D-resultant and subresultants
M’hammed El Kahoui · Proceedings of the American Mathematical Society · 2005
We establish a connection between the D -resultant of two polynomials f ( t ) f(t) and g ( t ) g(t) and the subresultant sequence of f ( t ) − x f(t)-x and g ( t ) − y g(t)-y . This connection is used to decide in a more explicit way whether K ( f ( t ) , g ( t ) ) = K ( t ) \mathcal {K}(f(t),g(t))=\mathcal {K}(t) or K [ f ( t ) , g ( t ) ] = K [ t ] \mathcal {K}[f(t),g(t)]=\mathcal {K}[t] . We also show how to extract a faithful parametrization from a given one.