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program Berechnung_ggT;
uses
arithmetik;
procedure teiler(n : integer);
var
i : integer;
first : boolean;
begin
first:=true;
write('\{');
for i:=1 to n do
if (n mod i=0) then begin
if (first) then write(' ',i) else write(',',i);
first:=false;
end;
write(' \}');
end; { teiler }
procedure teilerzwei(n, m : integer);
var
i : integer;
first : boolean;
min : integer;
begin
if (n < m) then
min := n
else
min := m;
first:=true;
write('\{');
for i:=1 to min do
if ((n mod i=0) and (m mod i=0)) then begin
if (first) then write(' ',i) else write(',',i);
first:=false;
end;
write(' \}');
end; { teilerzwei }
procedure teilerdrei(n, m, p: integer);
var
i : integer;
first : boolean;
min : integer;
begin
if (n < m) then
min := n
else
min := m;
if (min < p) then
min := min
else
min:=p;
first:=true;
write('\{');
for i:=1 to min do
if ((n mod i=0) and (m mod i=0) and (p mod i = 0)) then begin
if (first) then write(' ',i) else write(',',i);
first:=false;
end;
write(' \}');
end; { teilerdrei }
procedure primfaktorzerlegung(n : integer);
var
i : integer;
first : boolean;
begin
if (n<=1) then writeln(n);
if (n>2) then begin
i:=2;
first:=true;
while (n>1) do begin
if (n mod i=0) then begin
n:=n div i;
if first then write(i) else write(' \* ',i);
first:=false;
end else i:=i+1;
end;
end;
end; { primfaktorzerlegung }
procedure vielfach(n,m : integer);
var
i : integer;
first : boolean;
begin
first:=true;
write('\{');
for i:=1 to m do
begin
if (first) then write(' ',i*n) else write(',',i*n);
first:=false;
end;
write(',\dots \}');
end; { vielfach }
procedure rechne_ggt(a,b : integer);
begin
writeln('\begin{figure}[H]');
writeln('\centerline{');
writeln('\xymatrix@R=3pt{');
writeln('&&& \txt{Rechnung} \\');
while (a<>b) do begin
write('\txt{$\ggT(',a,';',b,')$} &\txt{$=$} &');
if (a}[dll] &');
writeln('\txt{$',b,'-',a,'=',b-a,'$} \\');
b:=b-a;
end else begin
write('\txt{$\ggT(',a-b,';',b,')$}\ar@{->}[dll] &');
writeln('\txt{$',a,'-',b,'=',a-b,'$} \\');
a:=a-b;
end;
end;
writeln('\txt{$\ggT(',a,';',b,')$} &\txt{$=$} & \txt{$',a,'$} \\');
writeln('}}');
writeln('\end{figure}');
end; { rechne_ggt }
var
x,y,z,t : integer;
eingabe : char;
i,k : integer;
begin
writeln;
writeln('Berechnung des ggT und kgV auf verschiedene Arten');
writeln('-------------------------------------------------');
writeln('Eingabe für ggT = g, Teilermengen = t, Primfaktorzerlegung = p und
kgV = k');
readln(eingabe);
case (eingabe) of
'p', 'P' : begin
writeln('Primfaktorzerlegung');
while (not eof) do begin
readln(x);
write('\item ');
write(' $ ',x, ' = ');
primfaktorzerlegung(x);
writeln('$');
end;
end;
'k', 'K' : begin
writeln('kgv normal = 1');
writeln('kgv schnell = 2');
writeln('kgv prim = 3');
readln(i);
case (i) of
1 : begin
while (not eof) do
begin
readln(x);
readln(y);
if ( x <= 0) or (y <= 0)
then writeln('dies ist keine ordentliche Eingabe')
else
begin
write('\item ');
write(' $V_{' ,x, '} = ');
vielfach(x,(2*kgv(x,y) ) div x);
writeln('$, \\ ');
write(' $V_{' ,y, '} = ');
vielfach(y,(2*kgv(x,y) ) div y);
writeln('$, \\ ');
write('$V = ');
vielfach(kgv(x,y),3);
writeln('$, \\ ');
write('$\kgV( ' ,x, '; ', y, ') = ' ,kgv(x,y), '$');
writeln;
end;
end;
end;
2 : begin
while (not eof) do
begin
readln(x);
readln(y);
if ( x <= 0) or (y <= 0)
then writeln('dies ist keine ordentliche Eingabe')
else
begin
write('\item');
writeln('$\kgV(',x,';',y,') = ?$ \\');
z:=max(x,y);
i:=z;
writeln('Wähle ' ,z,'. \\');
while (i< kgv(x,y)) do
begin
writeln('Ist ',i,' Vielfaches von ' ,min(x,y),'? \quad nein \\');
i:=i+z;
end;
writeln('Ist ',kgv(x,y),' Vielfaches von ' ,min(x,y),'? \quad ja
\\');
writeln('Also ist: \\');
writeln('$\kgV( ' ,x, '; ', y, ') = ' ,kgv(x,y), '$');
writeln;
end;
end;
end;
3 : begin
while (not eof) do
begin
readln(x);
readln(y);
if ( x <= 0) or (y <= 0)
then writeln('dies ist keine ordentliche Eingabe')
else
begin
write('\item ');
write(' $ ',x, ' = ');
primfaktorzerlegung(x);
writeln('$, \\ ');
write('$ ',y, ' = ');
primfaktorzerlegung(y);
writeln('$, \\ ');
z:= kgv(x,y);
write('$\kgV( ' ,x, '; ', y, ') = ');
primfaktorzerlegung(z);
write(' = ' ,kgv(x,y), '$');
writeln;
writeln;
end;
end;
end;
end; { case }
end;
't', 'T' : begin
writeln('Teilermengen normal = 1');
writeln('Schnittmengen von zwei = 2');
writeln('Schnittmengen von drei = 3');
readln(i);
writeln;
case (i) of
1 : begin
while (not eof) do
begin
readln(x);
write('\item');
write(' $T_{' ,x, '} = ');
teiler(x);
write('$');
writeln;
end;
end;
2 : begin
while (not eof) do
begin
readln(x);
readln(y);
write('\item');
write(' $T_{' ,x, '} = ');
teiler(x);
write('$ \\');
writeln;
write(' $T_{' ,y, '} = ');
teiler(y);
write('$ \\');
writeln;
write('$T_{' ,x, ' \cap ' ,y,'} = ');
teilerzwei(x,y);
writeln('$');
end;
end;
3 : begin
while (not eof) do
begin
readln(x);
readln(y);
readln(z);
write('\item');
write(' $T_{' ,x, '} = ');
teiler(x);
write('$ \\');
writeln;
write(' $T_{' ,y, '} = ');
teiler(y);
write('$ \\');
writeln;
write(' $T_{' ,z, '} = ');
teiler(z);
write('$ \\');
writeln;
write('$T_{' ,x, ' \cap ' ,y,' \cap ' ,z,'} = ');
teilerdrei(x,y,z);
writeln('$');
end;
end;
end; { case }
end;
else
writeln('ggT normal = 1');
writeln('ggT schnell = 2');
writeln('ggT prim = 3');
writeln('ggT euklid = 4');
writeln('ggT für drei Zahlen (normal) = 5');
writeln('ggT für drei Zahlen (prim) = 6');
writeln('ggT teilerfremd = 7');
readln(i);
writeln;
case (i) of
1 : begin
while (not eof) do
begin
readln(x);
readln(y);
if ( x <= 0) or (y <= 0)
then writeln('dies ist keine ordentliche Eingabe')
else
begin
write('\item ');
write(' $T_{' ,x, '} = ');
teiler(x);
writeln('$, \\ ');
write(' $T_{' ,y, '} = ');
teiler(y);
writeln('$, \\ ');
write('$T_{' ,x, ' \cap ' ,y,'} = ');
teilerzwei(x,y);
writeln('$, \\ ');
