Adapting double math-mode accents for different math styles

Question

I'm using a slightly generalized version of @wipet's excellent code for double hats in math mode that allows for arbitrary double accents (see below for the code). This works fine, but I now noticed that the spacing is (once again) off when you use different math styles (i.e. \displaystyle and friends). Here is an example:

\documentclass{article}
\usepackage{mathtools}
\makeatletter
\def\measureaccent#1#2{%
   \setbox0=\vbox{$#1{#2}\hfil\break$\null\par
      \setbox0=\lastbox\unskip\unpenalty\global\setbox1=\lastbox}%
   \setbox0=\hbox{\unhbox1 \unskip\unpenalty\unskip \global\setbox2=\lastbox}%
   \setbox0=\vbox{\unvbox2 \setbox0=\lastbox}%
}
\def\doubleaccent#1#2{%
   \measureaccent{#1}{#2}\dimen0=\wd0 \measureaccent{#1}{\kern0pt#2}%
   \raise.35ex\rlap{\kern\dimexpr\dimen0-\wd0$#1{\phantom{#2}}$}{#1#2}%
}
\def\doubletilde#1{\doubleaccent\tilde#1}
\makeatother
\begin{document}
\[ \textstyle \doubletilde k \qquad \scriptstyle \doubletilde k \qquad \scriptscriptstyle \doubletilde k \]
\end{document}

As you can see, in \textstyle (and \displaystyle) the result looks fine, but it gets worse from there.

Ideally I'd like for \doubleaccent to work with no further further intervention from my side in all styles. I imagine \measureaccent would have to be adapted for this; it looks like the measuring is done without regard for the current style, but I yet lack the skills to do this myself, and would therefore greatly appreciate the help of the resident wizards. Thanks!

EDIT: I should note that @wipet's answer solved a problem with horizontal alignment of the accents that I'd ideally like to not reintroduce.

EDIT 2: here's another snippet showing why I'm creating double accents this way to begin with:

\documentclass{article}
\usepackage{statmath}
\def\measureaccent#1#2{%
   \setbox0=\vbox{$#1{#2}\hfil\break$\null\par
      \setbox0=\lastbox\unskip\unpenalty\global\setbox1=\lastbox}%
   \setbox0=\hbox{\unhbox1 \unskip\unpenalty\unskip \global\setbox3=\lastbox}%
   \setbox0=\vbox{\unvbox3 \setbox0=\lastbox}%
}
\def\doubleaccent#1#2{%
   \measureaccent{#1}{#2}\dimen0=\wd0 \measureaccent{#1}{\kern0pt#2}%
   \raise.35ex\rlap{\kern\dimexpr\dimen0-\wd0$#1{\phantom{#2}}$}{#1#2}%
}
\def\doubletilde#1{\doubleaccent\tilde#1}
\makeatother
\begin{document}
\[ \tilde\beta \quad \tilde{\tilde\beta} \quad \doubletilde\beta \quad \tilde\bfbeta \quad \tilde{\tilde\bfbeta} \quad \doubletilde\bfbeta \]
\end{document}

The single \tilde is fine for both \beta and \bfbeta. Nested \tildes are too far apart and give the impression of two single tildes rather than a one double tilde (unsurprising, given that that's what they are). In addition, on the \bfbeta, they're positioned too far on the left.

(I usually don't use double accents outside of \displaystyle or \textstyle, and when I do it's usually on bold-face Greek or Latin letters. I just so happened to reach for \doubletilde today when defining another abbreviation in an \underbrace and when I already had k and \tilde k, and then noticed the above.)

What's wrong with \tilde{\tilde{k}} (using amsmath or mathtools)? — egreg, May 02 '21 at 12:56
@egreg The horizontal spacing is off (see the question to the answer linked); and I'd prefer for the two tildes to be a little closer as well, giving the visual impression of a double tilde rather than two single tildes. — chsk, May 02 '21 at 13:30
@chsk what is wrong with the horizontal position of the standard amsmath version ? or hat on beta ? — David Carlisle, May 02 '21 at 15:15
also don't use even boxes for global settings \global\setbox2= that should be box3 not box2 — David Carlisle, May 02 '21 at 15:37
@DavidCarlisle thanks for the pointer re: even boxes. Out of curiosity, why's that? And is there a "List O' Pitfalls" somewhere that tells you about things like these? — chsk, May 02 '21 at 19:24
@DavidCarlisle re: what's wrong with the standard stuff, I'll edit my post. — chsk, May 02 '21 at 19:25
the convention on odd and even scratch registers is set out in the texbook, I'm sure there is an answer on site I'll find... More generally even for registers allocated with \new... they should always be local or always global. — David Carlisle, May 02 '21 at 23:42
not the one I was thinking of but https://tex.stackexchange.com/a/406227/1090 — David Carlisle, May 02 '21 at 23:43

Steven B. Segletes · Accepted Answer · 2021-05-03T09:31:09.330

An approach with stackengine and scalerel.

EDITED to provide a version that accounts for italic font slant; namely, \tsup for upright symbols and \tsit for italic symbols. The italic font slant is specified in the definition \fontslant, here estimated as .3.

A SUPPLEMENT is provided at end to answer OP's wish list of doing this with arbitrary accents.

