Abstract
This paper addresses some concerns, and describes some proposals, on the ellusive concept of envelope of an algebraic family of varieties, and on its automatic computation.We describe how to use the recently developed Gröbner Cover algorithm to study envelopes of families of algebraic curves, and we give a protocol towards its implementation in dynamic geometry environments. The proposal is illustrated through some examples. A beta version of GeoGebra is used to highlight new envelope abilities in interactive environments, and limitations of our approach are discussed, since the computations are performed in an algebraically closed field.
Highlights
Preprint submitted to ElsevierWe will deal with these issues by restricting our framework to families of algebraic plane curves; in the context of dynamic geometry software (DGS).Yet, as we will show below, even in this restricted setting we will need to reflect about the very basic concept of envelope, in order to be able to propose some sound algorithmic protocols for its computation.1.1
This paper addresses some concerns, and describes some proposals, on the ellusive concept of envelope of an algebraic family of varieties, and on its automatic computation
We have described a protocol for the automatic computation of families of algebraic plane curves
Summary
Families of algebraic plane curves; in the context of dynamic geometry software (DGS). As we will show below (see examples ), even in this restricted setting we will need to reflect about the very basic concept of envelope, in order to be able to propose some sound algorithmic protocols for its computation
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