The Intersection Curve of an Hyperbolic Cylinder with a Torus Sharing the Same Center

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This work aims to classify the families of curves obtained by the intersection of an arbitrary hyperbolic cylinder with an arbitrary torus sharing the same center, based on the number of their connected components and the number of their self-intersections points. The graphic geometric representation of these curves, in GeoGebra, and the respective algebraic descriptions, supported from a theoretical and computational point of view, are of fundamental importance for the development of this work. In this paper, we describe the procedure and the necessary implementation to achieve the outlined objective.