are not printed. You can use \x`\pmatrix``{<data>}` +instead `\matrix{<data>}`: the vertically scalable parentheses () are inserted +around the table. Examples: + +\begtt +$$ + {\bf A} = \pmatrix{a_{1,1} & a_{1,2} & \cdots & a_{1,n} \cr + a_{2,1} & a_{2,2} & \cdots & a_{2,n} \cr + \vdots & \vdots & \ddots & \vdots \cr + a_{m,1} & a_{m,2} & \cdots & a_{m,n} }, +$$ +\endtt +$$ + {\bf A} = \pmatrix{a_{1,1} & a_{1,2} & \cdots & a_{1,n} \cr + a_{2,1} & a_{2,2} & \cdots & a_{2,n} \cr + \vdots & \vdots & \ddots & \vdots \cr + a_{m,1} & a_{m,2} & \cdots & a_{m,n} }, +$$ +or: + +\begtt +\def\qmatrix[#1]{\left[\matrix{#1}\right]} +$$ + \qmatrix[a&b&c\cr d&e&f\cr g&h&i] \cdot \qmatrix[x_1\cr x_2\cr x_3] + = \qmatrix[b_1\cr b_2\cr b_3]. +$$ +\endtt +$$ + \def\qmatrix[#1]{\left[\matrix{#1}\right]} + \qmatrix[a&b&c\cr d&e&f\cr g&h&i] \cdot \qmatrix[x_1\cr x_2\cr x_3] + = \qmatrix[b_1\cr b_2\cr b_3]. +$$ + +If you need to align the columns by another way than to center, then you can +use the phantom. Compare: + +\begtt +$$ + \pmatrix{ 1 & -1 & 0 \cr + 0 & 2 & 13 \cr + -3 & 0 & 5 } \quad \hbox{or} \quad + \def\0{\phantom0} \def\+{\phantom+} + \pmatrix { \+1 & -1 & \00 \cr + \+0 & \+2 & 13 \cr + -3 & \+0 & \05 } +$$ +\endtt +$$ + \pmatrix{ 1 & -1 & 0 \cr + 0 & 2 & 13 \cr + -3 & 0 & 5 } \quad \hbox{or} \quad + \def\0{\phantom0} \def\+{\phantom+} + \pmatrix { \+1 & -1 & \00 \cr + \+0 & \+2 & 13 \cr + -3 & \+0 & \05 } +$$ + +\new\OpTeX/ +Another option to set the right aligned matrix is setting the \x`\lmfil`: +Its value is used on the left side in each `\matrix` item. The right side is +set directly to `\hfil`. +\begtt +$$ + \lmfil={\hfill} % left matrix filler = \hfill + \pmatrix{ 1 & -1 & 0 \cr 0 & 2 & 13 \cr -3 & 0 & 5 } +$$ +\endtt + +\new \OpTeX/ +If you want to draw a vertical line inside the matrix, you can use `\adef|` +as in the following example: +\begtt +$$ + \adef|{\kern-.2em&\strut\vrule&\kern-.2em} + \def\+{\phantom+} + \pmatrix{1 & 2 & 3 | 0 \cr 4 & 5 & 6 | 1 \cr 7 & 8 & 9 | 2 } \sim + \pmatrix{1 & \+2 & \+3 | 0 \cr 0 & -3 & -6 | 1 \cr 0 & -6 & -12 | 2} \sim + \pmatrix{1 & 2 & 3 | 0 \cr 0 & 1 & 2 | -1/3 \cr 0 & 0 & 0 | 1 } +$$ +\endtt +$$ + \adef|{\kern-.2em&\strut\vrule&\kern-.2em} + \def\+{\phantom+} + \pmatrix{1 & 2 & 3 | 0 \cr 4 & 5 & 6 | 1 \cr 7 & 8 & 9 | 2 } \sim + \pmatrix{1 & \+2 & \+3 | 0 \cr 0 & -3 & -6 | 1 \cr 0 & -6 & -12 | 2} \sim + \pmatrix{1 & 2 & 3 | 0 \cr 0 & 1 & 2 | -1/3 \cr 0 & 0 & 0 | 1 } +$$ + +If you want to put something before the opening bracket in the matrix, you can +use another `\matrix`. Example: + +\begtt +$$ + \adef|{\kern-.2em&\strut\vrule&\kern-.2em} + \def\+{\phantom+} + \def\r{{\bf r}} + \pmatrix{1 & 2 & 3 | 0 \cr 4 & 5 & 6 | 1 \cr 7 & 8 & 9 | 2 } \ \sim \ + \matrix{\cr 2.\r - 4\cdot 1.\r: \cr 3.\r -7\cdot 1.\r: } + \pmatrix{1 & \+2 & \+3 | 0 \cr 0 & -3 & -6 | 1 \cr 0 & -6 & -12 | 2} +$$ +\endtt +$$ + \adef|{\kern-.2em&\strut\vrule&\kern-.2em} + \def\+{\phantom+} + \def\r{{\bf r}} + \pmatrix{1 & 2 & 3 | 0 \cr 4 & 5 & 6 | 1 \cr 7 & 8 & 9 | 2 } \ \sim \ + \matrix{\cr 2.\r - 4\cdot 1.\r: \cr 3.\r -7\cdot 1.