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

A method is presented for computing all the affine equivalences between tworational ruled surfaces defined by rational parametrizations that worksdirectly in parametric rational form, i.e. without computing or making use ofthe implicit equation of the surface. The method translates the problem intoparameter space and relies on polynomial system solving. Geometrically, theproblem is related to finding the projective equivalences between twoprojective curves (corresponding to the directions of the rulings of thesurfaces). This problem was recently addressed in a paper by Hauer andJ\"uttler, and we exploit the ideas by these authors in the algorithm presentedin this paper. The general idea is adapted to computing the isometries betweentwo rational ruled surfaces, and the symmetries of a given rational ruledsurface. The efficiency of the method is shown through several examples.

Affine equivalences, isometries and symmetries of ruled rational surfaces