step one: use a Computer Algebra system?
Needs to be an open source (reviewable) free (accessible) software
--> Eigenmath is free, opensource, available for Windows, no setup EXE, and EASY
However, does not export to Latex (png only)
http://en.wikipedia.org/wiki/Eigenmath
http://eigenmath.cvs.sourceforge.net/viewvc/eigenmath/
Other Computer algebra systems:
Already integrated into LaTeX!!!
http://www.ctan.org/tex-archive/macros/latex/contrib/sagetex/
http://www.sagemath.org/tour-research.html#latex
http://maxima.sourceforge.net/
http://math-blog.com/2007/06/02/3-awesome-free-math-programs/
Given the statement
A=B
add 2 to both sides
A+2 = B+2
Every step in math and physics homework can be broken down into simple operations
To carry this out using a computer algebra system, we'll need to include handles on the equations
A=B [1]
add 2 to both sides of equation [1]
A+2 = B+2 [2]
Luckily, Donald Knuth already wrote LaTeX, and LaTex does this type of equation labeling. Additionally, LaTeX is the standard language for math and physics peer-reviewed papers.
So what is being attempted looks like integrating a CAS with LaTeX. This has been done, as with Maple-Scientific workplace, Mupad-Scientific workplace, and Sage-LaTeX. However, as built, the CASs do not handle arguments like above. Specifically, one starts with a true statement, A==B, and then performs operations on the LHS and RHS, while maintaining equality.
To adapt Mathematica (a propriatary CAS) to the desired functionality, I wrote functions to verify operations.
addXtoBothSides[X_,LHS_,RHS_]:=
The plan is to demonstrate feasibility with mathematica, then translate to Sage (open source), then integrate into LaTeX.
The operating motto is, "hard things should only need to be done once."
The motivation is to make math and physics executions more readable.