On computational aspects of the generalized differential Lüroth's theorem

LISI D'ALFONSO; GABRIELA JERONIMO; PABLO SOLERNÓ

Buenos Aires

Congreso; XXI Coloquio Latinoamericano de Álgebra; 2016

We will discuss effectivity issues of the generalized differential Lüroth theorem. We will present the first known upper bounds for the order and the degree of any Lüroth generator of a subextension with differential transcendence degree 1 of a differential rational function field in an arbitrary number of differential variables. In the univariate case, these bounds improve the previous degree bounds.In addition, we will show that a Lüroth generator can be computed by means of classical techniques from computer algebra applied to a polynomial ideal associated with the given generators.