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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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# Normal run; a is involn, 3 columns ...

Wo:10k;
mess:100000;

gr:a,b;
rel:aa,abAbabAb;
end;
stat;
dump:1;

# Now a PT run; note that the presentation has already been munged,
#   but that we switch to 4 columns (this affects Fi too!) ...

pt;
stat;
dump:1;

# Now a PT run ab initio; a is no longer treated as as involn, so a & A
#   are different, and we get dedns/coincs ...

gr:a,b;
rel:aa,abAbabAb;
pt;
stat;
dump:1;