{VERSION 2 3 "SUN SPARC SOLARIS" "2.3" } {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 "" -1 256 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 100 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 208 0 220 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 0 1 74 0 202 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 64 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 32 125 10 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 "" 0 1 0 0 5 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 64 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 } {CSTYLE "" -1 269 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 0 1 0 0 127 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 271 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 272 "" 0 1 69 88 84 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 273 "" 0 1 0 0 140 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 274 "" 0 1 185 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 276 "" 0 1 79 118 48 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 277 "" 0 1 10 123 72 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 278 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 279 "" 0 1 0 0 5 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 280 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 281 "" 0 1 0 0 17 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 282 "" 0 1 185 0 1 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 283 "" 0 1 255 255 68 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 285 "" 0 1 184 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 286 "" 0 1 184 0 7 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 287 "" 0 1 2 0 11 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 288 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 289 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 290 "" 0 1 0 0 232 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 291 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 292 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 293 "" 0 1 255 255 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 294 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 295 "" 0 1 0 0 255 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 296 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 297 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 298 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 299 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 300 "" 0 1 10 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 301 "" 0 1 0 0 0 0 1 0 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 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading \+ 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 4 4 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 "Heading 4" 5 20 1 {CSTYLE "" -1 -1 "" 1 10 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 } } {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 18 "" 0 "" {TEXT -1 10 "4. Sitzung" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 30 "Erinnerung an die 3.te Sitzung" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 73 "a) Ge he zurueck zur 3. Sitzung, falls diese noch nicht abgeschlossen war." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 89 "b) Es sind i n den ersten 3 Sitzungen die folgenden Operatoren und Funktionen aufge taucht:" }}{PARA 0 "" 0 "" {TEXT -1 2 " " }{TEXT 257 267 "$ , ` ` \+ , ' ' , . , add , BesselJ , cat , convert , diff , evalf , evaln , expand , factor , fsolve , help , ifactor , int , isprime , lhs, mu l , nops , op , plot , print , product , rhs , seq , simplify , sort , sqrt , subs , subsop , sum , taylor , writeto" }{TEXT -1 1 " " }} {PARA 0 "" 0 "" {TEXT -1 58 "Was ist die jeweilige Bedeutung? Benutze \+ im zweifelsfalle " }{TEXT 256 4 "help" }{TEXT -1 35 " , um die Erinner ung aufzufrischen." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "help( );" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "c) Ergibt " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "subs( f(x)=1 , diff(f(x),x) );" }}{PARA 0 "" 0 "" {TEXT -1 19 "sofort den Wert 0 ?" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "d) Sei " }{TEXT 258 5 "Folge" }{TEXT -1 40 " eine MAPLE-Folge. Wi e haengt die durch" }}{PARA 0 "" 0 "" {TEXT -1 2 " " }{TEXT 259 52 "n :=nops([Folge]); neueFolge:= Folge[n-i]$i=0..n-1;" }}{PARA 0 "" 0 " " {TEXT -1 10 "erzeugte " }{TEXT 260 9 "neueFolge" }{TEXT -1 7 " mit " }{TEXT 261 5 "Folge" }{TEXT -1 13 " zusammen? " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "e) Was liefert " }{TEXT 262 9 "op(1,a^b)" } {TEXT -1 8 " bzw. " }{TEXT 263 9 "op(2,a^b)" }{TEXT -1 2 " ?" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "f) Sei" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "t:=taylor( a7*x^7+a9*x^9+a14*x^14 , x=0, 10);" }}{PARA 0 "" 0 "" {TEXT -1 30 "Was sind die Operanden von \+ t ?" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "Platz;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 76 "g) Finde heraus, welche numerischen Loesungen polyno mialer Gleichungen von " }{TEXT 265 6 "fsolve" }{TEXT -1 18 " gefund en werden!" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "help(fsolve);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "h) Finde numerische Approximatione n aller " }{TEXT 266 7 "reellen" }{TEXT -1 15 " Loesungen von " } {TEXT 264 25 " x + x^2 + ... + x^10 = 1" }{TEXT -1 2 " !" }{MPLTEXT 1 0 1 " " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "Platz;" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 8 "Loesung:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "Probiere zunaechst eine eigene Loesung !" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 8 "Loesung:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "x:='x': fsolve( sum(x^'i','i'=1..10) = 1 , x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "Graphische Kontrolle:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "plot( sum(x^'i','i'=1..10) -1 , x=-1.2 ..0.8);" }}}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "i) Finde numerische Approximationen " } {TEXT 268 5 "aller" }{TEXT -1 27 " (komplexen) Loesungen von " }{TEXT 267 25 " x + x^2 + ... + x^10 = 1" }{TEXT -1 2 " !" }{MPLTEXT 1 0 1 " \+ " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "Platz;" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 8 "Loesung:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "P robiere zunaechst eine eigene Loesung !" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 8 "Loesung:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "x:=' x': fsolve( sum(x^'i','i'=1..10) = 1 ,x,complex);" }}}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "j) Finde numerisch die ersten 10 positiven Null stellen von " }{TEXT 269 13 " BesselJ(0,x)" }{TEXT -1 66 " (finde zun aechst graphisch grobe Lokalisierungen, dann benutze " }{TEXT 277 6 " fsolve" }{TEXT -1 47 " mit Vorgabe eines Suchintervalls). Nenne sie \+ " }{TEXT 270 13 "x[1],..,x[10]" }{TEXT -1 3 " . " }}{PARA 0 "" 0 "" {TEXT -1 34 "Berechne hiermit die Differenzen " }{TEXT 271 31 "y[i]:= evalf( (x[i]-x[i-1])/Pi )" }{TEXT -1 4 " ! " }}{PARA 0 "" 0 "" {TEXT -1 29 "Welche Vermutung ergibt sich?" }}{PARA 0 "" 0 "" {TEXT -1 7 "Fi nde " }{TEXT 272 13 "c[1],..,c[10]" }{TEXT -1 12 ", so dass " } {TEXT 273 18 "x[i]=c[i] + i * Pi" }{TEXT -1 9 " gilt! " }}{PARA 0 " " 0 "" {TEXT -1 24 "Finde unter der Annahme " }{TEXT 278 5 "c[10]" } {TEXT -1 18 " ungefaehr gleich " }{TEXT 279 6 "c[999]" }{TEXT -1 18 " \+ ungefaehr gleich " }{TEXT 280 7 "c[1000]" }{TEXT -1 12 " numerisch " }{TEXT 274 17 "x[999] , x[1000]," }{TEXT -1 1 " " }{TEXT 275 7 "y[1000 ]" }{TEXT -1 7 " und " }{TEXT 276 7 "c[1000]" }{TEXT -1 3 " !" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "Platz;" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 8 "Loesung:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "Vers uche zunaechst eine eigene Loesung !" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 8 "Loesung:" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Grobe Loka lisierung der Nullstellen:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "f:=Be sselJ; plot(f(0,x),x=0..33 );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 77 " Finde die ersten Nullstellen mit aus der Graphik abgelesenen Suchinter vallen:" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "x[1]: =fsolve(f(0,x),x,2..3);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "x[2]:=fs olve(f(0,x),x,5..6);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "x[3]:=fsolv e(f(0,x),x,8..9);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "x[4]:=fsolve(f (0,x),x,11..12);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "x[5]:=fsolve(f( 0,x),x,14..15);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "x[6]:=fsolve(f(0 ,x),x,17..19);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "x[7]:=fsolve(f(0, x),x,21..22);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "x[8]:=fsolve(f(0,x ),x,24..25);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "x[9]:=fsolve(f(0,x) ,x,27..28);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "x[10]:=fsolve(f(0,x) ,x,30..31);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "Bestimme den Absta nd aufeinander folgender Nullstellen:" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "for i from 2 to 10 do \n y[i]:=evalf((x[i]-x [i-1])/Pi);\nod;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "Vermutung: \+ " }{XPPEDIT 18 0 "limit( y[i],i=infinity)=Pi " "/-%&limitG6$&%\"yG6#% \"iG/F)%)infinityG%#PiG" }{TEXT -1 41 " . Damit liegt nahe, dass fue r grosses " }{TEXT 295 1 "i" }{TEXT -1 31 " die Nullstellen von der Fo rm " }{TEXT 294 27 "x[i] approx const + i*Pi " }{TEXT -1 4 "sind" } {TEXT 296 2 ". " }{TEXT -1 10 "Fuehrt man" }{TEXT 298 18 " c[i]:=x[i]- i*Pi " }{TEXT -1 39 "ein, so liegt die Vermutung nahe, dass " }{TEXT 297 4 "c[i]" }{TEXT -1 13 " konvergiert:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "for i from 1 to 10 do\n c[i]:= evalf( x[i]- i*Pi);\no d;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "Dies fuehrt zur Vorhersage \+ " }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "approx:= -0. 