{VERSION 5 0 "HP RISC UNIX" "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 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } 3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 " " 1 14 0 0 0 0 1 1 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 1 1 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 30 "8. \334bungsblatt Comput eralgebra" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 257 "" 0 "" {TEXT -1 11 "Aufgabe 3b)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "restart:\nF10 := 2^(2^10)+1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "2 &^(F10-1) mod F10;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "3 &^(F10-1) mod F10;" }}}{EXCHG {PARA 258 "" 0 "" {TEXT -1 11 "Aufgabe 4b)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "p := 10^20 + 39;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 452 "printf(\"Quadratische Erg\344nzung:\");\nprint((x + \+ 1/2)^2 = -3/4);\nprintf(\"In F_p ist dies:\");\na := (-3/4 mod p):\npr int((x + 1/2)^2 = a);\nprintf(\"Zur Berechnung der Wurzel aus der rech ten Seite heben wir diese zur %d-ten Potenz\", (p+1)/4);\nx := a &^ (( p+1)/4) mod p;\nif x^2 mod p = a then\nprintf(\"Da %d^2 = %d ist, habe n wir eine Wurzel gefunden;\\nDie L\366sungen der Gleichung sind\", x, a);\nprint('x'[1] = (-1/2+x) mod p);\nprint('x'[2] = (-1/2-x) mod p); \nfi;\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "f := x -> (x^2 + x + 1) mod p;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "f(8059250 5861524411514);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "f(194074 94138475588524);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "2 0 0" 9 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }