The problem is indeed related to waveform. The computer, at least if it's somewhat recently made, uses a switching power supply derived from a rectifier off the power line. So worrying about power line waveform being sinusoidal isn't the important thing. The wave needs to be such that the required 170 Volts or so comes out of the filter to the switching circuit. Many kinds of waves will produce that but unless you have a UPS designed specifically for recent computer power supply circuits, you can't do much.
If you are really concerned, especially if the computer seems not to operate properly, you will need to measure the rectified voltage inside the computer power supply and verify that it's within specification.
In addition, since a UPS is a switching device, it will generate noise that may interfere with computer operation or, for that matter, other devices in the vicinity. Unless the UPS feature is vital to your operation, I'd suggest you remove it from the system until such time as it's needed (power line issues). Of course that would mean the computer shuts off or something and you could lose information, but for most people it's not an important thing.