\mnb150<nb><cmd><![CDATA[PRETTYPRINT:=FALSE:
web:=FALSE:



if not web=FALSE then web:=TRUE end:

initialnoweb:=proc()
begin
if  web
then myreturn:=return@webreturn
else
myreturn:=return@lprint
end
end:

initialnoweb():


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:

syntaktisch:=go:

go:=proc(Matrikelnummer, Primzahl) 
  name go;
  local aaa, n, mnr, myset, toolnummer, 
  myfirst,  firstleft, firstright, mystring, mysecond, 
  zwert, i, k, m, 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); 
  m:=n;
  if n=10 then m:=a end;
    if n=11 then m:=b end;
      if n=12 then m:=c end;
        if n=13 then m:=d end;
          if n=14 then m:=e end;
            if n=15 then m:=f end;
              if n=16 then m:=g end;
                if n=17 then m:=h end;
  if not m_isdefined(n) then 
      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; 
  toolnummer:=   text2expr(Matrikelnummer);
  if not (mnr=toolnummer or toolnummer=3000000) and web then 
      mystring:="Fehler: \n";
      mystring:=mystring."Sie können für die Matrikelnummer ".expr2text(mnr)." keine Miniprojekte abgeben.";
      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 Eintraege haben,\n";
      mystring:=mystring."der dritte Eintrag muss eine Liste sein.";
      myreturn(mystring);
  end_if; 
 TRUE,m, mnr
end_proc:




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


m_isdefined(0):=TRUE:
m_isdefined(1):=TRUE:
m_isdefined(2):=TRUE:
m_isdefined(3):=TRUE:
m_isdefined(4):=TRUE:
m_isdefined(5):=TRUE:
m_isdefined(6):=TRUE:
m_isdefined(7):=TRUE:
m_isdefined(8):=TRUE:
m_isdefined(9):=TRUE:
m_isdefined(10):=TRUE:
m_isdefined(11):=TRUE:
m_isdefined(12):=TRUE:
m_isdefined(13):=TRUE:
m_isdefined(14):=TRUE:
m_isdefined(15):=TRUE:
m_isdefined(16):=TRUE:
m_expired(2):=FALSE:
m_expired(3):=FALSE:
m_expired(5):=FALSE:
m_expired(4):=FALSE:
m_expired(6):=FALSE:
m_expired(7):=FALSE:
m_expired(8):=FALSE:
m_expired(9):=FALSE:
m_expired(10):=FALSE:
m_expired(11):=FALSE:
m_expired(12):=FALSE:
m_expired(13):=FALSE:
m_expired(14):=FALSE:
m_expired(15):=FALSE:
m_expired(16):=FALSE:








initialnoweb:=proc()
begin
if  web
then myreturn:=return@webreturn
else
myreturn:=return@lprint
end
end:

initialnoweb():


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:

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



aufgabe_pur:=proc()
local wurzel, zahl, a,b,c, mnr,mnr_org, pol, VZ;
begin
if args(0)>0 then mnr_org:=args(1) else 
if not testtype(Matr_Nr,DOM_INT) then 
myreturn("Matrikelnummer nicht definiert");
return(null()) else 
mnr_org:=Matr_Nr end_if; end_if;
mnr:=mnr_org;
mnr:=mnr*(mnr mod 2)*(mnr mod 3);
wurzel:=((nextprime(mnr) mod nextprime(173)) mod 9)-1;
if testtype(sqrt(wurzel), DOM_INT) then wurzel:=wurzel+1 end;
VZ:=(-1)^((mnr mod nextprime(27)) mod 2);
zahl:=  ((nextprime(mnr*50-2000) mod nextprime(53)) mod 3);
if zahl =0 or zahl=2 then zahl:=3 end;
if mnr_org=1234560 then zahl:=2 end;
a:=  ((nextprime(mnr) mod nextprime(212)) mod 7)+2;
a:=VZ*a;
b:=  ((nextprime(mnr) mod nextprime(94)) mod 5);
b:=-VZ*b;
c:=  ((mnr mod nextprime(56)) mod 9)+1;
c:=VZ*c;
pol:=c*wurzel^2 + b*x*wurzel^2 + a*x^6*zahl^4 + b*x^5*zahl^4 + 
c*x^4*zahl^4 + a*x^2*wurzel^2 - 2*a*x^4*zahl^2*wurzel - 
2*b*x^3*zahl^2*wurzel - 2*c*x^2*zahl^2*wurzel
end:

meine_Aufgabe:=aufgabe_pur:





oldpoly:= proc(ll)
local grad ,i, erg, koff;
begin 
if not testtype(ll,DOM_LIST)
then print(Unquoted,"Eingabe muss liste sein");
return(null())
else
erg:=0:
for i in ll do erg:=erg+op(i,1)*hold(x)^op(i,2) 
end
end
end:



go12:=proc(irgend,eingabe)
local  eing, loes,nullst, pols,anfpol, abl, mnr,ggt, zw1, ls, zw2 ;
begin
eing:=text2expr(eingabe);
nullst:=op(eing,[3,1]);
mnr:=op(eing,2);
pols:=oldpoly(op(eing,[3,2]));
anfpol:=aufgabe_pur(mnr);
abl:=diff(anfpol,x);
ggt:=gcd(anfpol,abl);
zw1:=op(divide(anfpol,pols),2);
zw2:=op(divide(pols,zw1),2);
ls:=eval(subs(anfpol,hold(x)=nullst));
if not ls=0 then 
mystring:="Fehler: Nullstelle falsch.";
myreturn(mystring);
end;
if not zw2=0 then 
mystring:="Fehler: Dies ist nicht der letzte Rest vor dem ggt.";
myreturn(mystring);
end;
TRUE
end:

probe:=proc(eingabe)
local mnr, vv;
begin 
mnr:=text2expr(eingabe);
mnr:=op(mnr,2);
mnr:=expr2text(mnr);
vv:=[go(mnr,eingabe)];
vv:=eval(vv);
if op(vv,1)=TRUE then
go12("12",eingabe)
else 
myreturn("Syntaxprobe negativ");
end
end:

PRETTYPRINT:=FALSE:
web:=FALSE:









initialnoweb:=proc()
begin
if  web
then myreturn:=return@webreturn
else
myreturn:=return@lprint
end
end:

initialnoweb():


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:

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



aufgabe_pur:=proc()
local wurzel, zahl, a,b,c, mnr,mnr_org, pol, VZ;
begin
if args(0)>0 then mnr_org:=args(1) else 
if not testtype(Matr_Nr,DOM_INT) then 
myreturn("Matrikelnummer nicht definiert");
return(null()) else 
mnr_org:=Matr_Nr end_if; end_if;
mnr:=mnr_org;
mnr:=mnr*(mnr mod 2)*(mnr mod 3);
wurzel:=((nextprime(mnr) mod nextprime(173)) mod 9)-1;
if testtype(sqrt(wurzel), DOM_INT) then wurzel:=wurzel+1 end;
VZ:=(-1)^((mnr mod nextprime(27)) mod 2);
zahl:=  ((nextprime(mnr*50-2000) mod nextprime(53)) mod 3);
if zahl =0 or zahl=2 then zahl:=3 end;
if mnr_org=1234560 then zahl:=2 end;
a:=  ((nextprime(mnr) mod nextprime(212)) mod 7)+2;
a:=VZ*a;
b:=  ((nextprime(mnr) mod nextprime(94)) mod 5);
b:=-VZ*b;
c:=  ((mnr mod nextprime(56)) mod 9)+1;
c:=VZ*c;
pol:=c*wurzel^2 + b*x*wurzel^2 + a*x^6*zahl^4 + b*x^5*zahl^4 + 
c*x^4*zahl^4 + a*x^2*wurzel^2 - 2*a*x^4*zahl^2*wurzel - 
2*b*x^3*zahl^2*wurzel - 2*c*x^2*zahl^2*wurzel
end:

meine_Aufgabe:=aufgabe_pur:





oldpoly:= proc(ll)
local grad ,i, erg, koff;
begin 
if not testtype(ll,DOM_LIST)
then print(Unquoted,"Eingabe muss liste sein");
return(null())
else
erg:=0:
for i in ll do erg:=erg+op(i,1)*hold(x)^op(i,2) 
end
end
end:



go12:=proc(irgend,eingabe)
local  eing, loes,nullst, pols,anfpol, abl, mnr,ggt, zw1, ls, zw2 ;
begin
eing:=text2expr(eingabe);
nullst:=op(eing,[3,1]);
mnr:=op(eing,2);
pols:=oldpoly(op(eing,[3,2]));
anfpol:=aufgabe_pur(mnr);
abl:=diff(anfpol,x);
ggt:=gcd(anfpol,abl);
zw1:=op(divide(anfpol,pols),2);
zw2:=op(divide(pols,zw1),2);
ls:=eval(subs(anfpol,hold(x)=nullst));
if not ls=0 then 
mystring:="Fehler: Nullstelle falsch.";
myreturn(mystring);
end;
if not zw2=0 then 
mystring:="Fehler: Dies ist nicht der letzte Rest vor dem ggt.";
myreturn(mystring);
end;
TRUE
end:

probe:=proc(eingabe)
local mnr, vv;
begin 
mnr:=text2expr(eingabe);
mnr:=op(mnr,2);
mnr:=expr2text(mnr);
vv:=[go(mnr,eingabe)];
vv:=eval(vv);
if op(vv,1)=TRUE then
go12("12",eingabe)
else 
myreturn("Syntaxprobe negativ");
end
end:

meine_Loesung:=proc(mnr)
local p0, p1, p2, p3;
begin
Matr_Nr:=mnr;
p0:=meine_Aufgabe();
p1:=diff(p0,x);
repeat
p3:=p0;
p2:=p1;
p1:=divide(p0,p1,Rem);
p0:=p2
until p1=0 end_repeat;
if testtype(op(op(p2,2)/-coeff(p2,2),1),DOM_INT) then p2:=sqrt(op(p2,2)/-coeff(p2,2))
else p2:=op(solve(p2,x),1)
end_if;
p3:=p3/lcoeff(p3);
mystring:=_concat("[12, ",Matr_Nr,", [",coerce(p2,DOM_STRING),", ",coerce(poly2list(p3), DOM_STRING),"]]")
end:]]></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\green128\blue0;\red255\green0\blue0;\red0\green0\blue255;}
\deflang1031\pard\ri4\plain\f3\fs40\cf1\b Miniprojekt 12: 
\par \plain\f4\fs44\cf1\b       Euklidischer Algorithmus f\'fcr Polynome\plain\f4\fs28\cf0 
\par 
\par Beachten Sie bitte die Drills zu diesem Thema. Beachten Sie weiterhin,
\par dass was in der zweiten Version des drill \'fcber Normalisierung steht. 
\par 
\par \plain\f4\fs32\cf1\b Aufgabe:
\par \plain\f4\fs28\cf0 In dem folgenden Feld sollen sie wieder die Matrikelnummer 1234560 
\par durch Ihre eigene ersetzen. Dann erhalten Sie durch Aktivierung ein
\par Polynom P(x), f\'fcr welches Sie  den ggt(P(x),P\'b4(x)) mit seiner Ableitung 
\par P\'b4(x) bestimmen sollen. Daf\'fcr verwenden sie den Euklidischen 
\par Algorithmus. 
\par 
\par Wie wir aus dem entsprechenden Drill wissen, l\'e4sst sich dann das Polynom 
\par P(x) durch das Quadrat des ggt(P(x),P\'b4(x)) teilen. In Ihrem Falle wird 
\par nach dieser Division sicher ein Polynom zweiten Grades \'fcberbleiben,
\par und Sie werden feststellen, dass auch Ihr ggt(P(x),P\'b4(x))  zweiten Grades ist.
\par 
\par Von diesen beiden Polynomen k\'f6nnen Sie die Nullstellen bestimmen
\par und haben dann alle Nullstellen Ihres Ausgangspolynoms. Wenn Sie es nicht
\par glauben, dann probieren sie es einfach aus. 
\par 
\par Hier nun Ihr Polynom:
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf0 {\pntext\f1\'b7\tab}  \plain\f3\fs24\cf2 Matr_Nr:=1234560:
\par \pard\li600\ri1\fi-300\plain\f3\fs24\cf2  meine_Aufgabe();
\par \pard\li50\ri6\plain\f3\fs24\cf3\protect    {\pict\wmetafile8\picw8701\pich993\picscalex99\picscaley99\picwgoal4933\pichgoal563
010009000003EB02000008001C0000000000050000000B0200000000050000000C02E103FD2103
0000001E00050000000C02E203FF21050000000B0200000000030000001E00030000001E000500
00000C0234024613050000000B0200000000050000000B020000000008000000FA020000000000
0000000000040000002D0100001C000000FB0238FF000000000000900100000001000000004172
69616C00C5774000000036080A971643C5771F43C57720C0C77700003000040000002D01010005
000000020101000000050000000102FFFFFF00050000002E011800000005000000090200000000
04000000080100001C000000FB02E8FE0000000000009001000000010000000054696D6573204E
657720526F6D616E001643C5771F43C57720C0C77700003000040000002D0102001C000000FB02
E8FE0000000000009001010000010000000054696D6573204E657720526F6D616E001643C5771F
43C57720C0C77700003000040000002D0103001C000000FB02E8FE000000000000900100000002
0000000053796D626F6C00774000000068070A011643C5771F43C57720C0C77700003000040000
002D010400040000002D010200040000002D0103001C000000FB023AFF00000000000090010000
00010000000054696D6573204E657720526F6D616E001643C5771F43C57720C0C7770000300004
0000002D010500040000002D010400040000002D010200040000002D010300040000002D010500
040000002D010400040000002D010200040000002D010300040000002D010500040000002D0104
00040000002D010200040000002D010300040000002D010500040000002D010400040000002D01
0200040000002D0104000500000009020000FF0007000000210501002D0092016400040000002D
0102000700000021050100380092010C01040000002D0104000700000021050100D7009201C201
040000002D0103000700000021050100780092013C02040000002D01040007000000210501002B
009201F002040000002D010200070000002105010033009201C203070000002105010032009201
4E04040000002D0104000700000021050100D70092010405040000002D010200040000002D0105
00040000002D0103000700000021050100780092017E05040000002D0105000700000021050100
33001501FA05040000002D01040007000000210501002D0092019506040000002D010200070000
0021050100340092016707070000002105010038009201F307040000002D010400070000002105
0100D7009201A908040000002D010200040000002D010500040000002D01030007000000210501
00780092012309040000002D0105000700000021050100340015019F09040000002D0104000700
0000210501002D0092013A0A040000002D0102000700000021050100330092010C0B0700000021
05010032009201980B040000002D0104000700000021050100D70092014E0C040000002D010200
040000002D010500040000002D010300070000002105010078009201C80C040000002D01050007
0000002105010035001501440D040000002D01040007000000210501002B009201DF0D04000000
2D010200070000002105010036009201B10E0700000021050100340092013D0F040000002D0104
000700000021050100D7009201F30F040000002D010200040000002D010500040000002D010300
0700000021050100780092016D10040000002D010500070000002105010036001501E910040000
002D01040007000000210501002B0092018411040000002D010200070000002105010034009201
561208000000FA0200000000000000000000040000002D0106001C000000FB0210000700000000
00BC02000000000102022253797374656D007740000000D2090A3F1643C5771F43C57720C0C777
00003000040000002D010700040000002701FFFF04000000F001000004000000F0010100040000
00F001020004000000F001030004000000F001040004000000F0010500040000002701FFFF0400
00002701FFFF030000000000
}\plain\f3\fs24\cf3\protect 
\par \pard\li50\ri2\plain\f3\fs24\cf3\protect 
\par \pard\ri4\plain\f4\fs28\cf0 Sie sollen daf\'fcr den oben beschriebenen Rechnungsgang durchgehen. 
\par Abgeben sollen Sie folgende Daten:
\par 1. wie \'fcblich Miniprojektnummer und Matrikelnummer
\par 2. den letzten Rest bevor Sie den Rest erhalten, der Ihnen den ggt gibt,
\par 3. eine Nullstelle der Art  Zahl + Wurzel aus Zahl
\par 
\par Die Daten m\'fcssen besonders kodiert werden: 
\par a. die Nullstelle in der Form \plain\f3\fs28\cf3 n+sqrt(m)\plain\f4\fs28\cf0  wobei das Vorzeichen wichtig ist,
\par     und sqrt f\'fcr die Wurzeloperation steht. 
\par b. Das durch den verlangten Rest gegebene Polynom in der Form  
\par     \plain\f4\fs28\cf3 [[z1,n1], [z2,n2], [z3,n3], ... [zk,nk]]\plain\f4\fs28\cf0  , wobei die Terme \plain\f4\fs28\cf3 [zk,nk]
\par \plain\f4\fs28\cf0     f\'fcr folgende Summanden stehen
\par 
\par \pard\li50\ri6\plain\f3\fs24\cf3    {\pict\wmetafile8\picw1591\pich931\picscalex99\picscaley99\picwgoal911\pichgoal532
0100090000034C02000008001C0000000000050000000B0200000000050000000C02A303370603
0000001E00050000000C02AB034706050000000B0200000000030000001E00050000000C02B703
4A06050000000B0200000000050000000B0200000000030000001E00050000000C02C1035A0605
0000000B0200000000050000000B0200000000050000000B0200000000030000001E0005000000
0C02CD036D06050000000B0200000000050000000B0200000000050000000B0200000000050000
000B0200000000030000001E00050000000C02E1038F06050000000B0200000000050000000B02
00000000050000000B0200000000050000000B0200000000050000000B0200000000030000001E
00050000000C02E2039006050000000B0200000000050000000B0200000000050000000B020000
0000050000000B0200000000050000000B0200000000050000000B0200000000030000001E0003
0000001E00050000000C023402B903050000000B0200000000050000000B020000000005000000
0B0200000000050000000B0200000000050000000B0200000000050000000B0200000000050000
000B020000000008000000FA0200000000000000000000040000002D0100001C000000FB0238FF
00000000000090010000000100000000417269616C00C577400000008C070AA81643C5771F43C5
7720C0C77700003000040000002D01010005000000020101000000050000000102FFFFFF000500
00002E01180000000500000009020000000004000000080100001C000000FB02E8FE0000000000
009001000000010000000054696D6573204E657720526F6D616E001643C5771F43C57720C0C777
00003000040000002D0102001C000000FB02E8FE0000000000009001010000010000000054696D
6573204E657720526F6D616E001643C5771F43C57720C0C77700003000040000002D0103001C00
0000FB023AFF0000000000009001000000010000000054696D6573204E657720526F6D616E0016
43C5771F43C57720C0C77700003000040000002D0104001C000000FB02E8FE0000000000009001
000000020000000053796D626F6C00774000000082050A491643C5771F43C57720C0C777000030
00040000002D0105000500000009020000FF00040000002D01020007000000210501007A009201
640007000000210501006B009201E000040000002D0105000700000021050100D7009201980104
0000002D010200040000002D010400040000002D01030007000000210501007800920112020400
00002D01040007000000210501006E0015018E0207000000210501006B001501F10208000000FA
0200000000000000000000040000002D0106001C000000FB021000070000000000BC0200000000
0102022253797374656D00774000000036080A981643C5771F43C57720C0C77700003000040000
002D010700040000002701FFFF04000000F001000004000000F001010004000000F00102000400
0000F001030004000000F001040004000000F0010500040000002701FFFF040000002701FFFF04
0000002701FFFF040000002701FFFF040000002701FFFF040000002701FFFF040000002701FFFF
030000000000
}\plain\f3\fs24\cf3 
\par \pard\li50\ri2\plain\f3\fs24\cf3 
\par \pard\ri4\plain\f4\fs28\cf0 Das oben stehende Polynom hat also die Form:
\par 
\par \pard\li50\ri6\plain\f3\fs24\cf3    {\pict\wmetafile8\picw10518\pich914\picscalex98\picscaley99\picwgoal6023\pichgoal519
0100090000032604000007001C0000000000050000000B0200000000050000000C029203162903
0000001E00050000000C0295038129050000000B0200000000030000001E00050000000C029E03
EF29050000000B0200000000050000000B0200000000030000001E00050000000C02A9035C2A05
0000000B0200000000050000000B0200000000050000000B0200000000030000001E0005000000
0C02B303CD2A050000000B0200000000050000000B0200000000050000000B0200000000050000
000B0200000000030000001E00050000000C02BD033C2B050000000B0200000000050000000B02
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}\plain\f3\fs24\cf3 
\par \pard\li50\ri2\plain\f3\fs24\cf3 
\par \pard\ri4\plain\f4\fs28\cf0 Wenn Sie pr\'fcfen wollen ob Sie Ihr Polynom richtig in dieser form geschrieben 
\par haben, dann k\'f6nnen Sie die folgende Funktion anwenden, sie muss Ihnen Ihr 
\par Ausgangspolynom geben: 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf0 {\pntext\f1\'b7\tab}    \plain\f3\fs24\cf2 oldpoly([[-8,1], [32,3], [-48,4],[-32,5], [64,6],[4,0]])
\par \pard\li600\ri1\fi-300\plain\f3\fs24\cf2 
\par \pard\li50\ri6\plain\f3\fs24\cf3\protect    {\pict\wmetafile8\picw8701\pich993\picscalex99\picscaley99\picwgoal4933\pichgoal563
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}\plain\f3\fs24\cf3\protect 
\par \pard\li50\ri2\plain\f3\fs24\cf3\protect 
\par \pard\ri4\plain\f4\fs28\cf0 Wir gehen jetzt die Rechnung f\'fcr die Beispielesmatrikelnummer 1234560 durch: 
\par Das Polynom und seine Ableitung sind
\par 
\par \pard\li50\ri6\plain\f3\fs24\cf3\protect    {\pict\wmetafile8\picw9344\pich971\picscalex98\picscaley98\picwgoal5352\pichgoal557
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}\plain\f3\fs24\cf3\protect 
\par \pard\li50\ri2\plain\f3\fs24\cf3\protect    {\pict\wmetafile8\picw8624\pich971\picscalex98\picscaley98\picwgoal4940\pichgoal557
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}\plain\f3\fs24\cf3\protect 
\par 
\par \pard\ri4\plain\f4\fs28\cf0 Der Euklidische Algorithmus liefert:
\par \pard\li50\ri6\plain\f3\fs24\cf3    {\pict\wmetafile8\picw5886\pich1024\picscalex98\picscaley99\picwgoal3371\pichgoal586
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\par \pard\li50\ri2\plain\f3\fs24\cf3 
\par    {\pict\wmetafile8\picw17975\pich1235\picscalex98\picscaley99\picwgoal10294\pichgoal706
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\par 
\par \pard\ri4\plain\f4\fs28\cf0 Der Rest vor dem ggt ist also: 
\par 
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\par \pard\li50\ri2\plain\f3\fs24\cf3 
\par \pard\ri4\plain\f4\fs28\cf0 Die f\'fcr die Abgabe vorgeschriebene Form ist dann
\par 
\par \pard\li50\ri6\plain\f3\fs24\cf3 [[26/55, 2], [-1/2, 1], [1, 3], [-13/55, 0]]
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0000002D010300040000002701FFFF04000000F001000004000000F0010100040000002701FFFF
040000002701FFFF040000002701FFFF040000002701FFFF040000002701FFFF040000002701FF
FF040000002701FFFF030000000000
}\plain\f3\fs24\cf3 
\par 
\par \pard\ri4\plain\f4\fs28\cf0 
\par 
\par Und eine L\'f6sung des Polynoms von der vorgeschriebenen Form erhalten 
\par wir durch die Nullstellen des ggt:
\par \pard\li50\ri6\plain\f3\fs24\cf3    {\pict\wmetafile8\picw2096\pich1548\picscalex98\picscaley98\picwgoal1200\pichgoal886
010009000003A302000009001C0000000000050000000B0200000000050000000C020C06300803
0000001E00050000000C021C064608050000000B0200000000030000001E00050000000C022E06
5D08050000000B0200000000050000000B0200000000030000001E00050000000C023E06730805
0000000B0200000000050000000B0200000000050000000B0200000000030000001E0005000000
0C0250068B08050000000B0200000000050000000B0200000000050000000B0200000000050000
000B0200000000030000001E00050000000C026106A308050000000B0200000000050000000B02
00000000050000000B0200000000050000000B0200000000050000000B0200000000030000001E
00050000000C026306A508050000000B0200000000050000000B0200000000050000000B020000
0000050000000B0200000000050000000B0200000000050000000B0200000000030000001E0003
0000001E00050000000C029F03E704050000000B0200000000050000000B020000000005000000
0B0200000000050000000B0200000000050000000B0200000000050000000B0200000000050000
000B020000000008000000FA0200000000000000000000040000002D0100001C000000FB0238FF
00000000000090010000000100000000417269616C00C57740000000F3050A031643C5771F43C5
7720C0C77700003000040000002D01010005000000020101000000050000000102FFFFFF000500
00002E01180000000500000009020000000004000000080100001C000000FB02E8FE0000000000
009001000000010000000054696D6573204E657720526F6D616E001643C5771F43C57720C0C777
00003000040000002D0102001C000000FB02E8FE0000000000009001010000010000000054696D
6573204E657720526F6D616E001643C5771F43C57720C0C77700003000040000002D0103001C00
0000FB023AFF0000000000009001000000010000000054696D6573204E657720526F6D616E0016
43C5771F43C57720C0C77700003000040000002D010400040000002D0102001C000000FB02E8FE
000000000000900100000001000000005346204D617468204578740068050A301643C5771F43C5
7720C0C77700003000040000002D010500040000002D0102001C000000FB02E8FE000000000000
9001000000020000000053796D626F6C0077400000008D090A591643C5771F43C57720C0C77700
003000040000002D010600040000002D0102000500000009020000FF00040000002D0103000700
000021050100780047026E00040000002D01040007000000210501003000BA02EA00040000002D
01060007000000210501003D0047029301040000002D010200040000002D010500070000002105
010070008C009B020700000021050100C5008C00B303040000002D010200070000002105010032
009201B30307000000210501003200FE023503040000002D0105000700000021050100C500F001
73020700000021050100C500F0011B030700000021050100C500F001C3030700000021050100C5
00F001DB0308000000FA0200000000000000000000040000002D0107001C000000FB0210000700
00000000BC02000000000102022253797374656D00774000000068070A171643C5771F43C57720
C0C77700003000040000002D010800040000002701FFFF04000000F001000004000000F0010100
04000000F001020004000000F001030004000000F001040004000000F001050004000000F00106
00040000002701FFFF040000002701FFFF040000002701FFFF040000002701FFFF040000002701
FFFF040000002701FFFF040000002701FFFF030000000000
}\plain\f3\fs24\cf3 
\par \pard\li50\ri2\plain\f3\fs24\cf3 
\par \pard\ri4\plain\f4\fs28\cf0 Wir m\'fcssen also abgeben 
\par 
\par \plain\f3\fs24\cf3 "[12,1234560, [sqrt(1/2), [[26/55, 2], 
\par    [-1/2, 1], [1, 3], [-13/55, 0]]]]"
\par    {\pict\wmetafile8\picw351\pich351\picscalex99\picscaley99\picwgoal199\pichgoal199
010009000003C100000004001C0000000000050000000B0200000000050000000C025F015F0103
0000001E00050000000C0260016001050000000B0200000000030000001E00030000001E000500
00000C02C800C800050000000B0200000000050000000B020000000008000000FA020000000000
0000000000040000002D0100001C000000FB0238FF000000000000900100000001000000004172
69616C00C577400000008C070ABD1643C5771F43C57720C0C77700003000040000002D01010005
000000020101000000050000000102FFFFFF00050000002E011800000005000000090200000000
04000000080100000500000009020000FF0008000000FA0200000000000000000000040000002D
0102001C000000FB021000070000000000BC02000000000102022253797374656D007740000000
8D090A5A1643C5771F43C57720C0C77700003000040000002D010300040000002701FFFF040000
00F001000004000000F0010100040000002701FFFF040000002701FFFF030000000000
}\plain\f3\fs24\cf3 
\par 
\par \plain\f4\fs28\cf0 Wie so h\'e4ufig bieten wir eine Probe an
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs24\cf2 {\pntext\f1\'b7\tab}probe("[12,1234560, [sqrt(1/2), [[26/55, 2], 
\par \pard\li600\ri1\fi-300\plain\f3\fs24\cf2 [-1/2, 1], [1, 3], [-13/55, 0]]]]")
\par 
\par \pard\li50\ri6\plain\f3\fs24\cf3\protect    {\pict\wmetafile8\picw1118\pich899\picscalex99\picscaley99\picwgoal634\pichgoal510
0100090000030101000005001C0000000000050000000B0200000000050000000C0283035E0403
0000001E00050000000C0285036004050000000B0200000000030000001E00030000001E000500
00000C02FF017B02050000000B0200000000050000000B020000000008000000FA020000000000
0000000000040000002D0100001C000000FB0238FF000000000000900100000001000000004172
69616C00C5774000000068070A1A1643C5771F43C57720C0C77700003000040000002D01010005
000000020101000000050000000102FFFFFF00050000002E011800000005000000090200000000
04000000080100001C000000FB02E8FE0000000000009001000000010000000054696D6573204E
657720526F6D616E001643C5771F43C57720C0C77700003000040000002D010200050000000902
0000FF00070000002105010074005E016400070000002105010072005E01B20007000000210501
0075005E010F01070000002105010065005E019B0108000000FA02000000000000000000000400
00002D0103001C000000FB021000070000000000BC02000000000102022253797374656D007740
00000068050A311643C5771F43C57720C0C77700003000040000002D010400040000002701FFFF
04000000F001000004000000F001010004000000F0010200040000002701FFFF040000002701FF
FF030000000000
}\plain\f3\fs24\cf3\protect 
\par \pard\li50\ri2\plain\f3\fs24\cf3\protect 
\par \pard\ri4\plain\f4\fs28\cf0 Sie sollten nat\'fcrlich etwas mehr tun, als f\'fcr die Abgabe verlangt,
\par Sie sollten nun noch wenigstens alle Nullstellen des Polynoms 
\par ausrechnen. 
\par 
\par Ich hab diese Version des Miniprojekts nochmal \'fcberarbeitet und habe
\par eine weitere Funktion hinzugef\'fcgt. Diese gibt direkt das Ergebnis aus, da\'df
\par Sie dann nur noch in das Abgabetool kopieren m\'fcssen.
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs24\cf2 {\pntext\f1\'b7\tab}meine_Loesung(1234560);
\par \pard\li50\ri6\plain\f3\fs22\cf3\protect    {\pict\wmetafile8\picw12885\pich874\picwgoal7304\pichgoal495
010009000003A705000007001C0000000000050000000B0200000000050000000C026A03553203
0000001E00030000001E00050000000C02F001891C050000000B020000000008000000FA020000
0000000000000000040000002D0100001C000000FB0238FF000000000000900100000001000000
00417269616C00C577400000008D090A5D1643C5771F43C57720C0C77700003000040000002D01
010005000000020101000000050000000102FFFFFF00050000002E011800000005000000090200
00000004000000080100001C000000FB0210FF000000000000900100000001000000005346204D
61746820457874008C070ABF1643C5771F43C57720C0C77700003000040000002D0102001C0000
00FB0210FF0000000000009001000000010000000054696D6573204E657720526F6D616E001643
C5771F43C57720C0C77700003000040000002D0103001C000000FB0210FF000000000000900100
0000020000000053796D626F6C007740000000D2090A551643C5771F43C57720C0C77700003000
040000002D010400040000002D010300040000002D010400040000002D010300040000002D0102
00040000002D010300040000002D010200040000002D010300040000002D010400040000002D01
0300040000002D010200040000002D010300040000002D010200040000002D010300040000002D
010200040000002D010400040000002D010300040000002D010200040000002D01030004000000
2D010400040000002D010300040000002D010200040000002D010400040000002D010300040000
002D010200040000002D010300040000002D010200040000002D010300040000002D0104000400
00002D010300040000002D010200040000002D010400040000002D010300040000002D01020004
0000002D010400040000002D010300040000002D010200040000002D010300040000002D010400
040000002D010300040000002D010200040000002D010400040000002D010300040000002D0102
00040000002D010400040000002D010300040000002D010200040000002D010300040000002D01
0400040000002D010300040000002D010200040000002D010300040000002D010200040000002D
010300040000002D010400040000002D010300040000002D010400040000002D01030004000000
2D010200040000002D010300040000002D010200040000002D010300040000002D010400040000
002D010300040000002D010200040000002D010300040000002D010200040000002D0103000400
00002D010200040000002D010400040000002D010300040000002D010200040000002D01030004
0000002D010400040000002D010300040000002D010200040000002D010400040000002D010300
040000002D010200040000002D010300040000002D010200040000002D010300040000002D0104
00040000002D010300040000002D010200040000002D010400040000002D010300040000002D01
0200040000002D010400040000002D010300040000002D010200040000002D010300040000002D
010400040000002D010300040000002D010200040000002D010400040000002D01030004000000
2D010200040000002D010400040000002D010300040000002D010200040000002D010300040000
002D010400040000002D010300040000002D0102000500000009020000FF00040000002D010300
0700000021050100220056016400040000002D01020007000000210501005B005601C600040000
002D01030007000000210501003100560109010700000021050100320056018101040000002D01
040007000000210501002C005601F901040000002D010300070000002105010020005601360207
00000021050100310056017202070000002105010032005601EA02070000002105010033005601
6203070000002105010034005601DA030700000021050100350056015204070000002105010036
005601CA040700000021050100300056014205040000002D01040007000000210501002C005601
BA05040000002D010300070000002105010020005601F705040000002D01020007000000210501
005B0056013306040000002D0103000700000021050100310056017606040000002D0102000700
0000210501002F005601EE06040000002D0103000700000021050100320056016607040000002D
01040007000000210501002A005601DE07040000002D0103000700000021050100320056015408
07000000210501005E005601CC08040000002D0102000700000021050100280056013D09040000
002D0103000700000021050100310056019A09040000002D01020007000000210501002F005601
120A040000002D0103000700000021050100320056018A0A040000002D01020007000000210501
0029005601020B040000002D01040007000000210501002C0056015F0B040000002D0103000700
000021050100200056019C0B040000002D01020007000000210501005B005601D80B0700000021
0501005B0056011B0C040000002D0103000700000021050100310056015E0C040000002D010400
07000000210501002C005601D60C040000002D010300070000002105010020005601130D070000
0021050100330056014F0D040000002D01020007000000210501005D005601C70D040000002D01
040007000000210501002C0056010A0E040000002D010300070000002105010020005601470E04
0000002D01020007000000210501005B005601830E040000002D01030007000000210501003200
5601C60E0700000021050100360056013E0F040000002D01020007000000210501002F005601B6
0F040000002D0103000700000021050100350056012E10070000002105010035005601A6100400
00002D01040007000000210501002C0056011E11040000002D0103000700000021050100200056
015B110700000021050100320056019711040000002D01020007000000210501005D0056010F12
040000002D01040007000000210501002C0056015212040000002D010300070000002105010020
0056018F12040000002D01020007000000210501005B005601CB12040000002D01040007000000
210501002D0056010E13040000002D0103000700000021050100310056019213040000002D0102
0007000000210501002F0056010A14040000002D01030007000000210501003200560182140400
00002D01040007000000210501002C005601FA14040000002D0103000700000021050100200056
0137150700000021050100310056017315040000002D01020007000000210501005D005601EB15
040000002D01040007000000210501002C0056012E16040000002D010300070000002105010020
0056016B16040000002D01020007000000210501005B005601A716040000002D01040007000000
210501002D005601EA16040000002D0103000700000021050100310056016E1707000000210501
0033005601E617040000002D01020007000000210501002F0056015E18040000002D0103000700
00002105010035005601D6180700000021050100350056014E19040000002D0104000700000021
0501002C005601C619040000002D010300070000002105010020005601031A0700000021050100
300056013F1A040000002D01020007000000210501005D005601B71A07000000210501005D0056
01FA1A07000000210501005D0056013D1B07000000210501005D005601801B040000002D010300
070000002105010022005601C31B08000000FA0200000000000000000000040000002D0105001C
000000FB021000070000000000BC02000000000102022253797374656D00774000000036080AAE
1643C5771F43C57720C0C77700003000040000002D010600040000002701FFFF04000000F00100
0004000000F001010004000000F001020004000000F001030004000000F0010400040000002701
FFFF030000000000
}\plain\f3\fs22\cf3\protect 
\par \pard\li50\ri2\plain\f3\fs22\cf3\protect 
\par \pard\ri4\plain\f4\fs28\cf0 Wie Sie sehen erhalten wir das gleiche Ergebnis, da\'df wir oben so m\'fchsam
\par berechnet haben. Viel Spa\'df mit dieser neuen Funktion w\'fcnscht
\par -Syne
\par 
\par }