Alignment tab character inside a starred command within align

Question

Here is a minimal example of what I want to do.
documentclass{article}

usepackage{amsmath}

makeatletter
newcommand{mylinebreak}{@ifstar@mylinebreak@@mylinebreak}
newcommand{@mylinebreak}{&}
newcommand{@@mylinebreak}{&&}
%letmylinebreak@@mylinebreak
makeatother

begin{document}
begin{align*}
 a&=bmylinebreak
  &=c.
end{align*}
end{document}

This gives the error message
! Misplaced alignment tab character &.
@@mylinebreak ->&
                  &
l.16 end{align*}

What is wrong?  How can I get this to work?
Curiously, I get no error message if I remove the % or if I use mylinebreak* instead.
I am guessing that the problem can be solved using the tricks involving master/balance counters, but I could not make this work.

David Carlisle · Accepted Answer

You are defining   to look ahead for a * (incidentally the standard command already looks ahead for a *) but in doing this it "sees" the & and the next cell starts before the previous row is ended by inserting the original  
The definition in amsmath is
defmath@cr{relaxiffalse{fiifnum0=`}fi
  @ifstar{global@eqpen@Mmath@cr@}%
          {global@eqpen
             ifnumdspbrk@lvl <z@ interdisplaylinepenalty
              else -@getpendspbrk@lvl fi
           math@cr@}}
defmath@cr@{new@ifnextchar[math@cr@@{math@cr@@[z@]}}
defmath@cr@@[#1]{ifnum0=`{fi iffalse}fimath@cr@@@
  noalign{vskip#1relax}}

The special relaxiffalse{fiifnum0=`}fi is designed to avoid this issue by preventing the halign template ending a cell at this point.
Note that it is already using @ifstar to define * to prevent a page break at this point.
It is not clear what is the intention of using &  as the behaviour of that construct is the same as   as the empty cells do not do anything in almost all circumstances.

egreg · Answer

TL;DR

Simple solution: use a more robust check for the *-variant.

documentclass{article}

usepackage{amsmath}

NewDocumentCommand{mylinebreak}{s}{%
  IfBooleanTF{#1}{&x}{&x&=y}%
}

begin{document}
begin{align*}
 a&=bmylinebreak
  &=c.
 a&=bmylinebreak*
  &=c.
end{align*}
end{document}

I added something in order to better see that the choices are made correctly.

If you're running a version of LaTeX prior to the 2020-10-01 release, you also need usepackage{xparse}.

Analysis of the issue

Let's see what happens: mylinebreak becomes

@ifstar@mylinebreak@@mylinebreak

According to the definition of @ifstar by amsmath

def@ifstar#1#2{new@ifnextchar *{defreserved@a*{#1}reserved@a}{#2}}

the above becomes

new@ifnextchar*{defreserved@a{@mylinebreak}reserved@a}{@@mylinebreak}

Let's see what new@ifnextchar does:

longdefnew@ifnextchar#1#2#3{%
  letreserved@d= #1%
  defreserved@a{#2}defreserved@b{#3}%
  futurelet@let@tokennew@ifnch
}

so the expansions continues as (newlines just for reading convenience)

letreserved@d= *
defreserved@a{defreserved@a*{@mylinebreak}reserved@a}
defreserved@b{@@mylinebreak}
futurelet@let@tokennew@ifnch &

The trailing & comes from the fact that the newline after mylinebreak is ignored during tokenization. Unfortunately, we're in an alignment, so as soon as TeX scans &, it inserts the v part of the template. And, indeed, the error message with a high value of errorcontextlines reads

! Misplaced alignment tab character &.
@@mylinebreak ->&
                  &
<to be read again> 
                   }
<template> }
            $}ifmeasuring@ savefieldlength@ fi set@field hfil endtempl...
<argument>  a&=bmylinebreak &
                              =c.

and @let@token is set to }. This is confirmed by injecting show@let@token at the beginning of new@ifnch:

@let@token=end-group character }

OK, let's go a step forward: the expansion of new@ifnch yields

ifx@let@tokenreserved@dletreserved@breserved@afireserved@b

In our case, the ifx test returns false, so we remain with

reserved@b}&

and this breaks, because reserved@b becomes @@mylinebreak.

Alignment tab character inside a starred command within align

2 Answers

TL;DR

Analysis of the issue

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