{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 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 10 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 1 18 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 1 18 0 0 0 0 0 0 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 "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 "Maple Outpu t" -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 "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 - Section Heading" -1 257 1 {CSTYLE "" -1 -1 "Times" 1 16 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 12 0 1 0 1 0 2 2 260 1 }{PSTYLE "AC - Title" -1 258 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" -1 259 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 " -1 260 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" -1 261 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 258 "" 0 "" {TEXT 262 43 "Interval type and basic interval operations" }{TEXT -1 0 "" }}{PARA 259 "" 0 "" {TEXT 257 234 "written by Grimmer, Markus, Department of Mathematics, Universit y of Wuppertal, Germany, http://www.math.uni-wuppertal.de/wrswt \n< \251 1999-2002 Scientific Computing/Software Engineering Research Grou p, University of Wuppertal, Germany>" }{TEXT 258 1 "\n" }}{PARA 260 " " 0 "" {TEXT -1 63 "NOTE: This worksheet demonstrates the use of the M aple package " }{TEXT 259 12 "intpakX v1.0" }{TEXT -1 25 " for interva l arithmetic." }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 102 "This document is not the package. It only shows how to work with the functions and types provided by " }{TEXT 261 12 "intpakX v1.0" }{TEXT -1 156 ". Yo u must create the package in an empty directory before loading the pac kage ( i.e., /usr/maple/intpakX/lib) Once created, load the package a s follows:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "restart;\nl ibname:=\"C:/mylib/interval\", libname;\nwith(intpakX);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%(libnameG6$Q2C:/mylib/interval6\"Q=C:\\Program ~Files\\Maple~8/libF'" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the nam e changecoords has been redefined\n" }}{PARA 7 "" 1 "" {TEXT -1 61 "Wa rning, the assigned name midpoint now has a global binding\n" }}{PARA 7 "" 1 "" {TEXT -1 85 "Warning, the protected names ilog10, max and mi n have been redefined and unprotected\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7ar%#&*G%$&**G%#&+G%#&-G%#&/G%-&Convex_HullG%(&arccosG%(&arcsinG %(&arctanG%&&cabsG%&&caddG%&&cdivG%*&cdiv_optG%'&cmultG%+&cmult_optG%% &cosG%&&coshG%&&csubG%%&expG%+&intersectG%*&intpowerG%$&lnG%%&sinG%&&s inhG%%&sqrG%&&sqrtG%%&tanG%&&tanhG%'&unionG%&EvalfG%6Interval_Integerp owerG%4Interval_Round_DownG%2Interval_Round_UpG%-Interval_addG%0Interv al_arccosG%0Interval_arcsinG%0Interval_arctanG%-Interval_cosG%.Interva l_coshG%0Interval_divideG%-Interval_expG%0Interval_hyp_rdG%0Interval_h yp_ruG%3Interval_intersectG%,Interval_lnG%2Interval_midpointG%5Interva l_option_zeroG%/Interval_powerG%6Interval_range_valuesG%4Interval_reci procalG%/Interval_scaleG%-Interval_sinG%.Interval_sinhG%-Interval_sqrG %.Interval_sqrtG%2Interval_subtractG%-Interval_tanG%.Interval_tanhG%/I nterval_timesG%1Interval_trig_rdG%1Interval_trig_ruG%-Interval_ulpG%/I nterval_unionG%/Interval_widthG%,addinfinityG%2centred_form_evalG%%cex pG%,cni_range3dG%2complex_disc_plotG%5complex_polynom_plotG%2compute_a ll_zerosG% \+ " 0 "" {MPLTEXT 1 0 31 "X:=[1.0,2.5];\ntype(X,interval);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"XG7$$\"#5!\"\"$\"#DF(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Y :=[0,infinity];\ntype(Y,interval);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%\"YG7$\"\"!%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "Z:=construct(1,2);\ntype(Z ,interval);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"ZG7$$\"\"\"\"\"!$\" \"#F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 27 "Procedures convert /inapply:" }}{PARA 0 "" 0 "" {TEXT -1 139 " Utility procedures to co nvert Maple expressions to interval arithmetic. \n convert(1+x + x^ 2,'interval') returns (1 &+ x) &+ (x &^ 2)," }}{PARA 0 "" 0 "" {TEXT -1 68 " whereas inapply(1+x+x^2,x) yields the operator x -> (1 &+ x) etc." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "convert(1+x + x^2, 'interval');\ninapply(1+x+x^2,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#- %-Interval_addG6$\"\"\"-F$6$%\"xG-%6Interval_IntegerpowerG6$F)\"\"#" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#f*6#%\"xG6\"6$%)operatorG%&arrowGF&-% -Interval_addG6$\"\"\"-F+6$9$-%6Interval_IntegerpowerG6$F0\"\"#F&F&F& " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 53 "Procedures is_in, midpoint, width, &intersect, &union" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "A:=[1.,4.];\nB:=[2.,3.];\nis_in(B,A );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG7$$\"\"\"\"\"!$\"\"%F(" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG7$$\"\"#\"\"!$\"\"$F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "midpoint(A);\nwidth(A);\nA &union [5.,6.];\nA &inters ect [3.,5.];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+*******\\#!\"*$ \"+,+++DF&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"\"$\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$7$$\"\"\"\"\"!$\"\"%F&7$$\"\"&F&$\"\"'F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"\"$\"\"!$\"\"%F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 128 "Arithmet ic operations &+,&-,&*,&/\nIn addition to &/, there is the operator ex t_int_div which can also handle \"division by zero\"." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "A &+ B;\nA &- B;\nA &* B;\nA &/ B; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+********H!\"*$\"+,+++qF&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7$$!+,+++?!\"*$\"+,+++?F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+********>!\"*$\"+,+++7!\")" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#7$$\"+JLLLL!#5$\"+,+++?!\"*" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 38 "C:=[-1.,1.];\nA &/ C;\next_int_div(A,C);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG7$$!\"\"\"\"!$\"\"\"F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$,$%)infinityG!\"\"F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$7$,$%)infinityG!\"\"$!**********!\"*7$$\"**********F)F% " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 91 "Trigonometric operations: \n&sin, &cos, &tan, &arcsin, &arccos, &a rctan, &sinh, &cosh, &tanh" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "&sin(A); " }{TEXT -1 7 " # etc." }}{PARA 11 "" 1 "" {XPPMATH 20 "6# 7$$!+h\\-ov!#5$\"\"\"\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 45 "Exponential Function and Logarithm:\n&exp , &ln" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "&exp(A); " }{TEXT -1 7 " # etc." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+F=G=F!\"*$\"+/] \")fa!\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 227 "Square, square root and power functions:\n&sqr, &sqrt, & intpower, &** \n&intpower raises an interval to an integer power, whil e &** raises an interval to the power of another interval.\nNote the d ifference between C*C and &sqr(C)!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "E:=[1.9,2.1];\nA &intpower 2;\nA &** E;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"EG7$$\"#>!\"\"$\"#@F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"**********!\"*$\"+,+++;!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"**********!\"*$\"+pt\"z$=!\")" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 14 "C&*C;\n&sqr(C);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$!+,+++5!\"*$\"+,+++5F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"!$\"+,+++5!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 261 "" 0 "" {TEXT 260 11 "Disclaimer:" }{TEXT -1 240 " While every eff ort has been made to validate the solutions in this worksheet, Waterlo o Maple Inc. and the contributors are not responsible for any errors c ontained and are not liable for any damages resulting from the use of \+ this material." }}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }