help with multiplying polynomials in lisp

Question

for example: (3x² - 5x + 2)(7x + 1) and you simplify it like this:

((3 2)(-5 1)(2 0))((7 1)(1 0))
((21 3)(3 2)(-35 2)(-5 1)(14 1)(2 0))
(21 3)(32 2)(9 1)(2 0)

and you get this answer: 21x³ + 32x² + 9x + 2

i need this solution in lisp please help

Answer 1

For the first stage, you need to pair up every LHS component with every RHS component; a cartesian product of the two sets. This requires a two-level map followed by a concatenation of the second-level lists of pairs into a single top level list (think (apply #'append ...).

The second stage can be done with a reduce that builds up an association list, keyed on the exponent.

EDIT: Let me solve a different problem for you, and let you figure out how to translate it into the solution for your problem:

Compute (a + b + ... + k) * (l + m + ... + z) by first expanding into pairs and then summing the products:

(defun mul-sums (aa bb)
  (reduce #'+
          (apply #'append
                 (map 'list
                      #'(lambda (a)
                          (map 'list
                               #'(lambda (b)
                                   (* a b))
                               bb))
                      aa))))
; Compute (1 + 2 + 3) * (3 + 4).
> (mul-sums '(1 2 3) '(3 4))
42