FWIW:

Hannes wrote in the Singular forum that he finds it a bad idea to use 64
bit integers, because it would behave differently on 32bit machines. He
also argues that bigint vectors exist in Singular, since there are bigint
*matrices* in Singular; right, but the syntax is different and thus it
isn't a drop-in replacement. And he wrote that making hilb(id,1) use
bigint vectors would imply a complete rewrite of the function, and if
I volunteer to implement it; although I'd expect that it is mainly
"search-and-replace", I am not so sure if I volunteer.

So, at the moment I am trying to implement something in Sage, using
sage.rings.polynomial.polydict.ETuple as data structure. I guess the
implementation will go to either sage.rings.polynomial.polydict or
better to a new module sage.rings.polynomial.hilbert.

Best regards,
Simon

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