We (a group of scientists) plan to co-author an open, online book. The idea is to collaboratively write an ebook hosted on a website, which is open for the public to read and comment. We are now looking for a web platform that has the following desired features:

• Entirely web-based
• Though we are all proficient in LaTeX, we would like to write in a simpler mark-up language, e.g. Markdown.
• Very good support for typesetting and displaying mathematical equations in LaTeX format: i.e. MathJax.
• Collaborative editing: like in Google Docs, preferably with a revision history feature, but not required.
• Allow commenting on each section or each paragraph (preferred but not required).
• Besides HTML (web), can export to PDF and ebook formats.
• Free or open-source, installable on our own host.
• Preferably data can be backed up on Dropbox, github, or the like.
• Preferably can embed interactive applets (e.g. Java, Python) because we'd love to have interactive examples and exercises in the book.

We found Authorea, which has most of the features we want, except that it is not really open and we can't install the software platform on our web host. In addition, though Authorea is good for writing articles, we don't know if it is up to the task of writing an entire book.

Do you have any suggestion for a web platform that satisfies our desired features? Of course, we can always write the book offline in a traditional way, then publish it online; but we think that with current technology, there would be a much better and modern solution.

Thanks!