\documentclass{article}
\usepackage{stackengine,scalerel}
\stackMath
\newcommand\tsup[2][2]{\ThisStyle{%
 \def\useanchorwidth{T}%
  \ifnum#1>1%
    \stackon[-5.5\LMpt]{\SavedStyle\tsup[\numexpr#1-1\relax]{#2}}{\SavedStyle\mathchar`~}%
  \else%
    \stackon[-4.5\LMpt]{\SavedStyle#2}{\SavedStyle\mathchar`~}%
  \fi%
}}
\def\fontslant{.3}
\newcommand\tsit[2][2]{\ThisStyle{%
 \sbox2{$\SavedStyle#2$}%
 \def\useanchorwidth{T}%
  \ifnum#1>1%
    \stackon[-5.5\LMpt]{\SavedStyle\tsit[\numexpr#1-1\relax]{#2}}{\hspace{\fontslant\ht2}\SavedStyle\mathchar`~}%
  \else%
    \stackon[-4.5\LMpt]{\SavedStyle#2}%
    {\hspace{\fontslant\ht2}\SavedStyle\mathchar`~}%
  \fi%
}}
\begin{document}
\[
\tsit[1]{z}\neq\tsup{\Lambda}\neq\tsup[3]{\Delta}\neq\tsit[4]{\psi}
\]
\[
\scriptstyle
\tsit[1]{z}\neq\tsup{\Lambda}\neq\tsup[3]{\Delta}\neq\tsit[4]{\psi}
\]
\[
\scriptscriptstyle
\tsit[1]{z}\neq\tsup{\Lambda}\neq\tsup[3]{\Delta}\neq\tsit[4]{\psi}
\]
\end{document}

SUPPLEMENT

Here, I create a macro \makeitupaccents that takes 3 arguments. The first is the name to use it creating the accent macros, to which it and up will be added. Thus, if ts is provided, macros \tsit and \tsup will be created.

Second is the accent itself and can include horizontal kerning, if needed (see MWE).

The third argument is a dimensional augmentation to the stacking gap between both the character and the accent as well as between accents. Because I am using scalerel, the dimensions \LMpt and \LMex are also available here, and refer to a pt and and ex, which get shrunk in the smaller math styles (.7pt and .5pt for script and scriptscript styles, by default, likewise for ex).

EDITED for efficiency, using fewer \mathchoices (by eliminating nested calls to \ThisStyle).

\documentclass{article}
\usepackage{stackengine,scalerel}
\stackMath
\newcommand\fontslant{.3}
\newcommand\makeitupaccents[3]{%
\expandafter\newcommand\csname #1up\endcsname[2][2]{\ThisStyle{%
  \csname #1upaux\endcsname[##1]{##2}}}
\expandafter\newcommand\csname #1upaux\endcsname[2][2]{%
  \def\useanchorwidth{T}%
  \ifnum##1>1%
    \stackon[\dimexpr#3-5.5\LMpt]{\SavedStyle\csname 
      #1upaux\endcsname[\numexpr##1-1\relax]{##2}}{\SavedStyle#2}%
  \else%
    \stackon[\dimexpr#3-4.5\LMpt]{\SavedStyle##2}{\SavedStyle#2}%
  \fi%
}
\expandafter\newcommand\csname #1it\endcsname[2][2]{\ThisStyle{%
  \csname #1itaux\endcsname[##1]{##2}}}
\expandafter\newcommand\csname #1itaux\endcsname[2][2]{%
 \sbox2{$\SavedStyle##2$}%
 \def\useanchorwidth{T}%
  \ifnum##1>1%
    \stackon[\dimexpr#3-5.5\LMpt]{\SavedStyle\csname
      #1itaux\endcsname[\numexpr##1-1\relax]{##2}}%
      {\hspace{\fontslant\ht2}\SavedStyle#2}%
  \else%
    \stackon[\dimexpr#3-4.5\LMpt]{\SavedStyle##2}%
    {\hspace{\fontslant\ht2}\SavedStyle#2}%
  \fi%
}
}
\begin{document}
\makeitupaccents{ts}{\mathchar`~}{0pt}
\makeitupaccents{cs}{\mathchar`^}{0pt}
\makeitupaccents{ds}{\mathchar'26}{.7\LMpt}
\makeitupaccents{as}{\kern-\LMpt\mathchar"017E}{.2\LMpt}
\def\tmp{\tsit[1]{z}\neq\tsup{\Lambda}
  \neq\csup[3]{\Delta}\neq\csit[4]{\psi}
  \neq\dsup[3]{\Omega}\neq\dsit[2]{\omega}
  \neq\asup[3]{\mathrm{A}}\neq\asit[2]{\nu}}
\[\tmp\]
\[\scriptstyle\tmp\]
\[\scriptscriptstyle\tmp\]
\end{document}

That's very cool -- thank you, +1 --, but it reintroduces the problem with horizontal alignment of the accents being off that @wipet's answer solved in the first place. — chsk, May 02 '21 at 14:30
@chsk I see your point. Maybe I'll get a chance to address that. — Steven B. Segletes, May 02 '21 at 14:31
Thanks --- that's great, now the only missing feature is arbitrary accents. (\doubleaccent in my question allows these; I merely used tildes as an example.) — chsk, May 02 '21 at 19:57
@chsk The accent in these definitions is \mathchar\~. It occurs twice in each definition. You can make a copy of the macro(s) and play with other accents. For example, replacing the four occurrences with\mathchar`^` gives a carat accent — Steven B. Segletes, May 02 '21 at 23:18
Thanks a lot again for all your work, much appreciated! I'll wait for a bit to see if there'll be any other answers before accepting. — chsk, May 03 '21 at 07:23

Adapting double math-mode accents for different math styles

1 Answers1

Linked