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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 119 "Hier geht es nur darum, e
in Beispiel aus dem Buch \"Algebraische Algorithmen\" von Attila Peth
\366 (Vieweg 1999) umzusetzen." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 16 "An dem  Polynom " }{XPPEDIT 18 0 "x^1155-
1;" "6#,&*$%\"xG\"%b6\"\"\"F'!\"\"" }{TEXT -1 57 "  mit vielen Primtei
lern wird demonstriert, dass moderne " }{TEXT 257 11 "polynomiale" }
{TEXT -1 80 " Primfaktorzerlegung schneller sein kann als das Ausmulti
plizieren der Faktoren." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "r
estart:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "t:=time():" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 17 "factor(x^1155-1);" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "t:=time()-t;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 134 "Mit Copy/Paste k\366nne
n wir die Ausgabe in eine Maple-Eingabezeile kopieren, dann haben wir \+
das komplette Produkt der Primfaktoren von  " }{XPPEDIT 18 0 "x^1155-1
;" "6#,&*$%\"xG\"%b6\"\"\"F'!\"\"" }{TEXT -1 368 "  vorliegen und k
\366nnen nun von Maple verlangen, das Produkt zu entwickeln (Maple gib
t die Primteiler nicht unbedingt jedesmal in derselben Reihenfolge an,
 deswegen kann das folgende Produkt anders aussehen, als die obige Aus
gabe, die Sie neu berechnet haben. Wenn Sei misstrauisch sind, l\366sc
hen Sie das folgende Argument von expand und kopieren Sie es erneut vo
n oben." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4555 "s:=time():expand((x-1)
*(1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x)*(1+x^6+x^5+x^4+x^3+x^2+x)*
(1-x+x^7-x^8+x^60+x^11+x^28+x^21+x^14+x^53-x^59+x^46+x^49-x^52-x^48+x^
39+x^42-x^45-x^41+x^32+x^35-x^37-x^34+x^25-x^26+x^18-x^23-x^19-x^15-x^
12-x^30)*(1+x^4+x^3+x^2+x)*(1-x+x^5-x^6+x^10-x^12+x^15-x^17+x^20-x^23+
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2-x^13+x^14-x^16+x^17-x^18+x^19-x^23+x^24)*(1+x+2*x^110+2*x^55+x^77-x^
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69+x^164+x^165+2*x^166-x^158-x^159+x^163-2*x^155-2*x^156-x^157-x^152-x
^153-x^154+x^148+x^149+x^150+x^145+x^146+x^147-2*x^139-x^140+x^144-x^1
36-x^137-x^138-x^47+2*x^132+x^133+x^134+2*x^129+2*x^130+2*x^131+x^126+
x^127+2*x^128-2*x^122-2*x^123-x^124-3*x^119-3*x^121-x^116-2*x^117-2*x^
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3-x^104+x^96-x^100-2*x^101+x^93+x^94+x^95+x^90+x^91+x^92+x^238+x^239-x
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-x^7-x^9-x^10-x^8+x^22-2*x^11+x^21-x^14+x^53+x^59-2*x^46-x^49-x^48+x^3
9-x^42-x^45+x^35+x^37+x^18+x^19-x^15-x^12+x^20+x^36)*(1+x^2+x)*(1-x+x^
3-x^4+x^6-x^7+x^9-x^10+x^11-x^13+x^14-x^16+x^17-x^19+x^20)*(1-x+x^3-x^
4+x^6-x^8+x^9-x^11+x^12)*(1+x-x^70+x^77-x^88+x^85+x^81-x^74-x^75-x^71+
x^68+x^64+x^56-x^50+x^120+x^119+x^118-x^112-x^113-x^109-x^111-x^107-x^
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x^9-x^29-x^8+x^60+x^22-x^11-x^28+x^21-x^46-x^49+x^52+x^39-x^45-x^32+x^
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22-x^28+x^14+x^46+x^48-x^39-x^42-2*x^41+x^32+x^35+x^34-x^26+x^15+x^12+
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^115+x^61+2*x^287-x^288-x^289-x^292-x^293+x^294-x^295-x^296-x^299-2*x^
77-x^87-x^83+x^84-x^85+2*x^81-2*x^82-2*x^74+x^75-x^76-x^71-x^72+x^73-2
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214+3*x^240-2*x^199+2*x^200-x^208+x^209-x^188-x^179-2*x^170+2*x^151+2*
x^142-x^143+2*x^135-2*x^201-x^196+2*x^193-3*x^194+x^195-x^191-x^192-x^
185+x^186-x^187-x^184-2*x^177+x^178-x^181+2*x^78-x^79-2*x^174+x^175+2*
x^171-2*x^172+x^173-2*x^167+x^168+x^164-x^165+x^166-x^163-x^152+x^153-
2*x^335-x^337+2*x^338+2*x^341-x^342+2*x^343-x^344+2*x^345+x^346-x^347+
2*x^336+2*x^149-2*x^150-2*x^145+3*x^146-x^147+2*x^139+2*x^144-x^136+2*
x^137-x^138+2*x^132-x^133+x^134+2*x^129-x^130+x^131+x^314+x^316-x^317+
x^327-x^328+2*x^329-2*x^330+2*x^331-x^333+3*x^334-x^315+x^126+x^128+2*
x^122-x^123+2*x^124-3*x^116+3*x^117+2*x^112-x^113-x^111+x^106-x^102+x^
103-2*x^96+x^100-3*x^94+3*x^95+x^90-2*x^91+x^92-2*x^381-2*x^384+3*x^38
5-3*x^386+x^388-2*x^389+x^390-x^391-x^393-x^395+x^382-3*x^364-x^367+2*
x^368-x^369+x^370+x^374-x^375+x^377-x^378+x^380+3*x^365+2*x^348-x^350+
2*x^351+x^352+x^354+2*x^356-x^357+2*x^358+x^360+3*x^363+x^349-x^239+x^
233+x^236+x^237-2*x^230+2*x^231-x^232+x^227-2*x^228+3*x^229+2*x^222-x^
225+x^226-x^219+2*x^220-2*x^221-x^205-x^38-x^43+x^44-x^451+x^453-x^454
+x^455+x^458+x^461-x^462+x^463+x^464-x^465+x^452-x^435-x^437+x^439-2*x
^440+2*x^441-x^442+x^444-x^445+x^446+x^450+x^436+x^421-x^423+x^424-x^4
25-x^426+x^427-x^428-x^429+x^430-x^431-x^422+x^407-x^409+x^410-2*x^411
-2*x^415+x^416-x^417-x^418+x^419-2*x^420-x^408+x^396-2*x^398+2*x^399-2
*x^400-x^401+2*x^402-2*x^403-x^404+x^405-2*x^406-x^397+x^98-2*x^99+x^3
+x^5-x^4-x^29+x^10+x^256+2*x^258-2*x^259+2*x^260-x^261+x^263-2*x^264+2
*x^265-x^266-x^257-2*x^60-x^51+x^22+x^28+x^14-x^270-x^272-x^275-2*x^27
9+2*x^280-2*x^281-x^284+x^285-3*x^286+x^271+x^53+x^59-x^49-x^52+2*x^39
-x^45+x^41-x^35+x^34+x^25-x^26-x^18+x^19-x^15+x^30-2*x^80+x^17-2*x^40+
x^466+x^470+x^475-x^476+x^477-x^479+x^36+x^27-x^89));" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 12 "s:=time()-s;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 4 "s/t;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 85 "Die Faktorzerlegung ist also deut
lich schneller als die Multiplikation der Faktoren !" }}}}{MARK "3 0 2
" 368 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }