/usr/share/app-install/desktop/euler:euler.desktop is in app-install-data 0.12.04.4.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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X-AppInstall-Package=euler
X-AppInstall-Popcon=86
X-AppInstall-Section=universe
Type=Application
Version=1.0
Exec=euler
Icon=euler-32
Categories=Education;Science;Math;
Name=Euler
GenericName=Computer Algebra System
Comment=An interactive mathematical program
X-Ubuntu-Gettext-Domain=app-install-data
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