A better long ≝ (defining equals, equals to by definition) without bumps

Question

For a long time, I've been defining a long „equals to by definition“ symbol ≝ for [pdf|lua|xe]latex via

\newcommand*{\longDefiningEquals}{\stackrel{\text{def}}{=\joinrel=}}

Its typical usage would be in a block formula such as

𝑅⨾𝑆 ≝ { (𝑥,𝑧) | ∃ 𝑦: (𝑥,𝑦) ∈ 𝑅 ∧ (𝑦,𝑧) ∈ 𝑆}

where there's enough space to accommodate a long equals-to-by-definition symbol (a short one, say, from TeX Gyre Termes Math, would semantically work, but here we wish to spend space on the main symbol of the formula). However, in my examples, the aforementioned command results in two small bumps in the middle of the equality sign. Here is an example to play with:

\documentclass{article}
\usepackage{iftex}
\ifTUTeX
  \usepackage[math-style=ISO]{unicode-math}
  \setmainfont[Ligatures=TeX]{TeX Gyre Termes}
  \setsansfont{TeX Gyre Heros}[Scale=0.88]%%% Somewhat ok scaling.
  \setmonofont{TeX Gyre Cursor}%%% No explicit turning on ligatures for the monospaced font.
  \setmathfont[Ligatures=TeX]{TeX Gyre Termes Math}
  \setmathfont[Ligatures=TeX,Extension=.otf,range={"2A3E},BoldFont=XITSMath-Bold]{XITSMath-Regular}%%% The fat semicolon comes from XITS.
\else
  \usepackage[helvratio=.9]{newtxtext}% Scale the sans font at 90%.
  \usepackage[slantedGreek,subscriptcorrection]{newtxmath}%% Should be loaded after the text font according to its manual. The default uppercase Greek letters should be slanted according to the SVMono manual.
\fi
\usepackage{graphics}
\newcommand*{\longDefiningEquals}{\stackrel{\text{def}}{=\joinrel=}}%%% long equality symbol that is used to define stuff
%\newcommand*{\longDefiningEquals}{\stackrel{\text{def}}{\scalebox{2}[1]{=}}}% Marjin's suggestion
\begin{document}
% \[R⨾𝑆\ \longDefiningEquals\ \{ (𝑥,𝑧) \mid ∃ 𝑦\colon (𝑥,𝑦) ∈ 𝑅 ∧ (𝑦,𝑧) ∈ 𝑆\}\]
% \[R⨾𝑆\ ≝ \{ (𝑥,𝑧) \mid ∃ 𝑦\colon (𝑥,𝑦) ∈ 𝑅 ∧ (𝑦,𝑧) ∈ 𝑆\}\]
\[\longDefiningEquals\]
\end{document}

The bumps sometimes become visible on the screen, especially at low resolutions:

Is there a better LONG ≝ symbol in a Type1 font or an OTF math font or, perhaps, can one construct a better symbol oneself? (Of course one can draw it via TikZ/PSTricks, but this would raise issues when such a symbol has to go into a TikZ/PS picture itself or when changing the font size.)

Answer 1

with luatex you can use extensible symbols:

\documentclass{article}
\usepackage[math-style=ISO]{unicode-math}
\setmathfont[Ligatures=TeX]{TeX Gyre Termes Math}

\newcommand*{\longDefiningEquals}
 {\Uoverdelimiter 0 "3D {\text{ \vphantom{j}definition }}}
\begin{document}
\[\longDefiningEquals\]
\end{document}

Answer 2

You don't have to draw it with PGF/TikZ. It's only two horizontal bars.

The value .225ex is half of TikZ “equal sign distance” (whereever that is from) and 2.57pt is from TikZ-CD's axis_height function. The value .56pt is from the rule_thickness function.

These values are different for each font and need to be evaluated better in the real use-case.

Only disadvantage is that it's not a = anymore and won't be selectable in the output.

Code

\documentclass{article}
\usepackage{iftex}
\ifTUTeX
  \usepackage[math-style=ISO]{unicode-math}
  \setmainfont[Ligatures=TeX]{TeX Gyre Termes}
  \setsansfont{TeX Gyre Heros}[Scale=0.88]%%% Somewhat ok scaling.
  \setmonofont{TeX Gyre Cursor}%%% No explicit turning on ligatures for the monospaced font.
  \setmathfont[Ligatures=TeX]{TeX Gyre Termes Math}
  \setmathfont[Ligatures=TeX,Extension=.otf,range={"2A3E},BoldFont=XITSMath-Bold]{XITSMath-Regular}%%% The fat semicolon comes from XITS.
\else
  \usepackage{newtxtext,newtxmath}
\fi
\usepackage{graphics}
\newcommand*{\longDefiningEquals}{\stackrel{\text{def}}{=\joinrel=}}
\makeatletter
\newcommand*\lde[1][def]{%
  \stackrel{\mathrm{#1}}{%
    \settowidth\dimen@{$\scriptstyle\mathrm{#1}$}%
    \rlap{\rule[\dimexpr-.225ex+2.57pt]{\dimen@}{.56pt}}%
          \rule[\dimexpr+.225ex+2.57pt]{\dimen@}{.56pt}}}
\makeatother

