\mnb150ÿ{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 System;}{\f3\froman\fcharset1 Times New Roman;}{\f4\fmodern\fprq1 Courier New;}{\f5\froman\fcharset1 Times New Roman;}} {\colortbl\red0\green0\blue0;\red0\green0\blue255;\red255\green0\blue0;} \deflang1031\pard\ri4\plain\f3\fs22\cf0 01. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf2 {\pntext\f1\'b7\tab}GradSchranke:=proc(A,B,C,k) \par \pard\li600\ri1\fi-300\plain\f4\fs22\cf2 local pol1,pol2,deg1,deg2,a,b; \par begin \par pol1:=collect(A-B,k); \par pol2:=collect(A+B,k); \par if pol1=0 \par then deg1:=-1 \par else deg1:=degree(pol1,k) \par end_if; \par if pol2=0 \par then deg2:=-1 \par else deg2:=degree(pol2,k) \par end_if; \par if deg1<=deg2 \par then print("Teil 1"); \par return(degree(C,k)-deg2); \par end_if; \par a:=coeff(pol1,k,deg1); \par if deg2=0) \par then print("Teil 2a"); \par return(degree(C,k)-deg1+1); \par else print("Teil 2b"); \par return(max(-2*b/a,degree(C,k)-deg1+1)); \par end_if; \par end_proc: \par \pard\ri4\plain\f3\fs22\cf0 02. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf2 {\pntext\f1\'b7\tab}GradSchranke(k-n,-(k+1),k+1,k) \par \pard\li50\ri6\plain\f4\fs22\cf1\protect \par \pard\li50\ri2\plain\f4\fs22\cf1\protect "Teil 2a" \par {\pict\wmetafile8\picw564\pich827\picwgoal319\pichgoal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}\plain\f4\fs22\cf1\protect \par \par \pard\ri4\plain\f3\fs22\cf0 03. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf2 {\pntext\f1\'b7\tab}GradSchranke(k*(k+1)^2,-k*(k+1),k^2*(k+1),k); \par \pard\li50\ri6\plain\f4\fs22\cf1\protect \par \pard\li50\ri2\plain\f4\fs22\cf1\protect "Teil 1" \par {\pict\wmetafile8\picw564\pich827\picwgoal319\pichgoal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}\plain\f4\fs22\cf1\protect \par \par \pard\ri4\plain\f3\fs22\cf0 04. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf2 {\pntext\f1\'b7\tab}GradSchranke(k+1,-1,1,k) \par \pard\li50\ri6\plain\f4\fs22\cf1\protect \par \pard\li50\ri2\plain\f4\fs22\cf1\protect "Teil 1" \par {\pict\wmetafile8\picw945\pich827\picwgoal535\pichgoal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}\plain\f4\fs22\cf1\protect \par \par \pard\ri4\plain\f3\fs22\cf0 05. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf2 {\pntext\f1\'b7\tab}REtoPol:=proc(A,B,C,k) \par \pard\li600\ri1\fi-300\plain\f4\fs22\cf2 local deg,g,j,rec,sol; \par begin \par deg:=GradSchranke(A,B,C,k); \par if deg<0 \par then return("keine Polynoml\'f6sung") \par end_if; \par g:=_plus(aa[j]*k^j $ j=0..deg); \par rec:=collect(A*subs(g,k=k+1)+B*g-C,k); \par sol:=solve(\{coeff(rec,k,i) $ i=0..degree(rec,k)\},\{aa[j] $ j=0..deg\},IgnoreSpecialCases); \par if sol=NIL or sol=\{\} \par then return("keine Polynoml\'f6sung") \par else subs(g,sol[1]); \par end_if; \par end_proc: \par \pard\ri4\plain\f3\fs22\cf0 06. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf2 {\pntext\f1\'b7\tab}REtoPol(k-n,-(k+1),k+1,k) \par \pard\li50\ri6\plain\f4\fs22\cf1\protect \par \pard\li50\ri2\plain\f4\fs22\cf1\protect "Teil 2a" \par {\pict\wmetafile8\picw1048\pich1141\picwgoal594\pichgoal646 0100090000032F0200000B001C0000000000050000000B0200000000050000000C027504180403 0000001E00030000001E00050000000C0287025202050000000B020000000014000000FF060000 0600F602000024000100020000800080FF7FFF7F02000080FF7F0080FF7F0200040000002D0100 0004000000F001000008000000FA0200000000000000000000040000002D01000007000000FC02 0000000000000000040000002D0101001C000000FB0210FF000000000000900100000001070000 00417269616C00F47740000000ED070AE37DA8F47786A8F4770100000000003000040000002D01 020005000000020101000000050000000102FFFFFF00050000002E011800000005000000090200 00000004000000080100001C000000FB0210FF0000000000009001000000010700000054696D65 73204E657720526F6D616E007DA8F47786A8F4770100000000003000040000002D0103000B0000 