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Dear gap-forum,

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.

Keith

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

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