Exact Sum Of Squares decomposition of univariate polynomials

Four algorithms for finding exact Sum Of Squares decompositions of univariate polynomials are proposed. The first algorithm allows to compute rational SOS decompositions, whereas the second and the third allow to compute SOS decompositions in appropriate finite algebraic extensions of the field of rational numbers. A fourth algorithm allows, when possible, to find an SOS decomposition having just two terms, in the same ring in which the given polynomial is defined.