Setze die folgenden Polynome 0 und die Koordinaten werden sich dir offenbaren.
\(x^{19}-38ix^{18}+108x^{18}-3884ix^{17}+4738x^{17}-\\ 176212ix^{16}+102038x^{16}-\\ 4655924ix^{15}+722120x^{15}-\\ 78508168ix^{14}-18363970x^{14}-\\ 856821804ix^{13}-620693422x^{13}-\\ 5529388772ix^{12}-9385217798x^{12}-\\ 9431509212ix^{11}-88779745113x^{11}+\\ 194056241550ix^{10} -554600410434x^{10}+\\ 2226689035560ix^{9}-2181975901620x^{9} +\\ 12742340556280ix^{8}-3930961370968x^{8}+\\ 44934579784896ix^{7} +8836579140912x^{7}+\\ 95360997465056ix^{6}+81117178220896x^{6} +\\ 89274444422528ix^{5}+253316293245504x^{5}-\\ 88958525620096ix^{4} +433086271827328x^{4}-\\ 368951311836160ix^{3}+392715209018880x^{3} -\\ 442339066649600ix^{2}+118691064652800x^{2}-\\ 233047696896000ix -67579633152000x-\\ 42567782400000i-43382476800000\)
\(x^{15}-29ix^{14}-70x^{14}+1892ix^{13}+1862x^{13}-53210ix^{12}-20590x^{12} +\\ 840558ix^{11}-38664x^{11}-8053516ix^{10}+4063266x^{10}+\\ 45502950ix^{9} -56586918x^{9}-109449614ix^{8}+433227338x^{8}-\\ 387637774ix^{7} -2082567769x^{7}+4459518793ix^{6}+6313338860x^{6}-\\ 18569668098ix^{5} -10833360096x^{5}+44400826424ix^{4}+4772075532x^{4}-\\ 63779758824ix^{3} +19938895712x^{3}+51926963472ix^{2}-43391154096x^{2}-\\ 20029408704ix +35997751872x+2050375680i-11095626240 \)
\(x^{15}+43ix^{14}+74x^{14}+2966ix^{13}+1625x^{13}+81741ix^{12}-4930x^{12} +\\ 1089562ix^{11}-813171x^{11}+5290289ix^{10}-15525598x^{10}-\\ 43018842ix^{9} -142225385x^{9}-829265417ix^{8}-609401950x^{8}-\\ 5487281074ix^{7} +170391374x^{7}-16970072472ix^{6}+14816803604x^{6}-\\ 10060020524ix^{5} +69672876660x^{5}+91444520576ix^{4}+136255845680x^{4}+\\ 269011922712ix^{3} +59215446696x^{3}+261748466640ix^{2}-172539280080x^{2}+\\ 29182258800ix -214723029600x-50409054000i-48937932000 \)
\(x^{20}+60ix^{19}-104x^{19}-5928ix^{18}+3382x^{18}+244188ix^{17}+4016x^{17} -\\ 5237088ix^{16}-3262965x^{16}+52681680ix^{15}+104478696x^{15} +\\ 147203784ix^{14}-1721623524x^{14}-\\ 12203909640ix^{13}+16279912000x^{13} +\\ 181282095696ix^{12}-69077087137x^{12}-\\ 1480685259204ix^{11} -307456248792x^{11}+\\ 6896486747304ix^{10}+6804183000246x^{10} -\\ 10811755268244ix^{9}-49918490974448x^{9}-\\ 80005308497568ix^{8} +206119739753085x^{8}+\\ 639128824541208ix^{7}-449082588539528x^{7} -\\ 2227922742896808ix^{6}+44798963024632x^{6}+\\ 4232797350840576ix^{5} +2752468479110272x^{5}-\\ 3395406408497040ix^{4}-8185209210948984x^{4} -\\ 2443769846859744ix^{3}+11330477104997728x^{3}+\\ 7779079636263648ix^{2} -7209429164740736x^{2}-\\ 5984596476050880ix+781124258940160x +\\ 1406076296664000i+762819459402000\)
Ein Computeralgebra System(CAS) wird zum Lösen empfohlen. z.B. Maxima (gratis), Mathematica, Matlab, etc. Ihr könnte auch rein numerische Pakete verwenden, z.B. Octave (gratis). Zur einfacheren Verwendung zum Herauskopieren in Maxima Syntax:
x^19-38*%i*x^18+108*x^18-3884*%i*x^17+4738*x^17-176212*%i*x^16+102038*x^16 -4655924*%i*x^15+722120*x^15-78508168*%i*x^14-18363970*x^14 -856821804*%i*x^13-620693422*x^13-5529388772*%i*x^12-9385217798*x^12 -9431509212*%i*x^11-88779745113*x^11+194056241550*%i*x^10 -554600410434*x^10+2226689035560*%i*x^9-2181975901620*x^9 +12742340556280*%i*x^8-3930961370968*x^8+44934579784896*%i*x^7 +8836579140912*x^7+95360997465056*%i*x^6+81117178220896*x^6 +89274444422528*%i*x^5+253316293245504*x^5-88958525620096*%i*x^4 +433086271827328*x^4-368951311836160*%i*x^3+392715209018880*x^3 -442339066649600*%i*x^2+118691064652800*x^2-233047696896000*%i*x -67579633152000*x-42567782400000*%i-43382476800000$
x^15-29*%i*x^14-70*x^14+1892*%i*x^13+1862*x^13-53210*%i*x^12-20590*x^12 +840558*%i*x^11-38664*x^11-8053516*%i*x^10+4063266*x^10+45502950*%i*x^9 -56586918*x^9-109449614*%i*x^8+433227338*x^8-387637774*%i*x^7 -2082567769*x^7+4459518793*%i*x^6+6313338860*x^6-18569668098*%i*x^5 -10833360096*x^5+44400826424*%i*x^4+4772075532*x^4-63779758824*%i*x^3 +19938895712*x^3+51926963472*%i*x^2-43391154096*x^2-20029408704*%i*x +35997751872*x+2050375680*%i-11095626240$
x^15+43*%i*x^14+74*x^14+2966*%i*x^13+1625*x^13+81741*%i*x^12-4930*x^12 +1089562*%i*x^11-813171*x^11+5290289*%i*x^10-15525598*x^10-43018842*%i*x^9 -142225385*x^9-829265417*%i*x^8-609401950*x^8-5487281074*%i*x^7 +170391374*x^7-16970072472*%i*x^6+14816803604*x^6-10060020524*%i*x^5 +69672876660*x^5+91444520576*%i*x^4+136255845680*x^4+269011922712*%i*x^3 +59215446696*x^3+261748466640*%i*x^2-172539280080*x^2+29182258800*%i*x -214723029600*x-50409054000*%i-48937932000$
x^20+60*%i*x^19-104*x^19-5928*%i*x^18+3382*x^18+244188*%i*x^17+4016*x^17 -5237088*%i*x^16-3262965*x^16+52681680*%i*x^15+104478696*x^15 +147203784*%i*x^14-1721623524*x^14-12203909640*%i*x^13+16279912000*x^13 +181282095696*%i*x^12-69077087137*x^12-1480685259204*%i*x^11 -307456248792*x^11+6896486747304*%i*x^10+6804183000246*x^10 -10811755268244*%i*x^9-49918490974448*x^9-80005308497568*%i*x^8 +206119739753085*x^8+639128824541208*%i*x^7-449082588539528*x^7 -2227922742896808*%i*x^6+44798963024632*x^6+4232797350840576*%i*x^5 +2752468479110272*x^5-3395406408497040*%i*x^4-8185209210948984*x^4 -2443769846859744*%i*x^3+11330477104997728*x^3+7779079636263648*%i*x^2 -7209429164740736*x^2-5984596476050880*%i*x+781124258940160*x +1406076296664000*%i+762819459402000$
Schreibweise:
- %i ist die imaginäre Einheit
- ^ ist der Potenzierungsoperator
- x ist die Variable
Je nach System, das ihr verwenden wollt, sind kleinere Anpassungen notwendig. z.B. %i durch i zu ersetzen.
Wenn ihr kein CAS-Software zur Verfügung habt, oder eine solche Software nicht installieren wollt, dann könnt Ihr auch ein Online CAS von Mathematica verwenden: http://www.mathe-online.at/Mathematica/
Initialer Inhalt:
- Cachenote
- Logbuch
- Münzen
- Stift