Definitely not caustic soda. Or Coca Cola. You don’t want to attack the aluminium or you’ll wreck the frame.
First step to try is leverage. Take the saddle off, and clamp the frame upside down in a vice, clamping by the head of the seatpost. Then twist. If you can, remove the bottle bosses and squirt loads of WD40 down there first to try to break the seal.
If that doesn’t work, then you need to cut it out. Chop off the post about an inch up from the frame, then using a hacksaw blade or a jabsaw cut down vertically inside the post. The aim is to slice the carbon post into sections without cutting the aluminium frame, then pry out the pieces.
Once you’ve got them all out, you’ll need to run a hone or reamer down there to clear out all the crud and corrosion.