How to make ≝ and „equivalent to by definition“ similar?

Question

We continue How to get two versions of the same math Unicode symbol from different fonts with XeLaTeX or LuLaTeX?, where we found out how to get ≝ in which “=” has roughly the same width as “def” using a math font.

We sometimes use “def“ also over the equivalence symbol. Is there a way to get similar and pleasant look of ≝ (in which “def” and “=” are roughly equally wide) such that it appears in the text layer of the PDF as a single symbol and also looks similar to “def” over “⇔”? Any other font besides Latin Modern Math, perhaps?

Here is some code to play with:

\documentclass{article}
\pagestyle{empty}
\usepackage[math-style=ISO]{unicode-math}
\setmainfont{TeX Gyre Termes}
\setsansfont{TeX Gyre Heros}[Scale=0.88]
\setmonofont{TeX Gyre Cursor}
\setmathfont{TeX Gyre Termes Math}
\newfontface{\latinmodernmath}{latinmodern-math.otf}% thx to Ulrike and egreg!!!
\newcommand*{\definingEquals}{\mathrel{\text{\latinmodernmath ≝}}}% thx to Ulrike and egreg!!!
\newcommand*{\definingEquiv}{\stackrel{\text{def}}{\Leftrightarrow}}
\begin{document}
\begin{align*}
𝑇\quad&\definingEquals\quad\{(𝐽, 𝑀) : 𝐽 ∈ ℤ ∧ 𝑀 ∈ ℕ_+ ∧ 𝑀 ≤ 12\}\\
(𝐽, 𝑀) ⪯ (𝐽′,𝑀′) \quad&\definingEquiv\quad 𝐽 < 𝐽′ ∨ (𝐽 = 𝐽′ ∧ 𝑀 ≤ 𝑀′)
\end{align*}
\end{document}

As you see, these def symbols don't look well together, but at least the upper one gets into the PDF text layer.

We are reluctant to take “⇔” from a non-main math font (i.e., we don't wish to deviate from TeX Gyre Termes Math much), since then, in a non-minimal document, we'd have to take also the left and right double arrows from that other font for visually pleasant looks, and this would possibly incur changing more and more characters. The publisher's guideline mentions “Times”, and we interpret this as “Times-like”.

What we could hypothetically do is replace “def“ above “⇔” by \textsmaller[2]{def} using the relsize package, though I'm really not sure whether this would be visually the best option: already now “def” above “=” is hardly visible, and we are reluctant to making “def” above “⇔” also hardly visible.

A font with a better ≝ (where “def” is Times-like) would be probably preferred, if it exists.

PS. The best scaling+stacking version so far is, IMHO, https://tex.stackexchange.com/a/35409. Related: A better long ≝ (defining equals, equals to by definition) without bumps .

Answer 1

Considering of your purpose, I give you the following options.

\documentclass{article}
\usepackage{amsfonts,amssymb,amsmath}
\usepackage{graphicx}%for \scalebox
\usepackage{mathtools}%for \cloneqq

\newcommand{\bedefine}{\stackrel{\scalebox{0.5}{\ensuremath{\mathsf{\,def}}}}{=}}
\newcommand{\eqdefine}{\stackrel{\scalebox{0.5}{\ensuremath{\mathsf{\,def}}}}{\equiv}}
\newcommand{\iffdefine}{\stackrel{\scalebox{0.5}{\ensuremath{\mathsf{\,def}}}}{\Leftrightarrow}}
\newcommand{\simdefine}{\stackrel{\scalebox{0.5}{\ensuremath{\mathsf{\,def}}}}{\sim}}

\newcommand{\bedefinet}{\stackrel{\scalebox{0.4}{\ensuremath{\mathbf{\,def}}}}{=}}
\newcommand{\eqdefinet}{\stackrel{\scalebox{0.4}{\ensuremath{\mathbf{\,def}}}}{\equiv}}
\newcommand{\iffdefinet}{\stackrel{\scalebox{0.4}{\ensuremath{\mathbf{\,def}}}}{\Leftrightarrow}}
\newcommand{\simdefinet}{\stackrel{\scalebox{0.4}{\ensuremath{\mathbf{\,def}}}}{\sim}}

\begin{document}
\huge
\[
\begin{array}{rclcrcl}
f&\bedefine& x+y,&&f&\bedefinet& x+y,\\
f&\eqdefine& x+y,&&f&\eqdefinet& x+y,\\
f&\iffdefine& x+y,&&f&\iffdefinet& x+y,\\
f&\simdefine& x+y,&&f&\simdefinet& x+y,\\
f&\coloneqq& x+y,&&&&\\
f&\triangleq& x+y.&&&&
\end{array}
\]
\end{document}

It's easy to understand \bedefine, \eqdefine, \iffdefine and \simdefine. I think you also see \coloneqq before. While I usually use \triangleq instead and I understand it as: Delta + equality ~ D + equality ~ define + equality ~ is defined to be.

By the way, to make "def" be more visible, the sans serif fonts are better choices than the serif fonts such as Times and so on. Now the font of def on the right side is Computer Modern Bold in default. And if you want def to be Times-like fonts, then you should set the bold fonts of the regular fonts to be Times Bold.