{VERSION 3 0 "IBM INTEL LINUX" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 24 0 0 0 0 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "" 2 6 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning " 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } 1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 24 0 0 0 0 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 24 0 0 0 0 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 41 "INTERNI DATOVA REPREZENTA CE A SUBSTITUCE" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 27 "Interni dato va reprezentace" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "pol:=x^4+ x^3-x^2-x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$polG,**$)%\"xG\"\"%\" \"\"\"\"\"*$)F(\"\"$F*F+*$)F(\"\"#F*!\"\"F(F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "subs(1=7, pol);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**$)%\"xG\"\"%\"\"\"\"\"(*$)F&\"\"$F(F)*$)F&\"\"#F(!\"\"F&F0" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "whattype(pol);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#%\"+G" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Po moci nops ziskame pocet scitancu:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "nops(pol);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "Posloupnost komponent ziskame procedurou \+ op (extract operands):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "op(pol);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&*$)%\"xG\"\"%\"\"\"*$)F%\"\"$F',$*$) F%\"\"#F'!\"\",$F%F/" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "Nyni si v simneme kazdeho podvyrazu zvlast:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "`prvni clen`:=op(1,pol);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+prv ni~clenG*$)%\"xG\"\"%\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "Na prvni operand se muzeme odkazat i pomoci" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 11 "op(pol)[1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)% \"xG\"\"%\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "whattype (%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"^G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "op(op(pol)[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%\"xG\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "op([1,1],p ol),op([1,2],pol);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%\"xG\"\"%" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 227 "Symbol ^ predstavuje datovy typ p ower (mocnina), pokud je exponent typu numeric, Maple provadi automati cke zjednoduseni na typ product (soucin).\nTreti clen je soucinem -1 a mocniny x^2. Maple vraci datovy typ product pomoci *.\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "`treti clen`:=op(3,pol);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+treti~clenG,$*$)%\"xG\"\"#\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "whattype(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"*G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "op( `treti clen`);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$!\"\"*$)%\"xG\"\"#\" \"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "`ctvrty clen`:=op(4 ,pol);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,ctvrty~clenG,$%\"xG!\"\" " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "op(`ctvrty clen`);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$!\"\"%\"xG" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 6 "-1, x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$!\"\"%\"xG " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "op([4,2],pol);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%\"xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "whattype(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%'sym bolG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 165 "Podobnym zpusobem muzeme v Maplu rozebrat jakykoliv vyraz, nejen polynomy.\nMusime vsak neusta le byt vedomi, ze identicke podvyrazy jsou interne ulozeny pouze jedno u." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "readlib(dismantle);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#R6\"F$6#%inCopyright~(c)~1994~by~Wat erloo~Maple~Inc.~All~rights~reserved.GF$C%-%'printfG6#Q\"|+6\"@)/9!.&% *dismantleG6#%$hexG-%/dismantle/dumpG6%-%*addressofG6#9\"\"\"!Q$%X,F,/ F/.&F26#%$decG-F66%F8F " 0 "" {MPLTEXT 1 0 15 "dismantle(pol); " }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 6 "SUM(9) " }}{PARA 6 "" 1 "" {TEXT -1 10 " PROD(3)" }}{PARA 6 "" 1 "" {TEXT -1 16 " NAME(4): x" }}{PARA 6 "" 1 "" {TEXT -1 18 " INTPOS(2 ): 4" }}{PARA 6 "" 1 "" {TEXT -1 15 " INTPOS(2): 1" }}{PARA 6 "" 1 " " {TEXT -1 10 " PROD(3)" }}{PARA 6 "" 1 "" {TEXT -1 16 " NAME(4 ): x" }}{PARA 6 "" 1 "" {TEXT -1 18 " INTPOS(2): 3" }}{PARA 6 "" 1 "" {TEXT -1 15 " INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 10 " P ROD(3)" }}{PARA 6 "" 1 "" {TEXT -1 16 " NAME(4): x" }}{PARA 6 "" 1 "" {TEXT -1 18 " INTPOS(2): 2" }}{PARA 6 "" 1 "" {TEXT -1 16 " \+ INTNEG(2): -1" }}{PARA 6 "" 1 "" {TEXT -1 13 " NAME(4): x" }} {PARA 6 "" 1 "" {TEXT -1 16 " INTNEG(2): -1" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "Odhadnete vyslede k nasledujici substituce:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "pol2:=Pi*x+x+1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%pol2G,(*&%#P iG\"\"\"%\"xGF(F(F)F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "dismantle(pol2);" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 " " {TEXT -1 6 "SUM(7)" }}{PARA 6 "" 1 "" {TEXT -1 10 " PROD(5)" }} {PARA 6 "" 1 "" {TEXT -1 30 " NAME(4): Pi #[protected]" }}{PARA 6 "" 1 "" {TEXT -1 18 " INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 16 " NAME(4): x" }}{PARA 6 "" 1 "" {TEXT -1 18 " INTPOS(2): \+ 1" }}{PARA 6 "" 1 "" {TEXT -1 15 " INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 13 " NAME(4): x" }}{PARA 6 "" 1 "" {TEXT -1 15 " INTPOS(2 ): 1" }}{PARA 6 "" 1 "" {TEXT -1 15 " INTPOS(2): 1" }}{PARA 6 "" 1 " " {TEXT -1 15 " INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "dismantle(x^4);" }}{PARA 6 " " 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 7 "PROD(3)" }}{PARA 6 "" 1 "" {TEXT -1 13 " NAME(4): x" }}{PARA 6 "" 1 "" {TEXT -1 15 " \+ INTPOS(2): 4" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "dismantle(x^a);" }}{PARA 6 "" 1 "" {TEXT -1 0 " " }}{PARA 6 "" 1 "" {TEXT -1 8 "POWER(3)" }}{PARA 6 "" 1 "" {TEXT -1 13 " NAME(4): x" }}{PARA 6 "" 1 "" {TEXT -1 13 " NAME(4): a" }} {PARA 6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "subs(1=3, pol2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&)%#PiG\" \"$\"\"\")%\"xGF'F(F'F*F'\"\"*\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "nops(pol2);op(pol2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%*&%#PiG\"\"\"%\"xGF%F&F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "whattype(op(1,pol2));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%\"*G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "op(op(1,pol2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%# PiG%\"xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "dismantle(pol2) ;" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 6 "SUM(7 )" }}{PARA 6 "" 1 "" {TEXT -1 10 " PROD(5)" }}{PARA 6 "" 1 "" {TEXT -1 30 " NAME(4): Pi #[protected]" }}{PARA 6 "" 1 "" {TEXT -1 18 " INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 16 " NAME(4): x" } }{PARA 6 "" 1 "" {TEXT -1 18 " INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 15 " INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 13 " NAME(4 ): x" }}{PARA 6 "" 1 "" {TEXT -1 15 " INTPOS(2): 1" }}{PARA 6 "" 1 " " {TEXT -1 15 " INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 15 " INTP OS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 57 "Dale si vsimneme interni reprezentace racionalni funkce. \n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "r:=(y^2-1)/(y-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG*&,&*$)%\"yG\"\"#\"\"\"\"\"\"!\"\"F,F+ ,&F)F,F-F,!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "dismantl e(r);" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 7 "P ROD(5)" }}{PARA 6 "" 1 "" {TEXT -1 9 " SUM(5)" }}{PARA 6 "" 1 "" {TEXT -1 13 " PROD(3)" }}{PARA 6 "" 1 "" {TEXT -1 19 " NA ME(4): y" }}{PARA 6 "" 1 "" {TEXT -1 21 " INTPOS(2): 2" }} {PARA 6 "" 1 "" {TEXT -1 18 " INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 19 " INTNEG(2): -1" }}{PARA 6 "" 1 "" {TEXT -1 18 " \+ INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 15 " INTPOS(2): 1" }} {PARA 6 "" 1 "" {TEXT -1 9 " SUM(5)" }}{PARA 6 "" 1 "" {TEXT -1 16 " NAME(4): y" }}{PARA 6 "" 1 "" {TEXT -1 18 " INTPOS(2): 1" } }{PARA 6 "" 1 "" {TEXT -1 19 " INTNEG(2): -1" }}{PARA 6 "" 1 "" {TEXT -1 18 " INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 16 " INT NEG(2): -1" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 19 "type(r, `ratpoly`);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "whattype(r );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"*G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "op(r);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,&*$)%\"y G\"\"#\"\"\"\"\"\"!\"\"F)*&F(F(,&F&F)F*F)!\"\"" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 8 "op(2,r);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*& \"\"\"F$,&%\"yG\"\"\"!\"\"F'!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "whattype(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"^G " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "op(%%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,&%\"yG\"\"\"!\"\"F%F&" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 10 "normal(r);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\" yG\"\"\"F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "dismantle(r );" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 7 "PROD (5)" }}{PARA 6 "" 1 "" {TEXT -1 9 " SUM(5)" }}{PARA 6 "" 1 "" {TEXT -1 13 " PROD(3)" }}{PARA 6 "" 1 "" {TEXT -1 19 " NAME(4): y" }}{PARA 6 "" 1 "" {TEXT -1 21 " INTPOS(2): 2" }}{PARA 6 " " 1 "" {TEXT -1 18 " INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 19 " INTNEG(2): -1" }}{PARA 6 "" 1 "" {TEXT -1 18 " INTPOS(2): \+ 1" }}{PARA 6 "" 1 "" {TEXT -1 15 " INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 9 " SUM(5)" }}{PARA 6 "" 1 "" {TEXT -1 16 " NAME(4): y " }}{PARA 6 "" 1 "" {TEXT -1 18 " INTPOS(2): 1" }}{PARA 6 "" 1 " " {TEXT -1 19 " INTNEG(2): -1" }}{PARA 6 "" 1 "" {TEXT -1 18 " \+ INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 16 " INTNEG(2): -1" }} {PARA 6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 155 " Opet vidime, ze interni datova struktura se lisi od externi, zobrazene na obrazovce. Racionalni funkce je soucinem\ncitatele a jmenovatele u mocneneho na -1." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "r:=(sin(x)^2-1) /(sin(x)-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG*&,&*$)-%$sinG6# %\"xG\"\"#\"\"\"\"\"\"!\"\"F/F.,&F)F/F0F/!\"\"" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 19 "type(r, `ratpoly`);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 " type(r, `ratpoly`(`integer`, sin(x)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "dismantle( r);" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 7 "PRO D(5)" }}{PARA 6 "" 1 "" {TEXT -1 9 " SUM(5)" }}{PARA 6 "" 1 "" {TEXT -1 13 " PROD(3)" }}{PARA 6 "" 1 "" {TEXT -1 20 " FU NCTION(3)" }}{PARA 6 "" 1 "" {TEXT -1 37 " NAME(4): sin #[p rotected]" }}{PARA 6 "" 1 "" {TEXT -1 21 " EXPSEQ(2)" }} {PARA 6 "" 1 "" {TEXT -1 25 " NAME(4): x" }}{PARA 6 "" 1 "" {TEXT -1 21 " INTPOS(2): 2" }}{PARA 6 "" 1 "" {TEXT -1 18 " INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 19 " INTNEG(2) : -1" }}{PARA 6 "" 1 "" {TEXT -1 18 " INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 15 " INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 9 " SU M(5)" }}{PARA 6 "" 1 "" {TEXT -1 17 " FUNCTION(3)" }}{PARA 6 "" 1 "" {TEXT -1 34 " NAME(4): sin #[protected]" }}{PARA 6 "" 1 " " {TEXT -1 18 " EXPSEQ(2)" }}{PARA 6 "" 1 "" {TEXT -1 22 " \+ NAME(4): x" }}{PARA 6 "" 1 "" {TEXT -1 18 " INTPOS(2): 1 " }}{PARA 6 "" 1 "" {TEXT -1 19 " INTNEG(2): -1" }}{PARA 6 "" 1 " " {TEXT -1 18 " INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 16 " I NTNEG(2): -1" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 66 "R je racionalni fce v promenne sin(x) s celociselnymi k oeficienty." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "normal(r);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%$sinG6#%\"xG\"\"\"F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 205 "Maple povazuje r za zobecnenou racionalni funk ci.\nProcedura normal automaticky \"uzavira\" funkci sin(x) pouze do j mena, provede zjednoduseni\na opet fci sin(x) \"otevira\". Obdobne se \+ chova i procedura factor." }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 10 "Su bstituce" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 132 "Nejjednodussi formou \+ substituce je prikaz\nsubs(var=replacement, expression).\nMa ten efekt , ze replacement je substituovan misto var " }}{PARA 0 "" 0 "" {TEXT -1 13 "v expression." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "subs(x=0, c os(x)*(sin(x)+x^2+1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%$cosG6# \"\"!\"\"\",&-%$sinGF&F(F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "eval(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 54 "Vysledek substituce je zjednodusen, ale n e vyhodnocen." }}{PARA 0 "" 0 "" {TEXT -1 19 "Nasobne substituce:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 " expression:=1+tan(x)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+expressionG,&\"\"\"F&*$)-%$tanG6#%\"xG\" \"#\"\"\"F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "subs(tan(x)= sin(x)/cos(x), sin(x)^2=1-cos(x)^2, expression);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"\"\"F$*&,&F$F$*$)-%$cosG6#%\"xG\"\"#\"\"\"!\"\"F.*$ )F)\"\"#F.!\"\"F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "normal (%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&\"\"\"F$*$)-%$cosG6#%\"xG\" \"#F$!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 240 "V tomto pripade se nejdrive provede prvni substituce, v ziskanem vyrazu se provede druha substituce.\nTomuto zpusobu se rika posloupnost substituci.\nDruhym z pusobem je tzv. soucasna substituce. (Substitucni rovnice uzavreme do \+ \{ \} zavorek).\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "subs(\{x=y, y= z\}, x*y^2); #soucasna substituce" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#* &%\"yG\"\"\")%\"zG\"\"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "subs(x=y, y=z, x*y^2); #posloupnost substituci" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)%\"zG\"\"$\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "subs(a=b, b=c, c=a, a+2*b+3*c);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%\"aG\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "subs(\{a=b, b=c, c=a\}, a+2*b+3*c);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"bG\"\"\"%\"cG\"\"#%\"aG\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 116 "Muzeme provadet i substituci za casti vyrazu.\nPodminkou je, ze Maple interne rozezna podvyraz (vystup procedury op)." }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "expr1:=x*y+z; expr2:=x*y*z; expr3:= (x*y)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&expr1G,&*&%\"xG\"\"\"% \"yGF(F(%\"zGF(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&expr2G*(%\"xG\" \"\"%\"yGF'%\"zGF'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&expr3G*&)%\"x G\"\"#\"\"\")%\"yGF(F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "s ubs(x*y=product, expr1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%(produc tG\"\"\"%\"zGF%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "subs(x*y =product, expr2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(%\"xG\"\"\"%\"y GF%%\"zGF%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "subs(x*y=prod uct, expr3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&)%\"xG\"\"#\"\"\")% \"yGF&F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "op(expr1);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$*&%\"xG\"\"\"%\"yGF%%\"zG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "op(expr2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%%\"xG%\"yG%\"zG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "op(expr3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$*$)%\"xG\"\"#\" \"\"*$)%\"yGF&F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "V druhem prip ade muzeme pouzit proceduru algsubs:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "algsubs(x*y=product, expr2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"zG\"\"\"%(productGF%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "algsubs(x*y=product, expr3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)%(productG\"\"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "applyrule(x*y=product, expr2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"zG\"\"\"%(productGF%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "applyrule(x*y=procucst, expr3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&)%\"xG\"\"#\"\"\")%\"yGF&F'" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 103 "Substituce se provadi za casti vyrazu (algebraicky), n e za casti ve smyslu interni datove reprezentace." }}{PARA 0 "" 0 "" {TEXT -1 51 "Muzeme pouzit i proceduru powsubs z baliku student." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(student):" }}{PARA 7 " " 1 "" {TEXT -1 29 "Warning, new definition for D" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 28 "powsubs(x*y=product, expr2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"zG\"\"\"%(productGF%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "powsubs(x*y=product, expr3);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#*$)%(productG\"\"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 26 "powsubs(x*y^2=s, x^3*y^4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&)%\"sG\"\"#\"\"\"%\"xG\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "subs(x*y^2=s, x^3*y^4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&)%\"xG\"\"$\"\"\")%\"yG\"\"%F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 124 "Procedura algsubs (algebraic substitution) funguje \+ i pro casti souctu a neni tak uzce spjata s interni strukturou jako su bs." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "vyraz:=a+b+c;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%&vyrazG,(%\"aG\"\"\"%\"bGF'%\"cGF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "subs(a+b=d, vyraz);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"aG\"\"\"%\"bGF%%\"cGF%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "algsubs(a+b=d, vyraz); " }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"dG\"\"\"%\"cGF%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "p:=a+2*b+3*c;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG,(%\"aG\"\"\"%\"bG\"\"#%\"cG\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "applyrule(a+b=d, p);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,(%\"aG\"\"\"%\"bG\"\"#%\"cG\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "algsubs(a+b=d,p);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"bG\"\"\"%\"dGF%%\"cG\"\"$" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 45 "Prikaz eliminoval a, chceme ale eliminovat b." }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "Jako dalsi argument procedury algs ubs muzeme zadat poradi promennych." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "algsubs(a+b=d,p,[b,a]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"aG!\"\"%\"dG\"\"#%\"cG\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "Dalsim volitelnym parametrem je 'exact': " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "algsubs(a+b=d,p,'exact');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"aG\"\"\"%\"bG\"\"#%\"cG\"\"$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "algsubs(a+b=d,2*a+2*b+3*c,'e xact');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"dG\"\"#%\"cG\"\"$" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 276 "Jinou substitucni moznosti je sub stituovat primo za operandy Maplovskeho vyrazu.\nK tomu slouzi procedu ra subsop(num1=replacement, num2=replacement, expression).\nSubstituce se provadi pouze v dane urovni (hloubce). (Subs prochazi celou strukt uru a kazdy vyskyt \nje nahrazovan.)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "vyraz:=x^2+x+1/x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&vyrazG,( *$)%\"xG\"\"#\"\"\"\"\"\"F(F+*&F*F*F(!\"\"F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "subsop(3=y, vyraz);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"xG\"\"#\"\"\"\"\"\"F&F)%\"yGF)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "Treti operand byl nahrazen y.\nSrovnejte " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "subsop(1=z, 2=y,vyraz);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"zG\"\"\"%\"yGF%*&\"\"\"F(%\"xG!\" \"F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 "a" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "subs(x=y, vyraz);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# ,(*$)%\"yG\"\"#\"\"\"\"\"\"F&F)*&F(F(F&!\"\"F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 106 "Dalsi vyhodou procedury subsop je to, ze nemusime p repisovat dlouhe casti vyrazu, ktere chceme nahrazovat." }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 38 "soucin:=(x^2+y^2+2*x*y) * ((x+y)^2+1);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%'soucinG*&,(*$)%\"xG\"\"#\"\"\"\"\" \"*$)%\"yGF*F+F,*&F)F,F/F,F*F,,&*$),&F)F,F/F,F*F+F,F,F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "factor(soucin);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#*&),&%\"xG\"\"\"%\"yGF'\"\"#\"\"\",**$)F&F)F*F'*$)F(F )F*F'*&F&F'F(F'F)F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " subsop(1=factor(op(1, soucin)), soucin);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&),&%\"xG\"\"\"%\"yGF'\"\"#\"\"\",&*$F$F*F'F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "applyop(factor,1,soucin);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&),&%\"xG\"\"\"%\"yGF'\"\"#\"\"\",&*$F$F*F' F'F'F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "applyop" }{TEXT 256 37 " (func, index, vyraz) je to same, jako" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }{TEXT 258 0 "" }{TEXT -1 6 "subsop" }{TEXT 259 38 "(index=func(op(i ndex, vyraz)), vyraz)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "v yraz:=(x^2+2*x+1)^2+(x^2-2*x+1)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%&vyrazG,&*$),(*$)%\"xG\"\"#\"\"\"\"\"\"F+F,F.F.F,F-F.