{VERSION 12 2 "Windows XP" "12.2" } {USTYLETAB {PSTYLE "Ordered List 1" -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 0 2 0 2 2 -1 1 } {PSTYLE "Ordered List 2" -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 36 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 "Ordered List 4" -1 203 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 "Ordered List 5" -1 204 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 "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 "Annotatio n Title" -1 205 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }3 1 0 0 12 12 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 "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 "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 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 "Line Prin ted 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 "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 "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 "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 "Normal258 " -1 206 1 {CSTYLE "" -1 -1 "Times" 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 "R3 Font 2" -1 207 1 {CSTYLE "" -1 -1 "Courier" 1 10 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 "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 10 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 "Maple Ou tput" -1 11 1 {CSTYLE "" -1 -1 "Times" 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 "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 "HyperlinkError" -1 208 1 {CSTYLE "" -1 -1 "Courier" 1 12 255 0 255 1 2 2 1 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 } {PSTYLE "R3 Font 0" -1 209 1 {CSTYLE "" -1 -1 "Times" 1 10 255 0 0 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 "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 "Error" -1 8 1 {CSTYLE "" -1 -1 "Cou rier" 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 "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 "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 "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 "Heading 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 "Hyperlink Warning" -1 210 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 255 1 2 2 1 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 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 "Left 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 "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 } {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 Math Italic Small223" -1 200 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Menus" -1 36 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small236" -1 201 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small234" -1 202 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic S mall235" -1 203 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D M ath Italic Small233" -1 204 "Times" 1 1 0 0 0 1 1 2 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 "Help Underlined" -1 44 "Times" 1 12 0 0 0 1 2 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 Italic Small208242" -1 205 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small208241" -1 206 "Times" 1 1 0 0 0 1 1 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 Nonterminal" -1 24 "Couri er" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small203 239248255" -1 207 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small208239" -1 208 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Emphasized" -1 22 "Times" 1 12 0 0 0 1 1 2 2 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 "2D Math Italic Small208" -1 209 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small207" -1 210 "Tim es" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small209" -1 211 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Ital ic Small202" -1 212 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE " 2D Math Italic Small201" -1 213 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small204" -1 214 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small203" -1 215 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small205" -1 216 "T imes" 1 1 0 0 0 1 1 2 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 "2D Math" -1 2 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Sma ll213" -1 217 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Mat h Italic Small210" -1 218 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 } {CSTYLE "2D Math Italic Small215" -1 219 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small214" -1 220 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small203236241" -1 221 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Smal l203236242" -1 222 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "H elp Italic" -1 42 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "H elp Italic Bold" -1 40 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 } {CSTYLE "2D Math Italic Small204240" -1 223 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small204242" -1 224 "Times" 1 1 0 0 0 1 1 2 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 Italic Small202230" -1 225 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Smal l" -1 7 "Times" 1 1 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Ital ic Small203239248" -1 226 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 } {CSTYLE "2D Math Italic Small204239" -1 227 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Maple Input Placeholder" -1 228 "Courier" 1 12 200 0 200 1 2 1 2 2 1 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 "2D Math Italic Small202207" -1 229 "Times" 1 1 0 0 0 1 1 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 "Equation Labe l" -1 230 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math I talic Small202206" -1 231 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 } {CSTYLE "2D Math Italic" -1 3 "Times" 1 12 0 0 0 1 1 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 Variable" -1 25 "Courier" 1 12 0 0 0 1 2 2 2 2 2 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 Italic Small203235240" -1 232 "Times" 1 1 0 0 0 1 1 2 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 "Prompt" -1 1 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small203235239" -1 233 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Itali c Small203240252" -1 234 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 } {CSTYLE "2D Math Italic Small201230" -1 235 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Code" -1 236 "Courier" 1 12 255 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small" -1 237 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small201229" -1 238 "Tim es" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small2012 23" -1 239 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math I talic Small201225" -1 240 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 } {CSTYLE "Header and Footer" -1 241 "Times" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "LaTeX" -1 32 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small201217" -1 242 "Times" 1 1 0 0 0 1 1 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 "Popup" -1 31 "Times" 1 12 0 128 128 1 1 2 1 2 2 2 0 0 0 1 }{CSTYLE "Help Fixed" -1 23 "Courier" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small203236242248" -1 243 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Ital ic Small203228" -1 244 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 } {CSTYLE "2D Math Italic Small203236242249" -1 245 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small203229" -1 246 "Time s" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small20322 7" -1 247 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math It alic Small203224" -1 248 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 } {CSTYLE "2D Math Italic Small203225" -1 249 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small203234" -1 