(in-package :cl-user)

(defun substitute-in-polynomial (plug-value &rest coefficients)
  (let ((sum-collector 0))
    (let ((iterator (- (length coefficients) 1)))
      (dolist (coefficient coefficients)
	(+ sum-collector (* coefficient (expt plug-value iterator)))
	(decf iterator)))
    sum-collector))

(defun polynomial-interface (&key order tolerance start end &rest coefficients)
  (if (not (equalp (length coefficients) (+ order 1)))
      (format nil "Invalid number of arguments"))
  (do ((test-expression (< (* (substitute-in-polynomial left coefficients) (substitute-in-polynomial right coefficients)) 0))
       (left start (if test-expression mid left))
       (right end (if test-expression right mid)))
      (<= (abs (- right left)) tolerance)
    (format nil "The root is in between ~a and ~a" left right)))