I'm not a chemical engineer after all

Patience. Research. Planning. Determination. They all played a part. As did my fear of messing about with caustic soda.

A dig through the scrap pile up-cycling, artisanal material section, plenty of grinding and here we have it. Crap photo, but how many phone calls have you made on your Nikon D4?

On the left is the bottom end of the seatpost, on the right is the protruding bit of the tool. Just enough of a lip to hook the seatpost. With some serious "pull hammer" action it came out, not without a fight, but gracefully resigned to it's fate. Park Tools take note ;)

Done. Out. Sanded. Polished. The post and it's saddle clamp re-epoxied.

Given the state of the inside of the seat-tube and the fact that I don't need 300mm of seat tube in a farm gate frame like this, it will be shortened.

Thanks to Graeme for the technical advice and to Babble for querying my commitment to the chemical option

That it should come to this

A lovely old 1997 GT Palomar has wandered into my stable, by a somewhat circuitous route (but that's a story for another post) Right now, the issue at hand is more dramatic. Stuck. Aluminium. In. Steel. %&*%$

..and the seatpost and saddle-clamp have parted ways.....

It's a matter of basic arithmetic:

Aluminium seatposts + steel seat tube + H2O + (2013-1997) = Trouble x Plenty x n+1

The saddle clamp has un-inserted itself from the seatpost, so no sideways leverage anymore. Next option is  my array of home made pullers combined with the CO2 shrinkage trick , but I fear it may end up being another equation:

NaOH + H2O + Aluminium  = Aluminium Hydroxide + Hydrogen + unharmed steel seat tube

              60 minutes

Yup. The observant faithful will have noticed that there is no longer a seatpost in the equation. Which is more or less what's supposed to happen.

Let the last resort remained untried. If you have connections with higher beings, please make appeals on my behalf (If George Carlin heard me say that, I'd be in shit)

Source: Sheldon Brown of course

13. Drastic solution, contributed by Matt Duff: Sodium Hydroxide - AKA Caustic Soda. ONLY FOR AN ALUMINUM SEATPOST IN A STEEL FRAME AS FAR AS I KNOW. It will destroy an aluminum frame. It won't affect steel, and as far as I know it won't affect most plastics.
    DISCLAIMER - don't attempt if you are unsure about anything and always use thick rubber gloves, face mask, overalls, boots. Sodium hydroxide will eat away at the aluminium but it will also eat off your skin faster than anything. [Getting it in the eyes can cause blindness. See precautions here. Have a source of running water, and for good measure, a bucket of water ready, in case of an accident. -- John Allen]
    PREPARE THE BIKE:
    Saw off the seat post at the top of the tube and bung it up with something plastic. You must do this because othersies, liquid would flow out when the caustic soda eats through the seatpost). Make sure it is liquid tight. Remove bottom bracket. I'd suggest removing anything else off the bike that is aluminium, and covering up any decals you may want to save. Take the bike outside and set upside down on a patch of dirt away from kids and animals.
    PREPARE THE SODIUM HYDROXIDE:
    Measure out 200g of sodium hydroxide powder into a plastic cup. Fill a 750ml bottle with 500ml of cool water.
    Put on all the safety gear - the mix will get hot, produce fumes, and may splash. Don't let it touch your skin!
    Place the bottle of water into an empty plastic bucket - the bottle may overflow so you want to catch that stuff. Slowly pour the 400g of powder into the 750ml bottle - use a thin wooden stick to stir it. It will get hot - make sure there is no powder left in the bottom of the bottle.
    POUR IT IN!
    Using a funnel and a thin hose pour in a small amount of the liquid mix into the frame of the bike through the bottom bracket . Maybe about 100ml at a time - wait about 5 minutes and it will start bubbling and gas coming out. When it starts to slow down pour another 100ml in Continue this so that the liquid is in the bike tube for about 1 hour. [No fire or flame nearby -- caustic soda releases hydrogen gas when it reacts with aluminum. -- John Allen].
    CLEAN UP:
    Break the seal on the seatpost hole - warning! lots of liquid will come out. Be covered up and check where it is all going to flow to. Run fresh water through the frame thoroughly to make sure it is all out Clean the area - dilute any that is on the ground with lots and lots of water Throw away any containers and wash tools really really well
    I found I had to do this twice. The second time I had to plug the top tube to stop the liquid flowing down there. [You might tilt the frame so liquid will not run down the top tube -- John Allen] Finally all that was left was a thin sliver of seat post. Hope this is good information. Cheers!

"Free at last! Free at last! Thank God almighty, I am free at last!"

--Dr. Martin Luther King, Jr.