I found this article interesting. I have not read it, but it gives an example of interaction between sage and Geogebra, thus it is possible to communicate with Geogebra via a plugin. Apparently it is possible to have an xml transcription of the construction; though it would be hard to support all what Geogebra allows...
Automatic Deduction in Dynamic Geometry using Sage http://arxiv.org/pdf/1202.4830.pdf Another posibility is to understand the language Asymptote, but that is harder to translate... I am in no position to tackle this in the near future, since I do not even know javascript, but I think it is interesting. Peace. -Adrián.
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