CoCoA » CoCoA-5

Andraschko's original email:

Arithmetic on Hilbert series or Hilbert functions. E.g. the code

/**/ S ::= QQ[x1,x2,x3,x4];
/**/ I := ideal(S,[RingElem(S,"x4")]);
/**/ H1 := HilbertSeries(R);
/**/ H2 := HilbertSeries(S/I);
/**/ H1 = H2;
produces two warnings that CoCoA is untagging the operators and then even says false. Also sth like H1 + H2 would be great. I have no idea whether it is possible to redefine operators as in C++, but even something like $hs.Equal(...) or $hs.Add(...) would be great.

Bernhard points out that currently a "hilbert series" is a record.
Perhaps it is best then to add a new field which contains a proper ratfn representation of the HS.
In which field should the ratfn reside? Should there be a QQ like QQ[t] for num and den?
Or perhaps instead of QQ[t]?