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For a project I need allow LaTeX input from a from website's users. I want a light weight LaTeX Editor that I can embed in my website and help them to write and edit their documents.

I want this editor be like LyX - i.e. WYSIWYG(M), tiny and of course open source - if it is possible. If it isn't, I want it to be as easy to use for authors as possible.

a editor like a text input box (my mean of tiny ) that user can use it in our site and some button(with that box) that help user write without any knowledge about TeX. then send what the user wrote for us in TeX format. we work on a educational site and want user write his mathematic questions without extra programs and easy.

Is there any kind of editor like that?

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Sharelatex is a collaborative web-based LaTeX editor.

I could not find any information on how to embed. Anyway, the web application and the services are completely decoupled, so it should not take great effort to customize it.

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The version of the tinymce HTML editor that is embedded in the Canvas LMS can accept raw LaTeX input in its equation editor component. A quick google shows quite a few different ways of using LaTeX with tinymce, but some seemed rather old and outdated.

A little more google searching turns up a list posted on GitHub,

https://github.com/mathjax/MathJax-docs/wiki/List-of-web-based-math-editors

and that list had a few entries that specified LaTeX support. This one seems good - http://visualmatheditor.equatheque.net/

Both free and Free (GPL3), runs locally or on a webserver, no plugin needed for current browsers.

From their site:

It now offers more than 730 LaTeX symbols and 210 AsciiMath symbols. It now works with LaTeX, AsciiMath, MathML and HTML syntaxes. It now can do PNG and SVG images exports. It improves the ergonomics of the user interface. It works in all modern browsers without plugin.

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