Software recommendation for FAST entry of equations I'm looking for a package that does for algebra what word processing software did for writing:

When I learned to type, my writing improved greatly because my fingers were closer to keeping up with my mind.

Similarly I think that students will be more willing to enter intermediate steps in solving problems if they can type math faster than they write it.

The package should in addition have drawing ability to make simple diagrams, and have the text formatting/editing ability roughly equivalent to the common rich text JavaScript modules commonly seen on forums.

It should be possible to create equations either through mouse or keyboard.  

I think I'm looking for something that is a subset of LaTeX. 

Added bonus: The ability to do simple symbolic consistency checks: for example, in a solution requiring several steps is each line a valid restatement of the previous line.

I am willing to consider a Windows program or Linux program running in a virtual machine, but I would prefer a Mac or iOS application.

The key feature is speed.  A user must be able to get the same sort of speed increase using this software as learning to type overcomes the slowness of handwriting.
On Windows, there is the Math-o-mir software. It should be able to provide all you asked for (rapid math typing, keyboard and mouse entry, basic CAS), but it requires some learning time to achieve speeds comparable to pencil-and-paper.