\mnb150ÿ{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 System;}{\f3\fmodern\fprq1 Courier New;}{\f4\froman\fcharset1 Times New Roman;}} {\colortbl\red0\green0\blue0;\red255\green0\blue0;\red0\green0\blue255;} \deflang1031\pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}Berlekamp:=proc(A,x,p) \par \pard\li600\ri1\fi-300\plain\f3\fs22\cf1 local n,lcoef,a,reste,eq,j,k,sol,b,tab,dimker; \par begin \par n:=degree(A,x); \par lcoef:=lcoeff(A,x); \par a:=poly(A*(lcoef^-1 mod p),[x],IntMod(p)); \par reste:=expr([divide(poly(x^(j*p),[x],IntMod(p)),a,Rem) $ j=0..n-1]); \par eq:=[coeff(expand(_plus(bet[k]*(reste[k+1]-x^k) $ k=0..n-1)),x,n-i) $ i=1..n]; \par MatA:=Dom::Matrix(Dom::IntegerMod(p))([[coeff(eq[i],bet[k]) $ k=0..n-1,0] $ i=1..nops(eq)]); \par sol:=linalg::matlinsolve(MatA); \par dimker:=nops(expr(sol[2])); \par sol:=[bet[k]=_plus(op(expr(sol[2])[i])[k+1]*y[i] $ i=1..dimker) $ k=0..n-1]; \par b:=subs(subs(_plus(bet[k]*x^k $ k=0..n-1),sol),[bet[i]=1 $ i=0..n-1]); \par b:=poly(subs(b,[y[i]=1 $ i=1..dimker]),[x],IntMod(p)); \par tab:=[expr(gcd(a,b-poly(k,[x],IntMod(p)))) $ k=0..p-1]; \par lcoef*_mult(op(tab)) \par end_proc: \par \pard\ri4\plain\f4\fs22\cf0 01. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}AnzahlFaktoren:=proc(a,x,p) \par \pard\li600\ri1\fi-300\plain\f3\fs22\cf1 local aa,n,reste,R,E,k,j,ns; \par begin \par aa:=poly(a,[x],IntMod(p)); \par n:=degree(aa); \par reste:=[divide(poly(x^(p*k),[x],IntMod(p)),aa,Rem) $ k=0..n-1]; \par R:=Dom::SquareMatrix(n,Dom::IntegerMod(p))([[coeff(reste[k],j) $ k=1..n] $ j=0..n-1]); \par E:=(Dom::SquareMatrix(n,Dom::IntegerMod(p)))::one; \par ns:=linalg::nullspace(R-E); \par nops(ns) \par end_proc: \par \pard\ri4\plain\f4\fs22\cf0 02. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}AnzahlFaktoren(x^6+x^5+x^4+x^3+x^2+x+1,x,2) \par \pard\li50\ri6\plain\f3\fs22\cf2\protect {\pict\wmetafile8\picw564\pich827\picwgoal319\pichgoal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}\plain\f3\fs22\cf2\protect \par \pard\li50\ri2\plain\f3\fs22\cf2\protect \par \pard\ri4\plain\f4\fs22\cf0 03. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}Berlekamp(x^6+x^5+x^4+x^3+x^2+x+1,x,2) \par \pard\li50\ri6\plain\f3\fs22\cf2\protect {\pict\wmetafile8\picw4860\pich928\picwgoal2755\pichgoal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}\plain\f3\fs22\cf2\protect \par \pard\li50\ri2\plain\f3\fs22\cf2\protect \par \pard\ri4\plain\f4\fs22\cf0 04. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}AnzahlFaktoren(x^6+x^5+x^4+x^3+x^2+x+1,x,3) \par \pard\li50\ri6\plain\f3\fs22\cf2\protect {\pict\wmetafile8\picw564\pich827\picwgoal319\pichgoal468 0100090000031701000005001C0000000000050000000B0200000000050000000C023B03340203 0000001E00030000001E00050000000C02D5014001050000000B020000000014000000FF060000 0600F602000024000100020000800080FF7FFF7F02000080FF7F0080FF7F0200040000002D0100 0004000000F001000008000000FA0200000000000000000000040000002D01000007000000FC02 0000000000000000040000002D0101001C000000FB0210FF000000000000900100000001070000 00417269616C00F4774000000031060A377DA8F47786A8F4770100000000003000040000002D01 020005000000020101000000050000000102FFFFFF00050000002E011800000005000000090200 00000004000000080100001C000000FB0210FF0000000000009001000000010700000054696D65 73204E657720526F6D616E007DA8F47786A8F4770100000000003000040000002D0103000B0000 0026060F000C004D6174685479706500007B000500000009020000FF0007000000210501003100 3B01640008000000FA0200000000000000000000040000002D01040004000000F0010000070000 00FC020000FFFFFF000000040000002D01000004000000F00101001C000000FB02100007000000 0000BC02000000000102022253797374656D00774000000043060AE57DA8F47786A8F477010000 0000003000040000002D010100040000002701FFFF04000000F001020004000000F00103000400 00002701FFFF030000000000 }\plain\f3\fs22\cf2\protect \par \pard\li50\ri2\plain\f3\fs22\cf2\protect \par \pard\ri4\plain\f4\fs22\cf0 05. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}AnzahlFaktoren(x^10+x^9+x^7+x^3+x^2+1,x,2) \par \pard\li50\ri6\plain\f3\fs22\cf2\protect {\pict\wmetafile8\picw564\pich827\picwgoal319\pichgoal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}\plain\f3\fs22\cf2\protect \par \pard\li50\ri2\plain\f3\fs22\cf2\protect \par \pard\ri4\plain\f4\fs22\cf0 06. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}faktoren:=Berlekamp(x^10+x^9+x^7+x^3+x^2+1,x,2) \par \pard\li50\ri6\plain\f3\fs22\cf2\protect {\pict\wmetafile8\picw5805\pich928\picwgoal3291\pichgoal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910B040000002D010A00040000002D010800040000002D010900040000002D010300040000002D 010A00040000002D010800040000002D010900040000002D010300040000002D010A0004000000 2D0108000700000021050100A2006400090C08000000FA0200000000000000000000040000002D 010B0004000000F001000007000000FC020000FFFFFF000000040000002D01000004000000F001 01001C000000FB021000070000000000BC02000000000102022253797374656D0077400000004E 060A277DA8F47786A8F4770100000000003000040000002D010100040000002701FFFF04000000 F001020004000000F001030004000000F001040004000000F001050004000000F0010600040000 00F001070004000000F001080004000000F001090004000000F0010A00040000002701FFFF0300 00000000 }\plain\f3\fs22\cf2\protect \par \pard\li50\ri2\plain\f3\fs22\cf2\protect \par \pard\ri4\plain\f4\fs22\cf0 07. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}AnzahlFaktoren(faktoren[1],x,2) \par \pard\li50\ri6\plain\f3\fs22\cf2\protect {\pict\wmetafile8\picw564\pich827\picwgoal319\pichgoal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