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|
% \iffalse meta-comment
%
%% Copyright (C) 2019--2022 by Marcel Krueger
%%
%% This file may be distributed and/or modified under the
%% conditions of the LaTeX Project Public License, either
%% version 1.3c of this license or (at your option) any later
%% version. The latest version of this license is in:
%%
%% http://www.latex-project.org/lppl.txt
%%
%% and version 1.3 or later is part of all distributions of
%% LaTeX version 2005/12/01 or later.
%
%<*batch>
%<*gobble>
\ifx\jobname\relax\let\documentclass\undefined\fi
\ifx\documentclass\undefined
\csname fi\endcsname
%</gobble>
\input l3docstrip.tex
\keepsilent
\preamble
\endpreamble
\generate{\file{luamathalign.sty}{\from{luamathalign.dtx}{package}}}
\begingroup
\def\MetaPrefix{--}
\preamble
\endpreamble
\postamble
\endpostamble
\generate{\file{luamathalign.lua}{\from{luamathalign.dtx}{lua}}}
\endgroup
\endbatchfile
%</batch>
%<*gobble>
\fi
\expandafter\ifx\csname @currname\endcsname\empty
\csname fi\endcsname
%</gobble>
%<*driver>
\documentclass[full]{l3doc}
\usepackage{luamathalign}
\usepackage{csquotes}
\MakeShortVerb{\|}
\setlength\IndexMin{100pt}
\begin{document}
\DocInput{luamathalign.dtx}
\PrintIndex
\PrintChanges
\end{document}
%</driver>
%<*gobble>
\fi
%</gobble>
% \fi
%
% \GetFileInfo{luamathalign.dtx}
% \title{The \pkg{luamathalign} package\thanks{This document
% corresponds to \pkg{luamathalign}~v0.1, dated~2022-04-18.}}
% \author{Marcel Kr\"uger \\ \href{mailto:tex@2krueger.de}{tex@2krueger.de}}
%
% \maketitle
%
% \begin{documentation}
% \section{The problem}
% In most cases, |amsmath| makes it simple to align multiple equations in a
% |align| environment. But sometimes, special requirements come up.
%
% Maybe one of your alignment points is in an exponent, or in a radical?
% The first attempts for such alignments often fail. For example, assume that
% you want to align the following radicals like this (at the $x^3$ term):
% \begin{align*}
% \sqrt{1-3x+3x^2+(\AlignHere x-1)^3}\\
% =\sqrt{1-3x+3x^2+{\AlignHere x}^3-3x^2+3x-1}\\
% =\sqrt{\AlignHere x^3}
% \end{align*}
% \enquote{Just adding \texttt{\&} at the alignment points} doesn't work:
% \begin{verbatim}
% \begin{align*}
% \sqrt{1-3x+3x^2+(&x-1)^3}\\
% =\sqrt{1-3x+3x^2+&x^3-3x^2+3x-1}\\
% =\sqrt{&x^3}
% \end{align*}
% \end{verbatim}
% fails with
% \begin{verbatim}
% ! Missing } inserted.
% <inserted text>
% }
% l.73 \end{align*}
% \end{verbatim}
%
% Another problem are nested alignments. Take this sample from \href{https://tex.stackexchange.com/questions/68547/alignment-across-nested-aligned-environments}{anonymous on \TeX\ -- \LaTeX\ StackExchange}: We want alignment like
% \begin{align*}
% aaaa &= 1 &&\text{for $X$} \\
% bbbb &= 1 &&\text{for $Y$} \\
% \left. \begin{aligned}
% c \SetAlignmentPoint1 &= 1 \\
% d &= 12
% \end{aligned} \right\}\ExecuteAlignment1 &&\text{for $Z$}
% \end{align*}
% but in
% \begin{verbatim}
% \begin{align*}
% aaaa &= 1 &&\text{for $X$} \\
% bbbb &= 1 &&\text{for $Y$} \\
% \left. \begin{aligned}
% c &= 1 \\
% d &= 12
% \end{aligned} \right\}&&&\text{for $Z$}
% \end{align*}
% \end{verbatim}
% there is not obvious way to align the equal signs in the nested |aligned| with the outer signs.
% \section{The solution}
% \pkg{luamathalign} provides solutions for both problems under Lua\LaTeX:
% \begin{function}{\AlignHere}
% The most important new macro is \cmd\AlignHere:
% It generates an alignment point like \texttt{\&},
% but it can be used almost everywhere.
%
% So problems like our first example can be implemented by just using \cmd\AlignHere\ instead of \texttt{\&}:
% \begin{verbatim}
% \begin{align*}
% \sqrt{1-3x+3x^2+(\AlignHere x-1)^3}\\
% =\sqrt{1-3x+3x^2+{\AlignHere x}^3-3x^2+3x-1}\\
% =\sqrt{\AlignHere x^3}
% \end{align*}
% \end{verbatim}
% \begin{align*}
% \sqrt{1-3x+3x^2+(\AlignHere x-1)^3}\\
% =\sqrt{1-3x+3x^2+{\AlignHere x}^3-3x^2+3x-1}\\
% =\sqrt{\AlignHere x^3}
% \end{align*}
% \end{function}
% Sadly, this doesn't really help with the nested alignment problem:
% Even if we use \cmd\AlignHere\ in the \env{aligned} environment, the alignment points
% would be inserted in the inner and not in the outer alignment.
% For such cases, there is a variant which allows to specify at which level the alignment should happen:
% \begin{function}{\SetAlignmentPoint,\ExecuteAlignment}
% The primary command for this is \cmd\SetAlignmentPoint\meta{number}. When called with a negative number it specifies the nesting level.
% For example when \meta{number} is -1 it is the same as \cmd\AlignHere, while for -2 it is aligning one level higher and so on.
%
% For example, our nested alignment above wanted to align the inner \env{aligned} and the outer \env{align*} at the same point,
% so |\SetAlignmentPoint-2| is used directly next to a inner alignment point (here |&|, \cmd\AlignHere\ would work too).
% Then the \cmd\ExecuteAlignment\ has to appear in the context of the outer \env{align*}, so it can be written e.g. directly before the next |&| of the outer \env{align*}:
% \begin{verbatim}
% \begin{align*}
% aaaa &= 1 &&\text{for $X$} \\
% bbbb &= 1 &&\text{for $Y$} \\
% \left. \begin{aligned}
% c \SetAlignmentPoint-2 &= 1 \\
% d &= 12
% \end{aligned} \right\}&&\text{for $Z$}
% \end{align*}
% \end{verbatim}
% \begin{align*}
% aaaa &= 1 &&\text{for $X$} \\
% bbbb &= 1 &&\text{for $Y$} \\
% \left. \begin{aligned}
% c \SetAlignmentPoint-2 &= 1 \\
% d &= 12
% \end{aligned} \right\}&&\text{for $Z$}
% \end{align*}
%
% If you do not want to keep track of the right nesting level you can explicitly mark a level and refer to it.
% To do so, use a non-negative \meta{number}.
% When \cmd\SetAlignmentPoint\ is used with a non-negative \meta{number} then \cmd\ExecuteAlignment\meta{number}
% must be executed afterwards with the same \meta{number} at a point where adding a |&| would add a valid alignment point at the right level.
%
% Our example above could therefore also be written as
% \begin{verbatim}
% \begin{align*}
% aaaa &= 1 &&\text{for $X$} \\
% bbbb &= 1 &&\text{for $Y$} \\
% \left. \begin{aligned}
% c \SetAlignmentPoint0 &= 1 \\
% d &= 12
% \end{aligned} \right\}\ExecuteAlignment0 &&\text{for $Z$}
% \end{align*}
% \end{verbatim}
% \begin{align*}
% aaaa &= 1 &&\text{for $X$} \\
% bbbb &= 1 &&\text{for $Y$} \\
% \left. \begin{aligned}
% c \SetAlignmentPoint0 &= 1 \\
% d &= 12
% \end{aligned} \right\}\ExecuteAlignment0 &&\text{for $Z$}
% \end{align*}
%
% This variant is also useful when working with custom alignment environment not prepared to work with luamathalign.
% By default \cmd\SetAlignmentPoint\meta{number} with negative numbers (and therefore also \cmd\AlignHere) only work with
% amsmath's \texttt{\{align\}}, \texttt{\{aligned\}} and their variants.
% If you have another environment which also follows similar alignment rules then you can either restrict yourself to
% non-negative \meta{number}s in combination with \cmd\ExecuteAlignment\ or patch these environments similar to what luamathalign does for amsmath.
% \end{function}
% \end{documentation}
% \begin{implementation}
% \section{The implementation}
% \subsection{Lua}
% \iffalse
%<*gobble>
\RequirePackage{docstrip-luacode}
\begin{docstrip-luacode}{luamathalign}
%</gobble>
%<*lua>
% \fi
% \begin{macrocode}
local luacmd = require'luamathalign-luacmd'
local luaprop = require'luamathalign-luaprop'('mathalign')
local hlist = node.id'hlist'
local vlist = node.id'vlist'
local whatsit = node.id'whatsit'
local kern = node.id'kern'
local user_defined = node.subtype'user_defined'
local whatsit_id = luatexbase.new_whatsit'mathalign'
local node_cmd = token.command_id'node'
local ampersand = token.new(38, 4)
-- We might want to add y later
local function is_marked(mark, list)
for n in node.traverse(list) do
local id = n.id
if id == hlist or id == vlist then
if is_marked(mark, n.head) then return true end
elseif id == whatsit and n.subtype == user_defined
and n.user_id == whatsit_id and n.value == mark then
return true
end
end
return false
end
local function assert_unmarked(mark, list, ...)
local marked = is_marked(mark, list)
if marked then
tex.error("Multiple alignment marks", "I found multiple alignment marks \z
of type " .. mark .. " in an alignment where I already had an \z
alignment mark of that type. You should look at both of them and \z
decide which one is right. I will continue with the first one for now.")
end
return ...
end
local measure do
local vmeasure
local function hmeasure(mark, list)
local x, last = 0, list.head
for n in node.traverse(last) do
local id = n.id
if id == hlist then
local w, h, d = node.rangedimensions(list, last, n)
x, last = x + w, n
local dx = hmeasure(mark, n)
if dx then return assert_unmarked(mark, n.next, dx + x) end
elseif id == vlist then
local w, h, d = node.rangedimensions(list, last, n)
x, last = x + w, n
local dx = vmeasure(mark, n)
if dx then return assert_unmarked(mark, n.next, dx + x) end
elseif id == whatsit and n.subtype == user_defined
and n.user_id == whatsit_id and n.value == mark then
local w, h, d = node.rangedimensions(list, last, n)
local after
list.head, after = node.remove(list.head, n)
return assert_unmarked(mark, after, x + w)
end
end
end
function vmeasure(mark, list)
for n in node.traverse(list.head) do
local id = n.id
if id == hlist then
local dx = hmeasure(mark, n)
if dx then return assert_unmarked(mark, n.next, dx + n.shift) end
elseif id == vlist then
local dx = vmeasure(mark, n)
if dx then return assert_unmarked(mark, n.next, dx + n.shift) end
elseif id == whatsit and n.subtype == user_defined
and n.user_id == whatsit_id and n.value == mark then
local after
list.head, after = node.remove(list.head, n)
return assert_unmarked(mark, after, 0)
end
end
end
function measure(mark, head)
local x, last = 0, head
for n in node.traverse(last) do
local id = n.id
if id == hlist then
local w, h, d = node.dimensions(last, n)
x, last = x + w, n
local dx = hmeasure(mark, n)
if dx then return assert_unmarked(mark, n.next, head, dx + x) end
elseif id == vlist then
local w, h, d = node.dimensions(last, n)
x, last = x + w, n
local dx = vmeasure(mark, n)
if dx then return assert_unmarked(mark, n.next, head, dx + x) end
elseif id == whatsit and n.subtype == user_defined
and n.user_id == whatsit_id and n.value == mark then
local w, h, d = node.dimensions(last, n)
local after
head, after = node.remove(head, n)
return assert_unmarked(mark, after, head, x + w)
end
end
return head
end
end
local isolate do
local visolate
local function hisolate(list, offset)
local x, last = 0, list.head
local newhead, newtail = nil, nil
local n = last
while n do
local id = n.id
if id == hlist then
local w, h, d = node.rangedimensions(list, last, n)
x, last = x + w, n
local inner_head, inner_tail, new_offset = hisolate(n, offset - x)
if inner_head then
if newhead then
newtail.next, inner_head.prev = inner_head, newtail
else
newhead = inner_head
end
newtail = inner_tail
offset = x + new_offset
end
n = n.next
elseif id == vlist then
local w, h, d = node.rangedimensions(list, last, n)
x, last = x + w, n
local inner_head, inner_tail, new_offset = visolate(n, offset - x)
if inner_head then
if newhead then
newtail.next, inner_head.prev = inner_head, newtail
else
newhead = inner_head
end
newtail = inner_tail
offset = x + new_offset
end
n = n.next
elseif id == whatsit and n.subtype == user_defined
and n.user_id == whatsit_id then
local w, h, d = node.rangedimensions(list, last, n)
x = x + w
list.head, last = node.remove(list.head, n)
if x ~= offset then
local k = node.new(kern)
k.kern, offset = x - offset, x
newhead, newtail = node.insert_after(newhead, newtail, k)
end
newhead, newtail = node.insert_after(newhead, newtail, n)
n = last
else
n = n.next
end
end
return newhead, newtail, offset
end
function visolate(list, offset)
local newhead, newtail = nil, nil
local n = list.head
while n do
local id = n.id
if id == hlist then
if dx then return assert_unmarked(mark, n.next, dx + n.shift) end
local inner_head, inner_tail, new_offset = hisolate(n, offset)
if inner_head then
if newhead then
newtail.next, inner_head.prev = inner_head, newtail
else
newhead = inner_head
end
newtail = inner_tail
offset = new_offset
end
n = n.next
elseif id == vlist then
if dx then return assert_unmarked(mark, n.next, dx + n.shift) end
local inner_head, inner_tail, new_offset = visolate(n, offset)
if inner_head then
if newhead then
newtail.next, inner_head.prev = inner_head, newtail
else
newhead = inner_head
end
newtail = inner_tail
offset = new_offset
end
n = n.next
elseif id == whatsit and n.subtype == user_defined
and n.user_id == whatsit_id then
local after
list.head, after = node.remove(list.head, n)
if 0 ~= offset then
local k = node.new(kern)
k.kern, offset = -offset, 0
newhead, newtail = node.insert_after(newhead, newtail, k)
end
newhead, newtail = node.insert_after(newhead, newtail, n)
n = last
else
n = n.next
end
end
return newhead, newtail, offset
end
function isolate(head)
local x, last = 0, head
local newhead, newtail, offset = nil, nil, 0
local n = last
while n do
local id = n.id
if id == hlist then
local w, h, d = node.dimensions(last, n)
x, last = x + w, n
local inner_head, inner_tail, new_offset = hisolate(n, offset - x)
if inner_head then
if newhead then
newtail.next, inner_head.prev = inner_head, newtail
else
newhead = inner_head
end
newtail = inner_tail
offset = x + new_offset
end
n = n.next
elseif id == vlist then
local w, h, d = node.dimensions(last, n)
x, last = x + w, n
local inner_head, inner_tail, new_offset = visolate(n, offset - x)
if inner_head then
if newhead then
newtail.next, inner_head.prev = inner_head, newtail
else
newhead = inner_head
end
newtail = inner_tail
offset = x + new_offset
end
n = n.next
elseif id == whatsit and n.subtype == user_defined
and n.user_id == whatsit_id then
local w, h, d = node.dimensions(last, n)
x = x + w
head, last = node.remove(head, n)
if x ~= offset then
local k = node.new(kern)
k.kern, offset = x - offset, x
newhead, newtail = node.insert_after(newhead, newtail, k)
end
newhead, newtail = node.insert_after(newhead, newtail, n)
n = last
else
n = n.next
end
end
return head, newhead
end
end
local mark, afterkern
luatexbase.add_to_callback('post_mlist_to_hlist_filter', function(n)
if mark then
local x
n, x = measure(mark, n)
local k = node.new'kern'
local off = x - n.width
k.kern, afterkern.kern = off, -off
node.insert_after(n.head, nil, k)
n.width = x
mark, afterkern = nil, nil
end
return n
end, 'luamathalign')
local function get_kerntoken(newmark)
assert(not mark)
mark, afterkern = newmark, node.new'kern'
return token.new(node.direct.todirect(afterkern), node_cmd)
end
local function insert_whatsit(mark)
local n = node.new(whatsit, user_defined)
n.user_id, n.type, n.value = whatsit_id, string.byte'd', mark
node.write(n)
end
luacmd("SetAlignmentPoint", function()
local mark = token.scan_int()
if mark < 0 then
for i=tex.nest.ptr,0,-1 do
local t = tex.nest[i].head
if luaprop.query(t) ~= nil then
mark = mark + 1
if mark == 0 then
luaprop.set(t, true)
return insert_whatsit(-i)
end
end
end
tex.error('No compatible alignment environment found',
'This either means that \\SetAlignmentPoint was used outside\n\z
of an alignment or the used alignment is not setup for use with\n\z
luamathalign. In the latter case you might want to look at\n\z
non-negative alignment marks.')
else
return insert_whatsit(mark)
end
end, "protected")
function handle_whatsit(mark)
token.put_next(ampersand, get_kerntoken(mark))
end
luacmd("ExecuteAlignment", function()
return handle_whatsit(token.scan_int())
end, "protected")
luacmd("LuaMathAlign@begin", function()
local nest = tex.nest.top
luaprop.set(nest.head, false)
end, "protected")
luacmd("LuaMathAlign@end@early", function()
local t = tex.nest.top.head
if luaprop.set(t, nil) == true then
handle_whatsit(-tex.nest.ptr)
end
end, "protected")
local delayed
luacmd("LuaMathAlign@end", function()
local nest = tex.nest.top
local t = nest.head
if luaprop.set(t, nil) == true then
assert(not delayed)
delayed = {get_kerntoken(-tex.nest.ptr), ampersand}
end
end, "protected")
luatexbase.add_to_callback("hpack_filter", function(head, groupcode)
if delayed and groupcode == "align_set" then
-- HACK: token.put_next puts the tokens into the input stream after the cell
-- is fully read, before the next starts. This will act as if the content was
-- written as the first element of the next field.
token.put_next(delayed)
delayed = nil
end
return true
end, "luamathalign.delayed")
luacmd("LuaMathAlign@IsolateAlignmentPoints", function()
local main = token.scan_int()
if not token.scan_keyword 'into' then
tex.error'Expected "into"'
end
local marks = token.scan_int()
local head, newhead = isolate(tex.box[main])
tex.box[marks] = node.direct.tonode(node.direct.hpack(
newhead and node.direct.todirect(newhead) or 0))
end, "protected")
% \end{macrocode}
% \subsection{LaTeX}
% \iffalse
%</lua>
%<*gobble>
\end{docstrip-luacode}
%</gobble>
%<*package>
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage
{luamathalign}
[2022-04-18 v0.1 additional math alignment tricks using Lua]
% \fi
% The actual \LaTeX\ package just loads the Lua module and patches \pkg{amsmath}:
% \begin{macrocode}
% \RequirePackage{scrlfile}
\directlua{require'luamathalign'}
\IfPackageLoadedTF{amsmath}{%
\@firstofone
}{%
\AddToHook{package/amsmath/after}
}
{%
\def\align@preamble{%
&\hfil
\strut@
\setboxz@h{\@lign$\m@th\displaystyle{%
\LuaMathAlign@begin##\LuaMathAlign@end}$}%
\ifmeasuring@\savefieldlength@\fi
\set@field
\tabskip\z@skip
&\setboxz@h{\@lign$\m@th\displaystyle{{}##}$}%
\ifmeasuring@\savefieldlength@\fi
\set@field
\hfil
\tabskip\alignsep@
}
\renewcommand{\start@aligned}[2]{%
\RIfM@\else
\nonmatherr@{\begin{\@currenvir}}%
\fi
\savecolumn@ % Assumption: called inside a group
\alignedspace@left
\if #1t\vtop \else \if#1b \vbox \else \vcenter \fi \fi \bgroup
\maxfields@#2\relax
\ifnum\maxfields@>\m@ne
\multiply\maxfields@\tw@
\let\math@cr@@@\math@cr@@@alignedat
\alignsep@\z@skip
\else
\let\math@cr@@@\math@cr@@@aligned
\alignsep@\minalignsep
\fi
\Let@ \chardef\dspbrk@context\@ne
\default@tag
\spread@equation % no-op if already called
\global\column@\z@
\ialign\bgroup
&\column@plus
\hfil
\strut@
$\m@th\displaystyle{\LuaMathAlign@begin##\LuaMathAlign@end}$%
\tabskip\z@skip
&\column@plus
$\m@th\displaystyle{{}##}$%
\hfil
\tabskip\alignsep@
\crcr
}
\edef\math@cr@@@alignedat{\LuaMathAlign@end@early
\unexpanded\expandafter{\math@cr@@@alignedat}}
\edef\math@cr{\LuaMathAlign@end@early
\unexpanded\expandafter{\math@cr}}
\edef\endaligned{\LuaMathAlign@end@early
\unexpanded\expandafter{\endaligned}}
}
\protected\def\AlignHere{\SetAlignmentPoint\m@ne}
\begingroup
\def\patch@finph@nt\setbox\tw@\null{%
\LuaMathAlign@IsolateAlignmentPoints\z@ into \tw@
}%
\expanded{\endgroup%
\protected\def\noexpand\finph@nt{%
\unexpanded\expandafter\expandafter\expandafter{%
\expandafter\patch@finph@nt\finph@nt
}%
}}
\ExplSyntaxOff
% \end{macrocode}
% \iffalse
%</package>
% \fi
% \end{implementation}
\endinput
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