write('$\ggT( ' ,x, '; ', y, ') = ' ,ggt(x,y), '$');
writeln;
end;
end;
end;
2 : begin
while (not eof) do
begin
readln(x);
readln(y);
if ( x <= 0) or (y <= 0)
then writeln('dies ist keine ordentliche Eingabe')
else
begin
write('\item ');
writeln('$\ggT(',x,';',y,') = ?$');
writeln('\begin{enumerate}[1)]');
write('\item ');
write('$T_{' ,min(x,y), '} = ');
teiler(min(x,y));
write('$');
writeln;
write('\item ');
k:=teilersuche(min(x,y),min(x,y));
while (max(x,y) mod k <> 0) do
begin
writeln('Ist ',k,' Teiler von ' ,max(x,y),'? \quad nein \\');
k:=teilersuche(min(x,y),k-1);
end;
writeln('Ist ',ggt(x,y),' Teiler von ' ,max(x,y),'? \quad ja');
writeln;
write('Also ist: ');
writeln('$\ggT( ' ,x, '; ', y, ') = ' ,ggt(x,y), '$');
writeln('\end{enumerate}');
end;
end;
end;
3 : begin
while (not eof) do
begin
readln(x);
readln(y);
if ( x <= 0) or (y <= 0)
then writeln('dies ist keine or dentliche Eingabe')
else
begin
write('\item ');
write('$ ',x, ' = ');
primfaktorzerlegung(x);
writeln('$, \\ ');
write('$ ',y, ' = ');
primfaktorzerlegung(y);
writeln('$, \\ ');
z:= ggT(x,y);
write('$\ggT( ' ,x, '; ', y, ') = ');
primfaktorzerlegung(z);
write(' = ' ,ggt(x,y), '$');
writeln;
end;
end;
end;
4 : begin
while (not eof) do
begin
readln(x);
readln(y);
if ( x <= 0) or (y <= 0)
then writeln('dies ist keine ordentliche Eingabe')
else begin
rechne_ggt(x,y);
end;
end;
end;
5 : begin
while (not eof) do
begin
readln(x);
readln(y);
readln(z);
if ( x <= 0) or (y <= 0) or (z <= 0)
then writeln('dies ist keine ordentliche Eingabe')
else
begin
write('\item ');
write(' $T_{' ,x, '} = ');
teiler(x);
write('$, \\ ');
write(' $T_{' ,y, '} = ');
teiler(y);
writeln('$, \\ ');
write(' $T_{' ,z, '} = ');
teiler(z);
writeln('$, \\ ');
write('$T_{' ,x, ' \cap ' ,y,' \cap ' ,z,'} = ');
teilerdrei(x,y,z);
writeln('$, \\ ');
write('$\ggT( ' ,x, '; ', y, '; ', z, ') = ' ,ggt(ggt(x,y), z), '$');
writeln;
end;
end;
end;
6 : begin
while (not eof) do
begin
readln(x);
readln(y);
readln(t);
if ( x <= 0) or (y <= 0) or (t<= 0)
then writeln('dies ist keine ordentliche Eingabe')
else
begin
write('\item ');
write(' $ ',x, ' = ');
primfaktorzerlegung(x);
writeln('$, \\ ');
write('$ ',y, ' = ');
primfaktorzerlegung(y);
writeln('$, \\ ');
write(' $ ',t, ' = ');
primfaktorzerlegung(t);
writeln('$, \\ ');
z:= ggT(ggT(x,y),t);
write('$\ggT( ' ,x, '; ', y, '; ' ,t,') = ');
primfaktorzerlegung(z);
write(' = ' ,ggT(ggt(x,y),t), '$');
writeln;
writeln;
end;
end;
end;
7 : begin
readln(y);
for x:=1 to y do
begin
if ( x <= 0) or (y <= 0)
then writeln('dies ist keine ordentliche Eingabe')
else
if ggt(x,y) = 1 then
begin
write('\item ');
write(' $T_{' ,x, '} = ');
teiler(x);
write('$, \\ ');
write(' $T_{' ,y, '} = ');
teiler(y);
write('$, \\ ');
write('$\ggT( ' ,x, '; ', y, ') = ' ,ggt(x,y), '$');
writeln;
writeln;
end;
end;
end;
end; { case }
end; { case }
end.
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