SMS sent from Arduino using software

I have an Arduino Due linked to a PC. The arduino monitors and controls some hardware, with data sent to the PC via BlueTooth. I would like the system to send me a message on my cell phone when something happens and that I'm away, not in front of the PC. I know that I can use a GPRS/GSM shield but I wonder if I could use the link from the Arduino to the PC to send the message using only software, as the PC is connected to wifi?

If you can add code to the PC software discussing with the arduino then you can use one of the many popular platform to send SMS.

Probably sending a twitter notification or facebook or an email will be even easier as there are tons of code already lying around for that and very well supported public API for doing so.

You can send the PC a message. It is entirely dependent on your PC programming skills as to whether or not you can make the PC send a text message. I could.