;----------------------------------------------------------------------------
; Original code and concept by Gordon Novak Jr.
; (http://www.cs.utexas.edu/users/novak)
;
; Some modifications by Yoonsuck Choe
; Thu Sep 11 11:41:03 CDT 2003
;
; To test: 
;
;	1. save as file deriv.lsp.
;
; 	2. run lisp
;
;	3. enter
;
;		(load "deriv.lsp")
;
;	4. test deriv
;
;		(deriv '(+ x (+ x 3)) 'x)
;
;	5. test splus
;
;		(splus 0 'x)
;
;	6. test derivplus
;
;		(derivplus '(+ x (+ 2 x)) 'x)
;
;	7. All of the above will work, out of the box.
;	   Extend and test one function at a time as you write.
;	
;	   First, modify derivplus by calling splus in derivplus.
;	  
;	   Then, test derivplus 
;	
;		(derivplus '(+ x (+ x x)) 'x)
;
;----------------------------------------------------------------------------


;----------------------------------------
; 	deriv
;----------------------------------------
(defun deriv (expr var)
  (if (atom expr)
    (if (equal expr var) 1 0)      
    (cond                       
        ((eq '+ (first expr))     ; PLUS 
            (derivplus expr var))
        ((eq '* (first expr))     ; MULT
            (derivmult expr var))                      
        (t                        ; Invalid
            (error "Invalid Expression!"))
     )
  )
)

;----------------------------------------
;	deriv plus
;----------------------------------------
(defun derivplus (expr var)
    (list '+
          (deriv (second expr) var)
          (deriv (third expr) var)
    )
)

;----------------------------------------
;	splus
;----------------------------------------
(defun splus (x y)
    (if (numberp x)
        (if (numberp y)
            (+ x y)    
            (if (zerop x) 
                y 
                (list '+ x y)
            )
        )
        (if (and (numberp y) (zerop y))
            x
            (list '+ x y)
        )
    )
)