accept both numbers and letters

[nakias]

Hey
I need your help for a program in common lisp. The program has to do with polynomial manipulation.
My problem is when i do simple arithmetic operations does not accept any letters e.g (p+ x 4)

(defun p+ (p1 p2)
(list '+ p1 p2))

(defun p+ (p1 p2)
(+ p1 p2))

How can i make it in order to accept letters as well ?

Thanks in advance

[bzoto]

I'm not sure to understand - do you need something like the following?
(defmacro p+ (p1 p2)
`(list '+ ',p1 ',p2))

ciao

[qbg]

Hey
I need your help for a program in common lisp. The program has to do with polynomial manipulation.
My problem is when i do simple arithmetic operations does not accept any letters e.g (p+ x 4)

(defun p+ (p1 p2)
(list '+ p1 p2))

(defun p+ (p1 p2)
(+ p1 p2))

How can i make it in order to accept letters as well ?

Thanks in advance

p+ is a function which means it gets its arguments evaluated. 4 evaluates to itself, but x would evaluate to what ever x is bound to, which looks like nothing in this case. To prevent evaluation of an object you quote it; (quote x) would be the quoted form of x. Because quoting is so common, you have a read macro to do it automatically, and so you can just write 'x

Now then while (list '+ 'x 4) makes sense, (+ 'x 4) does not because 'x is not a number, so only your first definition for p+ would work with (p+ 'x 4)

[nakias]

But how can i use the defmacro in order to simplify any given polynomial e.g (x + y)(x + y) → x2 + 2xy + y2


Thanks for replying.

Code: Select all

;; 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))

;;
;; Unevaluated derivative
;;

(defun make-derivative (poly x)
    (list 'd poly x))

(defun derivative-p (poly)
  (and (listp poly) (eq (first poly) 'd)))



;;
;; 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))))






[danb]

how can i use the defmacro in order to simplify any given polynomial e.g (x + y)(x + y) → x2 + 2xy + y2

There's some code here.

You don't need a macro if you're doing the simplification at runtime. You just quote the arguments, as in (simplify '(* (+ x 1) (+ x -1))).

Once a product is expanded, you can sort it by the symbols in each term, group the terms, and add up their coefficients.