Can I run Unity and compile a game on iPad?

Now, I would like to build games for playing on iPad and iPhone. So if I buy an iPad, can I run Unity on it an compile a game right on my iPad?

No, you'd need a mac to create games and compile them for the iPad.

You can't compile directly on the iPad - you can only deploy fully built games to the device. In order to deploy games, you need the Unity iOS license and an Apple developer license. Without the Apple developer license, you can only run programs in the iOS simulator that comes with the Xcode SDK (although I haven't tried running Unity games in the simulator).

EDIT: Apparently, you can run Unity games in the simulator:

Not to forget that you need a Unity license to build for the iPad and iPhone. Probably also some license from Apple to do it.

No, you cannot currently develop on your mobile device or tablet. It only runs apps.