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Diffstat (limited to 'doc')
| -rw-r--r-- | doc/context/documents/general/manuals/math-mkiv.pdf | bin | 2866911 -> 2906190 bytes | |||
| -rw-r--r-- | doc/context/sources/general/manuals/math/math-mkiv.tex | 697 |
2 files changed, 16 insertions, 681 deletions
diff --git a/doc/context/documents/general/manuals/math-mkiv.pdf b/doc/context/documents/general/manuals/math-mkiv.pdf Binary files differindex 74bd9eedb..49b992f65 100644 --- a/doc/context/documents/general/manuals/math-mkiv.pdf +++ b/doc/context/documents/general/manuals/math-mkiv.pdf diff --git a/doc/context/sources/general/manuals/math/math-mkiv.tex b/doc/context/sources/general/manuals/math/math-mkiv.tex index f16359fcb..8f3a62705 100644 --- a/doc/context/sources/general/manuals/math/math-mkiv.tex +++ b/doc/context/sources/general/manuals/math/math-mkiv.tex @@ -1,693 +1,28 @@ % language=uk -\setupbodyfont - [pagella] +\environment math-layout -\setupwhitespace - [big] +\startproduct math-mkiv -\setuppagenumbering - [alternative=doublesided] +\startdocument -\setuplayout - [backspace=2cm, - width=middle, - cutspace=2cm, - topspace=2cm, - header=2cm, - height=middle, - footer=0pt, - bottomspace=2cm] +\component math-titlepage -\usemodule[x][setups-basics] +\startfrontmatter + \component math-contents + \component math-introduction +\stopfrontmatter -\usemodule[visual] +\startbodymatter + \component math-spacing + \component math-framing + \component math-numbering + \component math-combining +\stopbodymatter -\loadsetups[i-context] +\stopdocument -\starttext - -\startMPpage - -StartPage; - fill Page withcolor .35magenta ; - picture p ; p := image ( draw outlinetext.b - ("\textdollar") - (withcolor .35green) - (withcolor .5yellow withpen pencircle scaled .1) ; - ) ; - p := p xysized(PaperWidth - 20pt,PaperHeight - 20pt ) ; - p := p shifted - llcorner p shifted (10pt,10pt) ; - draw p ; - picture p ; p := image ( draw outlinetext.b - ("math") - (withcolor .35green) - (withcolor .5yellow withpen pencircle scaled .2) ; - ) ; - p := p xsized(PaperWidth/2 - 40pt) ; - p := p shifted - llcorner p shifted (10pt,10pt) ; - draw p shifted (PaperWidth/2 + 20pt,20pt); -StopPage; - -\stopMPpage - -\page[empty] \setuppagenumber[number=1] - -\setuplayout - [backspace=2cm, - topspace=2cm, - header=2cm, - height=middle, - width=middle] - -\setuphead - [chapter] - [header=high, - style=\bfc, - color=darkmagenta] - -\setuphead - [section] - [style=\bfb] - -\setuphead - [subsection] - [style=\bfa] - -\starttitle[title=Introduction] - -This manual is not a systematic discussion about math in \CONTEXT\ but more a -collection of wrap|-|ups. The file also serves as testcase. The content can -change over time and can also serve as a trigger for discussions on the mailing -list. Feel free to contribute. - -\startlines -Hans Hagen -Hasselt NL -% May 2016 -\stoplines - -\stoptitle - -\startchapter[title=Vertical spacing] - -The low level way to input inline math in \TEX\ is - -\starttyping -$ e = mc^2 $ -\stoptyping - -while display math can be entered like: - -\starttyping -$$ e = mc^2 $$ -\stoptyping - -The inline method is still valid, but for display math the \type {$$} method -should not be used. This has to do with the fact that we want to control spacing -in a consistent way. In \CONTEXT\ the vertical spacing model is rather stable -although in \MKIV\ the implementation is quite different. It has always been a -challenge to let this mechanism work well with space round display formulas. This -has to do with the fact that (in the kind of documents that we have to produce) -interaction with already present spacing is somewhat tricky. - -Of course much can be achieved in \TEX\ but in \CONTEXT\ we need to have control -over the many mechanisms that can interact. Given the way \TEX\ handles space -around display math there is no real robust solution possible that gives visually -consistent space in all cases so that is why we basically