{VERSION 5 0 "Windows XP" "5.0" }
{USTYLETAB {PSTYLE "Heading 4" -1 20 1 {CSTYLE "" -1 -1 "Times" 1 10 0
 0 0 1 1 1 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Ord
ered List 5" -1 200 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 
2 1 0 0 1 }1 1 0 0 3 3 2 144 2 0 2 2 -1 1 }{PSTYLE "Ordered List 1" -1
 201 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 
0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 
-1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2
 2 -1 1 }{PSTYLE "Bullet Item" -1 15 1 {CSTYLE "" -1 -1 "Times" 1 12 0
 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Lef
t Justified Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 
1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Help" -1
 10 1 {CSTYLE "" -1 -1 "Courier" 1 9 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 
1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Author" -1 19 1 {CSTYLE "" -1 -1 
"Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 8 8 2 0 2 0 2 2 -1 1
 }{PSTYLE "Diagnostic" -1 9 1 {CSTYLE "" -1 -1 "Courier" 1 10 64 128 
64 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Headi
ng 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 0 0 1
 }1 1 0 0 8 2 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 3" -1 202 1 
{CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3
 2 72 2 0 2 2 -1 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Tim
es" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "R3 Font 0" -1 203 1 {CSTYLE "" -1 -1 "Helvetica" 1 14 0 0 255
 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Normal"
 -1 0 1 {CSTYLE "" -1 -1 "MS Serif" 1 14 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }
1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "R3 Font 2" -1 204 1 {CSTYLE "" 
-1 -1 "Courier" 1 14 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 
2 2 -1 1 }{PSTYLE "Dash Item" -1 16 1 {CSTYLE "" -1 -1 "Times" 1 12 0 
0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Head
ing 3" -1 5 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 1 0 0 
1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 4" -1 205 1 
{CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3
 2 108 2 0 2 2 -1 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "
Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 
}{PSTYLE "Line Printed Output" -1 6 1 {CSTYLE "" -1 -1 "Courier" 1 10 
0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
List Item" -1 14 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1
 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Normal258" -1 206 1 
{CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0
 2 0 2 0 2 2 -1 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier"
 1 10 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "Error" -1 8 1 {CSTYLE "" -1 -1 "Courier" 1 10 255 0 255 1 2 2
 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Fixed Width" 
-1 17 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3
 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 
-1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 8 4 2 0 2 0 2 2 
-1 1 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 
1 1 2 2 2 1 0 0 1 }3 1 0 0 12 12 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered Li
st 2" -1 207 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0
 1 }1 1 0 0 3 3 2 36 2 0 2 2 -1 1 }{CSTYLE "Help Variable" -1 25 "Cour
ier" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Text" -1 200 "Times" 1
 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Bold" -1 39 "Times" 1 
12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Page Number" -1 33 "Times" 1 
12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small" -1 201 
"Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Nonterminal" -1
 24 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Default" -1 
38 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Maple Comment" 
-1 21 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Maple Input
" -1 0 "Courier" 1 12 255 0 0 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "2D Math \+
Small" -1 7 "Times" 1 1 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Fix
ed" -1 23 "Courier" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Popup" 
-1 31 "Times" 1 12 0 128 128 1 1 2 1 2 2 2 0 0 0 1 }{CSTYLE "Plot Titl
e" -1 27 "Times" 1 10 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Input" 
-1 19 "Times" 1 12 255 0 0 1 2 2 2 2 1 2 0 0 0 1 }{CSTYLE "Copyright" 
-1 34 "Times" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Maple Input P
laceholder" -1 202 "Courier" 1 12 200 0 200 1 2 1 2 2 1 2 0 0 0 1 }
{CSTYLE "2D Math Bold Small" -1 10 "Times" 1 1 0 0 0 1 2 1 2 2 2 2 0 0
 0 1 }{CSTYLE "2D Math" -1 2 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 
}{CSTYLE "Help Notes" -1 37 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }
{CSTYLE "Help Underlined Bold" -1 41 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 
0 0 0 1 }{CSTYLE "Hyperlink" -1 17 "Times" 1 12 0 128 128 1 2 2 1 2 2 
2 0 0 0 1 }{CSTYLE "2D Math Symbol 2" -1 16 "Times" 1 12 0 0 0 1 2 2 2
 2 2 2 0 0 0 1 }{CSTYLE "Plot Text" -1 28 "Times" 1 8 0 0 0 1 2 2 2 2 
2 2 0 0 0 1 }{CSTYLE "Help Italic" -1 42 "Times" 1 12 0 0 0 1 1 2 2 2 
2 2 0 0 0 1 }{CSTYLE "Output Labels" -1 29 "Times" 1 8 0 0 0 1 2 2 2 2
 2 2 0 0 0 1 }{CSTYLE "Help Heading" -1 26 "Times" 1 14 0 0 0 1 2 1 2 
2 2 2 0 0 0 1 }{CSTYLE "Help Normal" -1 30 "Times" 1 12 0 0 0 1 2 2 2 
2 2 2 0 0 0 1 }{CSTYLE "2D Comment" -1 18 "Times" 1 12 0 0 0 1 2 2 2 2
 2 2 0 0 0 1 }{CSTYLE "Help Maple Name" -1 35 "Times" 1 12 104 64 92 1
 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Output" -1 20 "Times" 1 12 0 0 255 1
 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Dictionary Hyperlink" -1 45 "Times" 1 
12 147 0 15 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "Help Emphasized" -1 22 "Ti
mes" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Italic Bold" -1 
40 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "LaTeX" -1 32 "Ti
mes" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Menus" -1 36 "Tim
es" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Prompt" -1 1 "Courier" 
1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Help Underlined" -1 44 "Tim
es" 1 12 0 0 0 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "Help Underlined Italic"
 -1 43 "Times" 1 12 0 0 0 1 1 2 1 2 2 2 0 0 0 1 }{CSTYLE "2D Math Bold
" -1 5 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Ital
ic" -1 3 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{PSTYLE "" -1 208 1
 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 
0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 209 1 {CSTYLE "" -1 -1 "Courier"
