ePuB and Command "run" of LaTeX

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In .TeX we use command "run" to operate file like .ggb in GeoGebra software itself.
But while exporting ePuB from same .TeX file .. opening a new window like run:1.ggb in internet browser and due to it .. we are not able to run .ggb file in the application of GeoGebra.

Please help.

There's no such thing as a "run:" command for browsers. You can only make use of the standard protocols like http:, mailto:, ftp:, file:, etc. from within href/src attributes. So, assuming these are hyperlinks, you'd have to translate to something like:

<a href="1.ggb">open some ggb file</a>

But, the first problem you have is that ggb files are not core media types in epub, so most reading systems simply aren't going to do anything with them if you host them in the container. Plus they'll require a fallback for your publication to be valid.

Those issues aside, if the reading system is purely browser based, it might launch the external application if there is one set as the default in the user's operating system. Same as you can include PDFs or any other file format inside an EPUB and hope for the best.

What you can't do is force the file to open in a new window across all reading systems if the content is in the container. Local content is typically rendered in the application viewport, and non-major browser hosted reading systems ignore the target attribute.

Such GeoGebra-files are obviously only zip-archives, this is the same approach as for EPUB.
Which part of the archive do you need?
In general it is not useful to put a zip-archive into another zip-archive.
The main content of an GeoGebra zip-archive seems to be an XML file without namespace relations.
The element names only provide the illusion of some semantic meaning.
With a namespace this would be more meaningful than the general SVG approach for vector graphics for the intented purpose, without it seems to be only intended for internal use, not for publications.

To use such a graphic within EPUB my suggestion is to use the export function of GeoGebra
to SVG. In the next step one uses for example Inkscape to indentify objects and to add title elements to them. After this one can use an own script for rounding and scour to clean up the code. After such an optimisation the result is already pretty good to be embedded in XHTML-documents within the EPUB archive.
Another option is to write and apply an XSLT to the GeoGebra XML-file to generate an SVG with better quality than the export SVG-output of the program.

Of course, because interactivity and animation is not allowed in EPUB, one can have only static graphics.

If really the GeoGebra is used within the book, one needs an accessible alternative, such a combination of SVG and XHTML does this job as well.

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