Asymmetric parentheses in bold equation

Question

I'm trying to create asymmetric parentheses so they will look nice in the equation that the following code produces. For this I defined a new command according to an answer I found here, and it looks indeed perfect, as you can see in the output.

The problem is, it does not work in bold math font for some reason. Can someone please help me produce the same second equation in the color and bold font shown in the first equation?

The commented code is what does not work.

\documentclass[a4paper,12pt]{article}
\usepackage[spanish]{babel}
\usepackage[utf8]{inputenc}
\usepackage{mathtools}
\usepackage{bm}
\usepackage[dvipsnames]{xcolor}

\newcommand{\lowerparen}[2]{%
\raisebox{-#1}{\(\displaystyle\left(\raisebox{#1}{\(\displaystyle#2\)}\right)\)}}

\begin{document} 

\[\textcolor{pink!20!purple}{\bm{\omega_f(x)\coloneqq\inf_{\delta>0}\bigg(\sup_{d(x,t),\hspace*{0.5mm}d(x,u)\leq\delta}|f(t)-f(u)|\bigg)}}\]

%\[\textcolor{pink!20!purple}{\bm{\omega_f(x)\coloneqq\inf_{\delta>0}\lowerparen{3pt}{\sup_{d(x,t),\hspace*{0.5mm}d(x,u)\leq\delta}|f(t)-f(u)|}}}\]

\[\omega_f(x_0)=D\hspace*{2mm}\overset{\big.\text{def}\big.}{\Leftrightarrow}\hspace*{2mm}\inf_{\delta>0}\lowerparen{3pt}{\sup_{d(x,t),d(x,u)\leq\delta}|f(t)-f(u)|}=D\]

\end{document}

Answer 1

Don't lower the parentheses. It's wrong.

If you insist on it and also in typesetting bold formulas, you can do much better.

\documentclass[a4paper,12pt]{article}
\usepackage[spanish]{babel}
\usepackage[utf8]{inputenc}
\usepackage{mathtools}
\usepackage{bm}
\usepackage[dvipsnames]{xcolor}

\newcommand{\lowerparen}[2]{%
  \raisebox{-#1}{\(\displaystyle\left(\raisebox{#1}{\(\displaystyle#2\)}\right)\)}}

\newenvironment{boldequation*}
 {\boldmath\begin{equation*}}
 {\end{equation*}\ignorespaces}

\begin{document} 

This has nice fences
\begin{boldequation*}\color{pink!20!purple}
\omega_f(x)\coloneqq\inf_{\delta>0}
  \biggl(\sup_{d(x,t),\,d(x,u)\leq\delta}|f(t)-f(u)|\biggr)
\end{boldequation*}
whereas this has much less nice fences
\begin{boldequation*}\color{pink!20!purple}
  \omega_f(x)\coloneqq\inf_{\delta>0}
  \lowerparen{3pt}{\sup_{d(x,t),\,d(x,u)\leq\delta}|f(t)-f(u)|}
\end{boldequation*}
On the other hand, this is better
\begin{boldequation*}\color{pink!20!purple}
  \omega_f(x_0)=D
  \overset{\text{def}}{\Leftrightarrow}
  \inf_{\delta>0}
  \Bigl(\,\sup_{\substack{d(x,t)\leq\delta\\d(x,u)\leq\delta}}|f(t)-f(u)|\Bigr)=D
\end{boldequation*}

\end{document}

Please, do consider the third case. There's no law requiring the brackets to cover the whole material.