 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 210 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 211 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 212 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 213 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 214 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 215 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 216 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 217 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 218 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 219 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 220 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 221 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 222 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 223 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 224 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 225 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 226 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 227 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 228 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 229 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 230 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 231 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 232 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 233 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 234 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 235 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 236 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 237 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 238 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 239 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 240 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 241 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 242 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 243 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 244 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 245 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 246 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 247 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 248 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 249 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 250 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 251 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 252 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 253 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 254 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 255 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 256 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 257 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 258 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 259 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 260 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 261 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 262 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 263 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 264 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 265 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 266 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 267 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 268 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 269 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 270 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 271 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 272 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 273 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 274 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 275 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 276 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 277 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 278 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 279 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 280 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 281 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 282 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 283 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 284 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 285 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 286 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 287 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 288 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 289 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 290 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 291 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 292 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 293 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 294 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 295 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 296 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 297 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 298 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 299 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 300 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 301 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 302 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 303 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 304 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 305 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 306 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 307 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 308 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 309 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 310 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 311 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 312 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 313 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 314 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 315 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 316 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 317 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 318 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 319 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 320 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 321 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 322 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 323 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 324 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 325 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 326 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 327 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 328 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 329 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 330 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 331 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 332 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 333 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 334 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 335 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 336 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 337 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 338 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 339 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 340 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 341 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 342 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 343 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 344 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 345 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 346 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 347 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 348 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 349 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 350 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 351 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 352 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 353 