250 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small203232" -1 251 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic S mall203230" -1 252 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "H elp Underlined Italic" -1 43 "Times" 1 12 0 0 0 1 1 2 1 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small210266" -1 253 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small210267" -1 254 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small203218" -1 255 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic \+ Small203219" -1 256 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE " 2D Math Italic Small203214" -1 257 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small203215" -1 258 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small203216" -1 259 "Time s" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small20322 1" -1 260 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math It alic Small203220" -1 261 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 } {CSTYLE "2D Math Italic Small203223" -1 262 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small203222" -1 263 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Plot Title" -1 27 "Times" 1 10 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small205242" -1 264 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic S mall205243" -1 265 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2 D Math Italic Small205245" -1 266 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small203236241246248" -1 267 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small203235" -1 268 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic S mall203236" -1 269 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2 D Math Italic Small203237" -1 270 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small203238" -1 271 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small203239" -1 272 "Times " 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small203240 " -1 273 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Ita lic Small203236241246247" -1 274 "Times" 1 1 0 0 0 1 1 2 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 "2D Math Italic Small214275" -1 275 "Times" 1 1 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 "2D Math Italic Small209209" -1 276 "Times" 1 1 0 0 0 1 1 2 2 2 2 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 "2D Math Italic Small215215" -1 277 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Annotation Text" -1 278 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Ita lic Small215217" -1 279 "Times" 1 1 0 0 0 1 1 2 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 Math Italic Small203237244" -1 280 "Times" 1 1 0 0 0 1 1 2 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 "Maple Comment" -1 21 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small203238246" -1 281 " Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Inert Output" -1 282 "Times" 1 12 144 144 144 1 2 2 2 2 1 2 0 0 0 1 }{CSTYLE "2D Commen t" -1 18 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Text" -1 283 "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 "2D Math Italic S mall207239" -1 284 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2 D Math Italic Small203236241246" -1 285 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{PSTYLE "" -1 211 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 4 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 212 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 4 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 213 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 4 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 214 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 4 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 215 1 {CSTYLE "" -1 -1 "Time s" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 8 4 2 0 2 0 2 2 -1 1 } {PSTYLE "" -1 216 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 "" -1 217 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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "restart;with(combin at):with(LinearAlgebra):" }{MPLTEXT 1 0 18 "with(GraphTheory):" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 283 15 "Press Return " }{TEXT 283 57 "( the preloading can take a few seconds) then Scroll down." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 211 "" 0 "" {TEXT 283 0 "" }}{PARA 212 "" 0 "" {TEXT 283 0 "" }}{PARA 213 "" 0 "" {TEXT 283 37 "Finite Directed Lattices, Causality, " }}{PARA 214 "" 0 "" {TEXT 283 26 "and Topological Partitions" }}{PARA 215 "" 0 "" {TEXT 283 21 " NBR = 3 and 4 points" }}{PARA 216 "" 0 "" {TEXT 283 83 "Using some portions of a Maple program for finite topology created by Didie r Deses," }}{PARA 217 "" 0 "" {TEXT 283 65 "along with a number of mod ifications, additions, and corrections." }}{PARA 19 "" 0 "" {TEXT 286 35 "by R. M. Kiehn September 22, 2009 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 283 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 283 40 "Press Enter to load Program subroutines:" }{TEXT 283 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 " \+ " }} {PARA 0 "" 0 "" {TEXT 287 94 "A procedure to check if a set is a subse t of another one, the implementation is quite trivial." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "issubset:=proc(A,B)\n" }{MPLTEXT 1 0 2 " " } {MPLTEXT 1 0 9 "local a;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 14 "for a in A do\n" }{MPLTEXT 1 0 1 " " }{MPLTEXT 1 0 47 " if not(member(a ,B)) then RETURN(false); fi;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 4 " od;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 14 "RETURN(true);\n" } {MPLTEXT 1 0 9 "end proc:" }}{PARA 0 "" 0 "" {TEXT 287 66 "Two procedu res to close a set under unions/intersections: `union` " }}{PARA 0 "" 0 "" {TEXT 287 73 "it recursively applied to the given set, until it d oesn't change anymore;" }}{PARA 0 "" 0 "" {TEXT 287 34 "T is a given, \+ or computed,Topology" }}{PARA 0 "" 0 "" {TEXT 287 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "clunion:=proc(T)\n" }{MPLTEXT 1 0 2 " " } {MPLTEXT 1 0 16 "local A,U;U:=T;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 14 "for A in T do\n" }{MPLTEXT 1 0 4 " " }{MPLTEXT 1 0 30 "U:= U \+ union map(`union`,U,A);\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 4 "od;\n " }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 36 "if U=T then U; else clunion(U ); fi;\n" }{MPLTEXT 1 0 9 "end proc:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "clintersect:=proc(T)\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 16 "l ocal A,U;U:=T;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 14 "for A in T do \n" }{MPLTEXT 1 0 4 " " }{MPLTEXT 1 0 34 "U:= U union map(`intersec t`,U,A);\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 4 "od;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 40 "if U=T then U; else clintersect(U); fi;\n" }{MPLTEXT 1 0 9 "end proc:" }}{PARA 0 "" 0 "" {TEXT 287 59 "A subbasis SB is used to generate a topology by closing SB " }}{PARA 0 "" 0 "" {TEXT 287 71 "under both finite intersections and finite unions and ad ding X and \{\}. " }}{PARA 0 "" 0 "" {TEXT 287 49 "Since X is a finite set the result is a topology." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "t opbase:=proc(X,SB)\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 39 "clunion(c lintersect(SB union \{X,\{\}\}));\n" }{MPLTEXT 1 0 9 "end proc:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "" 0 "" {TEXT 283 0 "" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "kinterior:=proc(A,X,T)\n" } {MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 21 "local i;global kINT;\n" } {MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 7 "kINT:=\{" }{MPLTEXT 1 0 3 "\}:\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 20 "for i to nops(T) do\n" } {MPLTEXT 1 0 36 " if issubset(T[i],A) then kINT:=\{" }{MPLTEXT 1 0 18 "\} union T[i]: fi:\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 6 "od: \+ \n" }{MPLTEXT 1 0 11 "end proc: " }}{PARA 0 "" 0 "" {TEXT 283 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "" 0 "" {TEXT 283 0 "" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "kintext:=proc(A,X,T)\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 24 "local i;global kINTEXT;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 13 "kINTEXT:=\{\}:\n" }{MPLTEXT 1 0 2 " " } {MPLTEXT 1 0 20 "for i to nops(T) do\n" }{MPLTEXT 1 0 67 " if issub set(T[i],(X)minus(A)) then kINTEXT:=\{\} union T[i]: fi:\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 6 "od: \n" }{MPLTEXT 1 0 11 "end proc: " }} {PARA 0 "" 0 "" {TEXT 287 46 "A finite topology on X must contains X a nd \{\}." }}{PARA 0 "" 0 "" {TEXT 287 78 "It must be closed under unio ns of open sets and intersections of closed sets." }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 18 "isTopo:=proc(X,T)\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 68 "clunion(T)=T and member(X,T) and member(\{\},T) and clinterse ct(T)=T;\n" }{MPLTEXT 1 0 9 "end proc:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "" 0 "" {TEXT 283 0 "" }}{PARA 0 "" 0 "" {TEXT 287 85 "The interior of a subset is the union of all open sets contained i n the given subset." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "akinterior:= proc(A,X,T)\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 24 "local i;global k INTEXT;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 14 "kINTEXT:=\{0\}:\n" } {MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 20 "for i to nops(T) do\n" }{MPLTEXT 1 0 58 " if issubset(T[i],A) then kINTEXT:=\{0\} union T[i]: fi:\n " }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 6 "od: \n" }{MPLTEXT 1 0 11 "end proc: " }}{PARA 0 "" 0 "" {TEXT 283 26 "Is the Topology connected?" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "isConn:=proc(X,T)\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 23 "evalb(CO(X,T)=\{X,\{\}\});\n" }{MPLTEXT 1 0 9 "end proc:" }}{PARA 0 "" 0 "" {TEXT 283 38 "Find the sets that are Open and Closed" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "CO:=proc(X,T)\n " }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 17 "local A,W;W:=\{\};\n" } {MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 14 "for A in T do\n" }{MPLTEXT 1 0 4 " " }{MPLTEXT 1 0 48 "if member(X minus A,T) then W:=W union \{A \}; fi;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 4 "od;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 3 "W;\n" }{MPLTEXT 1 0 9 "end proc:" }}{PARA 0 "" 0 "" {TEXT 283 0 "" }}{PARA 0 "" 0 "" {TEXT 283 21 "Find the closure \+ of T" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "CLO:=proc(X,T)\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 34 "\{seq(X minus T[i],i=1..nops(T))\};\n" } {MPLTEXT 1 0 47 "end proc: " }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "" 0 "" {TEXT 287 79 "Th e following are a set of procedures testing for some topological prope rties, " }}{PARA 0 "" 0 "" {TEXT 287 78 "the used algorithms are simpl y exhaustive ones, all possibilities are checked." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "isT0:=proc(X,T)\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 18 "local x,y,A,test;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 14 "for \+ x in X do\n" }{MPLTEXT 1 0 3 " " }{MPLTEXT 1 0 25 " for y in X minus \{x\} do\n" }{MPLTEXT 1 0 20 " for A in T do\n" }{MPLTEXT 1 0 58 " test:=evalb((member(x,A) and not(member(y,A))) or\n" } {MPLTEXT 1 0 57 " (member(y,A) and not(member(x,A)) )):\n" }{MPLTEXT 1 0 32 " if test then break; fi;\n" }{MPLTEXT 1 0 10 " od:\n" }{MPLTEXT 1 0 35 " if not(test) then break; \+ fi;\n" }{MPLTEXT 1 0 8 " od:\n" }{MPLTEXT 1 0 33 " if not(test) \+ then break; fi;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 4 "od:\n" } {MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 6 "test;\n" }{MPLTEXT 1 0 9 "end pro c:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "isT1:=proc(X,T)\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 47 "issubset(\{seq(\{X[i]\},i=1..nops(X))\},C LO(X,T));\n" }{MPLTEXT 1 0 9 "end proc:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "isHd:=proc(X,T)\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 21 "loca l x,y,A,B,test; \n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 14 "for x in X \+ do\n" }{MPLTEXT 1 0 28 " for y in X minus \{x\} do\n" }{MPLTEXT 1 0 20 " for A in T do\n" }{MPLTEXT 1 0 32 " for B in T minu s \{A\} do\n" }{MPLTEXT 1 0 73 " test:=evalb(member(x,A) and \+ member(y,B) and A intersect B=\{\}):\n" }{MPLTEXT 1 0 6 " " } {MPLTEXT 1 0 28 " if test then break; fi;\n" }{MPLTEXT 1 0 12 " \+ od:\n" }{MPLTEXT 1 0 32 " if test then break; fi;\n" } {MPLTEXT 1 0 10 " od:\n" }{MPLTEXT 1 0 35 " if not(test) the n break; fi;\n" }{MPLTEXT 1 0 8 " od:\n" }{MPLTEXT 1 0 33 " if n ot(test) then break; fi;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 4 "od: \n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 6 "test;\n" }{MPLTEXT 1 0 9 "en d proc:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "" 0 "" {TEXT 283 55 "The exterior of a se t is the interior of its complement" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "exteriorb:=proc(A,X,T)\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 15 "l ocal i,C,ClX;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 15 "ClX:=CLO(X,T); \n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 6 "C:=X;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 22 "for i to nops(ClX) do\n" }{MPLTEXT 1 0 58 " if \+ issubset(A,ClX[i]) then C:=C intersect ClX[i]; fi;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 4 "od;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 21 "pr int(`Exterior`=C);\n" }{MPLTEXT 1 0 9 "end proc:" }}{PARA 0 "" 0 "" {TEXT 287 63 "Subspaces are found by taking intersections with the ope n sets." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "subspace:=proc(A,X,T)\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 23 "map2(`intersect`,A,T);\n" } {MPLTEXT 1 0 9 "end proc:" }}{PARA 0 "" 0 "" {TEXT 287 79 "Given a lis t of sets this procedure finds all element in the cartesian product." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "expandcart:=proc(PX)\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 13 "local C,P,i;\n" }{MPLTEXT 1 0 2 " " } {MPLTEXT 1 0 7 "C:=\{\};\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 47 "P:= cartprod([seq([op(PX[i])],i=1..nops(PX))]);\n" }{MPLTEXT 1 0 2 " " } {MPLTEXT 1 0 57 "while not P[finished] do C:=C union \{P[nextvalue]() \} od;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 3 "C;\n" }{MPLTEXT 1 0 9 "end proc:" }}{PARA 0 "" 0 "" {TEXT 287 78 "Implementation of the inve rse projections, this is needed in later procedures." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "iprj:=proc(k,S,PX) \n" }{MPLTEXT 1 0 2 " " } {MPLTEXT 1 0 11 "local i,O;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 21 " for i to nops(PX) do\n" }{MPLTEXT 1 0 4 " " }{MPLTEXT 1 0 41 "if i= k then O[i]:=S else O[i]:=PX[i] fi;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 4 "od;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 39 "expandcart([seq(O [i],i=1..nops(PX))]);\n" }{MPLTEXT 1 0 9 "end proc:" }}{PARA 0 "" 0 "" {TEXT 287 79 "Procedure to find a subbasis for a product topology usi ng inverse projections. " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "prodbas e:=proc(PX,PS)\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 19 "local i,k,S;S :=\{\};\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 21 "for k to nops(PX) do \n" }{MPLTEXT 1 0 4 " " }{MPLTEXT 1 0 24 "for i to nops(PS[k]) do\n " }{MPLTEXT 1 0 6 " " }{MPLTEXT 1 0 34 "S:=S union \{iprj(k,PS[k] [i],PX)\};\n" }{MPLTEXT 1 0 4 " " }{MPLTEXT 1 0 4 "od;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 4 "od;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 3 "S;\n" }{MPLTEXT 1 0 9 "end proc:" }}{PARA 0 "" 0 "" {TEXT 287 77 "Given a list of sets and a list of topologies, the product topology i s found." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "prodtop:=proc(PX,PT)\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 41 "topbase(expandcart(PX),prodbas e(PX,PT));\n" }{MPLTEXT 1 0 9 "end proc:" }}{PARA 0 "" 0 "" {TEXT 287 70 "A topology is weakly zero-dimensional iff the clopen sets form a b ase." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "isWzd:=proc(X,T)\n" } {MPLTEXT 1 0 30 " evalb(topbase(X,CO(X,T))=T)\n" }{MPLTEXT 1 0 9 "end proc:" }}{PARA 0 "" 0 "" {TEXT 287 60 "A topology is connected iff th ere are no proper clopen sets." }}{PARA 0 "" 0 "" {TEXT 287 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "isConn:=proc(X,T)\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 23 "evalb(CO(X,T)=\{X,\{\}\});\n" }{MPLTEXT 1 0 9 "end proc:" }}{PARA 0 "" 0 "" {TEXT 287 83 "A connection component i s the largest connected subspace, containing a given point." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "K:=proc(x,X,T)\n" }{MPLTEXT 1 0 2 " " } {MPLTEXT 1 0 14 "local i,S,SK;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 8 "SK:=\{\};\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 34 "S:=map2(`union` ,\{x\},powerset(X));\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 20 "for i t o nops(S) do\n" }{MPLTEXT 1 0 4 " " }{MPLTEXT 1 0 63 "if isConn(S[i ],subspace(S[i],X,T)) then SK:=SK union S[i]; fi;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 4 "od;\n" }{MPLTEXT 1 0 6 " SK;\n" }{MPLTEXT 1 0 9 "end proc:" }}{PARA 0 "" 0 "" {TEXT 287 80 "A topology is totally disc onnected if all connections components are singletons." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "isTotDisc:=proc(X,T)\n" }{MPLTEXT 1 0 2 " " } {MPLTEXT 1 0 9 "local i;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 20 "for i to nops(X) do\n" }{MPLTEXT 1 0 4 " " }{MPLTEXT 1 0 50 "if not(K( X[i],X,T)=\{X[i]\}) then RETURN(false) fi;\n" }{MPLTEXT 1 0 2 " " } {MPLTEXT 1 0 4 "od;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 14 "RETURN(t rue);\n" }{MPLTEXT 1 0 9 "end proc:" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" } {MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" } {MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" } {MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" } {MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" } {MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 0 "" } {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "prLatpt3:=proc( GS,NBR)\n" }{MPLTEXT 1 0 31 " local VA,EA,De,i,j,k,LS3,LS:\n" } {MPLTEXT 1 0 58 " global GA,G,H,Dee,SS3,SSS3,XS,ZS,QS,TS,STop1,STop1d ual:\n" }{MPLTEXT 1 0 1 " " }{MPLTEXT 1 0 9 " LS:=GS;\n" }{MPLTEXT 1 0 16 " if NBR=3 then\n" }{MPLTEXT 1 0 29 " LS:=(LS)union(\{\{a,b,c \}\})\n" }{MPLTEXT 1 0 7 " else\n" }{MPLTEXT 1 0 31 " LS:=(LS)unio n(\{\{a,b,c,d\}\})\n" }{MPLTEXT 1 0 6 " fi;\n" }{MPLTEXT 1 0 2 " " } {MPLTEXT 1 0 45 "XS:=\{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b,c\},\{a,b ,c\}\}:\n" }{MPLTEXT 1 0 28 " ZS:=[a,b,c,ab,ac,bc,abc]:\n" }{MPLTEXT 1 0 27 " j:=nops(LS)-1;QS:=LS[1];\n" }{MPLTEXT 1 0 36 " for i to j d o QS:=QS,LS[i+1]: od:\n" }{MPLTEXT 1 0 34 " LS3:=\{QS\}; k:=nops(LS3) : TS:=0:\n" }{MPLTEXT 1 0 16 " for j to k do\n" }{MPLTEXT 1 0 18 " \+ for i to 7 do\n" }{MPLTEXT 1 0 45 " if LS3[j]=XS[i] then TS:=TS, ZS[i]; fi;\n" }{MPLTEXT 1 0 8 " od;\n" }{MPLTEXT 1 0 6 " od;\n" } {MPLTEXT 1 0 21 " if nops(LS)=2 then\n" }{MPLTEXT 1 0 30 " print(` Nothing to draw`);\n" }{MPLTEXT 1 0 7 " else\n" }{MPLTEXT 1 0 27 " \+ drawLat63pt([TS],NBR);\n" }{MPLTEXT 1 0 6 " fi;\n" }{MPLTEXT 1 0 10 "end proc: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "prLatpt3g:=p roc(GS,NBR)\n" }{MPLTEXT 1 0 31 " local VA,EA,De,i,j,k,LS3,LS:\n" } {MPLTEXT 1 0 58 " global GA,G,H,Dee,SS3,SSS3,XS,ZS,QS,TS,STop1,STop1d ual:\n" }{MPLTEXT 1 0 10 " LS:=GS;\n" }{MPLTEXT 1 0 16 " if NBR=3 th en\n" }{MPLTEXT 1 0 29 " LS:=(LS)union(\{\{a,b,c\}\})\n" }{MPLTEXT 1 0 7 " else\n" }{MPLTEXT 1 0 31 " LS:=(LS)union(\{\{a,b,c,d\}\}) \n" }{MPLTEXT 1 0 6 " fi;\n" }{MPLTEXT 1 0 47 " XS:=\{\{a\},\{b\},\{ c\},\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\}:\n" }{MPLTEXT 1 0 28 " ZS:=[a ,b,c,ab,ac,bc,abc]:\n" }{MPLTEXT 1 0 27 " j:=nops(LS)-1;QS:=LS[1];\n" }{MPLTEXT 1 0 36 " for i to j do QS:=QS,LS[i+1]: od:\n" }{MPLTEXT 1 0 34 " LS3:=\{QS\}; k:=nops(LS3): TS:=0:\n" }{MPLTEXT 1 0 16 " for j to k do\n" }{MPLTEXT 1 0 18 " for i to 7 do\n" }{MPLTEXT 1 0 44 " \+ if LS3[j]=XS[i] then TS:=TS,ZS[i];fi;\n" }{MPLTEXT 1 0 8 " od; \n" }{MPLTEXT 1 0 6 " od;\n" }{MPLTEXT 1 0 21 " if nops(LS)=2 then\n " }{MPLTEXT 1 0 30 " print(`Nothing to draw`);\n" }{MPLTEXT 1 0 7 " else\n" }{MPLTEXT 1 0 28 " drawLat63ptg([TS],NBR);\n" }{MPLTEXT 1 0 6 " fi;\n" }{MPLTEXT 1 0 10 "end proc: " }}}{EXCHG {PARA 0 "" 0 " " {TEXT 283 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "prLatpt4:=proc(G S,NBR)\n" }{MPLTEXT 1 0 31 " local VA,EA,De,i,j,k,LS4,LS:\n" } {MPLTEXT 1 0 58 " global GA,G,H,Dee,SS4,SSS4,XS,ZS,QS,STop1,STop1dual ,TS:\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 8 "LS:=GS;\n" }{MPLTEXT 1 0 16 " if NBR=3 then\n" }{MPLTEXT 1 0 29 " LS:=(LS)union(\{\{a,b,c \}\})\n" }{MPLTEXT 1 0 7 " else\n" }{MPLTEXT 1 0 31 " LS:=(LS)unio n(\{\{a,b,c,d\}\})\n" }{MPLTEXT 1 0 6 " fi;\n" }{MPLTEXT 1 0 2 " " } {MPLTEXT 1 0 74 "XS:=\{\{a\},\{b\},\{c\},\{d\},\{a,b\},\{a,c\},\{b,c\} ,\{a,d\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\n" }{MPLTEXT 1 0 35 " \+ \{a,c,d\},\{b,c,d\},\{a,b,c,d\}\};\n" }{MPLTEXT 1 0 51 " ZS:=[a,b ,c,d,ab,ac,bc,ad,bd,cd,abc,abd,acd,bcd]:\n" }{MPLTEXT 1 0 28 " j:=nop s(LS)-1; QS:=LS[1];\n" }{MPLTEXT 1 0 36 " for i to j do QS:=QS,LS[i+1 ]: od:\n" }{MPLTEXT 1 0 34 " LS4:=\{QS\}; k:=nops(LS4): TS:=0:\n" } {MPLTEXT 1 0 16 " for j to k do\n" }{MPLTEXT 1 0 19 " for i to 14 \+ do\n" }{MPLTEXT 1 0 44 " if LS4[j]=XS[i] then TS:=TS,ZS[i];fi;\n" }{MPLTEXT 1 0 8 " od;\n" }{MPLTEXT 1 0 6 " od;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 19 "if nops(LS)=2 then\n" }{MPLTEXT 1 0 30 " p rint(`Nothing to draw`);\n" }{MPLTEXT 1 0 7 " else\n" }{MPLTEXT 1 0 26 " drawLat64pt([TS],NBR);\n" }{MPLTEXT 1 0 6 " fi;\n" }{MPLTEXT 1 0 10 "end proc: " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 283 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "prLatpt4g:=proc(GS,NBR)\n" }{MPLTEXT 1 0 31 " local VA,EA,De,i,j,k,LS4,LS:\n" }{MPLTEXT 1 0 58 " global GA,G, H,Dee,SS4,SSS4,XS,ZS,QS,STop1,STop1dual,TS:\n" }{MPLTEXT 1 0 10 " LS: =GS;\n" }{MPLTEXT 1 0 16 " if NBR=3 then\n" }{MPLTEXT 1 0 29 " LS: =(LS)union(\{\{a,b,c\}\})\n" }{MPLTEXT 1 0 7 " else\n" }{MPLTEXT 1 0 31 " LS:=(LS)union(\{\{a,b,c,d\}\})\n" }{MPLTEXT 1 0 6 " fi;\n" } {MPLTEXT 1 0 76 " XS:=\{\{a\},\{b\},\{c\},\{d\},\{a,b\},\{a,c\},\{b,c \},\{a,d\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\n" }{MPLTEXT 1 0 35 " \+ \{a,c,d\},\{b,c,d\},\{a,b,c,d\}\};\n" }{MPLTEXT 1 0 51 " ZS:=[a ,b,c,d,ab,ac,bc,ad,bd,cd,abc,abd,acd,bcd]:\n" }{MPLTEXT 1 0 28 " j:=n ops(LS)-1; QS:=LS[1];\n" }{MPLTEXT 1 0 36 " for i to j do QS:=QS,LS[i +1]: od:\n" }{MPLTEXT 1 0 34 " LS4:=\{QS\}; k:=nops(LS4): TS:=0:\n" } {MPLTEXT 1 0 16 " for j to k do\n" }{MPLTEXT 1 0 19 " for i to 14 \+ do\n" }{MPLTEXT 1 0 44 " if LS4[j]=XS[i] then TS:=TS,ZS[i];fi;\n" }{MPLTEXT 1 0 8 " od;\n" }{MPLTEXT 1 0 6 " od;\n" }{MPLTEXT 1 0 21 " if nops(LS)=2 then\n" }{MPLTEXT 1 0 30 " print(`Nothing to dr aw`);\n" }{MPLTEXT 1 0 7 " else\n" }{MPLTEXT 1 0 28 " drawLat64ptg ([TS],NBR);\n" }{MPLTEXT 1 0 6 " fi;\n" }{MPLTEXT 1 0 10 "end proc: " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 278 64 "Changes input LX = [\{ab\},\{ a\},\{d\},\{\},\{c\},\{\}] to LEXorder, both" }}{PARA 0 "" 0 "" {TEXT 278 41 " AAA = [\{\},\{a\},\{ab\},\{c\},\{d\}] or " }} {PARA 0 "" 0 "" {TEXT 278 34 " BBB = \{\{\},\{a\},\{ab\},\{c\},\{ d\}\} " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "LEXorder:=proc(LX ,NBR)\n" }{MPLTEXT 1 0 27 " local k,i,AA,BB,LEXsort:\n" }{MPLTEXT 1 0 18 " global AAA,BBB:\n" }{MPLTEXT 1 0 26 " k:=nops(LX): AA:=LX[1]: \n" }{MPLTEXT 1 0 20 " for i to (k-1) do\n" }{MPLTEXT 1 0 20 " AA: =AA,LX[i+1]:\n" }{MPLTEXT 1 0 6 " od:\n" }{MPLTEXT 1 0 13 " AAA:=\{A A\}:\n" }{MPLTEXT 1 0 27 " k:=nops(LX); BB:=AAA[1]:\n" }{MPLTEXT 1 0 41 " for i to (k-1) do BB:=BB,AAA[i+1]: od:\n" }{MPLTEXT 1 0 13 " BB B:=[BB]:\n" }{MPLTEXT 1 0 9 "end proc:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "drawLat64pt:=proc(TS,NBR)\n" }{MPLTEXT 1 0 18 " loca l EA,i,j,k:\n" }{MPLTEXT 1 0 72 " global GA,G,H,Dee,SS,SSS,LS,XS,ZS,L S8,CLTop1,CLTop1dual,SS4,SSS4,De,VA" }{MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 65 " GA:=Graph([0,a,b,c,d,ab,ac,ad,bc,bd,cd,abc,abd,acd,bcd,abcd] );\n" }{MPLTEXT 1 0 68 " #XS:=[\{a\},\{b\},\{c\},\{d\},\{a,b\},\{a,c \},\{b,c\},\{a,d\},\{b,d\},\{c,d\},\{a,b,c\}," }{MPLTEXT 1 0 36 "\{a,b ,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}];\n" }{MPLTEXT 1 0 52 " #ZS:=[a, b,c,d,ab,ac,bc,ad,bd,cd,abc,abd,acd,bcd]:\n" }{MPLTEXT 1 0 21 " LS8:= TS;De:=[0,0];\n" }{MPLTEXT 1 0 34 " VA:=Vertices(GA);EA:=Edges(GA);\n " }{MPLTEXT 1 0 35 " #HighlightVertex(GA, VA, white);\n" }{MPLTEXT 1 0 34 " #HighlightEdges(GA, EA, green);\n" }{MPLTEXT 1 0 23 " #SS4:=D rawGraph(GA);\n" }{MPLTEXT 1 0 19 " De:=[0,0]; k:=0;\n" }{MPLTEXT 1 0 24 " if member(a,LS8) then " }{MPLTEXT 1 0 17 "De:=De,[a,0] fi;\n" }{MPLTEXT 1 0 24 " if member(b,LS8) then " }{MPLTEXT 1 0 13 "De:=De,[ b,0] " }{MPLTEXT 1 0 4 "fi;\n" }{MPLTEXT 1 0 24 " if member(c,LS8) th en " }{MPLTEXT 1 0 17 "De:=De,[c,0] fi;\n" }{MPLTEXT 1 0 23 " if memb er(d,LS8) then" }{MPLTEXT 1 0 1 " " }{MPLTEXT 1 0 17 "De:=De,[d,0] fi; \n" }{MPLTEXT 1 0 43 " if member(ab,LS8) and member(a,LS8) then " } {MPLTEXT 1 0 18 "De:=De,[ab,a] fi;\n" }{MPLTEXT 1 0 43 " if member(ab ,LS8) and member(b,LS8) then " }{MPLTEXT 1 0 18 "De:=De,[ab,b] fi;\n" }{MPLTEXT 1 0 43 " if member(ac,LS8) and member(a,LS8) then " } {MPLTEXT 1 0 18 "De:=De,[ac,a] fi;\n" }{MPLTEXT 1 0 43 " if member(ac ,LS8) and member(c,LS8) then " }{MPLTEXT 1 0 18 "De:=De,[ac,c] fi;\n" }{MPLTEXT 1 0 43 " if member(ad,LS8) and member(a,LS8) then " } {MPLTEXT 1 0 18 "De:=De,[ad,a] fi;\n" }{MPLTEXT 1 0 43 " if member(ad ,LS8) and member(c,LS8) then " }{MPLTEXT 1 0 18 "De:=De,[ad,c] fi;\n" }{MPLTEXT 1 0 43 " if member(bc,LS8) and member(b,LS8) then " } {MPLTEXT 1 0 18 "De:=De,[bc,b] fi;\n" }{MPLTEXT 1 0 43 " if member(bc ,LS8) and member(c,LS8) then " }{MPLTEXT 1 0 18 "De:=De,[bc,c] fi;\n" }{MPLTEXT 1 0 43 " if member(bd,LS8) and member(b,LS8) then " } {MPLTEXT 1 0 18 "De:=De,[bd,b] fi;\n" }{MPLTEXT 1 0 43 " if member(bd ,LS8) and member(d,LS8) then " }{MPLTEXT 1 0 18 "De:=De,[bd,d] fi;\n" }{MPLTEXT 1 0 43 " if member(cd,LS8) and member(c,LS8) then " } {MPLTEXT 1 0 18 "De:=De,[cd,c] fi;\n" }{MPLTEXT 1 0 43 " if member(cd ,LS8) and member(d,LS8) then " }{MPLTEXT 1 0 18 "De:=De,[cd,d] fi;\n" }{MPLTEXT 1 0 45 " if member(abc,LS8) and member(ab,LS8) then " } {MPLTEXT 1 0 20 "De:=De,[abc,ab] fi;\n" }{MPLTEXT 1 0 45 " if member( abc,LS8) and member(bc,LS8) then " }{MPLTEXT 1 0 20 "De:=De,[abc,bc] f i;\n" }{MPLTEXT 1 0 45 " if member(abc,LS8) and member(ac,LS8) then " }{MPLTEXT 1 0 20 "De:=De,[abc,ac] fi;\n" }{MPLTEXT 1 0 45 " if membe r(abd,LS8) and member(ab,LS8) then " }{MPLTEXT 1 0 20 "De:=De,[abd,ab] fi;\n" }{MPLTEXT 1 0 45 " if member(abd,LS8) and member(bd,LS8) then " }{MPLTEXT 1 0 20 "De:=De,[abd,bd] fi;\n" }{MPLTEXT 1 0 45 " if mem ber(abd,LS8) and member(ad,LS8) then " }{MPLTEXT 1 0 20 "De:=De,[abd,a d] fi;\n" }{MPLTEXT 1 0 45 " if member(acd,LS8) and member(ac,LS8) th en " }{MPLTEXT 1 0 20 "De:=De,[acd,ac] fi;\n" }{MPLTEXT 1 0 45 " if m ember(acd,LS8) and member(ad,LS8) then " }{MPLTEXT 1 0 20 "De:=De,[acd ,ad] fi;\n" }{MPLTEXT 1 0 45 " if member(acd,LS8) and member(cd,LS8) \+ then " }{MPLTEXT 1 0 20 "De:=De,[acd,cd] fi;\n" }{MPLTEXT 1 0 45 " if member(bcd,LS8) and member(cd,LS8) then " }{MPLTEXT 1 0 20 "De:=De,[b cd,cd] fi;\n" }{MPLTEXT 1 0 45 " if member(bcd,LS8) and member(bc,LS8 ) then " }{MPLTEXT 1 0 20 "De:=De,[bcd,bc] fi;\n" }{MPLTEXT 1 0 45 " \+ if member(bcd,LS8) and member(bd,LS8) then " }{MPLTEXT 1 0 20 "De:=De, [bcd,bd] fi;\n" }{MPLTEXT 1 0 25 " if member(abc,LS8)then " }{MPLTEXT 1 0 22 "De:=De,[abcd,abc] fi;\n" }{MPLTEXT 1 0 25 " if member(acd,LS 8)then " }{MPLTEXT 1 0 22 "De:=De,[abcd,acd] fi;\n" }{MPLTEXT 1 0 25 " if member(abd,LS8)then " }{MPLTEXT 1 0 22 "De:=De,[abcd,abd] fi;\n" }{MPLTEXT 1 0 25 " if member(bcd,LS8)then " }{MPLTEXT 1 0 22 "De:=De, [abcd,bcd] fi;\n" }{MPLTEXT 1 0 19 " j:=nops([De])-1;\n" }{MPLTEXT 1 0 49 " Dee:=De[2]; for i to j do Dee:=Dee,De[i+1] od;\n" }{MPLTEXT 1 0 24 " H:=Digraph(VA,\{Dee\}):\n" }{MPLTEXT 1 0 74 " SetVertexPositi ons(H,[[-2,-4],[-8,1],[-4,1],[0,1],[4,1],[-12,6],[-8,6],\n" }{MPLTEXT 1 0 70 " [-4,6],[0,6],[4,6],[8,6],[-8,11],[-4,11],[0,11],[4,11],[-2 ,16]]):\n" }{MPLTEXT 1 0 42 " HighlightVertex(H, Vertices(H), white); \n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 96 " if member(a,LS8) then Hig hlightVertex(H,a,red) fi; " }{MPLTEXT 1 0 376 "if member(b,LS8) then HighlightVertex(H,b,red) fi; if member(c,LS8) then High lightVertex(H,c,red) fi; if member(d,LS8) then HighlightVertex(H,d,red) fi; \+ if member(e,LS8) then HighlightVertex(H,e,red) f i; " }{MPLTEXT 1 0 36 "High lightEdges(H, Edges(H), black);\n" }{MPLTEXT 1 0 22 " SSS4:=DrawGraph (H);\n" }{MPLTEXT 1 0 9 "end proc:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "drawLat64ptg :=proc(TS,NBR)\n" }{MPLTEXT 1 0 18 " lo cal EA,i,j,k:\n" }{MPLTEXT 1 0 74 " global GA,G,H,Dee,SS,SSS,LS,XS,ZS ,LS8,CLTop1,CLTop1dual,SS4,SSS4,De,VA:\n" }{MPLTEXT 1 0 65 " GA:=Grap h([0,a,b,c,d,ab,ac,ad,bc,bd,cd,abc,abd,acd,bcd,abcd]);\n" }{MPLTEXT 1 0 68 " #XS:=\{\{a\},\{b\},\{c\},\{d\},\{a,b\},\{a,c\},\{b,c\},\{a,d\} ,\{b,d\},\{c,d\},\{a,b,c\}," }{MPLTEXT 1 0 36 "\{a,b,d\},\{a,c,d\},\{b ,c,d\},\{a,b,c,d\}\};\n" }{MPLTEXT 1 0 70 " #ZS:=[a,b,c,d,ab,ac,bc,ad ,bd,cd,abc,abd,acd,bcd]:LS8:=TS;De:=[0,0];\n" }{MPLTEXT 1 0 45 " #Hig hlightVertex(GA, Vertices(GA), white);\n" }{MPLTEXT 1 0 41 " #Highlig htEdges(GA, Edges(GA), green);\n" }{MPLTEXT 1 0 23 " #SS4:=DrawGraph( GA);\n" }{MPLTEXT 1 0 34 " VA:=Vertices(GA);EA:=Edges(GA);\n" } {MPLTEXT 1 0 13 " De:=[0,0];\n" }{MPLTEXT 1 0 8 " k:=0;\n" }{MPLTEXT 1 0 61 " if member(ab,LS8) and member(a,LS8) then De:=De,[ab,a] fi; \n" }{MPLTEXT 1 0 61 " if member(ab,LS8) and member(b,LS8) then De:=D e,[ab,b] fi;\n" }{MPLTEXT 1 0 61 " if member(ac,LS8) and member(a,LS8 ) then De:=De,[ac,a] fi;\n" }{MPLTEXT 1 0 61 " if member(ac,LS8) and \+ member(c,LS8) then De:=De,[ac,c] fi;\n" }{MPLTEXT 1 0 61 " if member( ad,LS8) and member(a,LS8) then De:=De,[ad,a] fi;\n" }{MPLTEXT 1 0 61 " if member(ad,LS8) and member(c,LS8) then De:=De,[ad,c] fi;\n" } {MPLTEXT 1 0 61 " if member(bc,LS8) and member(b,LS8) then De:=De,[bc ,b] fi;\n" }{MPLTEXT 1 0 61 " if member(bc,LS8) and member(c,LS8) the n De:=De,[bc,c] fi;\n" }{MPLTEXT 1 0 61 " if member(bd,LS8) and membe r(b,LS8) then De:=De,[bd,b] fi;\n" }{MPLTEXT 1 0 61 " if member(bd,LS 8) and member(d,LS8) then De:=De,[bd,d] fi;\n" }{MPLTEXT 1 0 61 " if \+ member(cd,LS8) and member(c,LS8) then De:=De,[cd,c] fi;\n" }{MPLTEXT 1 0 61 " if member(cd,LS8) and member(d,LS8) then De:=De,[cd,d] fi;\n " }{MPLTEXT 1 0 65 " if member(abc,LS8) and member(ab,LS8) then De:=D e,[abc,ab] fi;\n" }{MPLTEXT 1 0 65 " if member(abc,LS8) and member(bc ,LS8) then De:=De,[abc,bc] fi;\n" }{MPLTEXT 1 0 65 " if member(abc,LS 8) and member(ac,LS8) then De:=De,[abc,ac] fi;\n" }{MPLTEXT 1 0 65 " \+ if member(abd,LS8) and member(ab,LS8) then De:=De,[abd,ab] fi;\n" } {MPLTEXT 1 0 65 " if member(abd,LS8) and member(bd,LS8) then De:=De,[ abd,bd] fi;\n" }{MPLTEXT 1 0 65 " if member(abd,LS8) and member(ad,LS 8) then De:=De,[abd,ad] fi;\n" }{MPLTEXT 