If you bought Aperture from the AppStore and your Desktop Mac is compatible with Aperture 3.5.1 (running MacOS X 10.9.x), then you can download Aperture directly from the AppStore and install it on your DeskTop Mac for free.
Sign into the AppStore with the same Apple ID you used to buy Aperture originally, and then download it from the "Purchased" tab and install it.
The AppStore licence entitles you to install one copy of Aperture on any Mac you own or control, as long as it is for private purposes.
Note however that Aperture does not allow a single user to synch a single Library between two computers even though the EULA permits a single user to use Aperture on two computers. A very serious limitation to the app.
Workarounds exist, none good. Perhaps the best of the poor workaround solutions is a "sneakernet" with a Library on an external drive that gets moved among computers.