SICP学习笔记 2.3.2 实例：符号求导

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    练习2.56

(define (deriv exp var)
  (cond ((number? exp) 0)
	((variable? exp)
	 (if (same-variable? exp var) 1 0))
	((sum? exp)
	 (make-sum (deriv (addend exp) var)
			       (deriv (augend exp) var)))
	((product? exp)
	 (make-sum
	  (make-product (multiplier exp)
			            (deriv (multiplicand exp) var))
	  (make-product (deriv (multiplier exp) var)
			            (multiplicand exp))))
	((exponentiation? exp)
	 (make-product
	  (make-product (exponent exp)
			            (make-exponentiation (base exp) (- (exponent exp) 1)))
	  (deriv (base exp) var)))
	
	(else (error "unknown expression type -- DERIV" exp))))

 

    练习2.57

;; 加法
(define (make-sum-list x list)
  (if (null? list)
      x
      (make-sum x
		            (make-sum-list (car list) (cdr list)))))
(define (make-sum-all x . y)
  (make-sum-list x y))

;; 被加数  
(define (augend-list s)
  (let ((l (length s)))
    (cond ((= l 1) 0)
	        ((= l 2) (cadr s))
	        ((= l 3) (augend s))
	        (else (cons '+ (cddr s))))))
	        
;; 乘法
(define (make-product-list x list)
  (if (null? list)
      x
      (make-product x
		                (make-product-list (car list) (cdr list)))))
(define (make-product-all x . y)
  (make-product-list x y))

;; 被乘数 
(define (multiplicand-list p)
  (let ((l (length p)))
    (cond ((= l 1) 1)
	        ((= l 2) (cadr p))
	        ((= l 3) (multiplicand p))
	        (else (cons '* (cddr p)))))) 
	        
;; 使用新的加法和乘法构造求导过程
(define (deriv exp var)
  (cond ((number? exp) 0)
	((variable? exp)
	 (if (same-variable? exp var) 1 0))
	((sum? exp)
	 (make-sum-all (deriv (addend exp) var)
			           (deriv (augend-list exp) var)))
	((product? exp)
	 (make-sum-all
	  (make-product-all (multiplier exp)
			                (deriv (multiplicand-list exp) var))
	  (make-product-all (deriv (multiplier exp) var)
			                (multiplicand-list exp))))
	((exponentiation? exp)
	 (make-product-all
	  (make-product-all (exponent exp)
			                (make-exponentiation (base exp) (- (exponent exp) 1)))
	  (deriv (base exp) var)))
	
	(else (error "unknown expression type -- DERIV" exp))))

1 ]=> (deriv '(* x y (+ x 3)) 'x)	
;Value : (+ (* x y) (* y (+ x 3)))

 

    练习2.58

;; 修改加法的构造函数、选择函数和谓词
(define (make-sum a1 a2)
  (cond ((=number? a1 0) a2)
	      ((=number? a2 0) a1)
	      ((and (number? a1) (number? a2)) (+ a1 a2))
	      ;;(else (list '+ a1 a2))))
	      (else (list a1 '+ a2))))
(define (addend s) (car s))
(define (augend s) (caddr s))
(define (sum? x)
  (and (pair? x) (eq? (cadr x) '+))
;; 使用类似的方法修改乘法的构造函数、选择函数和谓词

1 ]=> (deriv '((x * y) * ( x + 3)) 'x)
;Value : ((x * y) + (y * (x + 3)))

1 ]=> (deriv '(x + (3 * (x + (y + 2)))) 'x) 
;Value: 4

 

    练习2.59

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