Mathematical Symbolic Reduction - Help!
One of my many side projects evolves mathematical expressions using LINQ expression trees. One issue that I'm trying to address is reducing or compressing  the size of the tree by finding simple conditions in the tree. For example, if I find "a * 1", I know that can be turned into "a", which gets rid of two nodes. The problem is that I know there's a lot more that I can do. For example, one time my program came up with this formula:
((a * ((a * a) - a)) + (a * a))
Doing some simple algebraic manipulations:
a * ((a ^ 2) - a) + (a ^ 2)
(a ^ 3) - (a ^ 2) + (a ^ 2)
(a ^ 3)
So what I really have is something that's far simpler than the original formula . Unfortunately, my rules are extremely simplistic at this point and don't catch the reduction that I can do by hand.
Now, I could figure out a lot of these rules (eventually), but what I'm wondering is, are there any engines/papers/information/etc. out there that can guide me in creating my own framework to reduce my expression trees. I know there has to be stuff out there - I mean, Mathematica handles my example with ease. But finding information hasn't been easy for some reason (I'm guessing my search-fu isn't using the right terms).
Any ideas are appreciated - just leave a comment. Thanks!
 I call it "compressing" because there's a
Reduce() method on the
Expression class, but it doesn't do anything that I'm looking for.
 I ran some tests that showed that the original expression is quicker than the one where you have to use
Math.Pow(). But my tests were thrown together really quick - I'd have to do more investigation to solidify my initial observations.
* Posted at 06.29.2010 01:46:29 PM CST | Link *