To check if packagename
was installed, type:
dpkg -s <packagename>
You can also use dpkg-query
that has a neater output for your purpose, and accepts wild cards, too.
dpkg-query -l <packagename>
To find what package owns the command
, try:
dpkg -S `which <command>`
For further details, see article Find out if package is installed in Linux and dpkg cheat sheet.