\r: } + \pmatrix{1 & \+2 & \+3 | 0 \cr 0 & -3 & -6 | 1 \cr 0 & -6 & -12 | 2} +$$ + +Plain \TeX/ defines the \x`\bordermatrix` macro which allows you to create a +top row above the brackets and left column before the opening bracket. +\TeX/book shows the following example: + +\begtt +$$ + M = \bordermatrix{ &C&I&C'\cr + C&1&0&0 \cr I&1-b&0 \cr C'&0&a&1-a } +$$ +\endtt +$$ + M = \bordermatrix{ &C&I&C'\cr + C&1&0&0 \cr I&1-b&0 \cr C'&0&a&1-a } +$$ + +The `\matrix` macro used in $D$ style creates all its items in $T$ style. +\new \OpTeX/ +If you are using the `\matrix` macro in $T$ style or $S$ style (but not in +fractions nor another matrices) then the resulting table is appropriately +smaller and all its items are processed in $S$ style. +If you are using `\matrix` in $SS$ style then the items are in $SS$ style too. +The following example shows one-column matrix in script style: +$$ + `\sum``_{\matrix{i\in M\cr j\in N\cr k\in P}} x_{i,j,k}` \ \hbox{ creates: } + \sum_{\matrix{i\in M\cr j\in N\cr k\in P}} x_{i,j,k} +$$ + + +\secc Cases + +The \x`\cases` macro can be used as in the following example: + +\begtt +$$ + f(x) = \cases{ 1 & for $x\le 0$, \cr + 100-x\over 100 & when $0 < x \le 100$, \cr + 0 & in other cases. } +$$ +\endtt +$$ + f(x) = \cases{ 1 & for $x\le 0$, \cr + 100-x\over 100 & when $0\string< x\le 100$, \cr + 0 & in other cases. } +$$ + +The `\cases` macro behaves like a special `\matrix` with two left-aligned +columns and with left vertically scaled brace $\{$. +The first column is processed in math mode and $T$ style, the second column +is processed in text mode. We have to use `$...$` in the second column if +there is math material. + + +\sec Lines in display mode + +\secc General principles + +The \ii display/math,display/math/mode +`$$<formula>$$` finalizes previous paragraph, prints centered <formula> on +single line with a vertical space above and below and opens next paragraph +with no indentation. + +From \TeX/'s point of view, the text above `$$<formula>$$` plus text +below is a single paragraph interrupted by display <formula>. If there is no +text above (i.e. the opening `$$` are in vertical mode), then the internal +`\noindent` is processed first and the empty line above <formula> is created. +Thus, it is definitely a bad idea to open display mode in vertical mode: never +put an empty line before `$$<formula>$$`. On the other hand, the empty line +just after `$$<formula>$$` says that the paragraph is finalized by the +<formula> and the next text (after the empty line) opens the next paragraph with +indentation. Summary: + +\begitems +* \"Text above `$$<formula>$$` text below": the <formula> interrupts the + paragraph with \"Text above" and \"text below". The \"text below" is + without indentation. +* \"Text above `$$<formula>$$` empty line Text below": the \"Text below" + opens new paragraph with indentation. +* \"Empty line `$$<formula>$$`" is bad practice. +\enditems + +In contrast with the paragraph breaking, there is no built-in algorithm for +breaking display <formula> to more lines. If the <formula> is too wide then +overfull `\hbox` occurs and human must decide about splitting the <formula> +to more lines. The macros `\displaylines` and `\eqalign` are intended to +such task, see sections~\ref[dlines] and~\ref[elines]. + +On the other hand, the in-line math <formula>, i.e.