I'm making a symbolic algebra program. I want it to have:
> different types of variables + rationals
> negative and positive exponents (maybe radicals)
> negative and positive coefficients
> ability to attempt to simplify an equation (reduce amount of unlike variables and terms)
> ability to attempt to solve for (isolate) a variable
What are some relevant abstract algebra concepts or theorems that I can apply to this?
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Give it support for generatingfunctionology and you'll be pretty much set.
what is functionology?
It doesn't sound like you know much about computer algebra or symbolic computation. I'd try looking for a textbook on these topics.
fair enough which one?
Use risch algorithm for integration
I wasn't gonna make it integrate anything yet but I might in the future
I am writing exactly the same, though it is specifically for solving equations and differentiating/integrating. My starting point was that you need to keep a database for variables to compare with and apply rules all the time.
matrix multiplication
what language are you using btw?
So long as it can do first and second year linear algebra it's good in my books.