Totally real algebraic number fields of degree 9 with small discriminant (Q2719788)

The author computes all totally real algebraic number fields of degree 9 and discriminant less than 12,000,000,000. (Those are known to be primitive.) He uses known and refined methods for producing a set of sufficiently many polynomials which is guaranteed to contain generating polynomials for any such field. The handling of that set is kept elementary and described in detail. Not all steps (irreducibility testing, calculation of the field discriminant from the polynomial discriminant, isomorphy tests) use the most efficient known methods. The output consists of two fields of discriminants 9,685,993,193 and 11,779,563,529, respectively.