How to convert an equation into formulas for individual variables?

Question

How to convert an equation into formulas for individual variables? I am thinking about a math equations like:

c^2 = a^2 + b^2

I would like to have a function that could process any formula, and give me the individual variable formulas. The above equation would produce the following:

a = (c^2 - b^2)^0.5
b = (c^2 - a^2)^0.5
c = (a^2 + b^2)^0.5

I would also like to start with:

a = (c^2 - b^2)^0.5

and output:

b = (c^2 - a^2)^0.5
c = (a^2 + b^2)^0.5

I have looked at expression trees, but I am having trouble visualizing how this will work. I would like a .NET (C#, VB.NET, or F#) solution. Any ideas?

Something like:

public string[] GetFormulas(string equation)
{
   ...
}

Thanks.

Answer 1

Symbolic equation solving is a complex problem and there is no closed solution for many equations. Writing your own Computer Algebra System is none trivial, but you may be able to write a program for simple equation.

You will have to build a expression tree of the input string and define transformation rules for manipulating the expression tree. To solve for a variable you might then perform a search (guided by good heuristics to keep the runtime acceptable) on the space of expression tree that can be derived from the orginal tree by multiple aplications of transformation rules.