Adding divisors on hyperelliptic curves via interpolation polynomials

Let C be an algebraic curve of genus g.  An effective procedure to reduce any non-special divisor on C to an equivalent divisor composed of g points is suggested.  The hyperelliptic case is considered as the simplest model.  The advantage of the proposed procedure is its explicitness: all steps are realized through arithmetic operations on polynomials.  The resulting reduced divisor is obtained in the form of the Jacobi inversion problem, which unambiguously defines the divisor.  At the same time, values of abelian functions on the divisor are obtained.