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 354 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 355 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 356 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 357 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 358 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 359 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 360 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 361 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 362 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 363 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 364 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 365 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 366 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 367 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 368 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 369 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 370 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 371 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 372 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 373 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 374 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 375 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 376 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 377 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 378 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 379 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 380 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 381 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 382 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 383 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 384 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 385 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 386 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 387 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 388 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 389 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 390 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 391 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 392 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 393 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 394 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 395 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 396 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 397 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 398 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 399 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 400 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 401 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 402 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 403 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 404 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 405 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 406 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 407 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 408 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 409 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 410 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 411 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 412 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 413 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 414 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 415 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 416 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 417 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "" -1 418 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 
1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 419 1 {CSTYLE
 "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 
0 2 0 2 2 -1 1 }{PSTYLE "" -1 420 1 {CSTYLE "" -1 -1 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "
" -1 421 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0
 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 422 1 {CSTYLE "" -1 -1
 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2
 -1 1 }{PSTYLE "" -1 423 1 {CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2
 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 424 1 
{CSTYLE "" -1 -1 "Courier" 1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0
 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 425 1 {CSTYLE "" -1 -1 "Courier" 
1 14 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }}
{SECT 0 {EXCHG {PARA 206 "" 0 "" {TEXT 203 23 "# Iteration of mappings
" }}{PARA 206 "" 0 "" {TEXT 203 4 "Iter" }}{PARA 206 "" 0 "" {TEXT 
203 0 "" }}{PARA 206 "" 0 "" {TEXT 203 106 "Iter is a package of simpl
e tools for studying the sequences a, f(a), f(f(a)), f(f(f(a))), ... o
btained by" }}{PARA 206 "" 0 "" {TEXT 203 101 "repeatedly applying a f
unction f to an initial value a. To iterate something is to do it repe
atedly. " }}{PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 206 "" 0 "" {TEXT
 203 5 "iter " }}{PARA 206 "" 0 "" {TEXT 203 95 "     Use iter( f, n, \+
a ) to compute the sequence which begins with a, f(a), f(f(a)) ... and
 has" }}{PARA 206 "" 0 "" {TEXT 203 27 "     a total of n+1 terms. " }
}{PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 206 "" 0 "" {TEXT 203 10 "it
erprint " }}{PARA 206 "" 0 "" {TEXT 203 97 "     Use iterprint( f, n ,
 a ) to apply f to a n times and print the results in vertical format.
 " }}{PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 206 "" 0 "" {TEXT 203 9 
"iterplot " }}{PARA 206 "" 0 "" {TEXT 203 93 "     Use iterplot( f, n,
 a ) instead of iterprint to plot the sequence a, f(a), f(f(a)), ... "
 }}{PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 206 "" 0 "" {TEXT 203 10 "
iterplot2 " }}{PARA 206 "" 0 "" {TEXT 203 97 "     Use iterplot( f, g,
 n, a ) to plot the sequences a, f(a), f(f(a)), ... and a, g(a), g(g(a
))," }}{PARA 206 "" 0 "" {TEXT 203 9 "     ... " }}{PARA 206 "" 0 "" 
{TEXT 203 0 "" }}{PARA 206 "" 0 "" {TEXT 203 7 "cobweb " }}{PARA 206 "
" 0 "" {TEXT 203 89 "     Use cobweb( f, n, s, a..b ) to show how the \+
sequence of iterates s, f(s), f(f(s)) is" }}{PARA 206 "" 0 "" {TEXT 
203 44 "     generated by the \"cobweb\" procedure. " }}{PARA 206 "" 0
 "" {TEXT 203 0 "" }}{PARA 206 "" 0 "" {TEXT 203 11 "printarray " }}
{PARA 206 "" 0 "" {TEXT 203 61 "     Use printarray(y) to print a list
 y in vertical format. " }}{PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 
206 "" 0 "" {TEXT 203 0 "" }}{PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 
206 "" 0 "" {TEXT 203 0 "" }}{PARA 208 "> " 0 "" {MPLTEXT 1 0 14 "# Ji
m Carlson " }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 0 36 "# http://ww
w.math.utah.edu/~carlson)" }}}{EXCHG {PARA 210 "> " 0 "" {MPLTEXT 1 0 
16 "# August 9, 1993" }}}{EXCHG {PARA 211 "> " 0 "" {MPLTEXT 1 0 31 "#
 Last revised: October 2, 1993" }}}{EXCHG {PARA 212 "> " 0 "" {MPLTEXT
 1 0 0 "" }}}{EXCHG {PARA 213 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 214 "> " 0 "" {MPLTEXT 1 0 23 "printarray := proc( L )" }}{PARA 
215 "> " 0 "" {MPLTEXT 1 0 10 "  local i;" }}{PARA 216 "> " 0 "" 
{MPLTEXT 1 0 40 "  for i from 0 to op(2,op(2,eval(L))) do" }}{PARA 217
 "> " 0 "" {MPLTEXT 1 0 18 "    print(i, L[i])" }}{PARA 218 "> " 0 "" 
{MPLTEXT 1 0 6 "   od;" }}{PARA 219 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}
}{EXCHG {PARA 220 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 221 "> "
 0 "" {MPLTEXT 1 0 20 "iter :=  proc(f,n,a)" }}{PARA 222 "> " 0 "" 
{MPLTEXT 1 0 13 "  local x, i;" }}{PARA 223 "> " 0 "" {MPLTEXT 1 0 19 
"  x := array(0..n);" }}{PARA 224 "> " 0 "" {MPLTEXT 1 0 12 "  x[0] :=
 a;" }}{PARA 225 "> " 0 "" {MPLTEXT 1 0 22 "  for i from 1 to n do" }}
{PARA 226 "> " 0 "" {MPLTEXT 1 0 28 "    x[i] := evalf(f(x[i-1]))" }}
{PARA 227 "> " 0 "" {MPLTEXT 1 0 5 "  od;" }}{PARA 228 "> " 0 "" 
{MPLTEXT 1 0 12 "  RETURN(x);" }}{PARA 229 "> " 0 "" {MPLTEXT 1 0 4 "e
nd:" }}}{EXCHG {PARA 230 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
231 "> " 0 "" {MPLTEXT 1 0 24 "iterprint := proc(f,n,a)" }}{PARA 232 "
> " 0 "" {MPLTEXT 1 0 13 "  local y, z;" }}{PARA 233 "> " 0 "" 
{MPLTEXT 1 0 21 "    y := iter(f,n,a);" }}{PARA 234 "> " 0 "" {MPLTEXT
 1 0 18 "    printarray(y);" }}{PARA 235 "> " 0 "" {MPLTEXT 1 0 4 "end
:" }}}{EXCHG {PARA 236 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 237
 "> " 0 "" {MPLTEXT 1 0 23 "iterplot := proc(f,n,a)" }}{PARA 238 "> " 
0 "" {MPLTEXT 1 0 13 "  local y, z;" }}{PARA 239 "> " 0 "" {MPLTEXT 1 
0 20 "  y := iter2(f,n,a);" }}{PARA 240 "> " 0 "" {MPLTEXT 1 0 23 "  z
 := convert(y,list);" }}{PARA 241 "> " 0 "" {MPLTEXT 1 0 29 "  plot(z,
 0..n, style=POINT);" }}{PARA 242 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}
{EXCHG {PARA 243 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 244 "> " 
0 "" {MPLTEXT 1 0 25 "iterplotna := proc(f,n,a)" }}{PARA 245 "> " 0 ""
 {MPLTEXT 1 0 13 "  local y, z;" }}{PARA 246 "> " 0 "" {MPLTEXT 1 0 
22 "  y := iter2na(f,n,a);" }}{PARA 247 "> " 0 "" {MPLTEXT 1 0 23 "  z
 := convert(y,list);" }}{PARA 248 "> " 0 "" {MPLTEXT 1 0 29 "  plot(z,
 0..n, style=POINT);" }}{PARA 249 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}
{EXCHG {PARA 250 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 251 "> " 
0 "" {MPLTEXT 1 0 29 "iterplot2 :=  proc(f,g,n,a,b)" }}{PARA 252 "> " 
0 "" {MPLTEXT 1 0 21 "  local y, z, y2, z2;" }}{PARA 253 "> " 0 "" 
{MPLTEXT 1 0 20 "  y := iter2(f,n,a);" }}{PARA 254 "> " 0 "" {MPLTEXT 
1 0 23 "  z := convert(y,list);" }}{PARA 255 "> " 0 "" {MPLTEXT 1 0 
21 "  y2 := iter2(g,n,b);" }}{PARA 256 "> " 0 "" {MPLTEXT 1 0 25 "  z2
 := convert(y2,list);" }}{PARA 257 "> " 0 "" {MPLTEXT 1 0 39 "  plot(
\{ z, z2 \}, 0..n, style=POINT);" }}{PARA 258 "> " 0 "" {MPLTEXT 1 0 
4 "end:" }}}{EXCHG {PARA 259 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 260 "> " 0 "" {MPLTEXT 1 0 24 "iterplotP := proc(f,n,a)" }}
{PARA 261 "> " 0 "" {MPLTEXT 1 0 22 "  local y, u, z, i, j;" }}{PARA 
262 "> " 0 "" {MPLTEXT 1 0 21 "  u := array(0..2*n);" }}{PARA 263 "> "
 0 "" {MPLTEXT 1 0 20 "  y := iter2(f,n,a);" }}{PARA 264 "> " 0 "" 
{MPLTEXT 1 0 9 "  j := 0;" }}{PARA 265 "> " 0 "" {MPLTEXT 1 0 24 "  fo
r i from 0 to n-1 do" }}{PARA 266 "> " 0 "" {MPLTEXT 1 0 31 "    u[j] \+
:= [y[i][2],y[i][1]] ;" }}{PARA 267 "> " 0 "" {MPLTEXT 1 0 13 "    j :
= j+1;" }}{PARA 268 "> " 0 "" {MPLTEXT 1 0 33 "    u[j] := [y[i+1][2],
y[i][1]] ;" }}{PARA 269 "> " 0 "" {MPLTEXT 1 0 13 "    j := j+1;" }}
{PARA 270 "> " 0 "" {MPLTEXT 1 0 5 "  od;" }}{PARA 271 "> " 0 "" 
{MPLTEXT 1 0 31 "  u[2*n] := [y[n][2],y[n][1]] ;" }}{PARA 272 "> " 0 "
" {MPLTEXT 1 0 23 "  z := convert(u,list);" }}{PARA 273 "> " 0 "" 
{MPLTEXT 1 0 34 "  plot(z, 0..y[n][2], style=LINE);" }}{PARA 274 "> " 
0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 275 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 276 "> " 0 "" {MPLTEXT 1 0 20 "iter2 := proc(f,n,
a)" }}{PARA 277 "> " 0 "" {MPLTEXT 1 0 13 "  local x, i;" }}{PARA 278 
"> " 0 "" {MPLTEXT 1 0 19 "  x := array(0..n);" }}{PARA 279 "> " 0 "" 
{MPLTEXT 1 0 17 "  x[0] := [0, a];" }}{PARA 280 "> " 0 "" {MPLTEXT 1 
0 22 "  for i from 1 to n do" }}{PARA 281 "> " 0 "" {MPLTEXT 1 0 31 " \+
   x[i] := [ i, f(x[i-1][2]) ]" }}{PARA 282 "> " 0 "" {MPLTEXT 1 0 5 "
  od;" }}{PARA 283 "> " 0 "" {MPLTEXT 1 0 12 "  RETURN(x);" }}{PARA 
284 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 285 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 286 "> " 0 "" {MPLTEXT 1 0 22 "iter2
na := proc(f,n,a)" }}{PARA 287 "> " 0 "" {MPLTEXT 1 0 13 "  local x, i
;" }}{PARA 288 "> " 0 "" {MPLTEXT 1 0 19 "  x := array(0..n);" }}
{PARA 289 "> " 0 "" {MPLTEXT 1 0 17 "  x[0] := [0, a];" }}{PARA 290 ">
 " 0 "" {MPLTEXT 1 0 22 "  for i from 1 to n do" }}{PARA 291 "> " 0 ""
 {MPLTEXT 1 0 33 "    x[i] := [ i, f(i,x[i-1][2]) ]" }}{PARA 292 "> " 
0 "" {MPLTEXT 1 0 5 "  od;" }}{PARA 293 "> " 0 "" {MPLTEXT 1 0 12 "  R
ETURN(x);" }}{PARA 294 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG 
{PARA 295 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 296 "> " 0 "" 
{MPLTEXT 1 0 29 "makethread := proc( f, n, a )" }}{PARA 297 "> " 0 "" 
{MPLTEXT 1 0 20 "   local T, i, x, y;" }}{PARA 298 "> " 0 "" {MPLTEXT 
1 0 20 "   T := array(0..n);" }}{PARA 299 "> " 0 "" {MPLTEXT 1 0 17 " \+
  x := evalf(a);" }}{PARA 300 "> " 0 "" {MPLTEXT 1 0 12 "   y := 0.0;"
 }}{PARA 301 "> " 0 "" {MPLTEXT 1 0 17 "   T[0] := [x,y];" }}{PARA 302
 "> " 0 "" {MPLTEXT 1 0 28 "   for i from 1 by 2 to n do" }}{PARA 303 
"> " 0 "" {MPLTEXT 1 0 21 "      x := T[i-1][1];" }}{PARA 304 "> " 0 "
" {MPLTEXT 1 0 25 "      y := evalf( f(x) );" }}{PARA 305 "> " 0 "" 
{MPLTEXT 1 0 23 "      T[i] := [ x, y ];" }}{PARA 306 "> " 0 "" 
{MPLTEXT 1 0 25 "      T[i+1] := [ y, y ];" }}{PARA 307 "> " 0 "" 
{MPLTEXT 1 0 6 "   od;" }}{PARA 308 "> " 0 "" {MPLTEXT 1 0 22 "   conv
ert( T, list );" }}{PARA 309 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}
{EXCHG {PARA 310 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 311 "> " 
0 "" {MPLTEXT 1 0 31 "discretize := proc( f, n, a, b)" }}{PARA 312 "> \+
" 0 "" {MPLTEXT 1 0 22 "  local T, i, x, y, h;" }}{PARA 313 "> " 0 "" 
{MPLTEXT 1 0 19 "  T := array(0..n);" }}{PARA 314 "> " 0 "" {MPLTEXT 
1 0 16 "  x := evalf(a);" }}{PARA 315 "> " 0 "" {MPLTEXT 1 0 12 "  y :
= f(x);" }}{PARA 316 "> " 0 "" {MPLTEXT 1 0 24 "  h := evalf( (b-a)/n \+
);" }}{PARA 317 "> " 0 "" {MPLTEXT 1 0 16 "  T[0] := [x,y];" }}{PARA 
318 "> " 0 "" {MPLTEXT 1 0 22 "  for i from 1 to n do" }}{PARA 319 "> \+
" 0 "" {MPLTEXT 1 0 15 "    x := x + h;" }}{PARA 320 "> " 0 "" 
{MPLTEXT 1 0 14 "    y := f(x);" }}{PARA 321 "> " 0 "" {MPLTEXT 1 0 
18 "    T[i] := [x,y];" }}{PARA 322 "> " 0 "" {MPLTEXT 1 0 5 "  od;" }
}{PARA 323 "> " 0 "" {MPLTEXT 1 0 21 "  convert( T, list );" }}{PARA 
324 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 325 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 326 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 327 "> " 0 "" {MPLTEXT 1 0 21 "xminoflist := proc(L)" }}
{PARA 328 "> " 0 "" {MPLTEXT 1 0 16 "  local i,x, xm;" }}{PARA 329 "> \+
" 0 "" {MPLTEXT 1 0 17 "    xm:= L[1][1];" }}{PARA 330 "> " 0 "" 
{MPLTEXT 1 0 30 "    for i from 2 to nops(L) do" }}{PARA 331 "> " 0 ""
 {MPLTEXT 1 0 20 "       x := L[i][1];" }}{PARA 332 "> " 0 "" {MPLTEXT
 1 0 34 "      if (x < xm) then xm := x fi;" }}{PARA 333 "> " 0 "" 
{MPLTEXT 1 0 7 "    od;" }}{PARA 334 "> " 0 "" {MPLTEXT 1 0 5 "  xm;" 
}}{PARA 335 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 336 "> " 0
 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 337 "> " 0 "" {MPLTEXT 1 0 21 "x
maxoflist := proc(L)" }}{PARA 338 "> " 0 "" {MPLTEXT 1 0 16 "  local i
,x, xm;" }}{PARA 339 "> " 0 "" {MPLTEXT 1 0 17 "    xm:= L[1][1];" }}
{PARA 340 "> " 0 "" {MPLTEXT 1 0 30 "    for i from 2 to nops(L) do" }
}{PARA 341 "> " 0 "" {MPLTEXT 1 0 20 "       x := L[i][1];" }}{PARA 
342 "> " 0 "" {MPLTEXT 1 0 34 "      if (x > xm) then xm := x fi;" }}
{PARA 343 "> " 0 "" {MPLTEXT 1 0 7 "    od;" }}{PARA 344 "> " 0 "" 
{MPLTEXT 1 0 5 "  xm;" }}{PARA 345 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}
{EXCHG {PARA 346 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 347 "> " 
0 "" {MPLTEXT 1 0 21 "yminoflist := proc(L)" }}{PARA 348 "> " 0 "" 
{MPLTEXT 1 0 16 "  local i,y, ym;" }}{PARA 349 "> " 0 "" {MPLTEXT 1 0 
17 "    ym:= L[1][2];" }}{PARA 350 "> " 0 "" {MPLTEXT 1 0 30 "    for \+
i from 2 to nops(L) do" }}{PARA 351 "> " 0 "" {MPLTEXT 1 0 20 "       \+
y := L[i][1];" }}{PARA 352 "> " 0 "" {MPLTEXT 1 0 34 "      if (y < ym
) then ym := y fi;" }}{PARA 353 "> " 0 "" {MPLTEXT 1 0 7 "    od;" }}
{PARA 354 "> " 0 "" {MPLTEXT 1 0 5 "  ym;" }}{PARA 355 "> " 0 "" 
{MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 356 "> " 0 "" {MPLTEXT 1 0 0 "" 
}}}{EXCHG {PARA 357 "> " 0 "" {MPLTEXT 1 0 21 "ymaxoflist := proc(L)" 
}}{PARA 358 "> " 0 "" {MPLTEXT 1 0 16 "  local i,y, ym;" }}{PARA 359 "
> " 0 "" {MPLTEXT 1 0 17 "    ym:= L[1][2];" }}{PARA 360 "> " 0 "" 
{MPLTEXT 1 0 30 "    for i from 2 to nops(L) do" }}{PARA 361 "> " 0 ""
 {MPLTEXT 1 0 20 "       y := L[i][1];" }}{PARA 362 "> " 0 "" {MPLTEXT
 1 0 34 "      if (y > ym) then ym := y fi;" }}{PARA 363 "> " 0 "" 
{MPLTEXT 1 0 7 "    od;" }}{PARA 364 "> " 0 "" {MPLTEXT 1 0 5 "  ym;" 
}}{PARA 365 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 366 "> " 0
 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 367 "> " 0 "" {MPLTEXT 1 0 35 "i
d := x -> x; # identity function #" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I
#idG6\"f*6#I\"xGF$F$6$I)operatorGF$I&arrowGF$F$F'F$F$F$" }}}{EXCHG 
{PARA 368 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 369 "> " 0 "" 
{MPLTEXT 1 0 33 "cobweb := proc( f, n, a, xrange )" }}{PARA 370 "> " 0
 "" {MPLTEXT 1 0 75 "          local thread1, thread2, thread3, epsilo
n, x1, x2, y1, y2, yrange," }}{PARA 371 "> " 0 "" {MPLTEXT 1 0 37 "   \+
              xmin,xmax,ymin,ymax;" }}{PARA 372 "> " 0 "" {MPLTEXT 1 
0 17 "                 " }}{PARA 373 "> " 0 "" {MPLTEXT 1 0 27 "      \+
    yrange := xrange;" }}{PARA 374 "> " 0 "" {MPLTEXT 1 0 25 "        \+
  epsilon := 0.1;" }}{PARA 375 "> " 0 "" {MPLTEXT 1 0 45 "          th
read1 := makethread( f, 2*n, a );" }}{PARA 376 "> " 0 "" {MPLTEXT 1 0 
49 "          x1 := op(1,xrange); x2 := op(2,xrange);" }}{PARA 377 "> \+
" 0 "" {MPLTEXT 1 0 49 "          y1 := op(1,yrange); y2 := op(2,yrang
e);" }}{PARA 378 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 379 "> " 0 "" 
{MPLTEXT 1 0 38 "          xmin := xminoflist(thread1);" }}{PARA 380 "
> " 0 "" {MPLTEXT 1 0 38 "          xmax := xmaxoflist(thread1);" }}
{PARA 381 "> " 0 "" {MPLTEXT 1 0 38 "          ymin := yminoflist(thre
ad1);" }}{PARA 382 "> " 0 "" {MPLTEXT 1 0 38 "          ymax := ymaxof
list(thread1);" }}{PARA 383 "> " 0 "" {MPLTEXT 1 0 10 "          " }}
{PARA 384 "> " 0 "" {MPLTEXT 1 0 44 "          if (x1 > xmin) then x1 \+
:= xmin fi;" }}{PARA 385 "> " 0 "" {MPLTEXT 1 0 44 "          if (x2 <
 xmax) then x2 := xmax fi;" }}{PARA 386 "> " 0 "" {MPLTEXT 1 0 44 "   \+
       if (y1 > ymin) then y1 := ymin fi;" }}{PARA 387 "> " 0 "" 
{MPLTEXT 1 0 44 "          if (y2 < ymax) then y2 := ymax fi;" }}
{PARA 388 "> " 0 "" {MPLTEXT 1 0 10 "          " }}{PARA 389 "> " 0 ""
 {MPLTEXT 1 0 37 "          x1 := x1 - epsilon*(x2-x1);" }}{PARA 390 "
> " 0 "" {MPLTEXT 1 0 37 "          x2 := x2 + epsilon*(x2-x1);" }}
{PARA 391 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 392 "> " 0 "" {MPLTEXT 
1 0 48 "          thread2 := discretize(f, 20, x1, x2 );" }}{PARA 393 
"> " 0 "" {MPLTEXT 1 0 48 "          thread3 := discretize(id, 1, x1, \+
x2 );" }}{PARA 394 "> " 0 "" {MPLTEXT 1 0 10 "          " }}{PARA 395 
"> " 0 "" {MPLTEXT 1 0 48 "          plot( \{ thread1, thread2, thread
3 \}," }}{PARA 396 "> " 0 "" {MPLTEXT 1 0 65 "                x = x1..
x2, y=y1..y2, style = LINE,thickness=2 );" }}{PARA 397 "> " 0 "" 
{MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 398 "> " 0 "" {MPLTEXT 1 0 0 "" 
}}}{EXCHG {PARA 399 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 400 ">
 " 0 "" {MPLTEXT 1 0 20 "double := x -> 2*x; " }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I'doubleG6\"f*6#I\"xGF$F$6$I)operatorGF$I&arrowGF$F$,$*&
\"\"#\"\"\"F'F.F.F$F$F$" }}}{EXCHG {PARA 401 "> " 0 "" {MPLTEXT 1 0 0 
"" }}}{EXCHG {PARA 402 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 206
 "" 0 "" {TEXT 203 0 "" }}{PARA 206 "" 0 "" {TEXT 203 9 "Example 1" }}
{PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 206 "" 0 "" {TEXT 203 18 "Def
ine a function " }}{PARA 403 "> " 0 "" {MPLTEXT 1 0 20 "double := x ->
 2*x; " }}{PARA 11 "" 1 "" {XPPMATH 20 ">I'doubleG6\"f*6#I\"xGF$F$6$I)
operatorGF$I&arrowGF$F$,$*&\"\"#\"\"\"F'F.F.F$F$F$" }}}{EXCHG {PARA 
206 "" 0 "" {TEXT 203 0 "" }}{PARA 404 "> " 0 "" {MPLTEXT 1 0 27 "iter
print( double, 4, 1 ); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"!\"\"\"
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"\"$\"\"#\"\"!" }}{PARA 11 "" 1
 "" {XPPMATH 20 "6$\"\"#$\"\"%\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
$\"\"$$\"\")\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"%$\"#;\"\"!" 
}}}{EXCHG {PARA 405 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 406 ">
 " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 206 "" 0 "" {TEXT 203 99 "ap
plies double a total of four times to compute and print the sequence 1
, 2, 4, 8, 16. The command " }}{PARA 407 "> " 0 "" {MPLTEXT 1 0 26 "it
erplot( double, 4, 1 ); " }}{PARA 13 "" 1 "" {TEXT 204 0 "" }
{GLPLOT2D 400 400 400 {PLOTDATA 2 "6&-%+AXESLABELSG6$Q!6\"F&-%'CURVESG
6$7'7$$\"\"!F.$\"\"\"F.7$F/$\"\"#F.7$F2$\"\"%F.7$$\"\"$F.$\"\")F.7$F5$
\"#;F.-%&COLORG6&%$RGBG$\"#5!\"\"$F.FEFF-%&STYLEG6#%&POINTG-%%VIEWG6$;
FF$\"#SFE;$\"#q!\"#$\"2-++++++j\"!#:" 1 5 2 1 10 1 2 6 1 4 2 1.0 45.0 
45.0 1 0 "Curve 1" }}{TEXT 204 0 "" }}}{EXCHG {PARA 206 "" 0 "" {TEXT 
203 78 "computes the same sequence but displays a plot of it instead o
f \"printing.\" " }}{PARA 206 "" 0 "" {TEXT 203 68 "Note: If you need \+
to store the sequence for later manipulation, try " }}{PARA 206 "" 0 "
" {TEXT 203 0 "" }}{PARA 206 "" 0 "" {TEXT 203 38 "     results := ite
r( double, 4, 1 ); " }}{PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 206 ""
 0 "" {TEXT 203 68 "To display this variable use print(results) or pri
ntarray(results). " }}{PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 206 "" 
0 "" {TEXT 203 9 "Example 2" }}{PARA 206 "" 0 "" {TEXT 203 0 "" }}
{PARA 206 "" 0 "" {TEXT 203 70 "The quadratic function f(x) = kx(1-x) \+
gives more interesting results. " }}{PARA 206 "" 0 "" {TEXT 203 0 "" }
}{PARA 408 "> " 0 "" {MPLTEXT 1 0 29 "     quad := x -> k*x*(1-x); " }
}{PARA 11 "" 1 "" {XPPMATH 20 ">I%quadG6\"f*6#I\"xGF$F$6$I)operatorGF$
I&arrowGF$F$*(I\"kGF$\"\"\"F'F-,&F-F-F'!\"\"F-F$F$F$" }}}{EXCHG {PARA 
409 "> " 0 "" {MPLTEXT 1 0 15 "     k := 3.0; " }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I\"kG6\"$\"#I!\"\"" }}}{EXCHG {PARA 410 "> " 0 "" 
{MPLTEXT 1 0 32 "     iterplot( quad, 40, 0.1 ); " }}{PARA 13 "" 1 "" 
{TEXT 204 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "6&-%+AXESLABELSG6$Q
!6\"F&-%'CURVESG6$7K7$$\"\"!F.$\"3/+++++++5!#=7$$\"\"\"F.$\"3;+++++++F
F17$$\"\"#F.$\"3[++++++8fF17$$\"\"$F.$\"3!)*******HH*\\sF17$$\"\"%F.$
\"3C+++WaM\")fF17$$\"\"&F.$\"3!******\\L)36sF17$$\"\"'F.$\"31+++6lKLgF
17$$\"\"(F.$\"3!******\\*3nzrF17$$\"\")F.$\"3=*****\\V5Z2'F17$$\"\"*F.
$\"3)4++?C*\\`rF17$$\"#5F.$\"3$)*****fIK(3hF17$$\"#6F.$\"3_+++.Q@JrF17
$$\"#7F.$\"3m*****zJyt8'F17$$\"#8F.$\"39+++n6\">6(F17$$\"#9F.$\"3I+++n
$\\>;'F17$$\"#:F.$\"3g*******4i\\4(F17$$\"#;F.$\"3')******R,M$='F17$$
\"#<F.$\"3++++M=\"*zqF17$$\"#=F.$\"3u*****z-!>-iF17$$\"#>F.$\"3[******
Q<UmqF17$$\"#?F.$\"39+++g.(*=iF17$$\"#@F.$\"3%******zPLU0(F17$$\"#AF.$
\"3B*****pcPSB'F17$$\"#BF.$\"3J+++&QXJ/(F17$$\"#CF.$\"3?+++#3nwC'F17$$
\"#DF.$\"3Z*****p0)*H.(F17$$\"#EF.$\"3U+++qc2giF17$$\"#FF.$\"3b+++#ziO
-(F17$$\"#GF.$\"3A*****>nO9F'F17$$\"#HF.$\"3\\*****zjM],(F17$$\"#IF.$
\"3G+++@1*=G'F17$$\"#JF.$\"3))******Hp-2qF17$$\"#KF.$\"39+++rGb\"H'F17
$$\"#LF.$\"3?+++`tc**pF17$$\"#MF.$\"3++++@\">0I'F17$$\"#NF.$\"3a*****R
+&f#*pF17$$\"#OF.$\"3x*****Rap)3jF17$$\"#PF.$\"3'******R:eg)pF17$$\"#Q
F.$\"3]*****>!>n;jF17$$\"#RF.$\"3%******>`7*zpF17$$\"#SF.$\"3d*****4\"
R)RK'F1-%&COLORG6&%$RGBG$F[o!\"\"$F.FixFjx-%&STYLEG6#%&POINTG-%%VIEWG6
$;FjxF`x;$\"1-++ST,]()!#<$\"1-++')y#\\P(!#;" 1 5 2 1 10 1 2 6 1 4 2 
1.0 45.0 45.0 1 0 "Curve 1" }}{TEXT 204 0 "" }}}{EXCHG {PARA 411 "> " 
0 "" {MPLTEXT 1 0 24 "quad := x -> k*x*(1-x); " }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I%quadG6\"f*6#I\"xGF$F$6$I)operatorGF$I&arrowGF$F$*(I\"k
GF$\"\"\"F'F-,&F-F-F'!\"\"F-F$F$F$" }}}{EXCHG {PARA 412 "> " 0 "" 
{MPLTEXT 1 0 15 "     k := 2.8; " }}{PARA 11 "" 1 "" {XPPMATH 20 ">I\"
kG6\"$\"#G!\"\"" }}}{EXCHG {PARA 413 "> " 0 "" {MPLTEXT 1 0 31 "     i
terplot( quad, 40, 0.1 );" }}{PARA 13 "" 1 "" {TEXT 204 0 "" }
{GLPLOT2D 400 400 400 {PLOTDATA 2 "6&-%+AXESLABELSG6$Q!6\"F&-%'CURVESG
6$7K7$$\"\"!F.$\"3/+++++++5!#=7$$\"\"\"F.$\"3-++++++?DF17$$\"\"#F.$\"3
Y********z)yF&F17$$\"\"$F.$\"35+++8zPypF17$$\"\"%F.$\"3?+++Me3/fF17$$
\"\"&F.$\"3#)*****p1O6x'F17$$\"\"'F.$\"3))******p:m@hF17$$\"\"(F.$\"3s
*****>4Dxk'F17$$\"\")F.$\"33+++n0!)RiF17$$\"\"*F.$\"3g*****fZ5'plF17$$
\"#5F.$\"3A+++E/<5jF17$$\"#6F.$\"3w*****f'pO>lF17$$\"#7F.$\"3/+++Dni`j
F17$$\"#8F.$\"3[*****H^ap['F17$$\"#9F.$\"3E******e0\"4Q'F17$$\"#:F.$\"
3#********3kgY'F17$$\"#;F.$\"3%******Hq$=)R'F17$$\"#<F.$\"3e*****R0BEX
'F17$$\"#=F.$\"3)******H:o\"4kF17$$\"#>F.$\"3d*****Hj))RW'F17$$\"#?F.$
\"3q*****46rhT'F17$$\"#@F.$\"3l*****pi[%QkF17$$\"#AF.$\"3D+++bBk?kF17$
$\"#BF.$\"3b*****>3(*[V'F17$$\"#CF.$\"3a*****>q*\\BkF17$$\"#DF.$\"3\"*
******3;iKkF17$$\"#EF.$\"3q*****HpE`U'F17$$\"#FF.$\"3Q+++pU;JkF17$$\"#
GF.$\"3B+++t_\\EkF17$$\"#HF.$\"3[+++X6BIkF17$$\"#IF.$\"3r*****f)GCFkF1
7$$\"#JF.$\"3U+++oPjHkF17$$\"#KF.$\"3`*****4C@xU'F17$$\"#LF.$\"3@+++v8
DHkF17$$\"#MF.$\"3.+++Ut-GkF17$$\"#NF.$\"3B*****fh1!HkF17$$\"#OF.$\"3N
+++CKAGkF17$$\"#PF.$\"3M+++f*\\)GkF17$$\"#QF.$\"3()*****Re[$GkF17$$\"#
RF.$\"3!)*****>p\\(GkF17$$\"#SF.$\"3x******4)G%GkF1-%&COLORG6&%$RGBG$F
[o!\"\"$F.FixFjx-%&STYLEG6#%&POINTG-%%VIEWG6$;FjxF`x;$\",uTCV!))!#7$\"
-Era%z4(Ffy" 1 5 2 1 10 1 2 6 1 4 2 1.0 45.0 45.0 1 0 "Curve 1" }}
{TEXT 204 0 "" }}}{EXCHG {PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 414 
"> " 0 "" {MPLTEXT 1 0 15 "     k := 4.0; " }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I\"kG6\"$\"#S!\"\"" }}}{EXCHG {PARA 415 "> " 0 "" 
{MPLTEXT 1 0 32 "     iterplot( quad, 40, 0.1 ); " }}{PARA 13 "" 1 "" 
{TEXT 204 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "6&-%+AXESLABELSG6$Q
!6\"F&-%'CURVESG6$7K7$$\"\"!F.$\"3/+++++++5!#=7$$\"\"\"F.$\"3')*******
******f$F17$$\"\"#F.$\"3v***********f@*F17$$\"\"$F.$\"33++++w8!*GF17$$
\"\"%F.$\"3J+++hAR>#)F17$$\"\"&F.$\"3#******pQ0U&eF17$$\"\"'F.$\"3l+++
kK83(*F17$$\"\"(F.$\"3$******pY#RL6F17$$\"\")F.$\"3t*****RZQ(>SF17$$\"
\"*F.$\"3b******Q\\j:'*F17$$\"#5F.$\"35+++WcOy9F17$$\"#6F.$\"3#)*****
\\eO#R]F17$$\"#7F.$\"3s+++'>%Q****F17$$\"#8F.$\"3!******RJkIY#!#@7$$\"
#9F.$\"3#)*****>eI)\\)*F]p7$$\"#:F.$\"3>+++m90OR!#?7$$\"#;F.$\"3-+++&e
B#o:!#>7$$\"#<F.$\"3g+++K8_uhF^q7$$\"#=F.$\"3$******zn4tJ#F17$$\"#>F.$
\"35+++a!p77(F17$$\"#?F.$\"3T+++Tq3+#)F17$$\"#@F.$\"3x*****4<xP!fF17$$
\"#AF.$\"3w*****zsuKn*F17$$\"#BF.$\"3%******pK,UE\"F17$$\"#CF.$\"3)***
