{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 64 "a:=x^8-46*x^7-1062*x^6+4028*x^5-4944*x^4+2104* x^3-66*x^2-35*x+2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG,4*$)%\"xG \"\")\"\"\"F**&\"#YF*)F(\"\"(F*!\"\"*&\"%i5F*)F(\"\"'F*F/*&\"%GSF*)F( \"\"&F*F**&\"%W\\F*)F(\"\"%F*F/*&\"%/@F*)F(\"\"$F*F**&\"#mF*)F(\"\"#F* F/*&\"#NF*F(F*F/FCF*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "02." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "liste:=[seq(Factor(a) mod it hprime(n),n=1..10)];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&listeG7,**, (*$)%\"xG\"\"$\"\"\"F,F*F,F,F,F,,&F*F,F,F,F,,(F(F,*$)F*\"\"#F,F,F,F,F, F*F,*(,&F/F,F,F,F,F-F,),&F*F,F1F,\"\"&F,*(,*F(F,F/F,F*F,\"\"%F,F,F-F,, **$)F*F9F,F,*&F1F,F)F,F,*&F1F,F0F,F,F+F,F,**,&F*F,F+F,F,,&F*F,F6F,F,,( F/F,*&F1F,F*F,F,F6F,F,,(F;F,F/F,\"\"'F,F,*&,,F;F,*&FEF,F)F,F,*&\"\"(F, F0F,F,*&F1F,F*F,F,\"\"*F,F,,*F;F,*&F+F,F)F,F,*&F1F,F0F,F,\"#5F,F,*,,&F *F,F9F,F,,(F/F,*&FJF,F*F,F,F,F,F,,(F/F,*&F+F,F*F,F,FEF,F,,&F*F,FEF,F,, (F/F,*&\"#7F,F*F,F,F1F,F,*(,*F(F,*&F9F,F0F,F,*&F1F,F*F,F,FLF,F,,*F;F,* &F6F,F)F,F,*&FEF,F0F,F,\"#;F,F,,&F*F,\"#8F,F,*(,&F*F,FZF,F,,,F;F,*&\"# F, F*F,F,\"\")F,F,,(F/F,*&FPF,F*F,F,\"#?F,F,*,,&F*F,FhoF,F,,&F*F,\"#FF,F, ,&F*F,\"#9F,F,,*F(F,*&FEF,F0F,F,*&F1F,F*F,F,F^oF,F,,(F/F,*&FZF,F*F,F, \"#GF,F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "03." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "map(nops,liste);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7,\"\"%\"\"$F%F$\"\"#\"\"&F%F%F%F'" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 3 "04." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "q :=ithprime(5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG\"#6" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "05." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "fac:=Factor(a) mod q;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$facG*&,,*$)%\"xG\"\"%\"\"\"F+*&\"\"'F+)F)\"\"$F+F+*&\"\"(F+)F )\"\"#F+F+*&F3F+F)F+F+\"\"*F+F+,*F'F+*&F/F+F.F+F+*&F3F+F2F+F+\"#5F+F+ " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "06." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "b:=mods(op(1,fac),q);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG,,*$)%\"xG\"\"%\"\"\"F**&\"\"&F*)F(\"\"$F*!\"\"*& F)F*)F(\"\"#F*F/*&F2F*F(F*F*F2F/" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "07." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "c:=mods(op(2,fac) ,q);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG,**$)%\"xG\"\"%\"\"\"F** &\"\"$F*)F(F,F*F**&\"\"#F*)F(F/F*F*F*!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "08." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "09." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "[Gcdex(b,c,x,'s','t') mod q,[s,t]];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"\"7$,**&\"\"$F$)%\"xGF(F$F$*&\"\"&F$)F*\"\"#F$ F$*&\"\"(F$F*F$F$F.F$,**&\"\")F$F)F$F$*&F3F$F-F$F$F*F$\"\"'F$" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "10." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 310 "HenselLifting:=proc(a,b,c,s,t,x,q)\nlocal k,B,C,d,S, T;\nk:=expand((a-b*c)/q);\nB:=mods(Rem(k*t,b,x) mod q,q);\nC:=mods(Rem (k*s,c,x) mod q,q);\nd:=s*(b+q*B)+t*(c+q*C)-1;\nS:=mods(Rem(s*d,c+q*C, x) mod q^2,q^2);\nT:=mods(Rem(t*d,b+q*B,x) mod q^2,q^2);\n[expand(b+q* B),expand(c+q*C),expand(s-S),expand(t-T),q^2];\nend proc:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "11." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "bcstq:=HenselLifting(a,b,c,s,t,x,q);\nb:=bcstq[1]:c:=bcstq[2]: s:=bcstq[3]:t:=bcstq[4]:q:=bcstq[5]:" }}{PARA 12 "" 1 "" {XPPMATH 20 " 6#>%&bcstqG7',,*$)%\"xG\"\"%\"\"\"F+*&\"#F+F.F+F4*&F/F+F2F+F 4*&\"#7F+F)F+F+\"#hF+\"$@\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "12. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "bcstq:=HenselLifting(a, b,c,s,t,x,q);\nb:=bcstq[1]:c:=bcstq[2]:s:=bcstq[3]:t:=bcstq[4]:q:=bcst q[5]:" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&bcstqG7',,*$)%\"xG\"\"%\" \"\"F+*&\"#F+F.F+F+*&\"%pQF+F2F+F+*&\"%+MF+F)F+F+\"%'3$ F+\"&TY\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "13." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,,*$)%\"xG\"\"%\"\"\"F)*&\"# " 0 "" {MPLTEXT 1 0 24 "[rem(a,b,x),rem(a,c,x)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"!F$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "15." } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 228 "ZassenhausSchranke:=proc( a,x,m)\nlocal n,M,R;\nn:=degree(a,x);\nM:=max(seq((abs(coeff(a,x,n-k)) )^(1/k)/binomial(n,k),k=1..n));\nR:=M/(2^(1/n)-1);\nmax(seq(binomial(m ,k)*R^k,k=1..n));\nend proc:\n\nceil(evalf(ZassenhausSchranke(a,x,4))) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\")%G!H;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "16." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Hense lLifting(a,b,c,s,t,x,q);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7',,*$)%\" xG\"\"%\"\"\"F)*&\"# " 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 }