\ the `$<formula>$` in a +paragraph, can be broken after a Bin atom (with penalty `\binoppenalty`) or +after a Rel atom (with penalty `\relpenalty`). If you don't want to break +such a formula at a specific place then use `\nobreak`, for example +`$a+\nobreak b$`. If you want never to break such formulas then you can set +`\binoppenalty=10000`, `\relpenalty=10000`. (Default values are 700 and 500.) + + +\secc References to display lines + +The `$$<formula>`\x`\eqno``<mark>$$` \ii mark prints centered <formula> and the <mark> at +right margin. The `$$<formula>`\x`\leqno``<mark>$$` prints centered <formula> and +the <mark> at left margin. Examples: + +\begtt +$$ a^2 + b^2 = c^2 \eqno (1) $$ +\endtt +$$ + a^2 + b^2 = c^2 \eqno (1) +$$ +\begtt \aftergroup\nobreak +$$ a^2 + b^2 = c^2 \leqno \rm Py $$ +\endtt +$$\predisplaypenalty=10000 + a^2 + b^2 = c^2 \leqno \rm Py +$$ +The <mark> \ii mark is processed in math mode and $T$ style. If you want to put a +text here then you have to use `\rm <text>` or `\hbox{<text>}`. + +\new \OpTeX/ +The auto-generated <mark> can be created by `$$<formula>`\x`\eqmark``$$`. The +<label> can be used previously declared by \x`\label``[<label>]`. +Then it is associated to such +auto-generated <mark> and you can write a reference in the form +`see equation~\ref[<label>]`. You can write `\eqmark[<label>]` instead of +`\label[<label>]...\eqmark`. See the \OpTeX/ manual, section~1.4.3. + +\secc[dlines] The `\displaylines` macro + +This macro creates more horizontally centered formulas in one display mode. +The syntax is +\begtt \catcode`\<=13 +$$ \displaylines{ + <formula> \cr + <formula> \cr + ... \cr + <formula> +} $$ +\endtt +Usage of \x`\displaylines` is more +prefered than doing more display modes just behind each other. +Example: +\begtt +$$ \displaylines{ + (3x^3 + 4x^2 + 5x + 6) \cdot (x^6 + x^2 + 5) = \cr + = 3x^9 + 4x^8 + 5x^7 + 6x^6 + 3x^5 + 4x^4 + 20x^3 + 26x^2 + 25x + 30. +} $$ +\endtt +$$ \displaylines{ + (3x^3 + 4x^2 + 5x + 6) \cdot (x^6 + x^2 + 5) = \cr + = 3x^9 + 4x^8 + 5x^7 + 6x^6 + 3x^5 + 4x^4 + 20x^3 + 26x^2 + 25x + 30. +} $$ + +The output from `\displaylines` macro is breakable to more pages because +the lines are not encapsulated in one box. The macro uses a special feature of +`\halign` primitive. The disadvantage is that you cannot use `\eqno` nor +`\leqno` nor `\eqmark`. + +\new \OpTeX/ +\OpTeX/ provides alternative form: `\displaylines to<dimen> {<data>}`. +Then the centered formulas are encapsulated in a `\vcenter` box of width <dimen> and +usage of `\eqno` or `\leqno` or `\eqmark` is allowed. +The individual lines have the form `\hbox to<dimen>` and formulas are centered using +`\hss` from both sides. This means that you can set arbitrary <dimen> +without visual change of the formulas. Use smaller <dimen> value than +`\hsize` (or `\displaywidth`\fnote +{`\displaywith` = `\hsize` in most cases but it is +real display width when `\parshape` or `\hangindent` is used.}) +if you want to center formulas with `\eqno` appended. +The internal \TeX/ rule says: the formula with `\eqno` (or `\leqno`) is centered +if its width is less or equal `\displaywidth-4<mark-width>`. So +\begtt \catcode`\<=13 +$$ \displaylines to\hsize-8em {<formula>\cr<formula>}\eqno (1) $$ +\endtt +does global centering, because size of `(1)` is less than 2\,em. +You can do more experiments with this example, +for example `\diplaylines to\hsize{...}` +puts the `\eqno` mark to the next line in the display environment. Read +\TeX/book or \TeX/book naruby, where the precise explanation about such +positioning is. + +\new \OpTeX/ +You can use \"`\displaylines to<dimen>`" for more applications. For example, +you can put more +\"`\displaylines to<dimen>`" in single display mode, one next to second in order +to creating more centered columns with formulas; the width of such columns +are controlled by the <dimen> parameter. +Or, you can give an exception for several lines: + +\begtt \catcode`\<=13 +$$\displaylines to 10cm {<formula>\hfill \cr + <formula>\cr + <formula>\cr + \hfill <formula>} +$$ +\endtt +The example above gives similar result as the \LaTeX/ `multline` environment: +$$\displaylines to \hsize { + (3x^3 + 4x^2 + 5x + 6) \cdot (x^6 + x^2 + 5) = \hfill \cr + = 3x^9 + 3x^5 + 15x^3 + 4x^8 + 4x^4 + 20x^2 + 5x^7 + 5x^3 + 25x + + 6x^6 + 6x^2 + 30 = \cr + \hfill = 3x^9 + 4x^8 + 5x^7 + 6x^6 + 3x^5 + 4x^4 + 20x^3 + 26x^2 + 25x + 30. } +$$ + + +\secc[elines] The `\eqalign` macro + +The \ii .eqalign \iis .eqalign {{\code{\\eqalign}}} usage is: +\begtt \catcode`\<=13 +$$ \eqalign { <left-side> & <right-side> \cr + <left-side> & <right-side> \cr + ... \cr + <left-side> & <right-side> +} $$ +\endtt +The `\vcenter` box is created with two columns, left column is right aligned +and right column is left aligned. Example: + +\vbox{ +\begtt +$$ \eqalign{ + x + 2y + 3z &= 600 \cr + 12x + y - 3z &= 7 \cr + 4x - y + 5z &= -5 \cr +} $$ +\endtt +\vskip-5.7\baselineskip +{\hsize=1.35\hsize +$$ \eqalign{ + x + 2y + 3z &= 600 \cr + 12x + y - 3z &= 7 \cr + 4x - y + 5z &= -5 \cr +} $$}} + +\bigskip\noindent +The tab \"`&`" should be used just before a relation, i.e. `&=` is right, `=&` +is wrong. All lines are aligned to the used tab. + +Maybe you want more precise alignment in the example above. You can use +`\phantom`: + +\par\nobreak\vbox{ +\begtt +$$ \def\1{\phantom1} \def\+{\phantom+} + \eqalign{ + x + 2y + 3z &= 600 \cr + 12x + \1y - 3z &= \+7 \cr + 4x - \1y + 5z &= -5 \cr +} $$ +\endtt +\vskip-5.7\baselineskip +{\hsize=1.35\hsize +$$ \def\1{\phantom1} \def\+{\phantom+} + \eqalign{ + x + 2y + 3z &= 600 \cr + 12x + \1y - 3z &= \+7 \cr + 4x - \1y + 5z &= -5 +} $$}} +\bigskip +Another typical usage of the `\eqalign` macro: + +\begtt \typosize[10/12] +$$ \eqalign{ + p(x)\,q(x) &= (3x^3 + 4x^2 + 5x + 6) \cdot (x^6 + x^2 + 5) = \cr + &= 3x^9 + 4x^8 + 5x^7 + 6x^6 + 3x^5 + 4x^4 + 20x^3 + 26x^2 + 25x + 30. +} $$ +\endtt +$$ \eqalign{ + p(x)\,q(x) &= (3x^3 + 4x^2 + 5x + 6) \cdot (x^6 + x^2 + 5) = \cr + &= 3x^9 + 4x^8 + 5x^7 + 6x^6 + 3x^5 + 4x^4 + 20x^3 + 26x^2 + 25x + 30. +} $$ + +In \OpTeX/, \new\OpTeX/ +the `\eqalign` macro is more flexible. You can set the +`\baselineskip` value by the \x`\eqlines` parameter and math style +by the \x`\eqstyle` parameter. +For example, you need to put the system of \"equations" as a subscript of a sum +operator: +\begtt \typosize[10/12] \adef/{} +$$ + \sum/_{\eqlines{\baselineskip=.7\baselineskip}\eqstyle{\scriptstyle}\eqalign{ + i &\in A \cr + \quad j &\in B\cup C \cr + m &\in C }} + i + j + m +$$ +\endtt +$$ + \sum_{\eqlines{\baselineskip=.7\baselineskip}\eqstyle{\scriptstyle}\eqalign{ + i &\in A \cr + \quad j &\in B\cup C \cr + m &\in C }} + i + j + m +$$ + +\indent \new\OpTeX/ +You can write more equation systems one next second: +\begtt +$$\eqalign{ + x + y + z &= 1 && a + b + c &= -1 \cr + u + v &= 20 && f + g &= -20 \cr + i &= j +}$$ +\endtt +You can use the third column for centered equations +without aligning point. For example: +\begtt \catcode`\<=13 +$$ \left( \eqspace=0pt \eqalign{&& <first equation>\cr + && <second equation>} \right) $$ +\endtt +The \x`\eqspace` is additional space used in the third column to separate +equation systems one next second. + +\new \OpTeX/ +\OpTeX/ extensions summary: +\begitems +* `\eqlines` and `\eqstyle` set baselineskip and math style of the formulas. +* `\eqalign` allows more than two columns: + The first column is right-aligned (no space). The second is left-aligned (no space). + The third column (if used) + is centered with `\eqspace/2` at the left and right boundary of the column. + The fourth is the same as the first. The fifth is the same as second etc. The number + of columns that can be used in `\eqalign` is unlimited. +\enditems + +\secc The `\eqalign` macro with references + +You can give common mark to whole equation system by +`$$\eqalign{<data>}\eqno <mark>$$`. If you want to give marks to individual +lines of the equation system, then you can use another macro: +\x`\eqalignno`. The usage is similar as `\eqalign` but the +third column (if used) is intended to the equation mark. Example: + +\begtt +$$ \eqalignno{ + x + 2y + 3z &= 600 & \rm(A) \cr + 12x + y - 3z &= 7 & \rm(B) \cr + 4x - y + 5z &= -5 & \rm(C) \cr +} $$ +\endtt +\vskip-\baselineskip +$$ \eqalignno{ + x + 2y + 3z &= 600 & \rm(A) \cr + 12x + y - 3z &= 7 & \rm(B) \cr + 4x - y + 5z &= -5 & \rm(C) \cr +} $$ + +The `\leqalignno` macro is similar to `\eqalignno` but the marks are at the left +margin. The \OpTeX/ extensions of `\eqalign` are not available in +`\eqalignno` nor `\leqalignno` macros. + +\new \OpTeX/ +You can use auto-generated marks by `\eqmark` macro: +`$$\eqalign{<data>}\eqmark$$` or: +\begtt +$$ \eqalignno{ + x + 2y + 3z &= 600 & \eqmark[A] \cr + 12x + y - 3z &= 7 & \eqmark[B] \cr + 4x - y + 5z &= -5 & \eqmark[C] \cr +} $$ +\endtt + + +\sec Concept of loading math fonts + +\secc[fams] Math families + +\TeX/ can use more than one math font in math mode. This was a +necessity in the old days when only 128-characters fonts existed. +Each math font used in math mode has its \ii math/family {\em math family} represented by a number. +Math family is a collection of three (almost) equal fonts in three sizes: +first for `\textstyle` and `\displaystyle`, second for `\scriptstyle` +and third for `\scriptscriptstyle`. + +\new Unicode +When Unicode math font is loaded then it includes all three optical sizes and +all characters needed for typesetting math formula. +Theoretically, we can use only one math family with this single font. But more math families +(i.e.\ more fonts in math mode) is still possible. You can combine +characters from more fonts (Unicode fonts and old TFM fonts together) in one math formula. + +\new \OpTeX/ +\OpTeX/ loads the main Unicode math font into math family 1. The math +families 2 and 3 are reserved for specific \TeX/nical reasons, family 4 is +used for `\script` font and families 5, 6, 7, etc. can be used by user for +loading more fonts. The default macro for loading math fonts looks like: + +\begtt \typosize[10/12] +\_def\_normalunimath{% + \_loadumathfamily 1 {\_unimathfont}{} % Main Unicode math font + \_loadmathfamily 4 rsfs % \script (old TFM font) + \_setunimathdimens % set dimen parameters used in math formulas internally +}% +\let\_normalmath=\_normalunimath % this is done when Unicode math is initialized +\endtt +% +Whenever \OpTeX/ needs to resize math fonts (for example in footnotes or +titles), it calls the `\_normalmath` macro to reload all math +families to the desired size. If you want to add the next font, you can add +`\_loadunimathfamily <family> {<Unicode-font>}{<features>}` or +`\_loadmathfamily <family> <TFM-font>` into the `\_normalmath` macro. +The example in section~\ref[newfam] shows how to do it. + +\secc Two variants of math fonts: normal and bold + +All math formulas in the whole document need only one Unicode font (or only one collection +of math fonts as mentioned in section~\ref[fams]). But this +is not really true if titles are in bold font. If a math formula is present in +such a bold title then all characters of this formula must be bolder. +For example \"normal" variables must be in bold italic in titles, symbols +like `+` `=` must be bold and \"normal bold" letters +(e.g., indicating vectors in math formula) must be extra bold in titles. +It means that all fonts from the collection of math fonts must be bolder. +We need a second collection of math fonts with bolder +shape. Unfortunately, it is not always available. + +\new \OpTeX/ +If you have bold variant of used Unicode math font, then you can use +\ii .loadmath \iis .loadmath {{\code{\\loadmath}}} \x`\loadboldmath` command, for example: +\begtt +\loadmath {[xitsmath-regular]} +\loadboldmath {[xitsmath-bold]} \to {[xitsmath-regular]} +\endtt +% +\OpTeX/ uses `\_normalmath` macro for loading collection of math fonts in +\"normal" cases and `\_boldmath` macro for bold titles. The font declared by +\x`\loadboldmath` is used in second case. But if the bold variant of the font is +not available (this is unfortunately more typical), then \OpTeX/ uses faked +bold of main Unicode math font (the `embolden` internal font feature is +used). So, the default `\_boldmath` macro defined by \OpTeX/ looks like: + +\begtt \typosize[10/12] +\_def\_boldunimath{% + \_ifx\_unimathboldfont \_undefined + \_loadumathfamily 1 {\_unimathfont}{embolden=1.7;} % Main faked bold + \_else + \_loadumathfamily 1 {\_unimathboldfont}{} % Main real bold font + \_fi + \_loadmathfamily 4 rsfs % rsfs in not in bold, unfortunately + \_setunimathdimens +}% +\let\_boldmath=\_boldunimath % this is done when Unicode math is initialized +\endtt + +\secc[newfam] Example of using additional math font + +The font `bbold10.tfm` includes double stroked characters, for example, +double stroked plus, double stroked Greek letters and digits. +Try to run `pdftex testfont`, then answer the question about the name of the +font: `bbold10` and then type command `\table\end`. The `testfont.pdf` is +printed with the table of characters of this font. +Most of these characters cannot be found in Unicode math fonts. + +\new \OpTeX/ +We show an example of how to add this font to the collection of used math fonts. +We can re-define the `\_normalmath` macro by: +\begtt \typosize[10/12] +\addto\_normalmath {\_loadmathfamily 5 bbold } + +\_regtfm bbold 0 bbold5 5.5 bbold6 6.5 bbold7 7.5 bbold8 8.5 bbold9 + 9.5 bbold10 11.1 bbold12 15 bbold17 * % using all bbold*.tfm +\_normalmath % reload the math fonts collection +\endtt +% +The string \"`bbold`" is declared by `\_regtfm` as a collection of all +`bbold*.tfm` fonts, the optical sizes are supported. + +\addto\_normalmath {\_loadmathfamily 5 bbold } +\_regtfm bbold 0 bbold5 5.5 bbold6 6.5 bbold7 7.5 bbold8 8.5 bbold9 + 9.5 bbold10 11.1 bbold12 15 bbold17 * % using all bbold*.tfm +\_normalmath +\Umathchardef \bbplus 2 5 "2B +\Umathchardef \bble 3 5 "3C +\Umathchardef \bbge 3 5 "3E + +Finally, we must to declare new \TeX/ sequences for accessing the characters +from the new font, for example: + +\begtt \typosize[10/12] +\Umathchardef \bbplus 2 5 "2B +\Umathchardef \bble 3 5 "3C +\Umathchardef \bbge 3 5 "3E +\endtt +% +The \x`\Umathchardef` \TeX/ primitive declares new \TeX/ sequence used in math +typesetting. The first parameter is a class number (2 means Bin, 3 means Rel, +see the table in the section~\ref[class]). The second parameter is a math +family number. It is 5, see the redefinition of the `\_normalmath` macro above. +The third parameter is a slot in the font. Now you can try to use these characters: +$$ + `a \bbplus b \bbge c` \quad \hbox{gives} \quad a \bbplus b \bbge c. +$$ +% +Maybe, you want to declare a special math selector which can be used as +`$\bball a+b>c$` in order to get $\bbchar a \bbplus b \bbge c$. +Then you can define: + +\begtt \typosize[10/12] +\def\bball {\bbchar \Umathcodenum `+ \bbplus + \Umathcodenum `> \bbge + \Umathcodenum `< \bble } +\endtt + +If you want to add all double stroked Greek letters into `\bball` +selector, then you can do something like this: + +\begtt \typosize[10/12] +\def\setbbgreek #1 {\tmpnum=#1\xargs\setbbgreekA} +\def\setbbgreekA #1{\Umathcode \_ea`#1 0 5 \tmpnum \advance\tmpnum by1 } + +\addto\bball {% + \setbbgreek "0B \alpha \beta \gamma \delta \epsilon \zeta \eta + \theta \iota \kappa \lambda \mu \nu \xi \pi \rho \sigma + \tau \upsilon \phi \chi ; + \setbbgreek "7F \omega ; + \setbbgreek "00 \Gamma \Delta \Theta \Lambda \Xi \Pi \Sigma \Upsilon + \Phi \Psi \Omega ; } +\endtt +% +The \x`\Umathcode`` <input-code> <class> <family> <font-slot>` primitive is used +here. The control sequences `\alpha`, `\beta`, `\gamma` etc. are macros which expand +to the Unicode character of appropriate (non-math) Greek letter. We set the +Umathcode to such character, for example +\code{\\Umathcode `}$\_rmgreek\alpha$` 0 5 "0B` is processed. + +The bold variant of the font `bbold*.tfm` is not available, unfortunately. +We have to settle for normal version of the font in the `\_boldmath` macro: + +\begtt \typosize[10/12] + \addto \_boldmath {\_loadmathfamily 5 bbold } +\endtt + +Another approach of using more Unicode math fonts in a single formula is +shown in +\ulink[http://petr.olsak.net/optex/optex-tricks.html\#addumathfont]{OpTeX trick 0030}. + +\sec Index + +Control sequences listed at pages \pgref[listA]--\pgref[listB] are not +mentioned here again. + +\begmulti 3 +\makeindex +\endmulti + +\bye |