A computer is a programmable machine that stores, organises, and manipulates data and then outputs it in a useful format.
The M-series multitronic system was invented by Dr. Richard Daystrom as a independent artificial intelligence that could control and operate a starship. Daystrom's fifth design, M-5, was considered operational enough to for field testing. It, like its predecessor, was also a failure. Coupled with the mental breakdown of Daystrom saw the project was cancelled. (TOS: "The Ultimate Computer")
Isolinear system was a computing technology used by several cultures, such as the Cardassians and Federation. Isolinear optical chips started to come into common use in Starfleet in 2329. (TNG: "Relics")