8 + 999* Pi;" }}{PARA 0 "" 0 "" {TEXT -1 76 "fuer die 999.te Nullstell e. Suche in einem kleinen Intervall um diesen Wert:" }{MPLTEXT 1 0 0 " " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "x[999]:= fsolve(f(0,x),x,approx -1 .. approx+1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Analog fuer d ie 1000.te Nullstelle:" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "approx:= -0.8 + 1000* Pi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "x[1000]:= fsolve(f(0,x),x,approx-1 .. approx+1);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Hiermit ergibt sich" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "y[1000]:=evalf((x[1000]-x[ 999])/Pi);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "c[ 999]:=evalf(x[ 999 ]- 999*Pi);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "c[1000]:=evalf(x[100 0]-1000*Pi);" }}}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 10 "Mehr MAPLE" } }{SECT 1 {PARA 4 "" 0 "" {TEXT -1 5 "Typen" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 96 "MAPLE-Ausdruecke werden ihres mathematischen Aufbaus gema ess in Typen eingeteilt. Die Funktion " }{TEXT 281 8 "whattype" } {TEXT -1 45 " liefert die Typ-Bezeichnung (einen String):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Integer:=2; whattype(Integer);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Rational:=2/3: whattype(Rational);" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 32 "Reell:=1.234; whattype(Reell);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "Name:=a; whattype(Name);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "Summe:=a+b; whattype(Summe);" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 34 "Produkt:=a*b; whattype(Produkt);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "Potenz:=a^b; whattype(Potenz);" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "Gleichung:=a=b; whattype(Gleichung) ;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Bereich:= a..b; whattype(Berei ch);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "Menge:=\{a,b\}; whattype( Menge);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "Liste:=[a,b]; whattype (Liste);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "Folge:= a,b ; whattyp e(Folge);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Funktion:=a(b); whatty pe(Funktion);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "Reihe:=taylor(exp( x),x=0,2); whattype(Reihe);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "Al ternativ liefert op(0,Ausdruck) den Typ-Bezeichner:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "op(0,2);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "op(0,1.234);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "op (0,Name);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "op(0,Summe);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "op(0,Menge);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "Achtung:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "whattype(Fu nktion); op(0,Funktion);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "Welch en Typ hat 10! ?" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "whattype(10!) ;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "Welchen Typ hat a! ?" } {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "a:=evaln(a); wh attype(a!);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 102 "Der Fakultaetsope rator ist also in Wirklichkeit ein Funktionsaufruf. Welchen Namen hat \+ diese Funktion?" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "op(0,a!);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "In der Tat ergibt sich" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "factorial(6); factorial(a);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Was steckt hinter dem $ -Operator ?" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "expr:= a$b;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "whattype(expr);op(0,expr);" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 11 "In der Tat:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "$(a[i ],i=1..5);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "In" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "whattype(a$1);" }}{PARA 0 "" 0 "" {TEXT -1 27 "e rgibt die Evaluierung von " }{TEXT 290 3 "a$1" }{TEXT -1 11 " zum Wert " }{TEXT 292 1 "a" }{TEXT -1 17 " den Typ-Namen " }{TEXT 293 6 "st ring" }{TEXT -1 2 " ," }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "in" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "whattype(a$3);" } }{PARA 0 "" 0 "" {TEXT -1 28 "ergibt sich der Folgen-Typ ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "op(20,a$50);" }}{PARA 0 "" 0 "" {TEXT -1 24 "funktioniert nicht, da " }{TEXT 291 2 "op" }{TEXT -1 25 " nicht auf Folgen wirkt." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Wel chen Typ haben" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "expr1:=a*b+c*d; e xpr2:=a*(b+c);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "Platz;" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Betrachte" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "Zerlegung:= ifactor(123);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 20 "whattype(Zerlegung);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "Faktor:=op(1,Zerlegung);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 17 "whattype(Faktor);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "op(0,Faktor);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 123 "Die Primfaktoren werden also als unevaluierte Funktionsaufrufe ei ner Funktion mit dem Namen `` (leerer String) dargestellt;" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "Es gibt viele verschie dene Typen in MAPLE:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "help(type); " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "Die Funktion " }{TEXT 283 22 "type( expr, Typ-Name )" }{TEXT -1 31 " dient zur Typ-Ueberpruefun g. " }{TEXT 282 60 "Achtung: ein Ausdruck kann durchaus verschieden Ty pen haben!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "type(1,intege r);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "type(1,posint);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "type(1,numeric);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "type(1,algebraic);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "type(1,constant);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "type(1+sqrt(2),`+`);" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 24 "type(1+sqrt(2),numeric);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "type(1+sqrt(2),algebraic);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "type(1+sqrt(2),constant);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "type(a+b,`+`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "type(a+b,polynom);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "Man kann direkt komplexere Typen abfragen :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "type(a^2,string^integer);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "type(a^2,string^float);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "type([a,b,a]^2.0,list^float) ;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "Lese die Help-Seite zum Them a " }{TEXT 288 16 "type[structured]" }{TEXT -1 3 " . " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "help(type[structured]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "Schreibe ein MAPLE-Funktion " }{TEXT 285 15 "f:= expr -> ..." }{TEXT -1 19 " , die tested, ob " }{TEXT 286 4 "expr" } {TEXT -1 38 " eine Menge von Integern ist (Ausgabe " }{TEXT 287 4 "tru e" }{TEXT -1 7 " oder " }{TEXT 289 5 "false" }{TEXT -1 3 " )!" } {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "Platz;" }}} {SECT 1 {PARA 5 "" 0 "" {TEXT -1 9 "Loesunng:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "versuche zunaechst eine eigene Loesung !" }}} {SECT 1 {PARA 20 "" 0 "" {TEXT -1 8 "Loesung:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "f:= expr -> type(expr,set(integer));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "f(\{1,2,3\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "f(\{1,2,a\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "f( [1,2,3]);" }}}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Eine Abfrage der \+ Form " }{TEXT 301 4 "type" }{XPPEDIT 18 0 "``( expr, \{Typ[1],Typ[2], ``..` `\})" "-%!G6$%%exprG<%&%$TypG6#\"\"\"&F(6#\"\"#;F#%\"~G" }{TEXT -1 11 " liefert " }{TEXT 299 4 "true" }{TEXT -1 11 " , falls " } {TEXT 300 4 "expr" }{TEXT -1 19 " entweder vom Typ " }{XPPEDIT 18 0 " Typ[1] " "&%$TypG6#\"\"\"" }{TEXT -1 14 " oder vom Typ " }{XPPEDIT 18 0 "Typ[2] " "&%$TypG6#\"\"#" }{TEXT -1 14 " oder ... ist:" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 25 "type( a , \{name,float\} );" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "type(2.0 , \{name,float\} );" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 27 "type(\{a,2.0\},\{name,float\});" }}}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "4 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }