{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 10 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 1 18 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 261 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times " 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 } {PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Text Output" -1 6 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 2 1 3 1 } 1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Map le Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "AC - Normal Text" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "AC - Title" -1 257 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 12 12 1 0 1 0 1 2 258 1 }{PSTYLE "AC \+ - Author" -1 258 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 1 1 1 1 }3 1 0 0 8 8 1 0 1 0 2 2 259 1 }{PSTYLE "AC - Note" -1 259 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "AC - Disclaimer" -1 260 1 {CSTYLE "" -1 -1 "Times" 1 9 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 12 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 257 "" 0 "" {TEXT -1 45 "Range Enclosure with gra phical representation" }}{PARA 258 "" 0 "" {TEXT 258 234 "written by \+ Grimmer, Markus, Department of Mathematics, University of Wuppertal, G ermany, http://www.math.uni-wuppertal.de/wrswt \n<\251 1999-2002 Scien tific Computing/Software Engineering Research Group, University of Wup pertal, Germany>" }{TEXT 259 1 "\n" }}{PARA 259 "" 0 "" {TEXT -1 63 "N OTE: This worksheet demonstrates the use of the Maple package " } {TEXT 260 12 "intpakX v1.0" }{TEXT -1 25 " for interval arithmetic." } }}{EXCHG {PARA 256 "" 0 "" {TEXT -1 102 "This document is not the pack age. It only shows how to work with the functions and types provided \+ by " }{TEXT 262 12 "intpakX v1.0" }{TEXT -1 156 ". You must create th e package in an empty directory before loading the package ( i.e., /us r/maple/intpakX/lib) Once created, load the package as follows:\n" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "restart;\nlibname:=\"C:/myl ib/interval\", libname;\nwith(intpakX);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(libnameG6$Q2C:/mylib/interval6\"Q=C:\\Program~Files\\Maple~8/ libF'" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords h as been redefined\n" }}{PARA 7 "" 1 "" {TEXT -1 61 "Warning, the assig ned name midpoint now has a global binding\n" }}{PARA 7 "" 1 "" {TEXT -1 85 "Warning, the protected names ilog10, max and min have been rede fined and unprotected\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7ar%#&*G%$& **G%#&+G%#&-G%#&/G%-&Convex_HullG%(&arccosG%(&arcsinG%(&arctanG%&&cabs G%&&caddG%&&cdivG%*&cdiv_optG%'&cmultG%+&cmult_optG%%&cosG%&&coshG%&&c subG%%&expG%+&intersectG%*&intpowerG%$&lnG%%&sinG%&&sinhG%%&sqrG%&&sqr tG%%&tanG%&&tanhG%'&unionG%&EvalfG%6Interval_IntegerpowerG%4Interval_R ound_DownG%2Interval_Round_UpG%-Interval_addG%0Interval_arccosG%0Inter val_arcsinG%0Interval_arctanG%-Interval_cosG%.Interval_coshG%0Interval _divideG%-Interval_expG%0Interval_hyp_rdG%0Interval_hyp_ruG%3Interval_ intersectG%,Interval_lnG%2Interval_midpointG%5Interval_option_zeroG%/I nterval_powerG%6Interval_range_valuesG%4Interval_reciprocalG%/Interval _scaleG%-Interval_sinG%.Interval_sinhG%-Interval_sqrG%.Interval_sqrtG% 2Interval_subtractG%-Interval_tanG%.Interval_tanhG%/Interval_timesG%1I nterval_trig_rdG%1Interval_trig_ruG%-Interval_ulpG%/Interval_unionG%/I nterval_widthG%,addinfinityG%2centred_form_evalG%%cexpG%,cni_range3dG% 2complex_disc_plotG%5complex_polynom_plotG%2compute_all_zerosG% \+ " 0 "" {MPLTEXT 1 0 12 "X:=[0.5,2.];" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%\"XG7$$\"\"&!\"\"$\"\"#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "f3:=x->exp(-x^2)*sin(Pi*x^3);" }}{PARA 11 "" 1 "" {XPPMATH 20 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" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 128 "\nThe numerical results are store d in the list_of_ranges variable while the graphical output is directl y displayed on the screen." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "list_of_ranges;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7\\o7$$\"+i:M!) 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"6#>%\"TG7$$\"+=3*p#R!#5$\"+Fj zq:!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"SG7$$\"+=3*p#R!#5$\"+Fj zq:!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "g:=(x,y)->exp(-x *y)*sin(Pi*x^2*y^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6$%\"x G%\"yG6\"6$%)operatorG%&arrowGF)*&-%$expG6#,$*&9%\"\"\"9$F4!\"\"F4-%$s inG6#*(%#PiGF4)F5\"\"#F4)F3F=F4F4F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "compute_range3d(g,T,S,4);" }}{PARA 6 "" 1 "" {TEXT -1 55 "`Start range enclosure = `, [-.8570898115, .8570898115]" }} {PARA 6 "" 1 "" {TEXT -1 58 "Range enclosure after step 1 = [-.857089 8115,.8570898115]" }}{PARA 6 "" 1 "" {TEXT -1 58 "Range enclosure afte r step 2 = [-.6800891261,.8570898115]" }}{PARA 6 "" 1 "" {TEXT -1 58 "Range enclosure after step 3 = [-.6800891261,.8486122905]" }}{PARA 6 "" 1 "" {TEXT -1 58 "Range enclosure after step 4 = [-.5093193828,. 7559256232]" }}{PARA 13 "" 1 "" {GLPLOT3D 476 476 476 {PLOTDATA 3 "6_q 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"Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" "Curve 12" "Curve 13" "Curve 14" "Curve 15" "Curve 16" "Curve 17 " "Curve 18" "Curve 19" "Curve 20" "Curve 21" "Curve 22" "Curve 23" "C urve 24" "Curve 25" "Curve 26" "Curve 27" "Curve 28" "Curve 29" "Curve 30" "Curve 31" "Curve 32" "Curve 33" "Curve 34" "Curve 35" "Curve 36 " "Curve 37" "Curve 38" "Curve 39" "Curve 40" "Curve 41" "Curve 42" "C urve 43" "Curve 44" "Curve 45" "Curve 46" "Curve 47" "Curve 48" "Curve 49" "Curve 50" "Curve 51" "Curve 52" "Curve 53" "Curve 54" "Curve 55 " "Curve 56" "Curve 57" "Curve 58" "Curve 59" "Curve 60" "Curve 61" "C urve 62" "Curve 63" "Curve 64" "Curve 65" "Curve 66" "Curve 67" "Curve 68" "Curve 69" "Curve 70" "Curve 71" "Curve 72" "Curve 73" "Curve 74 " "Curve 75" "Curve 76" "Curve 77" "Curve 78" "Curve 79" "Curve 80" "C urve 81" "Curve 82" "Curve 83" "Curve 84" "Curve 85" "Curve 86" "Curve 87" "Curve 88" "Curve 89" "Curve 90" "Curve 91" "Curve 92" "Curve 93 " "Curve 94" "Curve 95" "Curve 96" "Curve 97" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "In addition, you can use the options of the plot3d map le command.\n" }}}}}{EXCHG {PARA 260 "" 0 "" {TEXT 261 11 "Disclaimer: " }{TEXT -1 240 " While every effort has been made to validate the sol utions in this worksheet, Waterloo Maple Inc. and the contributors are not responsible for any errors contained and are not liable for any d amages resulting from the use of this material." }}}}{MARK "1 0 0" 36 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }