> OK, as a conscious decision it is certainly justified. Of course,
> mathematically you are right that an object and a particular basis of
> that object are two different things. Only i was surprised, because i
> grew up with Singular and not with Magma...

FYI, magma has both commands GroebnerBasis, which returns
a sequence, and Groebner, which is actually a procedure that
modifies the ideal basis in place so that

Basis(Groebner(I)) eq GroebnerBasis(I);

returns true.  Interestingly, the syntax is not Groebner(~I), which
is what one would expect for a call-by-reference, modifying the
object in place.  But that seems to be a design decision that the
user-defined ideal generators are not an immutable attribute of
the ideal, so GroebnerBasis also changes the ideal generators
in place.

--David


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