We consider the algorithmic problem of constructing a maximal order in a semisimple algebra over an algebraic number field. A polynomial time ff-algorithm is presented to solve the problem. (An ffalgorithm is a deterministic method which is allowed to call oracles for factoring integers and for factoring polynomials over finite fields. The cost of a call is the size of the input given to the oracle.) As an application, we give a method to compute the degrees of the irreducible representations over an algebraic number field K of a finite group G, in time polynomial in the discriminant of the defining polynomial of K and the size of a multiplication table of G.
- Subject classifications: 68Q40, 11Y40, 68Q25, 11Y16
ASJC Scopus subject areas
- Theoretical Computer Science
- Computational Theory and Mathematics
- Computational Mathematics