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/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

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

Zendy Tools

Zendy Open

In this paper, a multiplicity preserving triangular set decompositionalgorithm is proposed for a system of two polynomials. The algorithm decomposesthe variety defined by the polynomial system into unmixed componentsrepresented by triangular sets, which may have negative multiplicities. In thebivariate case, we give a complete algorithm to decompose the system intomultiplicity preserving triangular sets with positive multiplicities. We alsoanalyze the complexity of the algorithm in the bivariate case. We implement ouralgorithm and show the effectiveness of the method with extensive experiments.

Multiplicity Preserving Triangular Set Decomposition of Two Polynomials