14.2 The Problem

Minimal factors exist if and only if there exist m1, m2, n1, n2, a, b, c, e, f and g such that the following polynomials is zero.

        Am   -  m a - m  f c    Am   -  m e
            1     1     2           2     2
          B -  m1b - m2f         - c + C m1
(FAC)        n1m1  - 1           n2m2  - 1

               n1m2                n2m1
             - g + C m2      m1n1  + m2n2  - 1
Each of these expressions must equal 0. Here A, B and C are known.

The problem is to solve these equations. That is, we want a constructive theorem which says when and how they can be solved.