Jacobi符号是Legendre符号的推广,在素性检验以及因子分解等诸多方面极为有用,所以先写一个备着,写其他算法时方便直接调用。
(defun jacobi (n m)
(let ((e 0)
(a1 0)(a n)
(s 0)(b m)
(n1 0))
(cond ((= a 0) 0)
((= a 1) 1)
(t
(if (/= 0 (mod a 2)) (progn (setf a1 a) (setf e 0))
(loop while (= 0 (mod a 2)) do
(setf a (/ a 2)) (setf a1 a) (incf e)))
(cond ((= 0 (mod e 2)) (setf s 1))
((or (= 1 (mod b 8)) (= 7 (mod b 8)))
(setf s 1))
((or (= 3 (mod b 8)) (= 5 (mod b 8)))
(setf s -1)))
(if (and (= 3 (mod b 4)) (= 3 (mod a1 4))) (setf s (- 0 s)))
(setf n1 (mod b a1))
(if (= 1 a1)
s
(* s (jacobi n1 a1)))))))