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2D010900040000002D010700070000002105010069016800E60708000000FA0200000000000000 000000040000002D010B0004000000F001000007000000FC020000FFFFFF000000040000002D01 000004000000F00101001C000000FB021000070000000000BC0200000000010202225379737465 6D00774000000041180AF5BDACF477C6ACF4770100000000003000040000002D01010004000000 2701FFFF04000000F001020004000000F001030004000000F001040004000000F0010500040000 00F001060004000000F001070004000000F001080004000000F001090004000000F0010A000400 00002701FFFF030000000000 }\plain\f4\fs22\cf2\protect \par \pard\li50\ri2\plain\f4\fs22\cf2\protect \par \pard\ri4\plain\f3\fs22\cf0 04./05. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf1 {\pntext\f1\'b7\tab}zlist:=[op(solve(res=0,z))] \par \pard\li50\ri6\plain\f4\fs22\cf2\protect {\pict\wmetafile8\picw1914\pich1129\picwgoal1085\pichgoal640 010009000003A70200000A001C0000000000050000000B0200000000050000000C0269047A0703 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{\pntext\f1\'b7\tab}vlist:=map(sol,y->gcd(subs(c-z*diff(d,x),y),d)) \par \pard\li50\ri6\plain\f4\fs22\cf2\protect {\pict\wmetafile8\picw2469\pich1369\picwgoal1399\pichgoal776 010009000003560300000D001C0000000000050000000B0200000000050000000C025905A50903 0000001E00030000001E00050000000C0208037805050000000B020000000014000000FF060000 0600F602000024000100020000800080FF7FFF7F02000080FF7F0080FF7F0200040000002D0100 0004000000F001000008000000FA0200000000000000000000040000002D01000007000000FC02 0000000000000000040000002D0101001C000000FB0210FF000000000000900100000001070000 00417269616C00F4774000000000110AC7BDACF477C6ACF4770100000000003000040000002D01 020005000000020101000000050000000102FFFFFF00050000002E011800000005000000090200 00000004000000080100001C000000FB0210FF0000000000009001000000010700000054696D65 73204E657720526F6D616E00BDACF477C6ACF4770100000000003000040000002D0103000B0000 0026060F000C004D617468547970650000D9001C000000FB0210FF000000000000900101000001 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{\pntext\f1\'b7\tab}makemonic:=(p,x)->map(p,z->expand(z/coeff(z,x,degree(z,x)))): \par \pard\ri4\plain\f3\fs22\cf0 08. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf1 {\pntext\f1\'b7\tab}makemonic(vlist,x) \par \pard\li50\ri6\plain\f4\fs22\cf2\protect {\pict\wmetafile8\picw2170\pich903\picwgoal1230\pichgoal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}\plain\f4\fs22\cf2\protect \par \pard\li50\ri2\plain\f4\fs22\cf2\protect \par \pard\ri4\plain\f3\fs22\cf0 21. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf1 {\pntext\f1\'b7\tab}factor(res) \par \pard\li50\ri6\plain\f4\fs22\cf2\protect {\pict\wmetafile8\picw8281\pich926\picwgoal4694\pichgoal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}\plain\f4\fs22\cf2\protect \par \pard\li50\ri2\plain\f4\fs22\cf2\protect \par \pard\ri4\plain\f3\fs22\cf0 22. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf1 {\pntext\f1\'b7\tab}RothsteinTrager:=proc(r,x) \par \pard\li600\ri1\fi-300\plain\f4\fs22\cf1 local c,d,dmonic,res,sol,zlist,vlist; \par begin \par c:=numer(r); \par d:=denom(r); \par dmonic:=makemonic([d],x)[1]; \par c:=normal(c*dmonic/d); \par d:=dmonic; \par res:=polylib::resultant(c-z*diff(d,x),d,x); \par sol:=[op(solve(res=0,\{z\}))]; \par zlist:=map(sol,y->subs(z,y)); \par vlist:=map(sol,y->gcd(subs(c-z*diff(d,x),y),d)); \par _plus(zlist[i]*ln(makemonic(vlist,x)[i]) $ i=1..nops(zlist)) \par end_proc: \par \pard\ri4\plain\f3\fs22\cf0 23. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf1 {\pntext\f1\'b7\tab}RothsteinTrager(1/(x^3+x),x) \par \pard\li50\ri6\plain\f4\fs22\cf2\protect {\pict\wmetafile8\picw3484\pich1300\picwgoal1975\pichgoal737 010009000003110400000D001C0000000000050000000B0200000000050000000C0214059C0D03 0000001E00030000001E00050000000C02E102B707050000000B020000000014000000FF060000 0600F602000024000100020000800080FF7FFF7F02000080FF7F0080FF7F0200040000002D0100 0004000000F001000008000000FA0200000000000000000000040000002D01000007000000FC02 0000000000000000040000002D0101001C000000FB0210FF000000000000900100000001070000 00417269616C00F47740000000E9020A75BDACF477C6ACF4770100000000003000040000002D01 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2D010500040000002D010600040000002D010700040000002D010300040000002D010500040000 002D0106000700000021050100A2006400C806040000002D010700040000002D01030007000000 2105010032007D021105040000002D010500040000002D0106000700000021050100C500A10147 030700000021050100C500A101D7030700000021050100C500A10167040700000021050100C500 A101F7040700000021050100C500A10187050700000021050100C500A101170607000000210501 00C500A101A7060700000021050100C500A101C30608000000FA02000000000000000000000400 00002D010C0004000000F001000007000000FC020000FFFFFF000000040000002D010000040000 00F00101001C000000FB021000070000000000BC02000000000102022253797374656D00774000 0000B8110AB1BDACF477C6ACF4770100000000003000040000002D010100040000002701FFFF04 000000F001020004000000F001030004000000F001040004000000F001050004000000F0010600 04000000F001070004000000F001080004000000F001090004000000F0010A0004000000F0010B 00040000002701FFFF030000000000 }\plain\f4\fs22\cf2\protect \par \pard\li50\ri2\plain\f4\fs22\cf2\protect \par \pard\ri4\plain\f3\fs22\cf0 24. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf1 {\pntext\f1\'b7\tab}RothsteinTrager(r,x) \par \pard\li50\ri6\plain\f4\fs22\cf2\protect {\pict\wmetafile8\picw6867\pich1305\picwgoal3893\pichgoal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