{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "01." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 43 "a:=x^8+x^6+3*x^5-9*x^4+6*x^3-13*x^2+11*x-2;" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG,2*$)%\"xG\"\")\"\"\"F**$)F(\" \"'F*F**&\"\"$F*)F(\"\"&F*F**&\"\"*F*)F(\"\"%F*!\"\"*&F-F*)F(F/F*F**& \"#8F*)F(\"\"#F*F6*&\"#6F*F(F*F*F " 0 "" {MPLTEXT 1 0 61 "mods(sum(k*x^ (k+1),k=0..10),9);\nsum(k*x^(k+1),k=0..10) mod 9;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,4*$)%\"xG\"\"#\"\"\"F(*&F'F()F&\"\"$F(F(*&F+F()F&\"\"% F(F(*&F.F()F&\"\"&F(F(*&F.F()F&\"\"'F(!\"\"*&F+F()F&\"\"(F(F5*&F'F()F& \"\")F(F5*$)F&\"\"*F(F5*$)F&\"#6F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#,4*$)%\"xG\"\"#\"\"\"F(*&F'F()F&\"\"$F(F(*&F+F()F&\"\"%F(F(*&F.F()F& \"\"&F(F(*&F1F()F&\"\"'F(F(*&F4F()F&\"\"(F(F(*&F7F()F&\"\")F(F(*&F:F() F&\"\"*F(F(*$)F&\"#6F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "03." } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "mods(a,9);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,0*$)%\"xG\"\")\"\"\"F(*$)F&\"\"'F(F(*&\"\"$F()F& \"\"&F(F(*&F-F()F&F-F(!\"\"*&\"\"%F()F&\"\"#F(F2*&F6F(F&F(F(F6F2" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "04." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 187 "ZassenhausSchranke:=proc(a,x,m)\nlocal n,M,R;\nn:=de gree(a,x);\nM:=max(seq((abs(coeff(a,x,n-k)))^(1/k)/binomial(n,k),k=1.. n));\nR:=M/(2^(1/n)-1);\nmax(seq(binomial(m,k)*R^k,k=1..n));\nend proc :" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "05." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "z:=ZassenhausSchranke(a,x,2);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"zG*&\"\"##\"\"\"\"\"%,&*$)F&#F(\"\")F(F(F(!\"\"! \"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "06." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 9 "evalf(z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$ \"+94t^9!\"(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "07." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "liste:=[seq(evalf(ZassenhausSchrank e(a,x,m)),m=1..4)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&listeG7&$\"+ nz([?\"!\")$\"+94t^9!\"($\"+\"fe\"\\ " 0 "" {MPLTEXT 1 0 15 "max(op(liste));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+XE_2@! \"&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "09." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 37 "p:=nextprime(ceil(2*max(op(liste))));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG\"&d@%" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 3 "10." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "fac:=F actor(a) mod p;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$facG**,&%\"xG\" \"\"\"&Cn\"F(F(,**$)F'\"\"$F(F(*&\"&=0#F()F'\"\"#F(F(*&\"&7i\"F(F'F(F( \"%f))F(F(,(F+F(F'F(\"&c@%F(F(,&F'F(\"%:\\F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "11." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "b:= mods(fac,p);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG**,&%\"xG\"\"\" \"&Cn\"F(F(,**$)F'\"\"$F(F(*&\"&=0#F()F'\"\"#F(F(*&\"&7i\"F(F'F(F(\"%f ))F(F(,(F+F(F'F(F(!\"\"F(,&F'F(\"%:\\F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "12." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "map(y->n ormal(a/y),convert(b,list));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7&*&,2 *$)%\"xG\"\")\"\"\"F**$)F(\"\"'F*F**&\"\"$F*)F(\"\"&F*F**&\"\"*F*)F(\" \"%F*!\"\"*&F-F*)F(F/F*F**&\"#8F*)F(\"\"#F*F6*&\"#6F*F(F*F*F " 0 "" {MPLTEXT 1 0 10 "factor(a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,**$) %\"xG\"\"&\"\"\"F)*&\"\"%F))F'\"\"#F)F)*&\"\"*F)F'F)!\"\"F-F)F),(*$)F' \"\"$F)F)F'F)F)F0F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} }{MARK "1 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }