\mnb150<nb><cmd><![CDATA[meineaufgabe:=proc()
local aa, bb;
save PRETTYPRINT;
begin
PRETTYPRINT:=FALSE;
if not testtype(Matr_Nr,DOM_INT) then 
error("Zuerst die Matrikelnummer der Größe Matr_Nr zuweisen") end;
print(Unquoted, "Miniprojekt 5: Aufgabe zur Matrikelnummer ".expr2text(Matr_Nr));
aa:=substring(expr2text(Matr_Nr),0..1).substring(expr2text(Matr_Nr),4..6);
aa:=(aa.".".aa);
print();
print(Unquoted,"Geben Sie zur Zahl:  ".aa);
print(Unquoted,"Eine bis zu 10-stellige Darstellung zur Basis 3 an.");
print(Unquoted,"Ich habe die Basis 2 nicht gewählt, weil es zuviel ");
print(Unquoted,"Programme gibt, die dies automatisch machen.");
print(Unquoted,"Geben Sie im Ãœbungstool folgende Liste ab:");
"[Miniprojektnummer, Matrikelnummer, 3-är-Darstellung]"
end:






A_benno_mini1:={1,2,3,4,5,6,a,s,d,f,g,h,j,K,B,N,G,F,H,K,U,Z,T}:
B_benno_mini1:= 3141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342\
1170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229\
4895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821\
3393607260249141274:



pinnumber:=proc(n1,n2,laenge,k)
name pinnumber;
  local a, b, bb, i;
begin
  if not testtype(Matr_Nr, DOM_INT) then 
    error("Zuerst die Matrikelnummer der Groesse Matr_Nr zuweisen")
  end_if; 
  a := []; 
  for i from n1 to n2 do 
    cc := ceil(10^laenge*(B_benno_mini1/10^i - ceil(B_benno_mini1/10^i))); 
    cc := Matr_Nr mod cc; 
    cc := cc mod k; 
    a := [op(a), cc]
  end_for; 
  a
end_proc:

selectmenge:=proc(A, anfang, n)
  name selectmenge;
  local m1, ll, nn, mm, g1, rs, rest, anz, ls, bildind, opbildind;
save Matr_Nr;
begin
if args(0)=4 then Matr_Nr:=args(4) end;
if not testtype(Matr_Nr,DOM_INT) then 
  error("Zuerst die Matrikelnummer der Groesse Matr_Nr zuweisen") 
end;
anz := nops(A); 
  ll := pinnumber(anfang, 200, 3, 375); 
  nn := 0; 
  m1 := {}; 
  while nops(m1) < n do
    nn := nn + 1; 
    mm := op(ll, nn) mod anz; 
    if mm = 0 then 
      mm := anz
    end_if; 
    if Matr_Nr=1234560 then
    m1 := {V,W,R,z,q,1,2}
    else
    m1 := {op(m1), op(A, mm)}
    end;
  end_while; 
  bildind := 10 + anfang; 
  opbildind := op(ll, bildind) mod n; 
  if opbildind = 0 then 
    opbildind := n
  end_if; 
  g1 := {[op(m1, 1), op(m1, opbildind)]}; 
  rs := {op(m1, opbildind)}; 
  while nops(g1) < n - 2 do
    bildind := bildind + 1; 
    opbildind := op(ll, bildind) mod n; 
    if opbildind = 0 then 
      opbildind := n
    end_if; 
    if not contains(rs, op(m1, opbildind)) then 
      rs := {op(rs), op(m1, opbildind)}; 
      g1 := {op(g1), [op(m1, nops(g1) + 1), op(m1, opbildind)]}
    end_if
  end_while; 
  ls:= {op(g1,[i,1])$i=1..n-2};
  rest := m1 minus ls; 
  g1 := {op(g1), [op(rest, 2), op(g1, [1, 1])], [op(rest, 1), op(g1, [3, 1])]}; 
  m1, g1
end_proc:

nachkommazahl:=proc(zahl)
local zz, pp;
begin
zahl:=abs(float(zahl));
zz:=expr2text(zahl); 
pp:=stringlib::pos(zz,"."); 
zz:=substring(zz,pp+1..length(zz)-1);
text2expr(zz)
end:


naersum:=proc(sumk)
local vz, aa, cc, k, bas;
begin
vz:=op(sumk,[1,1]);
bas:=op(sumk,[1,3]);
k:=2;
cc:=hold(_power)(bas,op(sumk,[1,2]));
aa:=hold(_plus)(hold(_mult)((op(sumk,k),hold(_power)(bas,-(k-2))))$k=2..nops(sumk));
aa:=hold(_mult)(cc,aa);
aa:=hold(_mult)(vz,aa);
if args(0)=2 and args(2)="block" then 
subs(block("aa"),"aa"=aa)
else
aa
end
end:

pruefenaer:=proc(zahl)
local basis;
begin
basis:=op(zahl,[1,3]);
naersum(zahl,basis);
float(eval(%))
end:

block:=proc(x) 
option hold; 
local ausn, erg;
begin
if args(0)=0 or args(0)> 2 then error("one or two arguments needed") 
end;
if args(0)=2 then ausn:={op(args(2))} else ausn:={} end;
if bool(op(x,1)=x) then
procname(x) 
elif bool(type(x) in ausn) then 
erg:=(map(x, block, ausn));
elif bool(type(x)="block") then
eval(x)
else
erg:=(map(x, block, ausn)); 
procname(erg)
end
end:


binkoeff:=proc(z, bas)
local aganz, bganz, 
     ganz,abgeschnitt,
     ganzv,abgeschnittv, 
     lganz, labgeschnitt, 
     k, vz, mant, z1, z2, 
     ll, anzahl;
begin 
vz:=1;if z < 0 then 
z:=-z;
vz:=hold(-1);
end_if;
 lganz:=[]; 
labgeschnitt:=[];
// lganzv:=[]; 
labgeschnittv:=[];
z1:=floor(z);
z2:=nachkommazahl(z);
z2:=z2/10^length(z2);
aganz:=10000;
if args(0)= 3 then 
anzahl:=args(3)
else
anzahl:=DIGITS
end_if;
for k from 0 to anzahl do 
aganz:=floor(z2*bas^(k+1)); 
bganz:=floor( z2*bas^(k))*bas;
lganzv:=[aganz,op(lganz)];
labgeschnittv:= [op(labgeschnittv), aganz-bganz];
end_for; 
ll:=op(labgeschnittv,nops(labgeschnittv));
while bool(ll=0) do 
labgeschnittv:= [op(labgeschnittv,1..nops(labgeschnittv)-1)];
ll:=op(labgeschnittv,nops(labgeschnittv));
end_while;
k:=-1;
repeat 
aganz:=floor(z*bas^(k+1)); 
bganz:=floor( z*bas^(k))*bas;
lganzv:=[aganz,op(lganz)];
labgeschnittv:= [aganz-bganz,op(labgeschnittv)];
k:=k-1; 
until aganz = 0 
end_repeat;
mant:=-k-3;
labgeschnittv:= [op(labgeschnittv,2..nops(labgeschnittv))];
[[vz,mant, bas], op(labgeschnittv), op(labgeschnitt)]
end:

initialnoweb:=proc()
begin
if args(1)="noweb"
then myreturn:=return@lprint
elif args(1)="web" then
myreturn:=return@webreturn
end
end:

webreturn:=proc(eintrag:DOM_STRING)
local vvvv;
begin
vvvv:=stringlib::subs(eintrag,"\n"=" ");
end:

lprint:=proc(ein)
save PRETTYPRINT;
begin 
PRETTYPRINT:=FALSE;
print(Unquoted,ein);
end:

probe:=proc(a)
save myreturn,PRETTYPRINT;
begin
PRETTYPRINT:=FALSE;
initialnoweb("noweb"); 
go(123,a)
end:





go:=proc(Matrikelnummer, Primzahl) 
  name go;
  // local mygeneral, n, mnr,aaa,  myset, myfirst, firstleft, firstright, mystring, mysecond, zwert, i, k, sollsecond, myselectmenge, mygraph;
  local mygeneral,pneu, n;
  save PRETTYPRINT;
begin
 mygeneral:=go_general(Matrikelnummer, Primzahl);
 if bool(mygeneral=TRUE) then
 pneu:=text2expr(Primzahl);
 n:=op(pneu,1); 
 case n
    of 1 do 
    go1(Matrikelnummer, Primzahl); break;
    of 2 do 
    go2(Matrikelnummer, Primzahl);break;
    of 3 do 
    go3(Matrikelnummer, Primzahl);break;
    of 4 do 
    go4(Matrikelnummer, Primzahl);break;
    of 5 do 
    go5(Matrikelnummer, Primzahl);break;
    of 6 do 
    go6(Matrikelnummer, Primzahl);break;
    of 7 do 
    go7(Matrikelnummer, Primzahl);break;
    of 8 do 
    go8(Matrikelnummer, Primzahl);break;
    of 9 do 
    go9(Matrikelnummer, Primzahl);break;
    of 10 do 
    go10(Matrikelnummer, Primzahl);break;
 end_case;
 // TRUE
 else mygeneral
 end_if
end_proc:


go1:=proc(Matrikelnummer, Primzahl) 
  name go;
  // local mygeneral, n, mnr,aaa,  myset, myfirst, firstleft, firstright, mystring, mysecond, zwert, i, k, sollsecond, myselectmenge, mygraph;
  local mygeneral, n, mnr,aaa,  myset, myfirst, firstleft, firstright, mystring, mysecond, zwert, i, k, sollsecond, myselectmenge, mygraph;
  save PRETTYPRINT;
begin
 mygeneral:=go_general(Matrikelnummer, Primzahl);
 if bool(mygeneral=TRUE) then
 Primzahl:=text2expr(Primzahl);
 n:=op(Primzahl,1); 
 mnr := op(Primzahl, 2);
 case n
    of 1 do 
      myselectmenge := selectmenge(A_benno_mini1, 12, 7, mnr); 
      myset := op(myselectmenge, 1); 
      mygraph := op(myselectmenge, 2); 
      myfirst := op(Primzahl, [3, 1]); 
      if not testtype(myfirst, DOM_SET) then 
      mystring:="Fehler: \n";
      mystring:=mystring."Graph muss eine Menge sein.";
      myreturn(mystring);
      end_if; 
      firstleft := [op(i, 1) $ i in myfirst]; 
      if not ({op(firstleft)} = myset and nops(firstleft) = nops(myset)) then
      mystring:="Fehler: \n";
      mystring:=mystring."Der angegebene Graph: \n";
      mystring:=mystring.expr2text(myfirst)."\n";
      mystring:=mystring."definiert keine Funktion auf: \n";
      mystring:=mystring.expr2text(myset);
      myreturn(mystring); 
      end_if; 
      firstright := [op(i, 2) $ i in myfirst]; 
      if not {op(firstright)} = myset then 
      mystring:="Fehler: \n";
      mystring:=mystring."Der angegebene Graph: \n";
      mystring:=mystring.expr2text(myfirst)."\n";
      mystring:=mystring."definiert keine injektive Funktion.";
      myreturn(mystring);
      end_if; 
      if nops(mygraph intersect myfirst) < 5 then 
      mystring:="Fehler: \n";
      mystring:=mystring."Sie haben mehr als zwei Elemente an dem \n";
      mystring:=mystring."Ihnen zugeteilten Graphen ge„ndert. ";
      myreturn(mystring);
      end_if; 
      mysecond := op(Primzahl, [3, 2]); 
      if not testtype(mysecond, DOM_SET) then 
      mystring:="Fehler: \n";
      mystring:=mystring."Zweiter Graph muss eine Menge sein.";
      myreturn(mystring);
      end_if; 
      sollsecond := {}; 
      zwert := ([op(i), op(k)] $ k in myfirst) $ i in myfirst; 
      for i in zwert do 
        if op(i, 3) = op(i, 2) then 
          sollsecond := {op(sollsecond), [op(i, 4), op(i, 1)]}
        end_if
      end_for; 
      if sollsecond = mysecond then 
         TRUE
      else 
         mystring:="Fehler: \n";
      mystring:=mystring."Zweiter Graph ist nicht Quadrat der Umkehrfunktion.";
      myreturn(mystring);
         end_if; 
      break
  end_case;
     TRUE
 else mygeneral
 end_if
end_proc:

go_general:=proc(Matrikelnummer, Primzahl) 
  name go;
  local aaa, n, mnr, myset, myfirst, firstleft, firstright, mystring, mysecond, zwert, i, k, sollsecond, myselectmenge, mygraph;
  save PRETTYPRINT;
begin
  k := 0; 
  i := 0; 
  mystring:="Fehler: ";
  PRETTYPRINT := FALSE; 
  if testtype(Primzahl, DOM_STRING) then 
    aaa := 0; 
    aaa := traperror(text2expr(Primzahl)); 
    if 0 < aaa then 
      mystring:="Syntaxfehler - Beachten Sie:\n";
      mystring:=mystring."Eingabe muss in Anfuehrungszeichen stehen. \n";
      mystring:=mystring."Zu jeder Klammer-auf gehoert eine Klammer-zu,\n";
      mystring:=mystring."benutzen Sie keine runden statt eckiger Klammern,\n";
      mystring:=mystring."trennen Sie Daten und Ausdruecke durch Kommata.";
      myreturn(mystring);
    else 
      Primzahl := text2expr(Primzahl)
    end_if
  else
      mystring:="Fehler - Beachten Sie:\n";
      mystring:=mystring."Die Eingabe muss in Anfuehrungszeichen stehen.";
      myreturn(mystring);
  end_if; 
  if not testtype(Primzahl, DOM_LIST) then 
      mystring:="Fehler: \n";
      mystring:=mystring."Eingabe muss Liste sein.";
      myreturn(mystring);
    end_if; 
  if not testtype(op(Primzahl, 1), DOM_INT) then 
      mystring:="Fehler: \n";
      mystring:=mystring."Erster Eintrag muss Miniprojektnummer sein.";
      myreturn(mystring);
  end_if; 
  n := op(Primzahl, 1); 
  if not m_isdefined(n) then 
      print(not m_isdefined(n));
      mystring:="Fehler: \n";
      mystring:=mystring."Ein Miniprojekt dieser Nummer ist noch nicht definiert.";
      myreturn(mystring);
  end_if; 
  if m_expired(n) then 
      mystring:="Fehler: \n";
      mystring:=mystring."Der Abgabetermin fuer Miniprojekt\n";
      mystring:=mystring.expr2text(n)."\n";
      mystring:=mystring."ist abgelaufen.";
      myreturn(mystring);
  end_if; 
  mnr := op(Primzahl, 2); 
  if not testtype(mnr, DOM_INT) then 
      mystring:="Fehler: \n";
      mystring:=mystring."Zweiter Eintrag muss Ihre Matrikelnummer sein.";
      myreturn(mystring);
  end_if; 
  if not (length(mnr) = 7 and (testtype(mnr/10, DOM_INT) or testtype(mnr/11, DOM_INT))) then 
      mystring:="Fehler: \n";
      mystring:=mystring."Keine gueltige Matrikelnummer!";
      myreturn(mystring);
  end_if; 
  erg := op(Primzahl, 3); 
  if not (nops(Primzahl) = 3 and testtype(erg, DOM_LIST)) then 
      mystring:="Fehler: \n";
      mystring:=mystring."Die Eingabe soll nur drei Eintr„ge haben,\n";
      mystring:=mystring."der dritte Eintrag muss eine Liste sein.";
      myreturn(mystring);
  end_if; 
  TRUE
end_proc:


go5:=proc(zz,Primzahl)
local aa_1, mnr, aa, par, mystring, myop;
begin
aa_1:=text2expr(Primzahl);
mnr:=(op(aa_1,2));
aa:=substring(expr2text(mnr),0..1).substring(expr2text(mnr),4..6);
aa:=(aa.".".aa); 
aa:=text2expr(aa);
erg:=binkoeff(aa,3);
if bool(erg=op(aa_1,3)) then TRUE
else
myop:=[3,1];
par:=op(aa_1,myop);
if not testtype(par,DOM_LIST) then 
mystring:="Fehler: \n";
mystring:=mystring."Beim dritten Eintrag, muss am Anfang eine Liste stehen";
myreturn(mystring)
end_if;
erg:=[1,1,erg];
myop:=[3,1,1];
par:=op(aa_1,myop);
if not bool(par=op(erg,myop)) then 
mystring:="Fehler: \n";
mystring:=mystring."Vorzeichen falsch";
myreturn(mystring)
end_if;
myop:=[3,1,2];
par:=op(aa_1,myop);
if not bool(par=op(erg,myop)) then 
mystring:="Fehler: \n";
mystring:=mystring."Mantisse falsch.";
myreturn(mystring)
end_if;
myop:=[3,1,3];
par:=op(aa_1,myop);
if not par=op(erg,myop) then 
mystring:="Fehler: \n";
mystring:=mystring."Basis falsch.";
myreturn(mystring)
end_if;
mystring:="Fehler: \n";
mystring:=mystring."Ziffern falsch.";
myreturn(mystring)
end
end:

m_isdefined:=proc()
begin
FALSE
end:
m_expired:=proc()
begin
TRUE
end:

initialnoweb("web"):
m_isdefined(0):=TRUE:
m_isdefined(1):=TRUE:
m_isdefined(5):=TRUE:
m_expired(1):=FALSE:
m_expired(5):=FALSE:
/*go:=proc(Matrikelnummer, Primzahl) 
  name go;
  local aaa, n, mnr, myset, myfirst, firstleft, firstright, mystring, mysecond, zwert, i, k, sollsecond, myselectmenge, mygraph;
  save PRETTYPRINT;
begin
  k := 0; 
  i := 0; 
  mystring:="Fehler: ";
  PRETTYPRINT := FALSE; 
  if testtype(Primzahl, DOM_STRING) then 
    aaa := 0; 
    aaa := traperror(text2expr(Primzahl)); 
    if 0 < aaa then 
      mystring:="Syntaxfehler - Beachten Sie:\n";
      mystring:=mystring."Eingabe muss in Anführungszeichen stehen. \n";
      mystring:=mystring."Zu jeder Klammer-auf gehört eine Klammer-zu,\n";
      mystring:=mystring."benutzen Sie keine runden statt eckiger Klammern,\n";
      mystring:=mystring."trennen Sie Daten und Ausdrücke durch Kommata.";
      myreturn(mystring);
    else 
      Primzahl := text2expr(Primzahl)
    end_if
  else
      mystring:="Fehler - Beachten Sie:\n";
      mystring:=mystring."Die Eingabe muss in Anführungszeichen stehen.";
      myreturn(mystring);
  end_if; 
  if not testtype(Primzahl, DOM_LIST) then 
      mystring:="Fehler: \n";
      mystring:=mystring."Eingabe muss Liste sein.";
      myreturn(mystring);
    end_if; 
  if not testtype(op(Primzahl, 1), DOM_INT) then 
      mystring:="Fehler: \n";
      mystring:=mystring."Erster Eintrag muss Miniprojektnummer sein.";
      myreturn(mystring);
  end_if; 
  n := op(Primzahl, 1); 
  if 1 < n then 
      mystring:="Fehler: \n";
      mystring:=mystring."Ein Miniprojekt dieser Nummer ist noch nicht definiert.";
      myreturn(mystring);
  end_if; 
  if n < 1 then 
      mystring:="Fehler: \n";
      mystring:=mystring."Der Abgabetermin für Miniprojekt\n";
      mystring:=mystring.expr2text(n)."\n";
      mystring:=mystring."ist abgelaufen.";
      myreturn(mystring);
  end_if; 
  mnr := op(Primzahl, 2); 
  if not testtype(mnr, DOM_INT) then 
      mystring:="Fehler: \n";
      mystring:=mystring."Zweiter Eintrag muss Ihre Matrikelnummer sein.";
      myreturn(mystring);
  end_if; 
  if not (length(mnr) = 7 and (testtype(mnr/10, DOM_INT) or testtype(mnr/11, DOM_INT))) then 
      mystring:="Fehler: \n";
      mystring:=mystring."Keine gültige Matrikelnummer!";
      myreturn(mystring);
  end_if; 
  erg := op(Primzahl, 3); 
  if not (nops(Primzahl) = 3 and testtype(erg, DOM_LIST)) then 
      mystring:="Fehler: \n";
      mystring:=mystring."Die Eingabe soll nur drei Einträge haben,\n";
      mystring:=mystring."der dritte Eintrag muss eine Liste sein.";
      myreturn(mystring);
  end_if; 
  case n
    of 1 do 
      myselectmenge := selectmenge(A_benno_mini1, 12, 7, mnr); 
      myset := op(myselectmenge, 1); 
      mygraph := op(myselectmenge, 2); 
      myfirst := op(Primzahl, [3, 1]); 
      if not testtype(myfirst, DOM_SET) then 
      mystring:="Fehler: \n";
      mystring:=mystring."Graph muss eine Menge sein.";
      myreturn(mystring);
      end_if; 
      firstleft := [op(i, 1) $ i in myfirst]; 
      if not ({op(firstleft)} = myset and nops(firstleft) = nops(myset)) then 
      mystring:="Fehler: \n";
      mystring:=mystring."Der angegebene Graph: \n";
      mystring:=mystring.expr2text(myfirst)."\n";
      mystring:=mystring."definiert keine Funktion auf: \n";
      mystring:=mystring.expr2text(myset);
      myreturn(mystring);
      end_if; 
      firstright := [op(i, 2) $ i in myfirst]; 
      if not {op(firstright)} = myset then 
      mystring:="Fehler: \n";
      mystring:=mystring."Der angegebene Graph: \n";
      mystring:=mystring.expr2text(myfirst)."\n";
      mystring:=mystring."definiert keine injektive Funktion.";
      myreturn(mystring);
      end_if; 
      if nops(mygraph intersect myfirst) < 5 then 
      mystring:="Fehler: \n";
      mystring:=mystring."Sie haben mehr als zwei Elemente an dem \n";
      mystring:=mystring."Ihnen zugeteilten Graphen geändert. ";
      myreturn(mystring);
      end_if; 
      mysecond := op(Primzahl, [3, 2]); 
      if not testtype(mysecond, DOM_SET) then 
      mystring:="Fehler: \n";
      mystring:=mystring."Zweiter Graph muss eine Menge sein.";
      myreturn(mystring);
      end_if; 
      sollsecond := {}; 
      zwert := ([op(i), op(k)] $ k in myfirst) $ i in myfirst; 
      for i in zwert do 
        if op(i, 3) = op(i, 2) then 
          sollsecond := {op(sollsecond), [op(i, 4), op(i, 1)]}
        end_if
      end_for; 
      if sollsecond = mysecond then 
        TRUE
      else 
        mystring:="Fehler: \n";
      mystring:=mystring."Zweiter Graph ist nicht Quadrat der Umkehrfunktion.";
      myreturn(mystring);
         end_if; 
      break
  end_case
end_proc:
*/



