連立方程式

逆行列を求める関数までかいた。
ベクトルの加減算、スカラ倍、内積、絶対値と
行列の表示、加減算、スカラ倍、行列同士の積、べき乗、n次の単位行列、逆行列をつくるなり計算するなりなもの。

(define (vecplus v1 v2)
  (map + v1 v2))

(define (vecminus v1 v2)
  (map - v1 v2))

(define (vecmulti s v)
  (map (lambda (a)
	 (* a s)) v))

(define (vecdiv v s)
  (map (lambda (a)
	 (/ a s)) v))

(define (innr_product v1 v2)
  (fold + 0 (map * v1 v2)))

(define (vecabs v)
  (sqrt (fold + 0
	      (map (lambda (a)
		     (* a a))
		   v))))

(define (matprint m)
  (define (iter t)
    (if (null? t)
	(print #\))
	(let ((a 1))
	  (print (car t))
	  (iter (cdr t)))))
    (print #\()
    (iter m))


(define (matplus m1 m2)
  (map vecplus m1 m2))

(define (matminus m1 m2)
  (map vecminus m1 m2))

(define (mattimes s m)
  (map (lambda (v)
	 (vecmulti s v))
       m))

(define (matmulti m1 m2)
  (map (lambda (v1)
	 (let loop ((v2 m2))
	   (if (null? (car v2))
	       '()
	       (cons (innr_product v1 (map car v2))
		     (loop (map cdr v2))))))
       m1))

(define (matpower m s)
  (let loop ((c m) (t s))
    (if (> t 1)
	(loop (matmulti c m) (- t 1))
	c)))

(define (mattranp m)
  (let loop ((t m))
    (if (null? (car t))
	'()
	(cons (map car t)
	      (loop (map cdr t))))))

(define (mkmatunit n)
  (let loop ((i n))
    (if (> i 0)
	(cons (let mkvec ((j n))
		(if (> j 0)
		    (cons (if (= i j)
			      1
			      0)
			  (mkvec (- j 1)))
		    '()))
	      (loop (- i 1)))
	'())))

(define (matrev m)
  (define (phase  m e c nf)
    (let ((d (vecdiv (car m)
		     (list-ref (car m)
			       c)))
	  (f (vecdiv (car e)
		     (list-ref (car m)
			       c))))
      (if (null? (cdr m))
	  (values (list d) (list f))
	  (receive (r1 r2)
	      (phase (map
		      (lambda (v)
			(vecminus v
				  (vecmulti (list-ref v c)
					    d)))
		      (cdr m))
		     (map
		      (lambda (v i)
			(vecminus v
				  (vecmulti (list-ref i c)
					    f)))
		      (cdr e) (cdr m))
		     (nf c 1) nf)
	    (values (cons d r1) (cons f r2))))))
  (let* ((n (length m)) (e (mkmatunit n)))
    (receive (t1 t2)
	(phase m e 0 +)
      (receive (r ans)
	  (phase (reverse t1) (reverse t2) (- n 1) -)
	(reverse ans)))))