*$),(F)F.F+!\"# F.F.F,F-F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "factor(vyraz) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"xG\"\"%\"\"\"\"\"#*$)F&F) F(\"#7F)\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "op(vyraz) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$*$),(*$)%\"xG\"\"#\"\"\"\"\"\"F(F )F+F+F)F**$),(F&F+F(!\"#F+F+F)F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "subsop(1=factor(op(1,vyraz)), 2=factor(op(2,vyraz)), \+ vyraz);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$),&%\"xG\"\"\"F(F(\"\"% \"\"\"F(*$),&F'F(!\"\"F(F)F*F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 238 "Tohoto vysledku muzeme snadno dosahnout pouzitim procedury map(pr oced, vyraz),\njez ma tento efekt: aplikuje proceduru proced na operan dy vyrazu (na kazdy zvlast), vysledek\nprevadi na puvodni datovy typ a provadi automaticke zjednoduseni.\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "map(factor, vyraz);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$),&% \"xG\"\"\"F(F(\"\"%\"\"\"F(*$),&F'F(!\"\"F(F)F*F(" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "Zjed noduseni z prvniho z prikladu je mozno provest i takto:" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 20 "subs(x+y=z, soucin);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*$)%\"xG\"\"#\"\"\"\"\"\"*$)%\"yGF(F)F**&F'F*F-F*F( F*,&*$)%\"zGF(F)F*F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&),&%\"xG\"\"\"%\"yGF' \"\"#\"\"\",&*$)%\"zGF)F*F'F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "subs(z=x+y, %);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*& ),&%\"xG\"\"\"%\"yGF'\"\"#\"\"\",&*$F$F*F'F'F'F'" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 52 "Toto je casto pouzivana technika pri zjednodusovan i." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "vyraz:=(x+y)^2+1/(x+y)^2;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%&vyrazG,&*$),&%\"xG\"\"\"%\"yGF*\"\" #\"\"\"F**&F-F-*$)F(\"\"#F-!\"\"F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "Chceme transformovat na tvar citatel/jmenovatel bez expanze (x+ y)^2." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "normal(vyraz);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,.*$)%\"xG\"\"%\"\"\"\"\"\"*&)F'\"\"#F))% \"yGF-F)\"\"'*&)F'\"\"$F)F/F*F(*&F'F*)F/F3F)F(*$)F/F(F)F*F*F*F)*$),&F' F*F/F*\"\"#F)!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 134 "Takto nedo stavame pozadovany vysledek. Docasne nahradime x+y pomoci napr. z , po uzijeme normal\na konecne provedeme zpetnou substituci." }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 19 "subs(x+y=z, vyraz);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"zG\"\"#\"\"\"\"\"\"*&F(F(*$)F&\"\"#F(!\"\"F)" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "normal(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&*$)%\"zG\"\"%\"\"\"\"\"\"F*F*F)*$)F'\"\"#F)!\" \"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "subs(z=x+y, %);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&*$),&%\"xG\"\"\"%\"yGF)\"\"%\"\"\" F)F)F)F,*$)F'\"\"#F,!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 120 "Pro zjednoduseni muzeme pouzit procedur freeze a thaw. Maple sam zvoli jm ena pro vyrazy, ktere chceme\ndocasne \"zmrazit\"." }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 16 "readlib(freeze);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #R6#%\"eG6#%#nnG6$%)rememberG%aoCopyright~(c)~1990~by~the~University~o f~Waterloo.~All~rights~reserved.GE\\s\",&%\"xG\"\"\"%\"yGF.%*freeze/R0 G@%-%%typeG6$9$<$%%nameG%(literalGF5C&>8$(%)freeze/RG%-freeze/countG>F >,&F>F.F.F.>-%%thawG6#F;F5F;6\"6#F>FE" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "subs(x+y=freeze(x+y), vyraz);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%*freeze/R0G\"\"#\"\"\"\"\"\"*&F(F(*$)F&\"\"#F(!\" \"F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "normal(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&*$)%*freeze/R0G\"\"%\"\"\"\"\"\"F* F*F)*$)F'\"\"#F)!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "tha w(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&*$),&%\"xG\"\"\"%\"yGF)\" \"%\"\"\"F)F)F)F,*$)F'\"\"#F,!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "2" 0 }{VIEWOPTS 1 1 0 3 2 1804 }