> I am very surprized that I.groebner_basis() does not return an ideal.

I don't think it should give back an ideal since a Grobner basis is a
particular basis for an ideal (particularly the one you started with).

sage: R.<a,b,c,d> = PolynomialRing(QQ)
sage: I = R.ideal(a*b-1, c*d-1)
sage: J = R.ideal(I.groebner_basis())
sage: I == J
True

--Mike

P.S.  It is better not to use strings everywhere but instead use the
actual variables.


> Is it really needed to say:
> sage: J=R.ideal(I.groebner_basis())
> sage: type(J)
> <class
> 'sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal'>
>
> This looks strange to me (close to a bug).
>
> Yours
>      Simon
>
> >
>

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