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\documentclass[a4paper,10pt,onecolumn]{article}
\usepackage[icelandic]{babel}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage{tocloft}
\usepackage{xstring}
\makeatletter
\numberwithin{equation}{section}
% we use this for our refernces as well
\AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
% redefinition of \equation for convenience
\let\oldequation = \equation
\let\endoldequation = \endequation
\AtBeginDocument{\let\oldlabel = \label}% \AtBeginDocument because hyperref redefines \label
\newcommand{\mynewlabel}[1]{%
\StrBehind{#1}{eq:}[\Str]% remove "eq:" from labels
\myequations{\Str}\oldlabel{#1}}
\renewenvironment{equation}{%
\oldequation
\let\label\mynewlabel
}{\endoldequation}
\newcommand{\listequationsname}{\Large{Jöfnur}}
\newlistof{myequations}{equ}{\listequationsname}
\newcommand{\myequations}[1]{%
\addcontentsline{equ}{myequations}{\protect\numberline{\theequation}#1}}
\setlength{\cftmyequationsnumwidth}{3em}
\makeatother
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\begin{equation}\label{eq:Hér þarf örn}
E = mc^2
\end{equation}