Singular

When writing facstd() output directly to a file, there is no way to distinguish the various ideals.
Also, I thought that the number of ideals produced by facstd() does not depend on the monomial order. Apparently it does.

As facstd is a Groebner base computation, it depends on the monomial
ordering. On its way it factorizes (and split) all new elements it came across, so it also depends on the implemented algorithm.
One only knows: the intersection of the ideals is between the radical
of the input and the input itself.

To distinguish the ideals in the list of ideal,
use

Danke schön. Until now I could tell from the order of variables. Sometimes it is clear from that where one ideal ends and the other begins. Alternatively, I have been printing the output in the shell, where it is obvious.

Best regards.