I would be grateful for any hints for a solution to this problem:
given an irreducible cubic polynomial p with integer coefficients
and three real roots, find a symmetric (preferably unimodular)
integer matrix with p as its characteristic polynomial, if such exists.
I presume this will involve transformations of the companion matrix.
Alternatively, it would be sufficient to have such a matrix whose
charpoly generates the same field as p.
Dr. Keith M. Briggs
Complexity Research, BTexact Technologies
email: Keith.Briggs@bt.com phone: +44(0)1473 work: 641 911 home: 625 972 fax: 647 410 web: www.btexact.com/people/briggsk2/ mail: Keith Briggs, Antares 2pp5, Adastral Park, Martlesham, Suffolk IP5 3RE, UK