Hello,

I need your help for the following application

The app has to do with polynomial manipulation and my question is how can i manipulate both letters and numbers.

in other words how can i collect together terms , e.g., (x + 1) + x → 2x + 1 rather than x + 1 + x

Thanks in advance for any help !

```
;; Constructors
(defun make-constant (num)
num)
(defun make-variable (sym)
sym)
;;(defun p+ (poly1 poly2)
;; (list '+ poly1 poly2))
(defmacro p+ (poly1 poly2)
`(list '+ ',poly1 ',poly2))
(defmacro p* (poly1 poly2)
`(list '* ',poly1 ',poly2))
;;(defun p* (poly1 poly2)
;; (list '* poly1 poly2))
(defun make-power (poly num)
(list '** poly num))
;;
;; Recognizers for polynomials
;;
(defun constant-p (poly)
(numberp poly))
(defun variable-p (poly)
(symbolp poly))
(defun sum-p (poly)
(and (listp poly) (eq (first poly) '+)))
(defun product-p (poly)
(and (listp poly) (eq (first poly) '*)))
(defun power-p (poly)
(and (listp poly) (eq (first poly) '**)))
;;
;; Selectors for polynomials
;;
(defun constant-numeric (const)
const)
(defun variable-symbol (var)
var)
(defun sum-arg1 (sum)
(second sum))
(defun sum-arg2 (sum)
(third sum))
(defun product-arg1 (prod)
(second prod))
(defun product-arg2 (prod)
(third prod))
(defun power-base (pow)
(second pow))
(defun power-exponent (pow)
(third pow))
;;
;; Simplification function
;;
(defun simplify (poly)
"Simplify polynomial POLY."
(cond
((constant-p poly) poly)
((variable-p poly) poly)
((sum-p poly)
(let ((arg1 (simplify (sum-arg1 poly)))
(arg2 (simplify (sum-arg2 poly))))
(make-simplified-sum arg1 arg2)))
((product-p poly)
(let ((arg1 (simplify (product-arg1 poly)))
(arg2 (simplify (product-arg2 poly))))
(make-simplified-product arg1 arg2)))
((power-p poly)
(let ((base (simplify (power-base poly)))
(exponent (simplify (power-exponent poly))))
(make-simplified-power base exponent)))
((derivative-p poly) poly)))
(defun make-simplified-sum (arg1 arg2)
"Given simplified polynomials ARG1 and ARG2, construct a simplified sum of ARG1 and ARG2."
(cond
((and (constant-p arg1) (zerop arg1)) arg2)
((and (constant-p arg2) (zerop arg2)) arg1)
(t (p+ arg1 arg2))))
(defun make-simplified-product (arg1 arg2)
"Given simplified polynomials ARG1 and ARG2, construct a simplified product of ARG1 and ARG2."
(cond
((and (constant-p arg1) (zerop arg1)) (make-constant 0))
((and (constant-p arg2) (zerop arg2)) (make-constant 0))
((and (constant-p arg1) (= arg1 1)) arg2)
((and (constant-p arg2) (= arg2 1)) arg1)
(t (p* arg1 arg2))))
(defun make-simplified-power (base exponent)
"Given simplified polynomials BASE and EXPONENT, construct a simplified power with base BASE and exponent EXPONENT."
(cond
((and (constant-p exponent) (= exponent 1)) base)
((and (constant-p exponent) (zerop exponent)) (make-constant 1))
(t (make-power base exponent))))
```