I would like to perform some symbolic calculations on lisp. I found useful derivative function and I would like to know how to write simple recursive function to add/substract/etc. polynomials.
Input (e.g.): (addpolynomial '(+ (^ (* 2 x) 5) 3) '(+ (^ (* 3 x) 5) (^ (* 3 x) 2)))
Output: (+ (^ (* 5 x) 5) (^ (* 3 x) 2)) 3)
Do you know how to do this? Or maybe you know other symbolic calculation examples?
When I've dealt with polynomials in Lisp in the past, I've used arrays of numbers (letting the variable be assumed, which means I couldn't trivially have things like "x*x + y", but since I didn't need that...).
That allows you to represent "2x^5 + 3" as #(3 0 0 0 0 2), finding the factor of x^n by (aref poly n) and other handy operations.
This also allows you to define addition as simply (map 'vector #'+ ...) (multiplication requires a bit more work).