\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;\red0\green0\blue255;\red255\green0\blue0;} \deflang1031\pard\ri4\plain\f4\fs22\cf0 02. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf2 {\pntext\f1\'b7\tab}Faktoren:=proc(a:DOM_POLY,x,p,s) \par \pard\li600\ri1\fi-300\plain\f3\fs22\cf2 local tab,k,i,j,bliste,faktorliste,pos; \par begin \par tab:=[k $ k=0..p-1]; \par bliste:=tab; \par for k from 1 to s do \par bliste:=[(bliste[i]+tab[j]*x^k $ j=1..p) $ i=1..p^k] \par end_for; \par delete bliste[1]; \par bliste:=map(bliste,y->poly(y,[x],IntMod(p))); \par faktorliste:=[]; \par for i from 1 to nops(bliste) do \par if divide(a,bliste[i])[2]=poly(0,[x],IntMod(p)) \par then faktorliste:=[op(faktorliste),bliste[i]] \par end_if; \par end_for; \par faktorliste \par end_proc: \par \pard\ri4\plain\f4\fs22\cf0 03. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf2 {\pntext\f1\'b7\tab}a:=poly(x^5+x^3+x,[x],IntMod(11)) \par \pard\li50\ri6\plain\f3\fs22\cf1\protect {\pict\wmetafile8\picw6315\pich907\picwgoal3580\pichgoal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}\plain\f3\fs22\cf1\protect \par \pard\li50\ri2\plain\f3\fs22\cf1\protect \par \pard\ri4\plain\f4\fs22\cf0 04. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf2 {\pntext\f1\'b7\tab}p:=11 \par \pard\li50\ri6\plain\f3\fs22\cf1\protect {\pict\wmetafile8\picw776\pich827\picwgoal439\pichgoal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}\plain\f3\fs22\cf1\protect \par \pard\li50\ri2\plain\f3\fs22\cf1\protect \par \pard\ri4\plain\f4\fs22\cf0 05. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf2 {\pntext\f1\'b7\tab}Faktoren(a,x,p,2) \par \pard\li50\ri6\plain\f3\fs22\cf1\protect \par \pard\li50\ri2\plain\f3\fs22\cf1\protect [poly(x, [x], IntMod(11)), poly(2 x, [x], IntMod(11)), \par \par poly(3 x, [x], IntMod(11)), poly(4 x, [x], IntMod(11)), \par \par poly(5 x, [x], IntMod(11)), poly((-5) x, [x], IntMod(11)), \par \par poly((-4) x, [x], IntMod(11)), poly((-3) x, [x], IntMod(11)), \par \par poly((-2) x, [x], IntMod(11)), poly((-1) x, [x], IntMod(11)), \par \par 2 \par poly(1, [x], IntMod(11)), poly(x + x + 1, [x], IntMod(11)), \par \par 2 \par poly(x - x + 1, [x], IntMod(11)), poly(2, [x], IntMod(11)), \par \par 2 \par poly(2 x + 2 x + 2, [x], IntMod(11)), \par \par 2 \par poly(2 x - 2 x + 2, [x], IntMod(11)), poly(3, [x], IntMod(11)), \par \par 2 \par poly(3 x + 3 x + 3, [x], IntMod(11)), \par \par 2 \par poly(3 x - 3 x + 3, [x], IntMod(11)), poly(4, [x], IntMod(11)), \par \par 2 \par poly(4 x + 4 x + 4, [x], IntMod(11)), \par \par 2 \par poly(4 x - 4 x + 4, [x], IntMod(11)), poly(5, [x], IntMod(11)), \par \par 2 \par poly(5 x + 5 x + 5, [x], IntMod(11)), \par \par 2 \par poly(5 x - 5 x + 5, [x], IntMod(11)), poly(-5, [x], IntMod(11)), \par \par 2 \par poly(- 5 x + 5 x - 5, [x], IntMod(11)), \par \par 2 \par poly(- 5 x - 5 x - 5, [x], IntMod(11)), poly(-4, [x], IntMod(11)), \par \par 2 \par poly(- 4 x + 4 x - 4, [x], IntMod(11)), \par \par 2 \par poly(- 4 x - 4 x - 4, [x], IntMod(11)), poly(-3, [x], IntMod(11)), \par \par 2 \par poly(- 3 x + 3 x - 3, [x], IntMod(11)), \par \par 2 \par poly(- 3 x - 3 x - 3, [x], IntMod(11)), poly(-2, [x], IntMod(11)), \par \par 2 \par poly(- 2 x + 2 x - 2, [x], IntMod(11)), \par \par 2 \par poly(- 2 x - 2 x - 2, [x], IntMod(11)), poly(-1, [x], IntMod(11)), \par \par 2 2 \par poly(- x + x - 1, [x], IntMod(11)), poly(- x - x - 1, [x], IntMod(11))] \par \par \pard\ri4\plain\f4\fs22\cf0 06. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf2 {\pntext\f1\'b7\tab}poly(x*(x^2+x+1)*(x^2+10*x+1),[x],IntMod(p)) \par \pard\li50\ri6\plain\f3\fs22\cf1\protect {\pict\wmetafile8\picw6315\pich907\picwgoal3580\pichgoal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0101001C000000FB021000070000000000BC02000000000102022253797374656D007740000000 4F060A987DA8F47786A8F4770100000000003000040000002D010100040000002701FFFF040000 00F001020004000000F001030004000000F001040004000000F001050004000000F00106000400 0000F001070004000000F001080004000000F001090004000000F0010A0004000000F0010B0004 0000002701FFFF030000000000 }\plain\f3\fs22\cf1\protect \par \pard\li50\ri2\plain\f3\fs22\cf1\protect \par \pard\ri4\plain\f4\fs22\cf0 07. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf2 {\pntext\f1\'b7\tab}rest:=divide(a,poly(x^2+x+1,[x],IntMod(p)))[1] \par \pard\li50\ri6\plain\f3\fs22\cf1\protect {\pict\wmetafile8\picw6315\pich907\picwgoal3580\pichgoal514 010009000003AC0400000D001C0000000000050000000B0200000000050000000C028B03AB1803 0000001E00030000001E00050000000C020202FC0D050000000B020000000014000000FF060000 0600F602000024000100020000800080FF7FFF7F02000080FF7F0080FF7F0200040000002D0100 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