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diff --git a/doc/context/sources/general/manuals/math/math-grouping.tex b/doc/context/sources/general/manuals/math/math-grouping.tex new file mode 100644 index 000000000..cc79ff198 --- /dev/null +++ b/doc/context/sources/general/manuals/math/math-grouping.tex @@ -0,0 +1,212 @@ +% language=uk + +\environment math-layout + +\startbuffer[oldcolor] + \disableexperiments[simplegroups]% + % when we no longer have it as experiment + \unprotect \pushoverloadmode + \permanent\protected\def\color[#1]% + {\bgroup % \beginsimplegroup + \edef\currentcolorname{#1}% + \ifempty\currentcolorprefix + \colo_helpers_activate_nop + \else + \colo_helpers_activate_yes + \fi + \let\nexttoken}% + \popoverloadmode \protect +\stopbuffer + +\startbuffer[newcolor] + \enableexperiments[simplegroups]% +\stopbuffer + +\startcomponent math-grouping + +\startchapter[title=Grouping] + +\startsection[title=Some details] + +In \TEX\ there are all kind of groups. When you start with a curly brace, you +often enter a group but when you start a box or table cell you also do that. When +you enter math a math group is started. Assignments are, unless explicitly done +global, nearly always local to the group. Here we discuss the following two +cases: + +\starttyping +{ .... } +\bgroup .... \egroup +\begingroup .... \endgroup +\stoptyping + +We say two cases, not three, because the first two are equivalent: the two macros +in the second line are not primitives but aliases to the curly braces. There is +however one fundamental difference between them. The verbose \type {\begingroup} +starts a so called simple group so let's call the other complex. A complex group +is bounded by equivalents to the two characters (braces) that have catcodes that +begin and end these groups. So, the following is valid. + +\starttyping +{ .... } +{ .... \egroup +\bgroup .... } +\bgroup .... \egroup +\stoptyping + +This means that a macro like this is okay: + +\starttyping +\def\foo{\bgroup\bf\let\next} \foo{text} +\stoptyping + +The \type {\foo} will start a complex group, switch font and then pick up the +brace. The group will be closed by the matching right brace or an equivalent. +The following two cases are invalid: + +\starttyping +\bgroup .... \endgroup +\begingroup .... \egroup +\stoptyping + +which means that: + +\starttyping +\def\foo{\begingroup\bf\let\next} \foo{text} +\stoptyping + +will trigger an error message. This is rather unfortunate because using braces +to wrap an argument in curly braces is rather convenient. The way out is this: + +\starttyping +\def\foo#1{\begingroup\bf#1\endgroup} \foo{text} +\stoptyping + +which is perfectly valid apart from the fact that the argument is first picked up +and then fed back into the input. Apart from a small performance hit and using +more memory it also adds noise to tracing. + +\stopsection + +\startsection[title=Side effects] + +In math mode matters are complicates by the fact that complex groups (the ones +started with the curly brace) start a math list. And that has side effects because +the spacing between math elements depends on what we deal with: math symbol, lists, +fenced material. The following example shows a whole lot of this: + +\startbuffer[example] +\starttabulate[|j1|j1||] + \NC $\sin{\left(xxx\right)}$ + \NC $f {\left(xxx\right)}$ + \NC $x {\left(xxx\right)}$ + \NR + \NC $\sin\begingroup\left(xxx\right)\endgroup$ + \NC $f \begingroup\left(xxx\right)\endgroup$ + \NC $x \begingroup\left(xxx\right)\endgroup$ + \NR + \NC $\sin\left(xxx\right)$\par + \NC $f \left(xxx\right)$\par + \NC $x \left(xxx\right)$\par + \NR + \NC $\sin\color[darkgreen]{(xxx)}$\par + \NC $f \color[darkgreen]{(xxx)}$\par + \NC $x \color[darkgreen]{(xxx)}$\par + \NR + \NC $\sin\startcolor[darkblue](xxx)\stopcolor$\par + \NC $f \startcolor[darkblue](xxx)\stopcolor$\par + \NC $x \startcolor[darkblue](xxx)\stopcolor$\par + \NR + \NC $\sin(xxx)$\par + \NC $f (xxx)$\par + \NC $x (xxx)$\par + \NR + \NC $\sin{\color[darkyellow]{(xxx)}}$\par + \NC $f {\color[darkyellow]{(xxx)}}$\par + \NC $x {\color[darkyellow]{(xxx)}}$\par + \NR + \NC $\sin\begingroup\color[darkred]{(xxx)}\endgroup$\par + \NC $f \begingroup\color[darkred]{(xxx)}\endgroup$\par + \NC $x \begingroup\color[darkred]{(xxx)}\endgroup$\par + \NR +\stoptabulate +\stopbuffer + +\typebuffer[example] + +A valid question is why we would want to add curly braces. One reason is that we +we want to apply something to a few characters, in this case color the argument +to the sinus. Now, when a color command is defined as the \type {\foo} before, we +start a complex group and that influences spacing! This is demonstrated in the +left part of \in {figure} [fig:grouping:sin] (you can zoom in on the table to +see the details; we also report the kind of spacing applied). + +\startplacefigure[reference=fig:grouping:sin,title=Grouping influencing math spacing (list).] + \startcombination[nx=2,ny=1,distance=2em,style=bold] + \startcontent + \showmakeup[math,fontkern,italic]% laps into the margin hence the -2em + \getbuffer[oldcolor]% + \scale[width=\dimexpr\measure{combination}-2em\relax]{\getbuffer[example]}% + \stopcontent + \startcaption + pseudo grouping + \stopcaption + \startcontent + \showmakeup[math,fontkern,italic]% laps into the margin hence the -2em + \getbuffer[newcolor]% + \scale[width=\dimexpr\measure{combination}-1em\relax]{\getbuffer[example]}% + \stopcontent + \startcaption + grouping + \stopcaption + \stopcombination +\stopplacefigure + +The right variant in that figure uses a different way of grouping, one that is +equivalent to: + +\starttyping +\def\foo{\beginsimplegroup\bf\let\next} +\stoptyping + +This time we effectively do \type {\begingroup} but permits both \type +{\endgroup} or a curly brace (or \type {\egroup} to wrap up the group. That means +that we don't get the side effect of starting a math list. + +\startbuffer[example] +$ x = y \quad x \color[red]{=} y$ +\stopbuffer + +This example shows the effect of coloring a single character (the result is shown +in \in {figure} [fig:grouping:char]): + +\typebuffer[example] + +\startplacefigure[reference=fig:grouping:char,title=Grouping influencing math spacing (symbol).] + \vkern4ex + \startcombination[nx=2,ny=1,distance=4em,style=bold] + \startcontent + \showmakeup[math,fontkern,italic]% laps into the margin hence the -2em + \getbuffer[oldcolor]% + \scale[width=\dimexpr\measure{combination}-2em\relax]{\getbuffer[example]}% + \stopcontent + \startcaption + pseudo grouping + \stopcaption + \startcontent + \showmakeup[math,fontkern,italic]% laps into the margin hence the -2em + \getbuffer[newcolor]% + \scale[width=\dimexpr\measure{combination}-2em\relax]{\getbuffer[example]}% + \stopcontent + \startcaption + grouping + \stopcaption + \stopcombination + \vkern2ex +\stopplacefigure + +\stopsection + +\stopchapter + +\stopcomponent |