{VERSION 4 0 "SGI MIPS UNIX" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 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 "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 }1 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 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Error" 7 8 1 {CSTYLE "" -1 -1 "" 0 1 255 0 255 1 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 "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 3 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 1 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 25 "Sequences, Lists and Sets " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 159 "A sequence is a tuple of exp ressions (values) separated by commas. The empty sequence is specifie d by NULL. A sequence of sequences becomes one big sequence." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "s := 3,2,1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG6%\"\"$\"\"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "t := NULL;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"tG6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "u := 3,1;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uG6$\"\"$\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "s,t,u;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6' \"\"$\"\"#\"\"\"F#F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 96 "The seq c ommand generates a sequence. It has the syntax seq( f(i), i=a..b \+ ) . For example" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "seq( i ^2, i=1..4 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&\"\"\"\"\"%\"\"*\"#; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "seq( x^i, i=1..4 );" }} {PARA 11 "" 1 "" {XPPMATH 20 "6&%\"xG*$)F#\"\"#\"\"\"*$)F#\"\"$F'*$)F# \"\"%F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "seq( isprime(i), i=1..4 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&%&falseG%%trueGF$F#" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 90 "Some Maple commands output sequenc es as their return value, for example, solve and fsolve." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "solve( x^4-x^2, x );" }}{PARA 11 " " 1 "" {XPPMATH 20 "6&\"\"!F#\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "fsolve( x^6-20*x^2+3, x );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&$!+xOY'4#!\"*$!+p'o^(Q!#5$\"+p'o^(QF($\"+xOY'4#F%" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 174 "All Maple commands take as input \+ a sequence of zero or more arguments. Some have a fixed number of arg uments and some allow for an arbirary number of arguments. For exampl e" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "max(3,2,1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "s := 3,2,1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG6%\"\"$\" \"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "max(s);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 181 "A list is created by enclosing a sequence in [ ... ] bra ckets. The empty list is just []. \nA set is created by enclosing a \+ sequence in \{ ... \} braces. The empty set is just \{ \} ." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "L := [3,2,1,3,1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG7'\"\"$\"\"#\"\"\"F&F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "S := \{3,2,1,3,1\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"SG<%\"\"\"\"\"#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "s, u; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6'\"\"$\" \"#\"\"\"F#F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "L := [s,u] ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG7'\"\"$\"\"#\"\"\"F&F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "S := \{s,u\};" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"SG<%\"\"\"\"\"#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 289 "The difference is that in a set, duplicates are rem oved and the entries are sorted (by Maple's internal ordering).\nYou c an access the i'th element of a list or set using subscript notation w here positive subscripts count from left to right and negative subscri pts count from right to left." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "L; L[1]; L[2]; L[3]; L[-1]; L[-2], L[-3];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7'\"\"$\"\"#\"\"\"F$F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"$\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "L[0]; L[6]; L[-6];" }}{PARA 8 "" 1 "" {TEXT -1 34 "Error, invalid subscript selector\n" }}{PARA 8 "" 1 "" {TEXT -1 34 "E rror, invalid subscript selector\n" }}{PARA 8 "" 1 "" {TEXT -1 34 "Err or, invalid subscript selector\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "S[1]; S[2]; S[-1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 106 "The numb er of values in a set or list is given by the nops function (which sta nds for number of operands)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "nops(L); nops(S);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 77 "You can test whether an element is in a list or set using the member function" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "mem ber( 2, L ); member( 0, L ); member( 3, S );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "The sequence of values in a list or set can be obtained u sing op. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "op(L);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6'\"\"$\"\"#\"\"\"F#F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "op(S);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6% \"\"\"\"\"#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 91 "Thus you can \+ append a new element 0 to a list (or insert a new element in a set) as follows" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "[ op(L), 0 ];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7(\"\"$\"\"#\"\"\"F$F&\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "\{ op(S), 0 \};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<&\"\"!\"\"\"\"\"#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 62 "Some useful functions for lists and sets are the set operators" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "L := [3,2,1,4 ,1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG7'\"\"$\"\"#\"\"\"\"\"%F (" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "sort(L);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#7'\"\"\"F$\"\"#\"\"$\"\"%" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 18 "L[2..3]; # sublist" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "S;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%\"\"\"\"\"#\"\"$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "T := \{3,4\};" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"TG<$\"\"$\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "S union T; # set union " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<&\"\"\"\"\"#\"\"$\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "S minus T; # set difference" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#< $\"\"\"\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 101 "What does all th is mean. We can discard all duplicate solutions from solve by putting them in a set." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "\{solve( x^4-x^2, x )\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%!\"\"\"\"!\"\"\" " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "We can compute the maximum so lution by putting the solutions in a max" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "max(solve( x^4-x^2, x ));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "We can k eep all entries for later use by putting them in a list" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "[solve( x^4-x^2, x )];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&\"\"!F$\"\"\"!\"\"" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 65 "We can create a list of [x,y] points using seq which we can plot." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "[seq([i,i^2], i=1..5)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7'7$\"\"\"F%7$\"\"#\"\"%7 $\"\"$\"\"*7$F(\"#;7$\"\"&\"#D" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "We can apply a function to each entry of a list or set as follows" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "L;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7'\"\"$\"\"#\"\"\"\"\"%F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "[seq( L[i]^2, i=1..nops(L) )];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7'\"\"*\"\"%\"\"\"\"#;F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "F := [seq( x^i,i=0..5 )];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG7(\"\"\"%\"xG*$)F'\"\"#F&*$)F'\"\"$F&*$)F'\"\"%F& *$)F'\"\"&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "dF := [seq( diff(F[i],x), i=1..6 )];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#dFG7( \"\"!\"\"\",$%\"xG\"\"#,$*$)F)F*F'\"\"$,$*$)F)F.F'\"\"%,$*$)F)F2F'\"\" &" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "We can iterate the tent map \+ until we enter a cycle as follows" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "tm := x -> piecewise( x<1/2, 2*x, 2-2*x );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#tmGR6#%\"xG6\"6$%)operatorG%&arrowGF(-%*p iecewiseG6%29$#\"\"\"\"\"#,$F0F3,&F3F2*&F3F2F0F2!\"\"F(F(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "x := 1/7;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"xG#\"\"\"\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "L := [];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG7\" " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "while not member(x,L) d o L := [op(L),x]; x := tm(x) od; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%\"LG7##\"\"\"\"\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG#\"\"#\" \"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG7$#\"\"\"\"\"(#\"\"#F(" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG#\"\"%\"\"(" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"LG7%#\"\"\"\"\"(#\"\"#F(#\"\"%F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG#\"\"'\"\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG7&#\"\"\"\"\"(#\"\"#F(#\"\"%F(#\"\"'F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG#\"\"#\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "64 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }