(*$B- Aufgabe  5.8 *)
PROGRAM cram;
TYPE vektor = ARRAY[1..10] OF real;
     matrix = ARRAY[1..10] OF vektor;
VAR i,j,n:integer; s,d:real;
    ai,a : matrix; b,x:ARRAY[1..10] OF real;
    stri: string[20]; ein,tf : text;

FUNCTION det(n:integer; a:matrix):real;
VAR i,j,k,jmax:integer;h:vektor; d, z, faktor:real;

BEGIN
  d :=1; i:=1;
  WHILE (i<=n) AND (d<>0) DO
  BEGIN
    (*PIVOTSUCHE *)
    jmax:=i;
    FOR j:=i+1 TO n DO
    IF abs(a[j,i])>abs(a[jmax,i]) THEN jmax:=j;
    IF a[jmax,i]=0 THEN d :=0
    ELSE
    BEGIN
      IF jmax<>i THEN
      BEGIN
        h:=a[i]; a[i]:=a[jmax]; a[jmax]:=h; d:=-d
      END;
      (*ELIMINATION*)
      d:=d*a[i,i];
      FOR k:=i+1 TO n DO
      BEGIN
        faktor:=a[k,i]/a[i,i];
        FOR j:= i+1 TO n DO
        a[k,j]:=a[k,j]-faktor*a[i,j];
      END
    END;
    i:=i+1;
  END;
  det := d;
END;

PROCEDURE print(n:integer; a:matrix);
VAR i,j : integer;
BEGIN
  FOR i := 1 TO n DO
  BEGIN
    writeln(tf);
    FOR j:=1 TO n DO write(tf,a[i,j]:12:3)
  END;
  writeln(tf)
END;

BEGIN
 writeln('Wohin mit dem Output ? ');
 read(stri); assign(tf,stri); rewrite(tf);
 writeln('woher kommt der Input ?');
 readln; readln(stri); assign(ein,stri); reset(ein);
 writeln('n eingeben'); read(ein,n);
 writeln('Matrix A zeilenweise eingeben');
 FOR i:=1 TO n DO FOR j:=1 TO n DO read(ein,a[i,j]);
 writeln('rechte Seite eingeben');
 FOR i := 1 TO n DO read(b[i]);
 writeln(tf,'Gegebene Matrix'); print(n,a); writeln(tf);
 writeln(tf,'rechte Seite');
 FOR i:=1 TO n DO writeln(tf,b[i]:12:7);

 d := det(n,a);
 writeln(tf,'Determinante von A =  ',d);
 FOR i := 1 TO n DO
 BEGIN
   ai:= a;
  FOR j := 1 TO n DO ai[j,i] := b[j];
  x[i] := det(n,ai)/d;
  writeln(tf,'x[',i:2,'] = ',x[i]);
 END;

 writeln(tf);writeln(tf, 'Residuenvektor');
 FOR i:=1 TO n DO
 BEGIN
  s:=-b[i];
  FOR j := 1 TO n DO s := s + a[i,j]*x[j];
  writeln(tf,s);
 END;
 close(tf); close(ein)
END.