disable the existing -spacing model. Disabling is easier in \LUATEX\ and recent versions of \MKIV\ have -been adapted to that. - -In pure \TEX\ what happens is this: - -\startbuffer -$$ x $$ -\stopbuffer - -\typebuffer \par \start \showboxes \getbuffer \par \stop - -A horizontal box get added which triggers a baselineskip. Then the formula is put -below it. We can get rid of that box with \type {\noindent}: - -\startbuffer -\noindent $$ x $$ -\stopbuffer - -\typebuffer \par \start \showboxes \getbuffer \par \stop - -In addition (not shown here) vertical space is added before and after the formula -and left- and rightskip on the edges. In fact typesetting display math goes like this: - -\startitemize[packed] - \startitem - typeset the formula using display mode and wrap it in a box - \stopitem - \startitem - add an equation number, if possible in the same line, otherwise on a line - below - \stopitem - \startitem - in the process center the formula using the available display width and - required display indentation - \stopitem - \startitem - add vertical space above and below (depending also in displays being - short in relation to the previous line - \stopitem - \startitem - at the same time also add penalties that determine the break across - pages - \stopitem -\stopitemize - -Apart from the spacing around the formula and the equation number, typesetting is -not different from: - -\starttyping -\hbox {$ \displaystyle x $} -\stoptyping - -This spacing around math is a sensitive issue. Because math itself can have a -narrow band, for instance a lone $x$, or relative much depth, as with $y$, or -both depth and height as in $(1,2)$ and $x^2 + y_2$ and because a preceding line -can have no or little depth and a following line little height, the visual -appearance can become inconsistent. The default approach is to force consistent -spacing, but when needed we can implement variants. - -Spacing around display math is set up with \type {\setupformulas}: - -\starttyping - \setupformulas - [spacebefore=big, - spaceafter=big] -\stoptyping - -When the whitespace is larger that setting wins because as usual the larger -of blanks or whitespace wins. - -% \showdefinition[setupformula] -% \showdefinition[setupmathematics] - -In \in {figures} [whitespace-no], \in {figures} [whitespace-medium] \in {and} -[whitespace-big] we see how things interact. We show lines with and without -maximum line height and depth (enforced by struts) alongside. - -% no whitespace - -\startbuffer[demo-1] -\disablemode[with-struts] -\showmakeup -\setupformulas[spacebefore=none,spaceafter=none] -\setupwhitespace[none] -\input math-spacing-001.tex -\stopbuffer - -\startbuffer[demo-2] -\enablemode[with-struts] -\showmakeup -\setupformulas[spacebefore=none,spaceafter=none] -\setupwhitespace[none] -\input math-spacing-001.tex -\stopbuffer - -\startbuffer[demo-3] -\disablemode[with-struts] -\showmakeup -\setupformulas[spacebefore=medium,spaceafter=medium] -\setupwhitespace[none] -\input math-spacing-001.tex -\stopbuffer - -\startbuffer[demo-4] -\enablemode[with-struts] -\showmakeup -\setupformulas[spacebefore=medium,spaceafter=medium] -\setupwhitespace[none] -\input math-spacing-001.tex -\stopbuffer - -\startplacefigure[location=page,reference=whitespace-no,title={No whitespace.}] - \startcombination[2*2] - {\typesetbuffer[demo-1][height=.45\textheight]} {\tttf natural + none + ws none} - {\typesetbuffer[demo-2][height=.45\textheight]} {\tttf strut + none + ws none} - {\typesetbuffer[demo-3][height=.45\textheight]} {\tttf natural + medium + ws none} - {\typesetbuffer[demo-4][height=.45\textheight]} {\tttf strut + medium + ws none} - \stopcombination -\stopplacefigure - -% whitespace medium same as medium spacing around math - -\startbuffer[demo-1] -\disablemode[with-struts] -\showmakeup -\setupformulas[spacebefore=none,spaceafter=none] -\setupwhitespace[medium] -\input math-spacing-001.tex -\stopbuffer - -\startbuffer[demo-2] -\enablemode[with-struts] -\showmakeup -\setupformulas[spacebefore=none,spaceafter=none] -\setupwhitespace[medium] -\input math-spacing-001.tex -\stopbuffer - -\startbuffer[demo-3] -\disablemode[with-struts] -\showmakeup -\setupformulas[spacebefore=medium,spaceafter=medium] -\setupwhitespace[medium] -\input math-spacing-001.tex -\stopbuffer - -\startbuffer[demo-4] -\enablemode[with-struts] -\showmakeup -\setupformulas[spacebefore=medium,spaceafter=medium] -\setupwhitespace[medium] -\input math-spacing-001.tex -\stopbuffer - -\startplacefigure[location=page,reference=whitespace-medium,title={Whitespace the same as display spacing.}] - \startcombination[2*2] - {\typesetbuffer[demo-1][height=.45\textheight]} {\tttf natural + none + ws medium} - {\typesetbuffer[demo-2][height=.45\textheight]} {\tttf strut + none + ws medium} - {\typesetbuffer[demo-3][height=.45\textheight]} {\tttf natural + medium + ws medium} - {\typesetbuffer[demo-4][height=.45\textheight]} {\tttf strut + medium + ws medium} - \stopcombination -\stopplacefigure - -% whitespace big wins from medium spacing around math - -\startbuffer[demo-1] -\disablemode[with-struts] -\showmakeup -\setupformulas[spacebefore=none,spaceafter=none] -\setupwhitespace[big] -\input math-spacing-001.tex -\stopbuffer - -\startbuffer[demo-2] -\enablemode[with-struts] -\showmakeup -\setupformulas[spacebefore=none,spaceafter=none] -\setupwhitespace[big] -\input math-spacing-001.tex -\stopbuffer - -\startbuffer[demo-3] -\disablemode[with-struts] -\showmakeup -\setupformulas[spacebefore=medium,spaceafter=medium] -\setupwhitespace[big] -\input math-spacing-001.tex -\stopbuffer - -\startbuffer[demo-4] -\enablemode[with-struts] -\showmakeup -\setupformulas[spacebefore=medium,spaceafter=medium] -\setupwhitespace[big] -\input math-spacing-001.tex -\stopbuffer - -\startplacefigure[location=page,reference=whitespace-big,title={Whitespace larger than display spacing.}] - \startcombination[2*2] - {\typesetbuffer[demo-1][height=.45\textheight]} {\tttf natural + none + ws big} - {\typesetbuffer[demo-2][height=.45\textheight]} {\tttf strut + none + ws big} - {\typesetbuffer[demo-3][height=.45\textheight]} {\tttf natural + medium + ws big} - {\typesetbuffer[demo-4][height=.45\textheight]} {\tttf strut + medium + ws big} - \stopcombination -\stopplacefigure - -Because we want to have control over the placement of the formula number but also -want to be able to align the formula with the left or right edge of the text -area, we don't use the native display handler by default. We still have a way to -force this, but this is only for testing purposes. By default a formula is placed -centered relative to the current text, including left and right margins. - -\startbuffer -\fakewords{20}{40} - -\startitemize - \startitem - \fakewords{20}{40} - \placeformula - \startformula - \fakeformula - \stopformula - \stopitem - \startitem - \fakewords{20}{40} - \stopitem -\stopitemize - -\fakewords{20}{40}\epar -\stopbuffer - -\typebuffer - -\start \getbuffer \stop - -In the next examples we explicitly align formulas to the left (\type -{flushleft}), center (\type {middle}) and right (\type {flushright}): - -\startbuffer[demo] -\setupformulas[align=flushleft] -\startformula\fakeformula\stopformula -\setupformulas[align=middle] -\startformula\fakeformula\stopformula -\setupformulas[align=flushright] -\startformula\fakeformula\stopformula -\stopbuffer - -\typebuffer[demo] - -The three cases show up as: - -\start \getbuffer[demo] \stop - -You can also set a left and|/|or right margin: - -\startbuffer[setting] -\setupformulas - [leftmargin=3cm, - rightmargin=3cm] -\stopbuffer - -\start \getbuffer[setting] \getbuffer[demo] \stop - -With formula numbers these formulas look as follows: - -\startbuffer[demo] -\setupformulas[align=flushleft] -\placeformula \startformula\fakeformula\stopformula -\setupformulas[align=middle] -\placeformula \startformula\fakeformula\stopformula -\setupformulas[align=flushright] -\placeformula \startformula\fakeformula\stopformula -\stopbuffer - -\start \getbuffer[demo] \stop - -and the same with margins: - -\start \getbuffer[setting] \getbuffer[demo] \stop - -\page - -When the \type {margin} option is set to \type {standard} or \type {yes} the -current indentation (when set) or left skip is added to the left side. - -\startbuffer -\setupformulas[align=flushleft] -\startformula \fakeformula \stopformula -\placeformula \startformula \fakeformula \stopformula -\stopbuffer - -\typebuffer \start \getbuffer \stop - -\startbuffer -\setupformulas[align=flushleft,margin=standard] -\startformula \fakeformula \stopformula -\placeformula \startformula \fakeformula \stopformula -\stopbuffer - -\typebuffer \start \getbuffer \stop - -The distance between the formula and the number is only applied when the formula -is left or right aligned. - -\startbuffer -\setupformulas[align=flushright,distance=0pt] -\startformula \fakeformula \stopformula -\placeformula \startformula \fakeformula \stopformula -\stopbuffer - -\typebuffer \start \getbuffer \stop - -\startbuffer -\setupformulas[align=flushright,distance=2em] -\startformula \fakeformula \stopformula -\placeformula \startformula \fakeformula \stopformula -\stopbuffer - -\typebuffer \start \getbuffer \stop - -\stopchapter - -% \startchapter[title=Numbering] - -% \stopchapter - -\startchapter[title=Framing] - -The \type {\framed} macro is one of the core constructors in \CONTEXT\ and it's -used all over the place. This macro is unlikely to change its behaviour and as it -has evolved over years it comes with quite some options and some can interfere -with the expectations one has. In general using this macro works out well but you -need to keep an eye on using struts and alignment. - -\startbuffer -\framed{$e=mc^2$} -\stopbuffer - -\typebuffer - -The outcome of this is: - -\startlinecorrection \getbuffer \stoplinecorrection - -There is a bit of offset (that you can set) but also struts are added as can be -seen when we visualize them: - -\startlinecorrection \showstruts \getbuffer \stoplinecorrection - -These struts can be disabled: - -\startbuffer -\framed[strut=no]{$e=mc^2$} -\stopbuffer - -\typebuffer - -Now the result is more tight. - -\startlinecorrection \showstruts \getbuffer \stoplinecorrection - -These struts are the way to get a consistent look and feel and are used -frequently in \CONTEXT. We mention these struts because they get in the way when -we frame a display formula. Let's first look at what happens when we -just package a formula in a box: - -\startbuffer -\vbox\bgroup - \startformula - e = mc^2 - \stopformula -\egroup -\stopbuffer - -\typebuffer - -We get: - -\startlinecorrection \start \showmakeup \getbuffer \stop \stoplinecorrection - -Now there are a few properties of displaymath that one needs to keep in mind when -messing around with them this way. First of all display math is meant to be used -as part of the page stream. This means that spacing above and below is adapted to -what comes before and after. It also means that, because formulas can be numbered, -we have some settings that relate to horizontal placement. - -The default vertical spacing is easy to get rid of: - -\startbuffer -\vbox\bgroup - \startformula[packed] - e = mc^2 - \stopformula -\egroup -\stopbuffer - -\typebuffer - -This gives: - -\startlinecorrection \start \showmakeup \getbuffer \stop \stoplinecorrection - -Another handy keyword is \type {tight}: - -\startbuffer -\vbox\bgroup - \startformula[tight] - e = mc^2 - \stopformula -\egroup -\stopbuffer - -\typebuffer - -This gives: - -\startlinecorrection \start \showmakeup \getbuffer \stop \stoplinecorrection - -We can combine these two: - -\startbuffer -\vbox\bgroup - \startformula[packed,tight] - e = mc^2 - \stopformula -\egroup -\stopbuffer - -\typebuffer - -This gives: - -\startlinecorrection \start \showmakeup \getbuffer \stop \stoplinecorrection - -Just in case you wonder why we need to go through these troubles: keep in mind -that we are wrapping something (math) that normally goes in a vertical list with -text above and below. - -The \type {packed} and \type {tight} options can help when we want to wrap -a formula in a frame: - -\startbuffer -\framed - [strut=no] - { - \startformula[packed,tight] - e = mc^2 - \stopformula - } -\stopbuffer - -\typebuffer - -which renders as: - -\startlinecorrection \getbuffer \stoplinecorrection - -There is a dedicated math framed instance that is tuned to give better results -and automatically switches to math mode: - -\startbuffer -\mframed { - e = mc^2 -} -\stopbuffer - -\typebuffer - -becomes: - -\startlinecorrection \getbuffer \stoplinecorrection - -Multiple formulas can be combined: - -\startbuffer -\startformulas - \startformula - a + b = c - \stopformula - \startformula - d - e = f - \stopformula -\stopformulas -\stopbuffer - -\typebuffer - -We might add some more control in the future, but this is what you get: - -\startlinecorrection \getbuffer \stoplinecorrection - -Framing a formula is also supported as a option, where the full power of framed can -be applied to the formula. We will illustrate this in detail on the next pages. For this -we use the following sample: - -\typefile{math-framing-001.tex} - -In \in {figure} [framing-flushleft], \in [framing-middle] \in {and} -[framing-flushright] you see some combinations. You can run this example on your -machine and see the details. - -\startplacefigure[location=page,reference=framing-flushleft,title={Framed formulas flushed left.}] - \startcombination[2*2] - {\typesetfile[math-framing-001.tex][page=01,height=.45\textheight]} {\tttf right + flushleft} - {\typesetfile[math-framing-001.tex][page=02,height=.45\textheight]} {\tttf right + flushleft} - {\typesetfile[math-framing-001.tex][page=07,height=.45\textheight]} {\tttf left + flushleft + tight} - {\typesetfile[math-framing-001.tex][page=08,height=.45\textheight]} {\tttf left + flushleft + tight} - \stopcombination -\stopplacefigure - -\startplacefigure[location=page,reference=framing-middle,title={Framed formulas centered.}] - \startcombination[2*2] - {\typesetfile[math-framing-001.tex][page=03,height=.45\textheight]} {\tttf right + middle} - {\typesetfile[math-framing-001.tex][page=04,height=.45\textheight]} {\tttf right + middle} - {\typesetfile[math-framing-001.tex][page=09,height=.45\textheight]} {\tttf left + middle + tight} - {\typesetfile[math-framing-001.tex][page=10,height=.45\textheight]} {\tttf left + middle + tight} - \stopcombination -\stopplacefigure - -\startplacefigure[location=page,reference=framing-flushright,title={Framed formulas flushed right.}] - \startcombination[2*2] - {\typesetfile[math-framing-001.tex][page=05,height=.45\textheight]} {\tttf right + flushright} - {\typesetfile[math-framing-001.tex][page=06,height=.45\textheight]} {\tttf right + flushright} - {\typesetfile[math-framing-001.tex][page=11,height=.45\textheight]} {\tttf left + flushright + tight} - {\typesetfile[math-framing-001.tex][page=12,height=.45\textheight]} {\tttf left + flushright + tight} - \stopcombination -\stopplacefigure - -\stopchapter - -With each formula class a framed variants is automatically created: - -\startbuffer -\defineformula - [foo] - -\setupformulaframed - [foo] - [frame=on, - framecolor=red] - -\startfooformula[frame] - e=mc^2 -\stopfooformula -\stopbuffer - -\typebuffer - -This time you get a red frame: - -\getbuffer - -You can also frame the number, as in: - -\startbuffer -\setupformulaframed[framecolor=red,frame=on,offset=1ex] -\setupformula[option=frame,color=blue] -\setupformula[numbercommand={\inframed[framecolor=green]}] - -\startplaceformula - \startformula - 2 + 2 = 2x - \stopformula -\stopplaceformula -\stopbuffer - -\typebuffer - -The boxes get properly aligned: - -\start \showboxes \getbuffer \stop - -\stoptext +\stopproduct % when we compare these tables with the one that the ff loader produces we notice % some differences: this is because (deduced from source) that ff does some kind |