{VERSION 3 0 "IBM INTEL NT" "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 Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "parancsok" -1 256 "" 0 0 128 0 0 1 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "opci\363 " -1 258 "" 0 0 255 0 255 1 0 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 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 "Headin g 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 3" 4 5 1 {CSTYLE "" -1 -1 " " 1 12 0 0 0 0 1 0 0 0 0 0 0 0 0 }0 0 0 -1 0 0 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 "bekezdes" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 0 0 0 0 0 0 0 0 0 }1 2 0 30 -1 -1 0 0 0 0 2 0 -1 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT 257 35 "Programoz\341s elemei, t ov\341bbi grafika" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 21 "Vez\351rl \351si szerkezetek" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 2 "if" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 96 "if feltetel1 then\n utasitas 1\n[elif feltetel2 then]\n utasitas2\n[else\n utasitas3]\nfi" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "a:=-5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "if a<3 then print(\"kicsi\") else print(\"n agy\") fi;\n " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 38 "rel\341ci\363s oper\341torok, logikai m \373veletek" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Rel\341ci\363s oper \341torok:\n<, >, <=, >=, =, <>" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Az " }{TEXT 256 5 "evalb" }{TEXT -1 53 " f\374gv\351nnyel lehet \+ egy logikai kifejez\351st ki\351rt\351kelni:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalb(3<>7);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Logikai m\373veletek:\n" }{TEXT 256 3 "and" }{TEXT -1 4 ", " }{TEXT 256 2 "or" }{TEXT -1 5 ", " }{TEXT 256 3 "not" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "a:=3;\nevalb(a<10 and a>0);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "" 0 " " {TEXT -1 8 "ciklusok" }}{EXCHG {PARA 0 "" 0 "" {TEXT 256 3 "for" } {TEXT -1 16 " ciklusv\341ltoz\363 " }{TEXT 256 4 "from" }{TEXT -1 13 " kezd\365\351rt\351k [" }{TEXT 256 2 "by" }{TEXT -1 12 " l\351p\351sk \366z] " }{TEXT 256 2 "to" }{TEXT -1 10 " v\351g\351rt\351k " }{TEXT 256 2 "do" }{TEXT -1 13 "\n utas\355t\341s\n" }{TEXT 256 2 "od" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "for i from 1 by 2 to 10 do i ; od;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 3 "for" }{TEXT -1 16 " ciklusv\341ltoz\363 " }{TEXT 256 4 "from" }{TEXT -1 13 " kezd\365\351rt\351k [" }{TEXT 256 2 "by" } {TEXT -1 12 " l\351p\351sk\366z] " }{TEXT 256 5 "while" }{TEXT -1 10 " felt\351tel " }{TEXT 256 2 "do" }{TEXT -1 13 "\n utas\355t\341s\n " }{TEXT 256 2 "od" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "for i from 3 by 110 while isprime(i) do i; od;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 3 "for" }{TEXT -1 10 " v\341ltoz\363 " }{TEXT 256 2 "in" }{TEXT -1 7 " lista " }{TEXT 256 2 "do" }{TEXT -1 13 "\n utas\355t\341s\n" }{TEXT 256 2 "od" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "for i in [1,2,5,12] do i^2; \+ od;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "for i in \{3,1,2,-12 ,7\} do i; od;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "i:=1;\nwh ile i<10 do\n i:=i+3;\nod;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "A ciklusb\363l a " }{TEXT 256 5 "break" }{TEXT -1 31 " utas\355t\341ssa l lehet kiugrani, a " }{TEXT 256 4 "next" }{TEXT -1 65 " utas\355t\341 s hat\341s\341ra a Maple visszaugrik a felt\351tel ki\351rt\351kel\351 s\351re." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "Ha a ciklus v\351g \351t jelz\365 od ut\341n \"" }{TEXT 256 1 ":" }{TEXT -1 70 "\"-ot tes z\374nk, akkor a cikluson bel\374li parancsok outputj\341t nem \355rja ki." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "for i from 1 to 10 \+ do i; od:\ni;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 21 "Programok l\351trehoz\341sa" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "programn\351v:=" }{TEXT 256 4 "pro c" }{TEXT -1 30 "(argumentumok)\n utas\355t\341sok\n" }{TEXT 256 3 "end" }{TEXT -1 1 ";" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "pl1 :=proc(x)\n x+8;\nend;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 " pl1(1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "pl1(y);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 134 "Minden elj\341r\341snak van outpu tja (azaz minden elj\341r\341s f\374ggv\351ny).