OK, I know that I have to set the new totilet on the base floor which in this case is cement. The carpet was cut around the existing totilet when the new carpet was installed. However now, I think the best way to open the carpet up, or cut the carpet around the totilet area is to intervert a v shape cut the existing carpet to open up the area to install the new totilet.
This idea vs: cutting the carpet along the edge of the tube, back wall, and side of cabnet.
Then just use for option double sided tape to hold in place with the new totilet.