****4L_<WF17$$\"#DF.$\"3#******>O)Gk)*F17$$\"#EF.$\"3#)*****f#\\za`F^q
7$$\"#FF.$\"3*******\\lAs-#F17$$\"#GF.$\"3Y+++Vz.lkF17$$\"#HF.$\"3G+++
IbYT\"*F17$$\"#IF.$\"3z*****fI0$RJF17$$\"#JF.$\"37++++h7:')F17$$\"#KF.
$\"3y*****>JXBx%F17$$\"#LF.$\"3s*****zLp#z**F17$$\"#MF.$\"3m*****fQu]F
)Fhp7$$\"#NF.$\"3++++7!REG$F^q7$$\"#OF.$\"37+++HF&*p7F17$$\"#PF.$\"3#*
*****>%*)pMWF17$$\"#QF.$\"3w*****p)Q<s)*F17$$\"#RF.$\"3u******fkoZ]F^q
7$$\"#SF.$\"3!*******H!er\">F1-%&COLORG6&%$RGBG$F[o!\"\"$F.F\\yF]y-%&S
TYLEG6#%&POINTG-%%VIEWG6$;F]yFcx;$!2+?(>$e`Z(>F1$\"2APj=EK*>5!#;" 1 5 
2 1 10 1 2 6 1 4 2 1.0 45.0 45.0 1 0 "Curve 1" }}{TEXT 204 0 "" }}}
{EXCHG {PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 206 "" 0 "" {TEXT 203 
131 "Try different values of the parameter k and the initial value. Us
e k in the range 1 to 4 and the initialvalue in the range 0 to 1. " }}
{PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 206 "" 0 "" {TEXT 203 9 "Exam
ple 3" }}{PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 206 "" 0 "" {TEXT 
203 120 "With iterplot2 you can compare two different sequences, e.g.,
 the ones generated by quad with different initial values. " }}{PARA 
206 "" 0 "" {TEXT 203 0 "" }}{PARA 416 "> " 0 "" {MPLTEXT 1 0 44 "    \+
 iterplot2( quad, quad, 40, 0.1, 0.9 ); " }}{PARA 13 "" 1 "" {TEXT 
204 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "6'-%+AXESLABELSG6$Q!6\"F&
-%'CURVESG6$7K7$$\"\"!F.$\"3/+++++++5!#=7$$\"\"\"F.$\"3')*************
f$F17$$\"\"#F.$\"3v***********f@*F17$$\"\"$F.$\"33++++w8!*GF17$$\"\"%F
.$\"3J+++hAR>#)F17$$\"\"&F.$\"3#******pQ0U&eF17$$\"\"'F.$\"3l+++kK83(*
F17$$\"\"(F.$\"3$******pY#RL6F17$$\"\")F.$\"3t*****RZQ(>SF17$$\"\"*F.$
\"3b******Q\\j:'*F17$$\"#5F.$\"35+++WcOy9F17$$\"#6F.$\"3#)*****\\eO#R]
F17$$\"#7F.$\"3s+++'>%Q****F17$$\"#8F.$\"3!******RJkIY#!#@7$$\"#9F.$\"
3#)*****>eI)\\)*F]p7$$\"#:F.$\"3>+++m90OR!#?7$$\"#;F.$\"3-+++&eB#o:!#>
7$$\"#<F.$\"3g+++K8_uhF^q7$$\"#=F.$\"3$******zn4tJ#F17$$\"#>F.$\"35+++
a!p77(F17$$\"#?F.$\"3T+++Tq3+#)F17$$\"#@F.$\"3x*****4<xP!fF17$$\"#AF.$
\"3w*****zsuKn*F17$$\"#BF.$\"3%******pK,UE\"F17$$\"#CF.$\"3)*******4L_
<WF17$$\"#DF.$\"3#******>O)Gk)*F17$$\"#EF.$\"3#)*****f#\\za`F^q7$$\"#F
F.$\"3*******\\lAs-#F17$$\"#GF.$\"3Y+++Vz.lkF17$$\"#HF.$\"3G+++IbYT\"*
F17$$\"#IF.$\"3z*****fI0$RJF17$$\"#JF.$\"37++++h7:')F17$$\"#KF.$\"3y**
***>JXBx%F17$$\"#LF.$\"3s*****zLp#z**F17$$\"#MF.$\"3m*****fQu]F)Fhp7$$
\"#NF.$\"3++++7!REG$F^q7$$\"#OF.$\"37+++HF&*p7F17$$\"#PF.$\"3#******>%
*)pMWF17$$\"#QF.$\"3w*****p)Q<s)*F17$$\"#RF.$\"3u******fkoZ]F^q7$$\"#S
F.$\"3!*******H!er\">F1-%&COLORG6&%$RGBG$F[o!\"\"$F.F\\yF]y-F)6$7K7$F-
$\"3A+++++++!*F1F2F7F<FAFFFKFPFUFZFinF^oFcoFhoF^pFcpFipF_qFdqFiqF^rFcr
FhrF]sFbsFgsF\\tFatFftF[uF`uFeuFjuF_vFdvFivF^wFcwFhwF]xFbx-Fhx6&FjxF]y
F[yF]y-%&STYLEG6#%&POINTG-%%VIEWG6$;F]yFcx;$!2+?(>$e`Z(>F1$\"2APj=EK*>
5!#;" 1 5 2 1 10 1 2 6 1 4 2 1.0 45.0 45.0 1 0 "Curve 1" "Curve 2" }}
{TEXT 204 0 "" }}}{EXCHG {PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 206 
"" 0 "" {TEXT 203 0 "" }}{PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 206 
"" 0 "" {TEXT 203 0 "" }}{PARA 206 "" 0 "" {TEXT 203 9 "Example 4" }}
{PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 206 "" 0 "" {TEXT 203 138 "Th
e function \"cobweb\" is useful for demonstrating graphicaly how a map
 is iterated. It is also useful for for finding fixed points. Try " }}
{PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 417 "> " 0 "" {MPLTEXT 1 0 
43 "     k := 3; cobweb( quad, 10, 0.1, 0..1); " }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I\"kG6\"\"\"$" }}{PARA 13 "" 1 "" {TEXT 204 0 "" }
{GLPLOT2D 400 400 400 {PLOTDATA 2 "6)-%+AXESLABELSG6$Q\"x6\"Q\"yF'-%'C
URVESG6$777$$\"3/+++++++5!#=$\"\"!F27$F.$\"3;+++++++FF07$F4F47$F4$\"3[
++++++8fF07$F8F87$F8$\"3!)*******HH*\\sF07$F<F<7$F<$\"3C+++WaM\")fF07$
F@F@7$F@$\"3!******\\L)36sF07$FDFD7$FD$\"31+++6lKLgF07$FHFH7$FH$\"3!**
****\\*3nzrF07$FLFL7$FL$\"3=*****\\V5Z2'F07$FPFP7$FP$\"3)4++?C*\\`rF07
$FTFT7$FT$\"3$)*****fIK(3hF07$FXFX-%&COLORG6&%$RGBG$\"#5!\"\"$F2F[oF