\usepackage{tikz}
\begin{document}
%\[R⨾𝑆\ \longDefiningEquals\ \{ (𝑥,𝑧) \mid ∃ 𝑦\colon (𝑥,𝑦) ∈ 𝑅 ∧ (𝑦,𝑧) ∈ 𝑆\}\]
%\[R⨾𝑆\ ≝ \{ (𝑥,𝑧) \mid ∃ 𝑦\colon (𝑥,𝑦) ∈ 𝑅 ∧ (𝑦,𝑧) ∈ 𝑆\}\]
\[\longDefiningEquals a = b \lde c \lde[definition] d = e\]
\tikz\node[draw,green,line cap=round]{$a \lde b$};
\end{document}

Answer 3

You can use the graphicx package that provides \scalebox and \resizebox to change the width of any content. If the content is text then it will remain as text, i.e., a widened = symbol can still be selected/copied/searched as a normal character.

For \scalebox you can set the horizontal and vertical scale separately. To make a symbol wider the vertical scale should remain at 1.

To make the symbol as wide as the text on top you can use \widthof from the calc package as width value for \resizebox. For the height value you can use the macro \height which contains the original height of the box. However, because the box containing def is slightly larger than the word itself, the symbol may appear to wide. The calc package provides the construct * \real{number} to modify the outcome of \widthof.

MWE:

\documentclass{article}
\usepackage{graphicx}
\usepackage{calc}
\usepackage[math-style=ISO]{unicode-math}
\setmainfont[Ligatures=TeX]{TeX Gyre Termes}
\setsansfont{TeX Gyre Heros}[Scale=0.88]%%% Somewhat ok scaling.
\setmonofont{TeX Gyre Cursor}%%% No explicit turning on ligatures for the monospaced font.
\setmathfont[Ligatures=TeX]{TeX Gyre Termes Math}
\setmathfont[Ligatures=TeX,Extension=.otf,range={"2A3E},BoldFont=XITSMath-Bold]{XITSMath-Regular}%%% The fat semicolon comes from XITS.
\newcommand*{\longDefiningEquals}{\stackrel{\text{def}}{=\joinrel=}}%%% long equality symbol that is used to define stuff
\newcommand*{\scaleDefiningEquals}{\stackrel{\text{def}}{\scalebox{2}[1]{=}}}%%% long equality symbol that is used to define stuff
\newcommand*{\wdDefiningEquals}{\stackrel{\text{def}}{\resizebox{\widthof{def} * \real{0.8}}{\height}{=}}}%%% long equality symbol that is used to define stuff

\begin{document}
\[R⨾𝑆\ \longDefiningEquals\ \{ (𝑥,𝑧) \mid ∃ 𝑦\colon (𝑥,𝑦) ∈ 𝑅 ∧ (𝑦,𝑧) ∈ 𝑆\}\]

\[R⨾𝑆\ \scaleDefiningEquals\ \{ (𝑥,𝑧) \mid ∃ 𝑦\colon (𝑥,𝑦) ∈ 𝑅 ∧ (𝑦,𝑧) ∈ 𝑆\}\]

\[R⨾𝑆\ \wdDefiningEquals\ \{ (𝑥,𝑧) \mid ∃ 𝑦\colon (𝑥,𝑦) ∈ 𝑅 ∧ (𝑦,𝑧) ∈ 𝑆\}\]
\end{document}

Result:

Note that the original symbol is stretched instead of repeated, so it is guaranteed not to have artifacts in the middle.

Answer 4

Something like this?

\documentclass[12pt]{article}
\usepackage{amsmath,amssymb}
\makeatletter
\def\equalsfill{$\m@th\mathord=\mkern-7mu
\cleaders\hbox{$\!\mathord=\!$}\hfill
\mkern-7mu\mathord=$}
\makeatother
\begin{document}
\[R \stackrel{\text{def}}{\hbox{\equalsfill}} S\]
\[R \stackrel{\text{definition}}{\hbox{\equalsfill}} S\]
\end{document}

PS: The macro is taken from the documentation symbols-a4.

Answer 5

The ≝ symbol is U+225D in Unicode, and \eqdef in unicode-math, stix or stix2.