## accept both numbers and letters

Discussion of Common Lisp
nakias
Posts: 3
Joined: Tue Dec 23, 2008 5:17 am

### accept both numbers and letters

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 ?

bzoto
Posts: 1
Joined: Mon Oct 27, 2008 5:26 am

### Re: accept both numbers and letters

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

ciao

qbg
Posts: 64
Joined: Mon Jun 30, 2008 1:05 pm
Location: Minnesota

### Re: accept both numbers and letters

nakias wrote: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 ?

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
Posts: 3
Joined: Tue Dec 23, 2008 5:17 am

### Re: accept both numbers and letters

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

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
Posts: 35
Joined: Sat Jun 28, 2008 1:05 pm
Location: Urbana, Illinois, US
Contact:

### Re: accept both numbers and letters

nakias wrote:how can i use the defmacro in order to simplify any given polynomial e.g (x + y)(x + y) â†’ 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.