You need an engineers vice on a sturdy bench.
Method 1;
Strip bike.
Turn upside down and clamp the jaws around the seatpost, it will get very good grip, crush post if needed.
Turn entire frame to break the corrosion seal.
Waggle back and forth and use upward pressure to help pull it out the frame.
Throw post in bin.
Method 2;
Remove bottom bracket, and stuff up the tube blocking it. Plasticine works good here.
Saw off seatpost about 1/2" from top of frame.
Pour in a strong drain cleaner.
Do outside as the fumes coming off are lethal
Peek in and watch the alloy seatpost dissolving. DO NOT use this method if the frame is alloy too. because the frame will also dissolve.
Method 3;
Saw off seatpost 1" from top of frame, then using bi-metal saw blade held in a cloth or hacksaw handle(theres a type for broken blades- I'll post up an example)
Carefully saw through the seatpost lengthwise, its a tricky job, but for some the preferred method.
When you feel you are 99% through, use something like mole grips to crush the post, one side of the cut and turn it inwards to itself, its like curling one side. This breaks the corrosion grip and makes the post smaller
Over on RetroBike, we are the home of stuck seatpost removal, theres literally dozens of threads pertaining to this, the three above are examples. I've personally used 1 and 3.
Heat or flame is really the last resort as it either wrecks the paint, or can cause the frame seat tube to crack, especially if an alloy frame.
After removal it is expected that you wave freed seatpost above your head shouting Way-hey, got ye ya bast$%^
There is a 4th way, involving something called Gallium. But suitable if only the post is alloy.
View attachment 48606
Gallium results-
They also try it on an alloy bicycle.