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\documentclass{article}
\usepackage[symbols,automake]{glossaries-extra}
\usepackage{glossary-mcols}
\makeglossaries[main]
\newglossaryentry{duck}{name=duck,%
description={a waterbird with webbed feet}}
\newglossaryentry{parrot}{name=parrot,%
description={mainly tropical bird with bright plumage}}
\newglossaryentry{zebra}{name=zebra,%
description={black and white striped African wild horse}}
\newglossaryentry{aardvark}{name=aardvark,%
description={African ant-eating mammal}}
\glsxtrnewsymbol[description={zeta}]{zeta}{$\zeta$}
\glsxtrnewsymbol[description={beta}]{beta}{$\beta$}
\glsxtrnewsymbol[description={alpha}]{alpha}{$\alpha$}
\glsxtrnewsymbol[description={gamma}]{gamma}{$\gamma$}
\begin{document}
General terms: \gls{duck}, \gls{zebra}, \gls{aardvark},
\gls{parrot}.
Symbols: \gls{beta}, \gls{gamma}, \gls{alpha}, \gls{zeta}.
\printglossary[style=mcolindexgroup]
\printnoidxglossary[type=symbols,sort=use,style=index]
\end{document}
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