nachkommazahl:=proc(zahl)
local zz, pp;
begin
zahl:=abs(float(zahl));
zz:=expr2text(zahl); 
pp:=stringlib::pos(zz,"."); 
zz:=substring(zz,pp+1..length(zz)-1);
text2expr(zz)
end:


naersum:=proc(sumk)
local vz, aa, cc, k, bas;
begin
vz:=op(sumk,[1,1]);
bas:=op(sumk,[1,3]);
k:=2;
cc:=hold(_power)(bas,op(sumk,[1,2]));
aa:=hold(_plus)(hold(_mult)((op(sumk,k),hold(_power)(bas,-(k-2))))$k=2..nops(sumk));
aa:=hold(_mult)(cc,aa);
aa:=hold(_mult)(vz,aa);
if args(0)=2 and args(2)="block" then 
subs(block("aa"),"aa"=aa)
else
aa
end
end:

pruefenaer:=proc(zahl)
local basis;
begin
basis:=op(zahl,[1,3]);
sumrep(zahl,basis);
float(eval(%))
end:

block:=proc(x) 
option hold; 
local ausn, erg;
begin
if args(0)=0 or args(0)> 2 then error("one or two arguments needed") 
end;
if args(0)=2 then ausn:={op(args(2))} else ausn:={} end;
if bool(op(x,1)=x) then
procname(x) 
elif bool(type(x) in ausn) then 
erg:=(map(x, block, ausn));
elif bool(type(x)="block") then
eval(x)
else
erg:=(map(x, block, ausn)); 
procname(erg)
end
end:


binkoeff:=proc(z, bas)
local aganz, bganz, 
     ganz,abgeschnitt,
     ganzv,abgeschnittv, 
     lganz, labgeschnitt, 
     k, vz, mant, z1, z2, 
     ll, anzahl;
begin 
vz:=1;if z < 0 then 
z:=-z;
vz:=hold(-1);
end_if;
 lganz:=[]; 
labgeschnitt:=[];
// lganzv:=[]; 
labgeschnittv:=[];
z1:=floor(z);
z2:=nachkommazahl(z);
z2:=z2/10^length(z2);
aganz:=10000;
if args(0)= 3 then 
anzahl:=args(3)
else
anzahl:=DIGITS
end_if;
for k from 0 to anzahl do 
aganz:=floor(z2*bas^(k+1)); 
bganz:=floor( z2*bas^(k))*bas;
lganzv:=[aganz,op(lganz)];
labgeschnittv:= [op(labgeschnittv), aganz-bganz];
end_for; 
ll:=op(labgeschnittv,nops(labgeschnittv));
while bool(ll=0) do 
labgeschnittv:= [op(labgeschnittv,1..nops(labgeschnittv)-1)];
ll:=op(labgeschnittv,nops(labgeschnittv));
end_while;
k:=-1;
repeat 
aganz:=floor(z*bas^(k+1)); 
bganz:=floor( z*bas^(k))*bas;
lganzv:=[aganz,op(lganz)];
labgeschnittv:= [aganz-bganz,op(labgeschnittv)];
k:=k-1; 
until aganz = 0 
end_repeat;
mant:=-k-3;
labgeschnittv:= [op(labgeschnittv,2..nops(labgeschnittv))];
[[vz,mant, bas], op(labgeschnittv), op(labgeschnitt)]
end:


aufgabe:=proc(zahl, glieder, basis)
local erg, summe;
save PRETTYPRINT;
begin 
PRETTYPRINT:=FALSE;
print(Unquoted,"Gebe (mit einer bis zu ".expr2text(glieder)."-stelligen Ziffernfolge) die ");
print(Unquoted,expr2text(basis)."-är-Darstellung der Zahl ".expr2text(zahl)."");
print();
if args(0)=4 then 
print(Unquoted,"Lösung: ");
erg:=binkoeff(zahl, basis, glieder);
print(Unquoted,expr2text(erg));
print(Unquoted,"Dies entspricht der Summe: ");
summe:=naersum(erg);
print(Unquoted,naersum(erg));
print(Unquoted,"und ergibt aufsummiert: ".expr2text(eval(summe)));
end_if;
null();
end:

null():]]></cmd></nb>ÿ{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 System;}{\f3\fmodern\fprq1 Courier New;}{\f4\froman\fprq2 Times New Roman;}}
{\colortbl\red0\green0\blue0;\red128\green0\blue128;\red0\green0\blue255;\red255\green0\blue0;}
\deflang1031\pard\ri4\plain\f3\fs40\cf1\b Miniprojekt 5: 
\par \plain\f3\fs44\cf0\b Bin\'e4r und n-\'e4r-Zahlen
\par \plain\f3\fs28\cf0\b 
\par 
\par Abgabetermin: so fr\'fch wie m\'f6glich, denn es kommen 
\par weitere Miniprojekte, sp\'e4testens bis Weihnachten. 
\par 
\par \plain\f4\fs28\cf0 
\par 
\par Zur Aufgabenstellung: 
\par 
\par 
\par F\'fcr Notation und Erkl\'e4rung schauen Sie sich bitte den Drill
\par \pard\plain\lang2057\f4\fs28\cf2\ul Drill: bin\'e4r und n-\'e4r Darstellungen \plain\f4\fs28\cf0  an.
\par 
\par Wenn der Computer Ihre Matrikelnummer nicht kennt, dann sollten Sie
\par \pard\ri4\plain\f4\fs28\cf0 sie ihm bekannt machen:
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs24\cf3 {\pntext\f1\'b7\tab}Matr_Nr:=6000000:
\par \pard\ri4\plain\f4\fs28\cf0 Dabei m\'fcssen Sie nat\'fcrlich die Beispielsmatrikelnummer 1234560
\par durch Ihre eigene Nummer ersetzen. 
\par \plain\lang2057\f4\fs24 
\par \plain\f4\fs28\cf0 Sie erhalten Ihre Aufgabe durch Ausf\'fchrung des Befehls:
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs24\cf3 {\pntext\f1\'b7\tab}meineaufgabe()
\par \pard\li600\ri1\fi-300\plain\f3\fs24\cf3 
\par \pard\li50\ri6\plain\f3\fs22\cf2\protect Miniprojekt 5: Aufgabe zur Matrikelnummer 6000000
\par \pard\li50\ri2\plain\f3\fs22\cf2\protect 
\par Geben Sie zur Zahl:  60000.60000
\par Eine bis zu 10-stellige Darstellung zur Basis 3 an.
\par Ich habe die Basis 2 nicht gew\'e4hlt, weil es zuviel 
\par Programme gibt, die dies automatisch machen.
\par Geben Sie im \'dcbungstool folgende Liste ab:
\par    {\pict\wmetafile8\picw10636\pich874\picwgoal6029\pichgoal495
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}\plain\f3\fs22\cf2\protect 
\par 
\par \pard\ri4\plain\f4\fs28\cf3 Hinweis: Vergessen Sie bitte die Anf\'fchrungszeichen nicht. 
\par 
\par \plain\f4\fs28\cf0 Beispiel:  Im Beispielsfall ist die Darstellung
\par 
\par \pard\li50\ri6\plain\f3\fs22\cf2\protect    {\pict\wmetafile8\picw10363\pich727\picscalex98\picscaley98\picwgoal5934\pichgoal416
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}\plain\f3\fs22\cf2\protect 
\par \pard\li50\ri2\plain\f3\fs22\cf2\protect 
\par \pard\ri4\plain\f4\fs28\cf0 Dass die L\'f6sung korrekt ist, sieht man, wenn man diesen Ausdruck  in eine 
\par Summe umwandelt 
\par \pard\li50\ri6\plain\f3\fs22\cf2\protect    {\pict\wmetafile8\picw31005\pich1012\picscalex99\picscaley98\picwgoal17751\pichgoal579
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00000000050000000B0200000000050000000B0200000000050000000B0200000000050000000B
020000000008000000FA0200000000000000000000040000002D0100001C000000FB0238FF0000
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C0C77700003000040000002D01010005000000020101000000050000000102FFFFFF0005000000
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01000000010000000054696D6573204E657720526F6D616E001643C5771F43C57720C0C7770000
3000040000002D0102001C000000FB02E8FE0000000000009001000000020000000053796D626F
6C007740000000400D0AF81643C5771F43C57720C0C77700003000040000002D01030004000000
2D0102000500000009020000FF00070000002105010032005E018C00070000002105010032005E
011801070000002105010032005E01A401070000002105010034005E0130020700000021050100
39005E01BC02070000002105010038005E014803070000002105010038005E01D4030700000021
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0207000000210501003100BD02480307000000210501003400BD02D40307000000210501003700
BD0260041C000000FB02E8FE000000000000900100000001000000005346204D61746820457874
00130D0A481643C5771F43C57720C0C77700003000040000002D0104000700000021050100C500
AF0164000700000021050100C500AF010C010700000021050100C500AF01B40107000000210501
00C500AF015C020700000021050100C500AF0104030700000021050100C500AF01AC0307000000
21050100C500AF0154040700000021050100C500AF01FC040700000021050100C500AF01840504
0000002D01030007000000210501003D0006027206040000002D01020007000000210501003100
06025207070000002105010032000602DE070700000021050100350006026A0807000000210501
0036000602F608070000002105010030000602820907000000210501002E0006020E0A07000000
2105010031000602540A070000002105010032000602E00A0700000021050100350006026C0B07
0000002105010036000602F80B08000000FA0200000000000000000000040000002D0105001C00
0000FB021000070000000000BC02000000000102022253797374656D0077400000003E0D0A4816
43C5771F43C57720C0C77700003000040000002D010600040000002701FFFF04000000F0010000
04000000F001010004000000F001020004000000F001030004000000F0010400040000002701FF
FF040000002701FFFF040000002701FFFF040000002701FFFF040000002701FFFF040000002701
FFFF040000002701FFFF040000002701FFFF040000002701FFFF040000002701FFFF0400000027
01FFFF040000002701FFFF040000002701FFFF040000002701FFFF040000002701FFFF04000000
2701FFFF040000002701FFFF040000002701FFFF040000002701FFFF040000002701FFFF040000
002701FFFF040000002701FFFF040000002701FFFF040000002701FFFF040000002701FFFF0400
00002701FFFF040000002701FFFF030000000000
}\plain\f3\fs22\cf2\protect 
\par \pard\li50\ri2\plain\f3\fs22\cf2\protect 
\par \pard\ri4\plain\f4\fs28\cf0 Im \'dcbungstool m\'fcssen wir also die Liste 
\par 
\par \plain\f3\fs24\cf2\b "[5,1234560,
\par [[1, 8, 3], 
\par 1, 2, 2, 0, 2, 0, 0, 1, 2, 0, 1, 0, 1, 0, 1, 1, 2, 0, 0, 1]]"\plain\f3\fs24\cf3\b 
\par \plain\f4\fs28\cf0 
\par abgeben.  
\par 
\par Um Ihnen Gelegenheit zu geben Ihr Ergebnis vorher zu \'fcberpr\'fcfen, habe ich 
\par Ihnen wieder eine \plain\f4\fs28\cf0\i Probe \plain\f4\fs28\cf0 programmiert. Sie rufen daf\'fcr einfach auf:
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs24\cf3 {\pntext\f1\'b7\tab}probe("[5, 1234560,
\par \pard\li600\ri1\fi-300\plain\f3\fs24\cf3 [[1, 8, 3], 
\par 1, 2, 2, 0, 2, 0, 0, 1, 2, 0, 1, 0, 1, 0, 1, 1, 2, 0, 0, 1]]"
\par )
\par \pard\li50\ri6\plain\f3\fs22\cf2\protect    {\pict\wmetafile8\picw999\pich816\picscalex98\picscaley98\picwgoal572\pichgoal467
0100090000031C01000005001C0000000000050000000B0200000000050000000C023003E70303
0000001E00050000000C023903F203050000000B0200000000030000001E00050000000C023B03
F403050000000B0200000000050000000B0200000000030000001E00030000001E00050000000C
02D5013E02050000000B0200000000050000000B0200000000050000000B020000000008000000
FA0200000000000000000000040000002D0100001C000000FB0238FF0000000000009001000000
0100000000417269616C00C57740000000480D0A711643C5771F43C57720C0C777000030000400
00002D01010005000000020101000000050000000102FFFFFF00050000002E0118000000050000
0009020000000004000000080100001C000000FB0210FF00000000000090010000000100000000
54696D6573204E657720526F6D616E001643C5771F43C57720C0C77700003000040000002D0102
000500000009020000FF00070000002105010074003B016400070000002105010072003B01A700
070000002105010075003B01F700070000002105010065003B016F0108000000FA020000000000
0000000000040000002D0103001C000000FB021000070000000000BC0200000000010202225379
7374656D007740000000400D0AF91643C5771F43C57720C0C77700003000040000002D01040004
0000002701FFFF04000000F001000004000000F001010004000000F0010200040000002701FFFF
040000002701FFFF040000002701FFFF030000000000
}\plain\f3\fs22\cf2\protect 
\par \pard\li50\ri2\plain\f3\fs22\cf2\protect 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf3 {\pntext\f1\'b7\tab}probe("[5, 6000000, [[1, 10, 3], 1,0,0,1,0,1,0,0,1,1,1,1,2,1,1,2,1,0,2,1,1,1]]"
\par \pard\li600\ri1\fi-300\plain\f3\fs22\cf3 )
\par \pard\li50\ri6\plain\f3\fs22\cf2\protect Fehler: 
\par \pard\li50\ri2\plain\f3\fs22\cf2\protect Ziffern falsch.
\par    {\pict\wmetafile8\picw352\pich352\picwgoal199\pichgoal199
010009000003AB00000004001C0000000000050000000B0200000000050000000C026001600103
0000001E00030000001E00050000000C02C800C800050000000B020000000008000000FA020000
0000000000000000040000002D0100001C000000FB0238FF000000000000900100000001000000
00417269616C00C577400000003E0D0A4B1643C5771F43C57720C0C77700003000040000002D01
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000000130D0A4A1643C5771F43C57720C0C77700003000040000002D010300040000002701FFFF
04000000F001000004000000F0010100040000002701FFFF030000000000
}\plain\f3\fs22\cf2\protect 
\par 
\par \pard\ri4\plain\f3\fs22\cf2 
\par   
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf3 {\pntext\f1\'b7\tab}floor(x*3^y) - 3* floor(x*3^(y-1)) $ y=-og..(-og+50)
\par \pard\li600\ri1\fi-300\plain\f3\fs22\cf3 
\par \pard\li50\ri6\plain\f3\fs22\cf2\protect    {\pict\wmetafile8\picw27066\pich873\picscalex99\picscaley99\picwgoal15345\pichgoal495
0100090000030506000006001C0000000000050000000B0200000000050000000C026903BA6903
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00000C02F001F23B050000000B0200000000050000000B020000000008000000FA020000000000
0000000000040000002D0100001C000000FB0238FF000000000000900100000001000000004172
69616C00C57740000000400D0AFC1643C5771F43C57720C0C77700003000040000002D01010005
000000020101000000050000000102FFFFFF00050000002E011800000005000000090200000000
04000000080100001C000000FB0210FF0000000000009001000000010000000054696D6573204E
657720526F6D616E001643C5771F43C57720C0C77700003000040000002D0102001C000000FB02
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0034005601163B08000000FA0200000000000000000000040000002D0104001C000000FB021000
070000000000BC02000000000102022253797374656D007740000000F00C0AEB1643C5771F43C5
7720C0C77700003000040000002D010500040000002701FFFF04000000F001000004000000F001
010004000000F001020004000000F0010300040000002701FFFF040000002701FFFF0300000000
00
}\plain\f3\fs22\cf2\protect 
\par \pard\li50\ri2\plain\f3\fs22\cf2\protect 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf3 {\pntext\f1\'b7\tab}floor(x*3^y) - 3* floor(x*3^(y-1)) $ y=-10..11
\par \pard\li50\ri6\plain\f3\fs22\cf2\protect    {\pict\wmetafile8\picw9934\pich873\picscalex99\picscaley99\picwgoal5632\pichgoal495
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0000000000040000002D0100001C000000FB0238FF000000000000900100000001000000004172
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0102000700000021050100300056016101040000002D01030007000000210501002C005601D901
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01020004000000F0010300040000002701FFFF040000002701FFFF030000000000
}\plain\f3\fs22\cf2\protect 
\par \pard\li50\ri2\plain\f3\fs22\cf2\protect 
\par \pard\ri4\plain\f3\fs22\cf2    
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf3 {\pntext\f1\'b7\tab}x:=60000.60000; og:=10
\par \pard\li600\ri1\fi-300\plain\f3\fs22\cf3 
\par \pard\li50\ri6\plain\f3\fs22\cf2\protect    {\pict\wmetafile8\picw1728\pich827\picwgoal979\pichgoal468
0100090000030001000005001C0000000000050000000B0200000000050000000C023B03C00603
0000001E00030000001E00050000000C02D501D403050000000B020000000008000000FA020000
0000000000000000040000002D0100001C000000FB0238FF000000000000900100000001000000
00417269616C00C57740000000F00C0AEE1643C5771F43C57720C0C77700003000040000002D01
010005000000020101000000050000000102FFFFFF00050000002E011800000005000000090200
00000004000000080100001C000000FB0210FF0000000000009001000000010000000054696D65
73204E657720526F6D616E001643C5771F43C57720C0C77700003000040000002D010200050000
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0000000000
}\plain\f3\fs22\cf2\protect 
\par \pard\li50\ri2\plain\f3\fs22\cf2\protect    {\pict\wmetafile8\picw776\pich827\picwgoal439\pichgoal468
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0000000000000000040000002D0100001C000000FB0238FF000000000000900100000001000000
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000102022253797374656D007740000000F00C0AEF1643C5771F43C57720C0C777000030000400
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0000002701FFFF030000000000
}\plain\f3\fs22\cf2\protect 
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf3 {\pntext\f1\'b7\tab}3^10*(0*3^0 +
\par \pard\li600\ri1\fi-300\plain\f3\fs22\cf3       1*3^-1 + 
\par       1*3^-2 + 
\par       2*3^-3 + 
\par       1*3^-4 + 
\par       0*3^-5 + 
\par       1*3^-6 + 
\par       2*3^-7 + 
\par       1*3^-8 + 
\par       0*3^-9 + 
\par       1*3^-10 + 
\par       0*3^-11 + 
\par       2*3^-12 + 
\par       2*3^-13 + 
\par       1*3^-14 + 
\par       1*3^-15 + 
\par       1*3^-16 + 
\par       1*3^-17 + 
\par       2*3^-18 + 
\par       0*3^-19 + 
\par       1*3^-20 + 
\par       2*3^-21 +
\par       0*3^-22 +
\par       1*3^-23 +
\par       0*3^-24 +
\par       1*3^-25 +
\par       2*3^-26 +
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