{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 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }0 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 0 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 "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 }} {SECT 0 {EXCHG {PARA 258 "" 0 "" {TEXT -1 30 "Grundregeln der Vektorad dition" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "with(plots, display): \+ Dicke := 5:" }}{PARA 256 "" 0 "" {TEXT -1 34 "Prozedur zum Zeichnen ei nes Pfeils" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 894 "v := proc(Anfang, Ende, Farbe)\nglobal Dicke;\nlocal dx, dy, phi, phi1, phi2, l1, l2, r1, r2;\ndx := Ende[1] - Anfang[1];\ndy := Ende[2] - An fang[2];\nif (abs(dy) > abs(dx)) then\n phi := Pi/2 - arctan(dx/dy) \nelif (abs(dx) > 0) then\n phi := arctan(dy/dx)\nelse return(plot([ Anfang[1], Anfang[2]], color=Farbe))\nfi;\n phi1 := phi + Pi/8;\n \+ phi2 := phi - Pi/8;\n l1 := Ende[1] - 0.2*sign(dy)*cos(phi1);\n l2 := Ende[2] - 0.2*sign(dy)*sin(phi1);\n r1 := Ende[1] - 0.2*sign(dy) *cos(phi2);\n r2 := Ende[2] - 0.2*sign(dy)*sin(phi2);\n plots[disp lay]([\n plot([[Anfang[1], Anfang[2]], [Ende[1], Ende[2]]], color=Fa rbe,\n thickness=Dicke, axes=none, scaling=constrained),\n plot( [[l1, l2], [Ende[1], Ende[2]]], color=Farbe,\n thickness=Dicke, ax es=none, scaling=constrained),\n plot([[r1, r2], [Ende[1], Ende[2]]] , color=Farbe,\n thickness=Dicke, axes=none, scaling=constrained)] );\nend:" }}{PARA 257 "" 0 "" {TEXT -1 33 "Demonstration der Vektoradd ition:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 668 "Parallelogramm := proc(a , b)\nlocal c;\nc := a + b;\ndisplay([\ndisplay([v([0,0], a, red), v([ 0,0], b, green)]),\ndisplay([v([0,0], a, red), v([0,0], b, green), v(a , c, green)]),\ndisplay([v([0,0], a, red), v([0,0], b, green),\n \+ v(a, c, green), v([0,0], c, blue)]),\ndisplay([v([0,0], a, red), v( [0,0], b, green)]),\ndisplay([v([0,0], a, red), v([0,0], b, green), v( b, c, red)]),\ndisplay([v([0,0], a, red), v([0,0], b, green),\n \+ v(b, c, red), v([0,0], c, blue)]),\ndisplay([v([0,0], a, red), v([0, 0], b, green), v(a, c, green),\n v(b, c, red), v([0,0], c, blu e)]),\ndisplay([v([0,0], a, red), v([0,0], b, green), v([0,0], c, blue )])],\ninsequence=true);\nend:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1140 "Assoziativgesetz := proc(a, b, c)\nlocal ab, bc, ac, abc;\nab := a+b; bc := b+c; ac := a+c; abc := a+b+c;\ndisplay([\ndisplay([v([0,0], a, \+ green), v([0,0], b, red), v([0,0], c, blue)]),\ndisplay([v([0,0], a, g reen), v([0,0], b, red),\n v([0,0], c, blue), v(a, ab, red)]), \ndisplay([v([0,0], a, green), v([0,0], b, red),\n v([0,0], c, blue), v(a, ab, red), v([0,0], ab, brown)]),\ndisplay([v([0,0], a, gr een), v([0,0], b, red),\n v([0,0], c, blue), v(a, ab, red),\n \+ v([0,0], ab, brown), v(ab, abc, blue)]),\ndisplay([v([0,0], a, green), v([0,0], b, red),\n v([0,0], c, blue), v(a, ab, red), v([0,0], ab, brown),\n v(ab, abc, blue), v([0,0], abc, cyan)] ),\ndisplay([v([0,0], a, green), v([0,0], b, red),\n v([0,0], \+ c, blue), v(a, ab, red), v([0,0], ab, brown),\n v(ab, abc, blu e), v([0,0], abc, cyan),\n v(b, bc, blue), v([0,0], bc, plum)] ),\ndisplay([v([0,0], a, green), v([0,0], b, red),\n v([0,0], \+ c, blue), v(a, ab, red), v([0,0], ab, brown),\n v(ab, abc, blu e), v([0,0], abc, cyan),\n v(b, bc, blue), v([0,0], bc, plum), v(a, abc, plum)])],\ninsequence=true);\nend:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 350 "Invers := proc(a)\nlocal s, l;\nl := sqrt(a[1]^2 + a [2]^2);\ns := [-a[2]/l*0.2, a[1]/l*0.2];\ndisplay([\nv([0, 0], a, red) ,\ndisplay([v([0, 0], a, red), v([0, 0], -a, blue)]),\ndisplay([v([0, \+ 0], a, red), v([0, 0], -a, blue),\nv(a + s, s, blue)]),\ndisplay([v([0 , 0], a, red), v([0, 0], -a, blue),\nv(a + s, s, blue), v(-a+s, s, red )])], insequence=true);\nend:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 819 "D istributiv := proc(a, b, lambda)\nglobal Dicke;\nlocal Summe1, Summe2, AlteDicke;\nAlteDicke := Dicke; \nif abs(lambda) > 1 then\nSumme1 := \+ display([\nv([0,0], a, red), v([0, 0], b, blue), v([0,0], a+b, plum), \nv(a, a+b, blue), v(b, a+b, red)]);\nDicke := floor(Dicke / 2);\nSumm e2 := display([\nv([0,0], lambda*a, orange), v([0, 0], lambda*b, cyan) , v([0,0], lambda*(a+b), coral), v(lambda*a, lambda*(a+b), cyan), v(la mbda*b, lambda*(a+b), orange)]);\nelse\nSumme1 := display([\nv([0,0], \+ lambda*a, red), v([0, 0], lambda*b, blue), v([0,0], lambda*(a+b), plum ), v(lambda*a, lambda*(a+b), blue), v(lambda*b, lambda*(a+b), red)]); \nDicke := floor(Dicke / 2);\nSumme2 := display([\nv([0,0], a, orange) , v([0, 0], b, cyan), v([0,0], a+b, coral),\nv(a, a+b, cyan), v(b, a+b , orange)]);\nfi;\nDicke := AlteDicke;\ndisplay([Summe1, Summe2])\nend :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Parallelogramm([3,5],[ 4,2]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "Assoziativgesetz( [3,5], [4,3], [3,1/2]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 " Invers([3,5]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "Distribut iv([3,5], [4,2], 1.6);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "1 0 0" 8 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }