Ideal Saturation over F(t)[x,y] for F a number field could be faster.

[simonbrandhorst]

The saturation of an ideal in F(t)[x,y] for F = QQ(a) a simple number field could be faster.

The following computation terminates in Magma in Total time: 85.219 seconds, Total memory usage: 64.12MB See the attached text file for the magma code saturation_with_magma.txt

It does not terminate with Oscar at all. Here is the file: saturation_with_oscar.txt

Here is the background where these computations came up. For our research @HechtiDerLachs and I had to compute an F(t)-rational point of a curve of genus one over F(t). We knew that the point is contained in a zero dimensional ideal J. To do so we first needed to saturate J by some principal ideal D1 whose vanishing locus would not contain the point. Then we would like to compute the minimal primes of the resulting ideal J1. (But we never got to this point in Oscar.)

@ederc @wdecker @hannes14 @jankoboehm @afkafkafk13 @HechtiDerLachs