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 Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

An efficient method of computing power expansions of algebraic functions isthe method of Kung and Traub and is based on exact arithmetic. This paper showsa numeric approach is both feasible and accurate while also introducing aperformance improvement to Kung and Traub's method based on the ramificationextent of the expansions. A new method is then described for computing radii ofconvergence using a series comparison test. Series accuracies are then fittedto a simple log-linear function in their domain of convergence and found tohave low variance. Algebraic functions up to degree 50 were analyzed and timed.A consequence of this work provided a simple method of computing the Riemannsurface genus and was used as a cycle check-sum. Mathematica ver. 13.2 was usedto acquire and analyze the data on a 4.0 GHz quad-core desktop computer.

A numeric study of power expansions around singular points of algebraic functions, their radii of convergence, and accuracy profiles