1 0 65 " if member(acd,LS8) \+ and member(ac,LS8) then De:=De,[acd,ac] fi;\n" }{MPLTEXT 1 0 65 " if \+ member(acd,LS8) and member(ad,LS8) then De:=De,[acd,ad] fi;\n" } {MPLTEXT 1 0 65 " if member(acd,LS8) and member(cd,LS8) then De:=De,[ acd,cd] fi;\n" }{MPLTEXT 1 0 65 " if member(bcd,LS8) and member(cd,LS 8) then De:=De,[bcd,cd] fi;\n" }{MPLTEXT 1 0 65 " if member(bcd,LS8) \+ and member(bc,LS8) then De:=De,[bcd,bc] fi;\n" }{MPLTEXT 1 0 65 " if \+ member(bcd,LS8) and member(bd,LS8) then De:=De,[bcd,bd] fi;\n" } {MPLTEXT 1 0 19 " j:=nops([De])-1;\n" }{MPLTEXT 1 0 49 " Dee:=De[2]; for i to j do Dee:=Dee,De[i+1] od;\n" }{MPLTEXT 1 0 24 " H:=Digraph( VA,\{Dee\}):\n" }{MPLTEXT 1 0 74 " SetVertexPositions(H,[[-2,-4],[-8, 1],[-4,1],[0,1],[4,1],[-12,6],[-8,6],\n" }{MPLTEXT 1 0 70 " [-4,6], [0,6],[4,6],[8,6],[-8,11],[-4,11],[0,11],[4,11],[-2,16]]):\n" } {MPLTEXT 1 0 42 " HighlightVertex(H, Vertices(H), white);\n" } {MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 94 "if member(a,LS8) then HighlightV ertex(H,a,red) fi; " } {MPLTEXT 1 0 378 "if member(b,LS8) then HighlightVertex(H,b,red) fi; \+ if member(c,LS8) then Highli ghtVertex(H,c,red) fi; if m ember(d,LS8) then HighlightVertex(H,d,red) fi; \+ if member(e,LS8) then HighlightVertex(H,e,red) fi; " }{MPLTEXT 1 0 36 "High lightEdges(H, Edges(H), black);\n" }{MPLTEXT 1 0 22 " SSS4:=DrawGraph (H);\n" }{MPLTEXT 1 0 9 "end proc:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "drawLat63pt:=proc(TS,NBR)\n" }{MPLTEXT 1 0 18 " loca l EA,i,j,k;\n" }{MPLTEXT 1 0 63 " global GA,G,H,Dee,SS,SSS,XS,ZS,CLTo p1,CLTop1dual,SS3,SSS3,VA," }{MPLTEXT 1 0 3 "De," }{MPLTEXT 1 0 6 "QS, LS7" }{MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 37 " GA:=Graph([0,a,b,c,ab,a c,bc,abc]);\n" }{MPLTEXT 1 0 70 " #SetVertexPositions(GA,[[0,0],[-1,1 ],[0,1],[1,1],[-1,2],[0,2],[1,2]," }{MPLTEXT 1 0 9 "[0,3]]):\n" } {MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 31 "VA:=Vertices(GA);EA:=Edges(GA);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 34 " #HighlightEdges(GA, EA, gree n);\n" }{MPLTEXT 1 0 19 " #HighlightVertex(" }{MPLTEXT 1 0 3 "GA," } {MPLTEXT 1 0 10 "VA,white);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 23 " \+ #SS3:=DrawGraph(GA);\n" }{MPLTEXT 1 0 48 " #XS:=[\{a\},\{b\},\{c\},\{ a,b\},\{a,c\},\{b,c\},\{a,b,c\}];\n" }{MPLTEXT 1 0 29 " #ZS:=[a,b,c,a b,ac,bc,abc]:\n" }{MPLTEXT 1 0 29 " LS7:=TS; De:=[0,0]; k:=0;\n" } {MPLTEXT 1 0 42 " if member(a,LS7) then De:=De,[a,0]; fi;\n" } {MPLTEXT 1 0 24 " if member(b,LS7) then " }{MPLTEXT 1 0 18 "De:=De,[b ,0]; fi;\n" }{MPLTEXT 1 0 24 " if member(c,LS7) then " }{MPLTEXT 1 0 18 "De:=De,[c,0]; fi;\n" }{MPLTEXT 1 0 43 " if member(ab,LS7) and mem ber(b,LS7) then " }{MPLTEXT 1 0 18 "De:=De,[ab,b] fi;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 59 "if member(ab,LS7) and member(a,LS7) then De :=De,[ab,a] fi;\n" }{MPLTEXT 1 0 43 " if member(ac,LS7) and member(a, LS7) then " }{MPLTEXT 1 0 18 "De:=De,[ac,a] fi;\n" }{MPLTEXT 1 0 43 " \+ if member(ac,LS7) and member(c,LS7) then " }{MPLTEXT 1 0 18 "De:=De,[ ac,c] fi;\n" }{MPLTEXT 1 0 43 " if member(bc,LS7) and member(b,LS7) t hen " }{MPLTEXT 1 0 18 "De:=De,[bc,b] fi;\n" }{MPLTEXT 1 0 43 " if me mber(bc,LS7) and member(c,LS7) then " }{MPLTEXT 1 0 18 "De:=De,[bc,c] \+ fi;\n" }{MPLTEXT 1 0 45 " if member(abc,LS7) and member(ab,LS7) then " }{MPLTEXT 1 0 20 "De:=De,[abc,ab] fi;\n" }{MPLTEXT 1 0 45 " if memb er(abc,LS7) and member(ac,LS7) then " }{MPLTEXT 1 0 20 "De:=De,[abc,ac ] fi;\n" }{MPLTEXT 1 0 45 " if member(abc,LS7) and member(bc,LS7) the n " }{MPLTEXT 1 0 20 "De:=De,[abc,bc] fi;\n" }{MPLTEXT 1 0 19 " j:=no ps([De])-1;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 47 "Dee:=De[2]; for \+ i to j do Dee:=Dee,De[i+1] od;\n" }{MPLTEXT 1 0 24 " H:=Digraph(VA,\{ Dee\}):\n" }{MPLTEXT 1 0 77 " SetVertexPositions(H,[[0,0],[-1,1],[0,1 ],[1,1],[-1,2],[0,2],[1,2],[0,3]]):\n" }{MPLTEXT 1 0 191 " HighlightV ertex(H, Vertices(H), white); \+ if member(a,LS7) then HighlightVertex(H,a,red) fi; \+ " }{MPLTEXT 1 0 94 "if member(b ,LS7) then HighlightVertex(H,b,red) fi; \+ " }{MPLTEXT 1 0 94 "if member(c,LS7) then HighlightVertex (H,c,red) fi; " }{MPLTEXT 1 0 94 "if member(d,LS7) then HighlightVertex(H,d,red) fi; \+ " }{MPLTEXT 1 0 50 "if member(e,LS7) t hen HighlightVertex(H,e,red) fi;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 38 " HighlightEdges(H, Edges(H), black);\n" }{MPLTEXT 1 0 22 " SSS3: =DrawGraph(H);\n" }{MPLTEXT 1 0 9 "end proc:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "drawLat63ptg:=proc(TS,NBR)\n" }{MPLTEXT 1 0 18 " \+ local EA,i,j,k;\n" }{MPLTEXT 1 0 74 " global GA,G,H,Dee,SS,SSS,XS,ZS ,CLTop1,CLTop1dual,SS3,SSS3,VA,De,QS,LS7:\n" }{MPLTEXT 1 0 37 " GA:=G raph([0,a,b,c,ab,ac,bc,abc]);\n" }{MPLTEXT 1 0 70 " #SetVertexPositio ns(GA,[[0,0],[-1,1],[0,1],[1,1],[-1,2],[0,2],[1,2]," }{MPLTEXT 1 0 9 " [0,3]]):\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 31 "VA:=Vertices(GA);EA :=Edges(GA);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 18 " #HighlightVerte x" }{MPLTEXT 1 0 15 "(GA,VA,white);\n" }{MPLTEXT 1 0 34 " #HighlightE dges(GA, EA, green);\n" }{MPLTEXT 1 0 23 " #SS3:=DrawGraph(GA);\n" } {MPLTEXT 1 0 48 " #XS:=[\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b,c\},\{a ,b,c\}];\n" }{MPLTEXT 1 0 29 " #ZS:=[a,b,c,ab,ac,bc,abc]:\n" } {MPLTEXT 1 0 29 " LS7:=TS; De:=[0,0]; k:=0;\n" }{MPLTEXT 1 0 61 " i f member(ab,LS7) and member(b,LS7) then De:=De,[ab,b] fi;\n" }{MPLTEXT 1 0 61 " if member(ab,LS7) and member(a,LS7) then De:=De,[ab,a] fi; \n" }{MPLTEXT 1 0 61 " if member(ac,LS7) and member(a,LS7) then De:=D e,[ac,a] fi;\n" }{MPLTEXT 1 0 61 " if member(ac,LS7) and member(c,LS7 ) then De:=De,[ac,c] fi;\n" }{MPLTEXT 1 0 61 " if member(bc,LS7) and \+ member(b,LS7) then De:=De,[bc,b] fi;\n" }{MPLTEXT 1 0 61 " if member( bc,LS7) and member(c,LS7) then De:=De,[bc,c] fi;\n" }{MPLTEXT 1 0 19 " j:=nops([De])-1;\n" }{MPLTEXT 1 0 49 " Dee:=De[2]; for i to j do De e:=Dee,De[i+1] od;\n" }{MPLTEXT 1 0 24 " H:=Digraph(VA,\{Dee\}):\n" } {MPLTEXT 1 0 77 " SetVertexPositions(H,[[0,0],[-1,1],[0,1],[1,1],[-1, 2],[0,2],[1,2],[0,3]]):\n" }{MPLTEXT 1 0 42 " HighlightVertex(H, Vert ices(H), white);\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 94 "if member(a ,LS7) then HighlightVertex(H,a,red) fi; \+ " }{MPLTEXT 1 0 376 "if member(b,LS7) then HighlightVerte x(H,b,red) fi; if member(c, LS7) then HighlightVertex(H,c,red) fi; \+ if member(d,LS7) then HighlightVertex(H,d,red) fi; \+ if member(e,LS7) then HighlightVer tex(H,e,red) fi; " } {MPLTEXT 1 0 36 "HighlightEdges(H, Edges(H), black);\n" }{MPLTEXT 1 0 22 " SSS3:=DrawGraph(H);\n" }{MPLTEXT 1 0 9 "end proc:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 283 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "Cl osure:=proc(X,LS) local k,i: global RCL;\n" }{MPLTEXT 1 0 1078 "k:=nop s(X)+1:RCL:=Matrix(k,5): \+ RCL[1,1]:=`Point`: \+ RCL[1,2]:=`Interior`: \+ RCL[1, 3]:=`Exterior`: \+ RCL[1,4]:=`Boundary`: \+ RCL[1,5]:=`Closure `: \+ for i \+ to nops(X) do RCL[i+1,1]:=\{X[i]\}: od: \+ for i to nops(X) do kinterior(\{X[i]\},X,LS): \+ RCL[i+1,2]:=kINT:kintext (\{X[i]\},X,LS): \+ RCL[i+1,3]:=kINTEXT: \+ RCL[i+1,4]:=(X)minus(RCL[i+1,2])minus(RCL[i+1, 3]): RCL[i+1,5]:=(RCL[i+1,4 ])union(RCL[i+1,2]):od:RCL;\n" }{MPLTEXT 1 0 12 " end proc: " }} {PARA 0 "" 0 "" {TEXT 283 33 "*********************************" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "CLOS:= proc(CLM,RCL1s,NBR)\n" }{MPLTEXT 1 0 15 " local i,j,k:\n" }{MPLTEXT 1 0 20 " global RCL1,RCL2;\n" }{MPLTEXT 1 0 60 " kinterior(\{a\},X,C LM);RCL1s[2,2]:=kINT:kintext(\{a\},X,CLM);\n" }{MPLTEXT 1 0 23 " RCL1 s[2,3]:=kINTEXT:\n" }{MPLTEXT 1 0 53 " RCL1s[2,4]:=(X)minus(RCL1s[2,2 ])minus(RCL1s[2,3]):\n" }{MPLTEXT 1 0 45 " RCL1s[2,5]:=(RCL1s[2,2])un ion(RCL1s[2,4]):\n" }{MPLTEXT 1 0 62 " kinterior(\{b\},X,CLM); RCL1s[ 3,2]:=kINT: kintext(\{b\},X,CLM);\n" }{MPLTEXT 1 0 23 " RCL1s[3,3]:=k INTEXT:\n" }{MPLTEXT 1 0 53 " RCL1s[3,4]:=(X)minus(RCL1s[3,2])minus(R CL1s[3,3]):\n" }{MPLTEXT 1 0 45 " RCL1s[3,5]:=(RCL1s[3,2])union(RCL1s [3,4]):\n" }{MPLTEXT 1 0 62 " kinterior(\{c\},X,CLM); RCL1s[4,2]:=kIN T: kintext(\{c\},X,CLM);\n" }{MPLTEXT 1 0 23 " RCL1s[4,3]:=kINTEXT:\n " }{MPLTEXT 1 0 53 " RCL1s[4,4]:=(X)minus(RCL1s[4,2])minus(RCL1s[4,3] ):\n" }{MPLTEXT 1 0 45 " RCL1s[4,5]:=(RCL1s[4,2])union(RCL1s[4,4]):\n " }{MPLTEXT 1 0 21 " if not(NBR=3) then\n" }{MPLTEXT 1 0 62 " kint erior(\{d\},X,CLM);RCL1s[5,2]:=kINT:kintext(\{d\},X,CLM);\n" }{MPLTEXT 1 0 76 " RCL1s[5,3]:=kINTEXT: RCL1s[5,4]:=(X)minus(RCL1s[5,2])minu s(RCL1s[5,3]):\n" }{MPLTEXT 1 0 47 " RCL1s[5,5]:=(RCL1s[5,2])union( RCL1s[5,4]):\n" }{MPLTEXT 1 0 11 " else fi;\n" }{MPLTEXT 1 0 12 " en d proc: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 283 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4927 " LATtop:=proc(GS,`Tit`,NBR) \+ local k,Q,i,W,SubStru,A: \+ global Top1,Top1dual,STop1, STop1dual,INEXT,kINT,RCL,RCLdual,SBrow,SBcol,R,RR,RM,topbasis,CLTop1,C LTop1dual,Relation,latticebasis,X,LQS,LS0,LSUB,LQSa,QS,SubStruc,LStru, CLL,CLT,CLTd,VCL,VCT,VCTd,STop12,SS,LS: \+ LS:=GS; \+ if NBR=3 then \+ X:=\{a,b,c\}:LS:=(LS)union(\{X\}): fi: \+ if NBR=4 then X:=\{a,b,c,d\};LS:=(LS)union(\{X\}):fi: \+ if NBR=5 then X:=\{a,b,c,d,e\} :LS:=(LS)union(\{X\}): fi; pr int(` `);print(` `);print(`******************************************* *******`); print(`Tit`);print(` X `=X); \+ i:=1; k:=nops(LS)-1;QS:=LS [1]; for i to k do QS:=QS,LS[i+1]: od: A:=\{ QS,X\}; if A[1]=\{\} then LStru:= A; else LStru:=\{\{\},QS,X\}; fi; \+ topbasis:=LStru;print(`Lattice Structure `=LSt ru); Top1:=topbase(X,topbasis);T op1dual:=CLO(X,Top1); print(` Does the Lattice structure form a Hausdorf T2 topology ?`=isHd(X,LStru )); print(`Does the Lattice structure form a Alexandroff T1 topology ?`=isT1(X,LStru)); print(`Does the Lattice structure form a Kolmogorov T0 topology ?`=isT0(X,LStru)); if not(isT0 (X,LStru)) then print( `Does the Lattice Structure form a NON T0 topol ogy ) `=isTopo(X,LStru));fi; \+ print(`*********`) ; \+ print(`The Lattice St ructure with Vertices connected by TOP-DOWN arrows = Causal order by \+ Exclusion.`); \+ if NBR=3 then print(prLatpt3(LS,NBR));fi; \+ if NBR=4 then print(prLa tpt4(LS,NBR));fi; pr int(`*********`); \+ print(`NOW use the LATTICE STRUCTURE to FORM Topo1 a nd Topo1dual `); print(`Topo1 `=Top1); print(`Top o1dual ` = Top1dual); pritnt(`************`); print(` Is Topo1 a topology `=isTopo(X,Top1)); \+ print(`Is Topo1 T0 ? `=isT0(X,Top1)); \+ print(`Is Topo1 T1 ? `=isT1(X,Top1)); \+ print(`Is Topo1 Ha usdorff T2 ? `=isHd(X,Top1)); \+ print(`Is Topo1 connected ? `=isConn(X,Top1)); print(`***********` ); print(`The closed-open sets for Topo1 are `= CO(X,Top1)); print(`*********`) ; \+ pr int(`The Lattice Structure for Top1`); \+ if NBR=3 then \+ print(prLatpt3(Top1,NBR)) else \+ print(prLatpt4(Top1,NBR)) fi; \+ \+ print(`*********`); \+ print(`The Lattice Structure for Top1 dual`); if NBR=3 then p rint(prLatpt3(Top1dual,NBR)); fi; \+ if NBR=4 then print(prLatpt4(Top1dual,NBR));fi; \+ print(`*********`); \+ print(`Now compa re the Singleton Closure of the Lattice and Top1 and Top1dual topologi es`); CLL:= Closure(X,LS); \+ CLT:= Closure(X,Top1); \+ CLTd:= Closure(X,Top1du al); SS: =CLL[2,5]; for i to nops(X)-1 do SS:=SS,CLL[i+2,5] od; \+ STop12:=\{SS\}; \+ SS:=CLT[2,5]; for i to nops (X)-1 do SS:=SS,CLT[i+2,5] od; STop1:= \{SS\}; \+ SS:=CLTd[2,5]; for i to nops(X)-1 do SS:=SS,CLTd[i+2,5] od; STop1dual:=\{SS\}; \+ " }{MPLTEXT 1 0 309 " print(`Lattice Closure `=STop12); \+ print(`Topo1 Closure `=STop1); \+ print(`Topo1du al Closure `=STop1dual); \+ fullprint(LS,NBR); end proc:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 283 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 2940 "fullprint:=proc(GS,NBR) global \+ Top1,Top1dual,STop1,STop1dual,STop12,INEXT,kINT,RCL,RCLdual,SBrow,SBco l,Relation,R,RR,RM,LSUB,topbasis,X,CLTop1,CLTop1dual,ZZ,BBB,LS; \+ LS:=GS; \+ if NBR=3 then X=\{a,b,c\}:LS:=(LS )union(\{X\}): fi: if NBR= 4 then X=\{a,b,c,d\};LS:=(LS)union(\{X\}):fi: \+ if NBR=5 then X:=\{a,b,c,d,e\}:LS:=(LS)union(\{X\}) : fi; print(`***********`); \+ prin t(`Topo1`=Top1); Closure(X,Top1); \+ print(`Pointset Closure of Topo1`=RCL); \+ print(`Topo1 subbasis of Singl eton Closure points, column 5.`=STop1); print(`To po1 Closure Topology from Topo1 subbasis is : `); \+ ZZ:=topbase(X,STop1): print(ZZ); \+ print(`Is Topo1 Closure a topology `=i sTopo(X,ZZ)); print(`Is Topo1 C losure topology T0 ?`=isT0(X,ZZ)); \+ print(`Is Topo1 Closure topology T1 ?`=isT1(X,ZZ)); \+ print(`Is Topo1 Closure topology T2 ?`=isHd(X,Z Z)); print(`***********`); \+ print(` Graph for Topo1 Closure Topology`); \+ if NBR=3 then print(prLatpt3g(STop1,NBR));fi; \+ if NBR=4 then print(prLatpt4g(S Top1,NBR)); fi; print(` ***********`); \+ print(`Topo1dual`=Top1dual); Closure(X,Top1dual); \+ print(`Pointset Closure of Topo1d ual`=RCL); print(`Topo1du al subbasis of Singleton Closure points, column 5.`=STop1dual); \+ print(`Topo1dual Closure Topology from Topo1dual subbasis is :` ); ZZ:=topbase(X,STop1dual); print(ZZ);LEXor der(ZZ,NBR); print(`Is Topo1dual C losure a topology `=isTopo(X,ZZ)); \+ print(`Is Topo1dual; Closure topology T0 ?`=isT0(X,Top1dual)); \+ print(`Is Topo1dual Closure topology T1 ?`= isT1(X,Top1dual)); print(`Is Topo1dual Closure topology T2 ?`=isHd(X,Top1dual)); \+ print(`***********`); \+ print(`Graph for Topo1dual Closure topology` ); " }{MPLTEXT 1 0 169 " if NBR=3 then print(prLatpt3g(STop1dual,NBR));fi; \+ if NBR=4 then print(prLatpt4g(STop1dual,NB R)); fi; " }{MPLTEXT 1 0 119 " p rint(`***********`); \+ end proc:" }}{PARA 0 "" 0 "" {TEXT 283 33 "******* **************************" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "sepAxioms:=proc(X,GS,NBR)\n" }{MPLTEXT 1 0 29 " print(` So let GS ` = GS);\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 57 "print(`Is the GS topology Kolmogorov T0 ?` =isT0(X ,GS));\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 58 "print(`Is the GS topo logy Alexandroff T1 ?` =isT1(X,GS));\n" }{MPLTEXT 1 0 43 " print(`Is \+ the GS topology Hausdorff T2 ? " }{MPLTEXT 1 0 15 "`=isHd(X,GS));\n" } {MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 94 "print(`Draw topological Graph if T0, other wise Draw NON T0 Lattice`); " } {MPLTEXT 1 0 3 "if " }{MPLTEXT 1 0 22 "isTopo(X,LS) and NBR=3" } {MPLTEXT 1 0 76 " then print(`GRAPHICS: T0-MODE`);print(prLatpt3g(GS,N BR)); fi; if not(" }{MPLTEXT 1 0 23 "isTopo(X,LS)) and NBR=3" } {MPLTEXT 1 0 6 " then " }{MPLTEXT 1 0 30 "print(`LATTICE: NON-T0-MODE` );" }{MPLTEXT 1 0 122 "print(prLatpt3(GS,NBR)); fi; \+ \+ " }{MPLTEXT 1 0 36 "if isTopo(X,LS) and NBR=4 then print" } {MPLTEXT 1 0 22 "(`GRAPHICS: T0-MODE`);" }{MPLTEXT 1 0 66 " print(prLa tpt4g(GS,NBR)); fi; if not(isTopo(X,LS)) and NBR=4" }{MPLTEXT 1 0 6 " then " }{MPLTEXT 1 0 31 "print(`LATTICE: NON-T0-MODE`); " } {MPLTEXT 1 0 31 "print(prLatpt4(GS,NBR)); fi; " }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 10 "end proc :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "checktop:=proc(GS,title,NBR)\n" }{MPLTEXT 1 0 73 " local LS,LSs c,LSsu,PLS,PLSsc,PLSsu,X,TopoLS,TopoLSsc,TopoLSsu,TopoPLS,\n" } {MPLTEXT 1 0 33 " TopoPLSsc,TopoPLSsu,CLS;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 25 "if NBR=3 then X:=\{a,b,c\};" }{MPLTEXT 1 0 1 " " }{MPLTEXT 1 0 42 "CLS:=\{\{\},\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b,c \},X\};" }{MPLTEXT 1 0 54 " fi; if NBR=4 then X:= \{a,b,c,d\}; " }{MPLTEXT 1 0 6 "CLS:=\{" }{MPLTEXT 1 0 60 "\{a\},\{b\} ,\{c\},\{d\},\{a,b\},\{a,c\},\{b,c\},\{a,d\},\{b,d\},\{c,d\},\{a,b,c\} ," }{MPLTEXT 1 0 34 "\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\}" } {MPLTEXT 1 0 1 ";" }{MPLTEXT 1 0 4 " fi;" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 10 " LS:=GS:\n" }{MPLTEXT 1 0 19 " LSsc:=CLO(X,LS):\n" }{MPLTEXT 1 0 25 " LSsu:=(LS)union(LSsc):\n" }{MPLTEXT 1 0 7 " PLS:= " }{MPLTEXT 1 0 14 "(CLS)minus(LS)" }{MPLTEXT 1 0 21 "union(\{\{\}\})u nion(\{X\})" }{MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 11 " PLSsc:= (" } {MPLTEXT 1 0 15 "CLS)minus(LSsc)" }{MPLTEXT 1 0 21 "union(\{\{\}\})uni on(\{X\})" }{MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 9 "PLSsu:= (" }{MPLTEXT 1 0 36 "CLS)minus(LSsu)union(\{\{\}\})union(\{X \})" }{MPLTEXT 1 0 1 ":" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 " " } {MPLTEXT 1 0 1 " " }{MPLTEXT 1 0 22 "print(` `);print(` `);" }{MPLTEXT 1 0 62 "print(`**************************************************`); \+ " }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 41 " print(`X `=X);print(title) ;print(` `);\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 33 "print(`Lattice \+ Topology issues`);" }{MPLTEXT 1 0 49 "print(`LS structure `=LS); TopoL S:=isTopo(X,LS):\n" }{MPLTEXT 1 0 50 " print(`Always show Lattice Str ucture Digraph`);\n" }{MPLTEXT 1 0 86 " print(`Singletons (level 1 Ve rtices) in the Lattice structure are highlighted in Red" }{MPLTEXT 1 0 4 "`);\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 19 "if nops(LS)=2 then \n" }{MPLTEXT 1 0 67 " print(`the topology is the Indiscrete Topolo gy, so no plot.`);\n" }{MPLTEXT 1 0 7 " else\n" }{MPLTEXT 1 0 74 " \+ if NBR=3 then print(`LATTICE MODE`);print(prLatpt3(LS,Title,NBR));fi; \n" }{MPLTEXT 1 0 18 " if NBR=4 then " }{MPLTEXT 1 0 22 "print(`LAT TICE MODE`);" }{MPLTEXT 1 0 113 "print(prLatpt4(LS,Title,NBR));fi; \+ print(`Next examine possible Topological Structur es`);\n" }{MPLTEXT 1 0 54 " print(`Is the lattice structure, LS, a \+ topology?`=" }{MPLTEXT 1 0 12 "isTopo(X,LS)" }{MPLTEXT 1 0 3 ");\n" } {MPLTEXT 1 0 7 " if " }{MPLTEXT 1 0 12 "isTopo(X,LS)" }{MPLTEXT 1 0 6 " then " }{MPLTEXT 1 0 21 "sepAxioms(X,LS,NBR);\n" }{MPLTEXT 1 0 9 " else\n" }{MPLTEXT 1 0 79 " print(`LS is not a topology, so no topological structure is available`);\n" }{MPLTEXT 1 0 8 " fi; \n" }{MPLTEXT 1 0 6 " fi;\n" }{MPLTEXT 1 0 14 " print(` `);\n" } {MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 21 "print(`LSsc `=LSsc);\n" } {MPLTEXT 1 0 3 " i" }{MPLTEXT 1 0 83 "f nops(LSsc)=2 then print(`the \+ topology is the Indiscrete Topology, so no plot.`);\n" }{MPLTEXT 1 0 7 " else\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 57 " print(`Is LSsc, t he set compliment of LS, a topology?`=i" }{MPLTEXT 1 0 13 "sTopo(X,LSs c)" }{MPLTEXT 1 0 3 ");\n" }{MPLTEXT 1 0 25 " if isTopo(X,LSsc) then " }{MPLTEXT 1 0 21 "sepAxioms(X,LSsc,NBR)" }{MPLTEXT 1 0 55 "; else \+ " }{MPLTEXT 1 0 72 "prin t(`LS is not a topology, so no topological structure is available`);" }{MPLTEXT 1 0 4 "fi;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 12 "print(` `);\n" }{MPLTEXT 1 0 6 " fi;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 21 "print(`LSsu `=LSsu);\n" }{MPLTEXT 1 0 5 " i" }{MPLTEXT 1 0 83 " f nops(LSsu)=2 then print(`the topology is the Indiscrete Topology, so no plot.`);\n" }{MPLTEXT 1 0 7 " else\n" }{MPLTEXT 1 0 77 " print(` Is LSsu, the union of LS and the set compliment of LS, a topology `=" }{MPLTEXT 1 0 14 "isTopo(X,LSsu)" }{MPLTEXT 1 0 3 ");\n" }{MPLTEXT 1 0 5 " i" }{MPLTEXT 1 0 2 "f " }{MPLTEXT 1 0 14 "isTopo(X,LSsu)" } {MPLTEXT 1 0 1 " " }{MPLTEXT 1 0 32 "then sepAxioms(X,LSsu,NBR) else " }{MPLTEXT 1 0 49 " " }{MPLTEXT 1 0 72 "print(`LS is not a topology, so no topological struc ture is available`);" }{MPLTEXT 1 0 18 "fi; " }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 94 "print(` `); \+ " }{MPLTEXT 1 0 4 "fi;\n" }{MPLTEXT 1 0 14 " print(` `);\n" }{MPLTEXT 1 0 2 " " } {MPLTEXT 1 0 36 "print(`**************************`);" }{MPLTEXT 1 0 34 "print(`Lattice Partition issues`);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 15 "print(`X `=X); " }{MPLTEXT 1 0 19 "print (`PLS `=PLS);\n" }{MPLTEXT 1 0 1 " " }{MPLTEXT 1 0 56 " print(`Is PLS , a partition of CLS by LS, a topology?`=" }{MPLTEXT 1 0 12 "isTopo(X, PLS" }{MPLTEXT 1 0 4 "));\n" }{MPLTEXT 1 0 22 " if nops(PLS)=2 then\n " }{MPLTEXT 1 0 66 " print(`The topology is the Indiscrete Topology , so no plot.`)\n" }{MPLTEXT 1 0 7 " else\n" }{MPLTEXT 1 0 7 " if " }{MPLTEXT 1 0 13 "isTopo(X,PLS)" }{MPLTEXT 1 0 1 " " }{MPLTEXT 1 0 25 "then sepAxioms(X,PLS,NBR)" }{MPLTEXT 1 0 6 "; fi;\n" }{MPLTEXT 1 0 16 " print(` `);\n" }{MPLTEXT 1 0 1 " " }{MPLTEXT 1 0 5 " fi;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 24 "print(`PLSsc `=PLSsc); \n" } {MPLTEXT 1 0 78 " print(`Is PLSsc, a partition of CLS by LSsc, a topo logy?`=isTopo(X,PLSsc));\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 22 "if \+ nops(PLSsc)=2 then\n" }{MPLTEXT 1 0 67 " print(`The topology is the Indiscrete Topology, so no plot.`);\n" }{MPLTEXT 1 0 7 " else\n" } {MPLTEXT 1 0 4 " " }{MPLTEXT 1 0 5 "if is" }{MPLTEXT 1 0 13 "Topo(X ,PLSsc)" }{MPLTEXT 1 0 1 " " }{MPLTEXT 1 0 27 "then sepAxioms(X,PLSsc, NBR)" }{MPLTEXT 1 0 6 "; fi;\n" }{MPLTEXT 1 0 16 " print(` `);\n" } {MPLTEXT 1 0 6 " fi;\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 24 "print( `PLSsu `=PLSsu); \n" }{MPLTEXT 1 0 60 " print(`Is PLSsu, a partition \+ of CLS by LSsu, a topology?`=" }{MPLTEXT 1 0 15 "isTopo(X,PLSsu)" } {MPLTEXT 1 0 3 ");\n" }{MPLTEXT 1 0 2 " " }{MPLTEXT 1 0 22 "if nops(P LSsu)=2 then\n" }{MPLTEXT 1 0 66 " print(`The topology is the Indis crete Topology, so no plot.`)\n" }{MPLTEXT 1 0 7 " else\n" }{MPLTEXT 1 0 4 " " }{MPLTEXT 1 0 3 "if " }{MPLTEXT 1 0 15 "isTopo(X,PLSsu)" }{MPLTEXT 1 0 1 " " }{MPLTEXT 1 0 27 "then sepAxioms(X,PLSsu,NBR)" } {MPLTEXT 1 0 6 "; fi;\n" }{MPLTEXT 1 0 16 " print(` `);\n" } {MPLTEXT 1 0 6 " fi;\n" }{MPLTEXT 1 0 9 "end proc:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 283 57 "E nter the Lattice Vertex Structure, the calling routine, " }}{PARA 0 "" 0 "" {TEXT 283 72 "which can be either checktop(LS,`Title`,NBR) or LA Ttop(LS,`Title`,NBR) " }}{PARA 0 "" 0 "" {TEXT 283 24 "and then press return. " }}{PARA 0 "" 0 "" {TEXT 283 90 "LATtop(LS,`Title`,NBR) co mputes the structures for both the top-down order by exclusion, " }} {PARA 0 "" 0 "" {TEXT 283 55 "and the order induced by the Closure of \+ the singletons." }}{PARA 0 "" 0 "" {TEXT 283 77 "checktop(LS,`Title`,N BR) computes the structures for the top-down order only." }}{PARA 0 "" 0 "" {TEXT 283 83 "NBR is either 3 or 4 and represents the Top Set as either X=\{a,b,c\} or X=\{a,b,c,d\}." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "LS:=\{\{\},\{\},\{a,c\},\{b,d\},\{a ,b\},\{a,b,c\}\}:\n" }{MPLTEXT 1 0 8 "checktop" }{MPLTEXT 1 0 30 "(LS, `Your title of Choice`,4):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "LS:=\{\{\},\{\},\{a\},\{\}, \{a,b\},\{c\},\{a,c\},\{a,b,c\}\}:\n" }{MPLTEXT 1 0 36 "LATtop(LS,`You r title of Choice`,3);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 283 78 "The connection between Top Down Directed Lattice structu res is examined below:" }}}{EXCHG {PAGEBK }{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "LS:=\{\{\},\{\},\{\},\{\},\{\},\{\},\{\},\{a,b,c \}\}:checktop(LS,`The Indiscrete Topology`,3);" }{MPLTEXT 1 0 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "LS:=\{\{\},\{a\},\{b\},\{c\},\{\}, \{\},\{\},\{a,b,c\}\}:checktop(LS,`Poset 1, three isolated singletons. `,3);" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "LS:=\{ \{\},\{\},\{a\},\{a,b\},\{c\},\{\},\{\},\{a,b,c\}\}:checktop(LS,`Poset 2, one isolated singleton.`,3);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "LS:=\{\{\},\{\},\{b\},\{a,b\},\{b,c\},\{\},\{\},\{a,b,c\}\}:checktop" }{MPLTEXT 1 0 17 "(LS,`Poset 3`,3);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "LS:=\{\{\},\{a\},\{\},\{c\},\{a,c\},\{\},\{\},\{a,b,c\}\}:" } {MPLTEXT 1 0 8 "checktop" }{MPLTEXT 1 0 17 "(LS,`Poset 4`,3);" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "LS:=\{\{\},\{a\},\{b\},\{c\},\{a,b \},\{a,c\},\{b,c\},\{a,b,c\}\}:" }{MPLTEXT 1 0 8 "checktop" }{MPLTEXT 1 0 38 "(LS,`Poset 9,the Complete Lattice`,3);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }