Exercise 2.94 · 习题

Exercise 2.94: Using div-terms, implement
the procedure remainder-terms and use this to define gcd-terms as
above. Now write a procedure gcd-poly that computes the polynomial
GCD of two polys. (The procedure should signal an error if the two
polys are not in the same variable.) Install in the system a generic operation
greatest-common-divisor that reduces to gcd-poly for polynomials
and to ordinary gcd for ordinary numbers. As a test, try

(define p1
(make-polynomial
'x '((4 1) (3 -1) (2 -2) (1 2))))

(define p2
(make-polynomial
'x '((3 1) (1 -1))))

(greatest-common-divisor p1 p2)

and check your result by hand.

练习 2.94：利用 div-terms 实现 remainder-terms 过程，并用它按上面的方式定义 gcd-terms。然后编写过程 gcd-poly，用于计算两个多项式的多项式 GCD。（若两个多项式的变量不同，该过程应报错。）在系统中安装一个通用操作 greatest-common-divisor，对多项式归结为 gcd-poly，对普通数归结为普通的 gcd。作为测试，尝试

(define p1
(make-polynomial
'x '((4 1) (3 -1) (2 -2) (1 2))))

(define p2
(make-polynomial
'x '((3 1) (1 -1))))

(greatest-common-divisor p1 p2)

并手动验证结果。