5 research outputs found
Parametric "Non-nested" Discriminants for Multiplicities of Univariate Polynomials
We consider the problem of complex root classification, i.e., finding the
conditions on the coefficients of a univariate polynomial for all possible
multiplicity structures on its complex roots. It is well known that such
conditions can be written as conjunctions of several polynomial equations and
one inequation in the coefficients. Those polynomials in the coefficients are
called discriminants for multiplicities. It is well known that discriminants
can be obtained by using repeated parametric gcd's. The resulting discriminants
are usually nested determinants, that is, determinants of matrices whose
entries are determinants, and so son. In this paper, we give a new type of
discriminants which are not based on repeated gcd's. The new discriminants are
simpler in that they are non-nested determinants and have smaller maximum
degrees
Solving polynomial constraints for proving termination of rewriting
A termination problem can be transformed into a set of polynomial constraints. Up to now, several approaches have been studied to deal with these constraints as constraint solving problems. In this thesis, we study in depth some of these approaches, present some advances in each approach.Navarro Marset, RA. (2008). Solving polynomial constraints for proving termination of rewriting. http://hdl.handle.net/10251/13626Archivo delegad