\\o-F*6$777$$!3/+++++++5F0$!3;+++++++LF07$$!3/++++++]R!#>$!31++++v!=B
\"F07$$\"39+++++++@Fho$\"3e**********pnhFho7$$\"3#*)***********\\\")Fh
o$\"3-++++DtXAF07$$\"3()************>9F0$\"3++++++3bOF07$$\"39++++++D?
F0$\"3v*******\\7[%[F07$$\"36++++++IEF0$\"3Q+++++$\\\"eF07$$\"35++++++
NKF0$\"3C++++DVllF07$$\"33++++++SQF0$\"3S+++++K'4(F07$$\"32++++++XWF0$
\"3!)*******\\#f2uF07$$\"3/++++++]]F0$\"3_*********\\#*\\(F07$$\"3-+++
+++bcF0$\"3e*******\\#HrtF07$$\"3-++++++giF0$\"3(**********>P-(F07$$\"
3)************\\'oF0$\"3c*******\\KlX'F07$$\"3)*************puF0$\"3[*
********H(pcF07$$\"3'************\\2)F0$\"3u*******\\7Lm%F07$$\"3%****
*********z')F0$\"3y*********zsV$F07$$\"3#************\\G*F0$\"3%)*****
**\\K;*>F07$$\"3!**************))*F0$\"3%***********pjKFho7$$\"35+++++
]\\5!#<$!35++++v]e:F07$$\"35++++++56Fcu$!39++++++jOF0-Ffn6&FhnF\\oFinF
\\o-F*6$7$7$FaoFao7$FguFgu-Ffn6&FhnFinFinF\\o-%*THICKNESSG6#\"\"#-%&ST
YLEG6#%%LINEG-%%VIEWG6$;$F[oF[o$\"$6\"!\"#;F\\oFin" 1 6 2 1 10 2 2 6 1
 4 2 1.0 45.0 45.0 1 0 "Curve 1" "Curve 2" "Curve 3" }}{TEXT 204 0 "" 
}}}{EXCHG {PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 206 "" 0 "" {TEXT 
203 90 "This example \"cobwebs\" quad 10 times on the interval 0..1 wi
th an initial value of 0.1. " }}{PARA 206 "" 0 "" {TEXT 203 0 "" }}
{PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 206 "" 0 "" {TEXT 203 0 "" }}
{PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 206 "" 0 "" {TEXT 203 9 "Exam
ple 5" }}{PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 206 "" 0 "" {TEXT 
203 99 "The iter function can be used to implement Newton's method for
 finding roots. Let us use it to find" }}{PARA 206 "" 0 "" {TEXT 203 
66 "the square root of two, which is a root of the quadratic function \+
" }}{PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 418 "> " 0 "" {MPLTEXT 1 
0 24 "     f := x -> x*x - 2; " }}{PARA 11 "" 1 "" {XPPMATH 20 ">I\"fG
6\"f*6#I\"xGF$F$6$I)operatorGF$I&arrowGF$F$,&*&F'\"\"\"F'F-F-\"\"#!\"
\"F$F$F$" }}}{EXCHG {PARA 419 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 206 "" 0 "" {TEXT 203 40 "New
ton tells us to iterate the function " }}{PARA 206 "" 0 "" {TEXT 203 
0 "" }}{PARA 420 "> " 0 "" {MPLTEXT 1 0 30 "     g :=x-> x - (f(x)/(2*
x));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I\"gG6\"f*6#I\"xGF$F$6$I)operat
orGF$I&arrowGF$F$,&F'\"\"\"*(#F,\"\"#F,-I\"fGF$F&F,F'!\"\"F2F$F$F$" }}
}{EXCHG {PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 206 "" 0 "" {TEXT 
203 101 "with a reasonable guess for the starting value. Try the examp
le below, which iterates g 10 times with" }}{PARA 206 "" 0 "" {TEXT 
203 20 "1 as initial value. " }}{PARA 206 "" 0 "" {TEXT 203 0 "" }}
{PARA 421 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 206 "" 0 "" 
{TEXT 203 0 "" }}{PARA 422 "> " 0 "" {MPLTEXT 1 0 28 "     iterprint( \+
g, 10, 1 ); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"!\"\"\"" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6$\"\"\"$\"+++++:!\"*" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$\"\"#$\"+nmm;9!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$
\"\"$$\"+'o:UT\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"%$\"+iN@99
!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"&$\"+iN@99!\"*" }}{PARA 11
 "" 1 "" {XPPMATH 20 "6$\"\"'$\"+iN@99!\"*" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$\"\"($\"+iN@99!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$
\"\")$\"+iN@99!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"*$\"+iN@99!
\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"#5$\"+iN@99!\"*" }}}{EXCHG 
{PARA 206 "" 0 "" {TEXT 203 0 "" }}{PARA 206 "" 0 "" {TEXT 203 0 "" }}
{PARA 423 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 424 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 425 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}

{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 15 10 1804 1 1 1 1 }{PAGENUMBERS 0 1 
2 33 1 1 }