\nA f\374ggv\351ny viss zat\351r\351si \351rt\351ke az utols\363 v\351grehajtott parancs outpu tja." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "pl2:=proc(x)\n a: =4;\n x+a;\nend;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "b:=pl 2(5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 22 "anim\341ci\363s alkalmaz\341sok" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 94 "N\351zz\374nk n\351h\341ny anim \341ci\363s alkalmaz\341st. El\365sz\366r rakjunk \366ssze egy 31 kock \341b\363l \341ll\363 anim\341ci\363t a " }{XPPEDIT 18 0 "sin(x);" "6 #-%$sinG6#%\"xG" }{TEXT -1 39 " f\374ggv\351ny f\374gg\365leges ir\341 ny\372 eltol\341s\341ra:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "for i fro m 0 to 30 do\n g.i:=plot(sin(x)+i*2/30,x=0..30):\nod:\ndisplay(seq(g .j,j=0..30),insequence=true);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 105 "Most k\351sz\355ts\374nk az el\365bbi feladatra egy olyan programot, \+ amelynek param\351terben kapja meg a kock\341k sz\341m\341t:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 161 "sineltolas:=proc(n)\n for i from 0 to n-1 do\n g.i:=plot(sin(x)+i*2/(n-1),x=0..(n-1)):\n \+ od:\n plots[display](seq(g.j,j=0..(n-1)),insequence=true);\nend: \+ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "sineltolas(40);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "A k\366vetkez\365 p\351ld\341ban rajzoljuk ki az \n " } {XPPEDIT 18 0 "x = 10*cos(t)-2*cos(5*t)+15*sin(2*t);" "6#/%\"xG,(*&\"# 5\"\"\"-%$cosG6#%\"tGF(F(*&\"\"#F(-F*6#*&\"\"&F(F,F(F(!\"\"*&\"#:F(-%$ sinG6#*&\"\"#F(F,F(F(F(" }{TEXT -1 3 "\n " }{XPPEDIT 18 0 "y = -15*co s(2*t)+10*sin(t)-2*sin(5*t);" "6#/%\"yG,(*&\"#:\"\"\"-%$cosG6#*&\"\"#F (%\"tGF(F(!\"\"*&\"#5F(-%$sinG6#F.F(F(*&\"\"#F(-F36#*&\"\"&F(F.F(F(F/ " }{TEXT -1 3 "\n " }{XPPEDIT 18 0 "z = 10*cos(3*t);" "6#/%\"zG*&\"#5 \"\"\"-%$cosG6#*&\"\"$F'%\"tGF'F'" }{TEXT -1 13 "\n 0 <= t <= " } {XPPEDIT 18 0 "2*Pi;" "6#*&\"\"#\"\"\"%#PiGF%" }{TEXT -1 117 "\ng\366r b\351t \372gy, hogy a grafikon folyamatosan rajzol\363djon ki a k\351p erny\365re. \nAz elj\341r\341s param\351tere a kock\341k sz\341ma legy en. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 302 "gorberajz:=proc(n) \n x:=t->-10*cos(t)-2*cos(5*t)+15*sin(2*t);\n y:=t->-15*cos(2*t)+1 0*sin(t)-2*sin(5*t);\n z:=t->10*cos(3*t);\n for i from 0 to n do \+ \n g.i:=plots[tubeplot]([x(t),y(t),z(t)], t=0..i*2*Pi/n, radius=0.5);\n od:\n plots[display](seq(g.j,j=0..n),insequence=tru e);\nend: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "gorberajz( 20);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 17 "plottools package" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "with(plottools);\nwith(plots):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "A " }{TEXT 258 9 "plottools" }{TEXT -1 155 " package \+ elemi geometriai alakzatokat defini\341l\363 parancsokat valamint geom etriai transzform\341ci\363kat v\351grehajt\363 parancsokat tartalmaz. Az elemi alakzatokat a " }{TEXT 256 7 "display" }{TEXT -1 32 " paranc csal lehet megjelen\355teni." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 3 "a rc" }{TEXT -1 44 " : k\366r\355v - k\366z\351ppont, sug\341r, sz\366gt artom\341ny " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "display(ar c([0,0],1,Pi/6..5*Pi/4),scaling=constrained);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 5 "arrow" }{TEXT -1 76 " : ny\355l - kezd\365pont, v\351 gpont, sz\351less\351g, fej sz\351less\351ge, fej-hossz ar\341nya " } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "display(arrow([0,0],[1,1], 0.1,0.2,0.25),scaling=constrained);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 6 "circle" }{TEXT -1 25 " : k\366r - k\366z\351ppont, sug\341r" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "display(circle([0,0],0.2),s caling=constrained);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 4 "line" } {TEXT -1 31 " : szakasz - kezd\365pont, v\351gpont" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "display(line([0,0],[1,2]),thickness=3,color =blue);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "display(line([1, 0,0],[0,1,2]),axes=boxed,thickness=3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 5 "point" }{TEXT -1 20 " : pont - koordin\341ta" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "display(point([1,1]),color=blue);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 7 "polygon" }{TEXT -1 10 " : soksz \366g" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "display(polygon([[ 0,0],[1,1],[2,-1],[0.5,-0.5]]),color=blue);" }}}{EXCHG {PARA 0 "" 0 " " {TEXT 256 6 "sphere" }{TEXT -1 26 " : g\366mb - k\366z\351ppont, sug \341r" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "display(sphere([1, 1,0],2),color=blue,axes=frame,scaling=constrained);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 10 "hexahedron" }{TEXT -1 32 " : kocka - k\366z \351ppont, oldalhossz" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "di splay(hexahedron([1,1,0],2),color=green,axes=frame,scaling=constrained );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 11 "tetrahedron" }{TEXT -1 35 " : tetra\351der - k\366z\351ppont, sz\351less\351g" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "display(tetrahedron([1,1,0],2),color=gree n,axes=frame,scaling=constrained);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 10 "octahedron" }{TEXT -1 34 " : okta\351der - k\366z\351ppont, sz \351less\351g" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "display(oc tahedron([1,1,0],2),color=green,axes=frame,scaling=constrained);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 256 12 "dodecahedron" }{TEXT -1 36 " : do deka\351der - k\366z\351ppont, sz\351less\351g" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 76 "display(dodecahedron([1,1,0],2),color=green,ax es=frame,scaling=constrained);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 11 "icosahedron" }{TEXT -1 35 " : ikoza\351der - k\366z\351ppont, sz \351less\351g" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "display(ic osahedron([0,1,0],1),color=magenta,axes=frame,scaling=constrained);" } }}{EXCHG {PARA 0 "" 0 "" {TEXT 256 7 "reflect" }{TEXT -1 40 " : t\374k r\366z\351s - grafika, pont koordin\341t\341ja" }}{PARA 0 "" 0 "" {TEXT -1 77 " vagy - grafika, egyenest meghat\341ro z\363 k\351t pont koordin\341t\341i" }}{PARA 0 "" 0 "" {TEXT -1 76 " \+ vagy - grafika, s\355kot meghat\341roz\363 h\341rom \+ pont koordin\341t\341i" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "a :=octahedron():\nb:=reflect(a,[0,0,1]):\ndisplay(a,b,axes=normal,scali ng=constrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 145 "a:=hex ahedron():\nb:=reflect(a,[[3,0,0],[0,3,0],[0,0,3]]):\nc:=polygon([[3,0 ,0],[0,3,0],[0,0,3]]):\ndisplay(a,b,c,axes=normal,orientation=[-45,75] );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 6 "rotate" }{TEXT -1 163 " : f orgat\341s - grafika, x-tengely forgat\341s k\366r\374li sz\366g, y-k \366r\374li sz\366g, z-k\366r\374li sz\366g\n vagy - g rafika, s\355kbeli forgat\341s sz\366ge, [forgat\341s k\366z\351ppontj a]" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 83 "\nA k\366vetkez\365 program a z-tengely k\366r\374l fogat k\366rbe egy t\351rbeli grafik\341t n l \351p\351sben:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 141 "forgat:= proc(gr,n)\nfor i from 0 to n-1 do \n g.i:=plottools[rotate](gr,0,0, i*2*Pi/n);\nod:\ndisplay(seq(g.j,j=0..(n-1)),insequence=true);\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "forgat(icosahedron(),20); " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 9 "translate" }{TEXT -1 66 " : e ltol\341s - grafika, x-ir\341ny\372, y-ir\341ny\372, z-ir\341ny\372 el tol\341s m\351rt\351ke" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "a :=octahedron():\nb:=translate(a,1,2,2):\ndisplay(a,b,axes=normal,scali ng=constrained);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 5 "scale" } {TEXT -1 74 " : ny\372jt\341s - grafika, x-ir\341ny\372, y-ir\341ny \372, z-ir\341ny\372 ny\372jt\341s szorz\363t\351nyez\365je" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "a:=sphere():\nb:=scale(a,0.3 ,2,1):\ndisplay(a,b,axes=boxed,scaling=constrained,style=wireframe);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "2 0 0" 6 } {VIEWOPTS 1 1 0 3 2 1804 }