{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 "" {MPLTEXT 1 0 450 "Berlekamp1:=proc(A, x,p)\nlocal n,lcoef,a,reste,j,k,sol,beta,b,tab;\nn:=degree(A,x);\nlcoe f:=lcoeff(A,x);\na:=A*(lcoef^(-1) mod p) mod p;\nreste:=[seq(Rem(x^(j* p),a,x) mod p,j=0..n-1)];\nsol:=msolve(\{seq(coeff(expand(sum(beta[k]* (reste[k+1]-x^k),k=0..n-1)),x,i),i=0..n-1)\},p);\nb:=subs(sol,sum(beta [k]*x^k,k=0..n-1));\nb:=subs(map(y->y=1,indets(b) minus \{x\}),b) mod \+ p;\ntab:=[seq(Gcd(a mod p,b-k mod p) mod p,k=0..p-1)];\nlcoef*convert( tab,`*`) mod p;\nend proc:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "01. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 286 "AnzahlFaktoren:=proc(a ,x,p)\nlocal aa,n,reste,R,E,k,j,ns;\naa:=a mod p;\nn:=degree(aa);\nres te:=[seq(Rem(x^(p*k),aa,x) mod p,k=0..n-1)];\nR:=matrix(n,n,[seq(seq(c oeff(reste[k],x,j),j=0..n-1),k=1..n)]);\nE:=LinearAlgebra[IdentityMatr ix](n);\nns:=Nullspace(evalm(R-E)) mod p;\nnops(ns);\nend proc:" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "02." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "AnzahlFaktoren(x^6+x^5+x^4+x^3+x^2+x+1,x,2);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "03." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "Berlekamp1(x^6+x^5+x^4+x^3+x^2+x+1,x,2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "04." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "AnzahlFaktoren(x^6+x^5+x^4+x^3+x^2+x+1,x,3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "05." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "AnzahlFaktoren(x^10+x^9+x^7+x^3+x^2+1,x,2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "06." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "fak toren:=Berlekamp1(x^10+x^9+x^7+x^3+x^2+1,x,2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "07." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Anz ahlFaktoren(op(1,faktoren),x,2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "08." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "AnzahlFaktoren(op (2,faktoren),x,2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "09." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "Berlekamp1(op(1,faktoren),x, 2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "10." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 37 "Factor(x^10+x^9+x^7+x^3+x^2+1) mod 2;" }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }