LuaLatex and large braces with MathTime Professional 2

Question

The following example behaves badly in LuaLatex:

\documentclass{article}
\usepackage{amsmath}
\usepackage[lite]{mtpro2}
\begin{document}
\[ x = \ccases{ x & 1,\\x & 2,\\x & \text{otherwise} } \]
\end{document}

With pdflatex (pdfTeX 3.14159265-2.6-1.40.15 (TeX Live 2014/W32TeX)) I get the following:

And, with lualatex (LuaTeX, Version beta-0.79.1 (TeX Live 2014/W32TeX) (rev 4971)) I get the following:

Why? And, is it fixable?

Answer 1

With the following experiment, I get different results during the run:

\documentclass{article}
\usepackage{amsmath}
\usepackage[lite]{mtpro2}
\usepackage{etoolbox}

\makeatletter
\patchcmd{\PEX@}{\ifdim}{\showthe\dp\Pbox@\ifdim}{}{}
\makeatother

\begin{document}
\[ x = \ccases{ x & 1,\\x & 2,\\x & \text{otherwise} } \]
\end{document}

The \PEX@ macro is used to decide the extension font to be used, either mt2exa (straight braces) or mt2exe (curly braces).

When compiling with pdflatex, the run stops twice with

> 41.53998pt.
\PEX@ ...setbox \z@ \hbox {#1}\showthe \dp \Pbox@ 
                                                  \ifdim \dp \Pbox@ >\dp \z@...
l.11 ...es{ x & 1,\\x & 2,\\x & \text{otherwise} }
                                                   \]
? 
> 42.0pt.
\PEX@ ...setbox \z@ \hbox {#1}\showthe \dp \Pbox@ 
                                                  \ifdim \dp \Pbox@ >\dp \z@...
l.11 ...es{ x & 1,\\x & 2,\\x & \text{otherwise} }
                                                   \]
? 

while with lualatex I get a single stop with

> 0.0pt.
\PEX@ ...setbox \z@ \hbox {#1}\showthe \dp \Pbox@ 
                                                  \ifdim \dp \Pbox@ >\dp \z@...
l.11 ...ases{ x & 1,\\x & 2,\\x & \text{otherwise} }
                                                   \]
? 

This seems to be evidence that something is going wrong.

Actually, the box that's being measured turns out to be very different when pdflatex or lualatex are used: with pdflatex we get

> \box29=
\vbox(0.45999+41.53998)x7.67
.\hbox(0.45999+17.54)x7.67
..\LMP3/mtt/m/n/10 1
.\hbox(0.0+6.0)x7.67
..\LMP3/mtt/m/n/10 C
.\hbox(0.45999+17.54)x7.67
..\LMP3/mtt/m/n/10 A

while lualatex shows

> \box29=
\vbox(41.99997+0.0)x7.67, direction TLT
.\hbox(0.45999+17.54)x7.67, direction TLT
..\LMP3/mtt/m/n/10 1
.\hbox(0.0+6.0)x7.67, direction TLT
..\LMP3/mtt/m/n/10 C
.\hbox(0.45999+17.54)x7.67, direction TLT
..\LMP3/mtt/m/n/10 A

The box that is being examined contains a \right delimiter, but apparently the models used by pdflatex and lualatex are quite different when such a box is appended. When we look at the box before \PEX@ dismantles it we see, with pdflatex,

...\vbox(0.45999+41.53998)x7.67, shifted -23.05998
....\hbox(0.45999+17.54)x7.67
.....\LMP3/mtt/m/n/10 1
....\hbox(0.0+6.0)x7.67
.....\LMP3/mtt/m/n/10 C
....\hbox(0.45999+17.54)x7.67
.....\LMP3/mtt/m/n/10 A

while lualatex has

...\vbox(41.99997+0.0)x7.67, shifted 18.48, direction TLT
....\hbox(0.45999+17.54)x7.67, direction TLT
.....\LMP3/mtt/m/n/10 1
....\hbox(0.0+6.0)x7.67, direction TLT
.....\LMP3/mtt/m/n/10 C
....\hbox(0.45999+17.54)x7.67, direction TLT
.....\LMP3/mtt/m/n/10 A

The problem can be replicated with a simpler document:

\documentclass{article}
\usepackage[lite]{mtpro2}
\begin{document}
\showboxbreadth=1000 \showboxdepth=1000 \tracingonline=1
\setbox0=\hbox{$\left.\vrule height 25pt\right)$}\showbox0

With pdflatex we see

> \box0=
\hbox(25.0+18.48)x9.26999
.\mathon
.\hbox(25.0+18.48)x9.26999
..\hbox(0.0+0.0)x1.2, shifted -2.51999
..\rule(25.0+*)x0.4
..\vbox(0.45999+41.53998)x7.67, shifted -23.05998
...\hbox(0.45999+17.54)x7.67
....\LMP3/mtt/m/n/10 1
...\hbox(0.0+6.0)x7.67
....\LMP3/mtt/m/n/10 C
...\hbox(0.45999+17.54)x7.67
....\LMP3/mtt/m/n/10 A
.\mathoff

while lualatex shows

> \box0=
\hbox(25.0+18.48)x9.26999, direction TLT
.\mathon
.\hbox(25.0+18.48)x9.26999, direction TLT
..\hbox(0.0+0.0)x1.2, shifted -2.51999, direction TLT
..\rule(25.0+*)x0.4
..\vbox(41.99997+0.0)x7.67, shifted 18.48, direction TLT
...\hbox(0.45999+17.54)x7.67, direction TLT
....\LMP3/mtt/m/n/10 1
...\hbox(0.0+6.0)x7.67, direction TLT
....\LMP3/mtt/m/n/10 C
...\hbox(0.45999+17.54)x7.67, direction TLT
....\LMP3/mtt/m/n/10 A
.\mathoff

If we remove the call to mtpro2, we get, with pdflatex,

> \box0=
\hbox(25.0+18.5002)x10.35
.\mathon
.\hbox(25.0+18.5002)x10.35
..\hbox(0.0+0.0)x1.2, shifted -2.5
..\rule(25.0+*)x0.4
..\vbox(0.39998+41.60042)x8.75002, shifted -23.10022
...\hbox(0.39998+17.60019)x8.75002
....\OMX/cmex/m/n/5 1
...\hbox(0.0+6.00006)x8.75002
....\OMX/cmex/m/n/5 C
...\hbox(0.39998+17.60019)x8.75002
....\OMX/cmex/m/n/5 A
.\mathoff

and, with lualatex,

> \box0=
\hbox(25.0+18.5002)x10.35, direction TLT
.\mathon
.\hbox(25.0+18.5002)x10.35, direction TLT
..\hbox(0.0+0.0)x1.2, shifted -2.5, direction TLT
..\rule(25.0+*)x0.4
..\vbox(42.0004+0.0)x8.75002, shifted 18.5002, direction TLT
...\hbox(0.39998+17.60019)x8.75002, direction TLT
....\OMX/cmex/m/n/10 1
...\hbox(0.0+6.00006)x8.75002, direction TLT
....\OMX/cmex/m/n/10 C
...\hbox(0.39998+17.60019)x8.75002, direction TLT
....\OMX/cmex/m/n/10 A
.\mathoff

so it's not a problem with the fonts, but a problem inherent to how LuaTeX transforms a math list into a horizontal list.

Solution?

Just a hack that's not guaranteed to give exact size of the brace:

\documentclass{article}
\usepackage{amsmath}
\usepackage[lite]{mtpro2}
\usepackage{etoolbox}

\makeatletter
\patchcmd{\PEX@}{\ifdim\dp\Pbox@>\dp\z@}{\ifdim\ht\Pbox@>\dp\z@}{}{}
\makeatother

\begin{document}
\[ x = \ccases{ x & 1,\\x & 2,\\x & \text{otherwise} } \]
\end{document}

Answer 2

Based on egreg's solution, I was able to patch the \SQRT command for slanted root symbol.

Before the patch, the code

$ \epsilon $ is a small positive quantity.

\[ \lim_{n\to +\infty} \SQRT{
    \frac{\displaystyle \int_{-\epsilon}^\epsilon \cos^n x \,\diff x}
    {\displaystyle \int_{-\pi/2}^{\pi/2} \cos^n x \,\diff x}}
  = 1 \]

\[ \PARENS{ \begin{matrix}
    a & b \\
    c & d \\
    e & f \\
    g & h
    \end{matrix} } \]

compiles into the following incorrect result.

After the patch

\usepackage{etoolbox,ifluatex}
\ifluatex
\makeatletter
\patchcmd{\PEX@}{\dp\Pbox@>\dp\z@}{\ht\Pbox@>\dp\z@}{}{}
\patchcmd{\SQEX@}{\dp\Sbox@>\dp0}{\ht\Sbox@>\dp0}{}{}
\makeatother
\fi

the code compiles into the intended result, as shown below.