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If you add some debugging print, you will notice that arent(aux) is first Univariate Polynomial Ring in x over Integer Ring but then Univariate Polynomial Ring in x over Rational Field, because you made a division, and though the resulting coefficient remain integers, they now belong to the rational field, see:

sage: parent(2)
Integer Ring
sage: 4/2
2
sage: parent(4/2)
Rational Field

So what you have to do is to convert the result back into ZX:

sage: primitive_part = lambda f : ZX(f / f.content())

Or, since ZX is the parent of f, you can do more generically:

sage: primitive_part = lambda f : parent(f)(f / f.content())