{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 }{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 }} {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;" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 70 "02.\nMaple erzeugt mit \"mods\" \+ Polynome mit symmetrischer Modulofunktion" }}}{EXCHG {PARA 0 "> " 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;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "03." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "mods(a,9);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "04." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 187 "Zass enhausSchranke:=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:" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 3 "05." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "z :=ZassenhausSchranke(a,x,2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "06 ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(z);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "07." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "liste:=[seq(evalf(ZassenhausSchranke(a,x,m)),m=1..4)];" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "08." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "max(op(liste));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "09." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "p:=nextprime(ceil (2*max(op(liste))));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "10." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "fac:=Factor(a) mod p;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "11." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "b:=mods(fac,p);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "12." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "map(y->normal(a/y ),convert(b,list));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "13." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(a);" }}}}{MARK "1 0 0 " 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }