Dear Mark,

I have had problems where a computer with bigger RAM has helped, though frankly 
if I had not had that larger computer I probably would have been able to do 
with a somewhat smaller machine and splitting up the job. In the end the 
benefit of more memory is somewhat logarithmic, if you give 512GB a 10, then 
128GB is a 9 or 9.5.

As far as ordering a computer, I think the question is of the tradeoff what you 
would have to forgo if buying the larger machine (at the funding level I have, 
512GB would be too high a tradeoff; you are probably better funded) and whether 
you already have calculations that you know failed at 128GB.  However, frankly, 
again my experience with (say) coset enumeration is that if it did not 
terminate in Memory x the chance to terminate in memory 2x is somewhere 5% or 
less, so a factor of 4 in memory is really only buying you a better success 
chance of 20% or less on these kinds of calculations.

Particularly concerning the calculations I expect you will be doing, also be 
aware that GAPs built-in Coset enumeration, knuth-bendix and groebner bases are 
far less powerful than the standalone c-programs and that there are packages 
that provide interfaces to ACE, KBMAG and singular.

Also often calculations tend to run for a long time and our system 
administrator wanted to reboot machines for safety updates -- I am now using 
DMTCP (http://dmtcp.sourceforge.net) to be able to save a running jobs to disk 
and to restart it after the machine reboot.

Best,

    Alexander



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