扩充练习—有理函数

练习2.92 通过加入强制性的变量序扩充多项式程序包，使多项式的加法和乘法能对其有不同变量的多项式进行。
;;其实就是实现多项式变量的转换
;;比如多项式(y+1)x^{2也可以看作(x}2)y+x^2
;;两者是相同的，主要是看变量的不同

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(define (term->poly term old-var new-var)(define (make-term-poly term var)(make-term var (adjoin term (the-empty-termlist))))(define (change-var old-order old-var new-var)(let ((tmp-term (make-term old-order 1)))(let ((tmp-poly (make-term-poly tmp-term old-var)))(let ((new-term (make-term 0 tmp-poly)))(make-term-poly new-term new-var)))))(let (p1 (obj->poly (coeff term) new-var))(p2 (change-var (order term) old-var new-var))(mul-poly p1 p2)))(define (term->polylist L old-var new-var)(if (empty-list? L)(make-poly new-var (the-empty-termlist))(add-poly (term->poly (first-term L) old-var new-var)(term->polylist (rest-of-termlist L) old-var new-var))))

练习2.93 修改有理数算数包，采用通用型操作。

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(define (install-ractional-package)(define (number x) (car x))(define (denom x) (cadr x))(define (make-rat n d) (cons n d))(define (add-rat x y)(make-rat (add (mul (number x) (denom y))(mul (number y) (denom x)))(mul (denom x) (denom y))))(define (sub-rat x y)(make-rat (sub (mul (number x) (denom y))(mul (number y) (denom x)))(mul (denom x) (denom y))))(define (mul-rat x y)(make-rat (mul (number x) (number y))(mul (denom x) (denom y))))(define (div-rat x y)(make-rat (mul (number x) (denom y))(mul (denom x) (number y))))(define (tag x) (attach-tag 'ractional x))(put 'add '(ractional ractional)(lambda (x y) (tag (add-rat x y))))(put 'sub '(ractional ractional)(lambda (x y) (tag (sub-rat x y))))(put 'mul '(ractional ractional)(lambda (x y) (tag (mul-rat x y))))(put 'div '(ractional ractional)(lambda (x y) (tag (div-rat x y))))(put 'make 'ractional(lambda (n d) (tag (make-rat n d)))))
(define (make-ractional n d)((get 'make 'ractional) n d))
(define (number-rat x) (car (contents x)))
(define (denom-rat x) (cdr (contents x)))