On Oct 21, 4:03 am, mmarco <mma...@unizar.es> wrote:
> That was my first idea when i encountered these problems. But then,
> things like primary decomposition rely on factorization of
> polynomials... which will differ a lot from QQbar to an algebraic
> extension of Q.

Indeed. Data point: Magma does allow QQbar as a base ring for
polynomial rings and supports primary decomposition. Magma uses a
finite field to track dependencies rather than interval arithmetic.
That's numerically a lot simpler, except in the rare event that you
run into a polynomial with bad reduction at the chosen prime.

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