English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

The problem of search for the dependence of GCD of algebraic parametrized objects on a parameter appears in some algorithms of computer algebra. In the case of usual polynomials such problem appears in solving systems of algebraic equations by the elimination method and in some others described in [1]. In the case of rings of polynomials which describe the rings of differential and difference operators such problem appears in solving differential equations in the terms of sparse power series [2]. So it makes interesting to consider this problem from the point of view of Ore polynomial rings which generalize the examples above. For the search for the GCRD of two Ore polynomials it was developed the fast modular algoritm [4]. If we need to determine the depedence of the GCRD on a parameter the next algorithm can be applied: find all the values of a parameter for which the resultant is zero and find the set of GCRDs of polynomials with substituting the parameter by such values. Here we present more efficient non-modular algorithm based on subresultant theory of Ore polynomials [4] which allows to determine the dependence of GCRD on a parameter.

On the greatest common right divisor of Ore polynomials with polynomial coefficients which depend on a parameter