0026060F000C004D617468547970650000BF001C000000FB0210FF000000000000900101000001 0700000054696D6573204E657720526F6D616E007DA8F47786A8F4770100000000003000040000 002D010400040000002D010300040000002D010400040000002D0103001C000000FB0210FF0000 000000009001000000020700000053796D626F6C0077400000004E080A4E7DA8F47786A8F47701 00000000003000040000002D0105001C000000FB0210FF00000000000090010000000207000000 53796D626F6C00774000000088070AD67DA8F47786A8F4770100000000003000040000002D0106 001C000000FB0210FF0000000000009001000000020700000054696D6573204E657720526F6D61 6E007DA8F47786A8F4770100000000003000040000002D010700040000002D010300040000002D 010500040000002D0106000500000009020000FF0007000000210501002D009801880004000000 2D010700040000002D010300040000002D01040007000000210501006B0027015A010700000021 0501006E00200259011C000000FB0210FF000000000000900100000001070000005346204D6174 68204578740053080A0B7DA8F47786A8F4770100000000003000040000002D0108001C000000FB 0210FF000000000000900100000002070000005346204D617468204578740058080A3F7DA8F477 86A8F4770100000000003000040000002D0109000700000021050100C50047013C010700000021 050100C50047015E0108000000FA0200000000000000000000040000002D010A0004000000F001 000007000000FC020000FFFFFF000000040000002D01000004000000F00101001C000000FB0210 00070000000000BC02000000000102022253797374656D00774000000066080A187DA8F47786A8 F4770100000000003000040000002D010100040000002701FFFF04000000F001020004000000F0 01030004000000F001040004000000F001050004000000F001060004000000F001070004000000 F001080004000000F0010900040000002701FFFF030000000000 }\plain\f4\fs22\cf1\protect \par \par \pard\ri4\plain\f3\fs22\cf0 07. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf2 {\pntext\f1\'b7\tab}REtoPol(k*(k+1)^2,-k*(k+1),k^2*(k+1),k) \par \pard\li50\ri6\plain\f4\fs22\cf1\protect \par \pard\li50\ri2\plain\f4\fs22\cf1\protect "Teil 1" \par {\pict\wmetafile8\picw564\pich827\picwgoal319\pichgoal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}\plain\f4\fs22\cf1\protect \par \par \pard\ri4\plain\f3\fs22\cf0 08. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf2 {\pntext\f1\'b7\tab}REtoPol(k+1,-1,1,k) \par \pard\li50\ri6\plain\f4\fs22\cf1\protect \par \pard\li50\ri2\plain\f4\fs22\cf1\protect "Teil 1" \par {\pict\wmetafile8\picw4376\pich827\picwgoal2480\pichgoal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}\plain\f4\fs22\cf1\protect \par \par \pard\ri4\plain\f3\fs22\cf0 09. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf2 {\pntext\f1\'b7\tab}a:=1/(k+1) \par \pard\li50\ri6\plain\f4\fs22\cf1\protect {\pict\wmetafile8\picw1318\pich1141\picwgoal747\pichgoal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0000001E00030000001E00050000000C02D5014001050000000B020000000014000000FF060000 0600F602000024000100020000800080FF7FFF7F02000080FF7F0080FF7F0200040000002D0100 0004000000F001000008000000FA0200000000000000000000040000002D01000007000000FC02 0000000000000000040000002D0101001C000000FB0210FF000000000000900100000001070000 00417269616C00F47740000000ED070AE77DA8F47786A8F4770100000000003000040000002D01 020005000000020101000000050000000102FFFFFF00050000002E011800000005000000090200 00000004000000080100001C000000FB0210FF0000000000009001000000010700000054696D65 73204E657720526F6D616E007DA8F47786A8F4770100000000003000040000002D0103000B0000 0026060F000C004D6174685479706500007B000500000009020000FF0007000000210501003100 3B01640008000000FA0200000000000000000000040000002D01040004000000F0010000070000 00FC020000FFFFFF000000040000002D01000004000000F00101001C000000FB02100007000000 0000BC02000000000102022253797374656D00774000000063080AD87DA8F47786A8F477010000 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\pard\li50\ri2\plain\f4\fs22\cf1\protect "Teil 2b" \par {\pict\wmetafile8\picw564\pich827\picwgoal319\pichgoal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