sicp每日一题[2.56]

合集 - sicp(77)
1.sicp每日一题[1.42]2.sicp每日一题[1.43]3.sicp每日一题[1.44]4.sicp每日一题[1.45]5.sicp每日一题[1.46]6.sicp每日一题[2.1]7.sicp每日一题[2.2]8.sicp每日一题[2.3]9.sicp每日一题[2.4]10.sicp每日一题[2.5]11.sicp每日一题[2.6]12.sicp每日一题[2.7]13.sicp每日一题[2.8]14.sicp每日一题[2.9]15.sicp每日一题[2.11]16.sicp每日一题[2.10]17.sicp每日一题[2.12]18.sicp每日一题[2.13-2.16]19.sicp每日一题[2.17]20.sicp每日一题[2.18]21.sicp每日一题[2.19]22.sicp每日一题[2.20]23.sicp每日一题[2.21]24.sicp每日一题[2.22-2.23]25.sicp每日一题[2.24-2.27]26.sicp每日一题[2.28]27.sicp每日一题[2.29]28.sicp每日一题[2.30]29.sicp每日一题[2.31]30.sicp每日一题[2.32]31.sicp每日一题[2.33]32.sicp每日一题[2.34]33.sicp每日一题[2.35]34.sicp每日一题[2.36-2.37]35.sicp每日一题[2.38-2.39]36.sicp每日一题[2.40]37.sicp每日一题[2.41]38.sicp每日一题[2.42]39.sicp每日一题[2.43]40.sicp每日一题[2.44]41.sicp每日一题[2.45]42.sicp每日一题[2.46]43.sicp每日一题[2.47]44.sicp每日一题[2.48]45.sicp每日一题[2.49]46.sicp每日一题[2.50]47.sicp每日一题[2.51]48.sicp每日一题[2.52]49.sicp每日一题[2.53-2.55]
50.sicp每日一题[2.56]
51.sicp每日一题[2.57]52.sicp每日一题[2.58]53.sicp每日一题[2.59]54.sicp每日一题[2.60]55.sicp每日一题[2.61]56.sicp每日一题[2.62]57.sicp每日一题[2.63-2.64]58.sicp每日一题[2.65]59.sicp每日一题[2.66]60.sicp每日一题[2.67-2.68]61.sicp每日一题[2.69]62.sicp每日一题[2.70]63.sicp每日一题[2.71]64.sicp每日一题[2.72]65.sicp每日一题[2.73]66.sicp每日一题[2.74]67.sicp每日一题[2.75]68.sicp每日一题[2.76]69.sicp每日一题[2.77]70.sicp每日一题[2.78]71.sicp每日一题[2.79]72.sicp每日一题[2.80]73.sicp每日一题[2.81]74.sicp每日一题[2.82]75.sicp每日一题[2.83]76.sicp每日一题[2.84]77.sicp每日一题[2.85-2.86]
收起

Exercise 2.56

Show how to extend the basic differentiator to handle more kinds of expressions. For instance, implement the differentiation rule

d(x^n)/dx = n x^(n-1)

by adding a new clause to the deriv program and defining appropriate procedures exponentiation?, base, exponent, and make-exponentiation.
(You may use the symbol ** to denote exponentiation.) Build in the rules that anything raised to the power 0 is 1 and anything raised to the power 1 is the thing itself.

这道题难度不大，先仿照 make-sum, make-product 写出 make-exponentiation 函数，剩下的部分就很简单了。

(define (make-exponentiation base exponent)
  (cond ((=number? base 0) 0)
        ((=number? base 1) 1)
        ((and (number? base) (=number? exponent 0)) 1)
        ((and (number? base) (=number? exponent 1)) base)
        ((and (number? base) (number? exponent)) (* base (make-exponentiation base (- exponent 1))))
        (else (list '** base exponent))))

(define (exponentiation? x) (and (pair? x) (eq? (car x) '**)))

(define (base e) (cadr e))

(define (exponent e) (caddr e))

(define (deriv exp var)
  (cond ((number? exp) 0)
        ((variable? exp) (if (same-variable? exp var) 1 0))
        ((exponentiation? exp)
         (let ((base (base exp))
               (n (exponent exp)))
           (if (same-variable? base var)
               (make-product n
                             (make-exponentiation base (- n 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))))
        (else
         (error "unknown expression type: DERIV" exp))))


(deriv '(** x 3) 'x)
(deriv '(** x 3) 'y)

; 执行结果
'(* 3 (** x 2))
0
posted @   再思即可  阅读(9)  评论(0)  编辑  收藏  举报
相关博文：
· sicp每日一题[2.73]
· sicp每日一题[2.57]
· 5.29 一些零碎的基础练习
· SymPy-1-13-中文文档-十-
· 2.27——..E1
阅读排行：
· DeepSeek 开源周回顾「GitHub 热点速览」
· 物流快递公司核心技术能力-地址解析分单基础技术分享
· .NET 10首个预览版发布：重大改进与新特性概览！
· AI与.NET技术实操系列（二）：开始使用ML.NET
· 单线程的Redis速度为什么快？
点击右上角即可分享
微信分享提示
AI FOR CODE 大赛