Leaving out the back story - which is emotional - here is how I got an alloy seatpost out of a Columbus SLX (steel) frame.
I got a bunch of optimistic advice and it all failed me.
Penetrating oil such as WD-40, Hard core penetrators like PBlaster and Kroil, Freeze spray, Hammers, and giant levers.
I was down to the last resort - sodium hydroxide, aka lye, aka drain cleaner.
I melted the seatpost out with drain cleaner. If you are going to do this you can't just buy drain cleaner. A lot of drain cleaners are not 100% sodium hydroxide. Get the pure stuff. This stuff is dangerous - use precautions. I wore safety glasses and huge gloves everytime I handled this stuff and I handled it a lot. This process takes time but if you persist you will get results with little more effort that the effort of mixing the lye and pouring the mixture.
What you are going to do is flip the bike upside down and pour lye down the seat tube so that it hits the seatpost and melts it from the inside. Lye is corrosive to aluminum, it does not affect steel. I cut the head off of my seatpost which in hindsight I would not do again. Seatposts are usually hollow and cutting the head off reveals an open hole which the lye runs out of. I plugged the hole with plumbers putty of all things. I also spring some leaks near the binder bolt so I plugged those with plumber putty also. Also my frame had holes in the top tube for cable routing so I plugged those also. I recommend experimenting with water to check for leaks! The water-test is also helpful to determine the volume that you want to use.
I pulled the wheels and fork off of my bike when I did mine because I did not want anything flopping around and also I wanted all aluminum away from the lye. You need to pull the bottom bracket because that is where you pour the lye. So with the bike upside down bike such that the seatpost is the furthest down, big gloves and eye protection donned, and your lye mixed according to instructions you pour the lye into the bottom bracket filling up the seatpost. Rinse out the container with water many many times and rinse your gloves many many times. At this point you can put your ear to the bottom bracket and you can hear the chemical sizzling. After a while - day or days - you will pour the lye out and pour some more in. I am not a chemist and I do not know how lye works, maybe if you agitate the stuff every few hours it works better. I just made sure to leave it in for at least a day and I never left it in for more than a few days.
Pour the old stuff out and pour some new stuff in.
So about that hole which is revealed when you cut the head off of the seatpost. On the one hand this is something you need to plug constantly. Because of this you might not want the hole. On the other hand it makes draining easy. I got to where I would pull the plug over the slop sink, replug the hole, and pour in the fresh stuff.
The hole is also nice to access because you can see if the stuff is working - the hole gets bigger, gets jagged, etc. So you might want access to the hole during the melting.
Eventually you will get a nicely corroded seatpost which is still stuck in the frame. Now it is hacksaw blade time.
Take a hacksaw blade, just the blade, and stick it into the seatpost hole and start cutting the seat post. These are long vertical cuts that run the length of the seatpost. You are basically cutting the round seatpost into pieces of pie. This is extremely tedious work and you will second guess yourself, thinking that you are sawing into the frame but eventually you will get a complete cut and you will realize that cutting the aluminum seatpost is very different than cutting steel.
Now you are making the vertical slices when you have time, and then plugging everything and using lye over the course of days and in between cutting sessions. The more mangled things get the more difficult it will be to keep the lye in the tube. Eventually pieces of the seatpost will come loose and you can pull them out with pliers. Keep going until everything is either corroded away or yanked out. What is left will be very rough. I recommend some files and then something attached to a drill, like a cylinder hone or perhaps a barrel hone:
You use that to clean up the inside of the seatpost.
When you are done give your frame a good shake to make sure that all of the bits are out, then rinse again with water. You might take this opportunity to apply framesaver. You are ready to put everything back on, using grease liberally.