Some issues on the automatic computation of plane envelopes in interactive environments
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This paper addresses some concerns, and describes some proposals, on the elusive 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 toward 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.