{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Error" 7 8 1 {CSTYLE "" -1 -1 "" 0 1 255 0 255 1 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "Komma 5.2.98" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 99 "Ein paar Tips zum Umgang mit st\374ckweise definierten Funktionen in Maple. Bitte selbs t kommentieren." }}{PARA 0 "" 0 "" {TEXT -1 23 "(Es gibt auch Bugs...) ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 33 "y:=piecewise(x<2,x-1,x>=2,x^2+2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG-%*PIECEWISEG6$7$,&%\"xG\"\"\"!\"\"F+2 F*\"\"#7$,&*$F*F.F+F.F+1F.F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "plot(y,discont=true);" }}{PARA 8 "" 1 "" {TEXT -1 60 "Error, (in plot) discontinuous plotting only for expressions" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot(y,x=-1..3,discont=true);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "ys:=diff(y,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ysG-%*PIECEWISEG6&7$\"\"\"2%\"xG\"\"#7$%*undefinedG/ F+F,7$,$F+F,2F,F+F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "plot (\{y,ys\},x=-1..3,discont=true);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "yi:=int(ys,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%# yiG-%*PIECEWISEG6%7$%\"xG2F)\"\"#7$%*undefinedG/F)F+7$,(!\"#\"\"\"F-F+ *$F)F+F22F+F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "plot(\{yi \},x=-1..3,discont=true);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "yi:=int(piecewise(x<2,1,x>2,2*x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#yiG-%*PIECEWISEG6$7$%\"xG1F)\"\"#7$,&!\"#\"\"\"*$F)F+F/2F+F) " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "plot(\{y,yi\},x=-1..3,d iscont=true);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "readlib(is cont);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#:6%'%\"fG%*algebraicG'%\"zG/ %%nameG%&rangeG%$optG63%\"wG%%openG%\"xG%\"aG%\"bG%$sbaG%%discG%\"rG% \"dG%%indsG%$solG%#loG%#hiG%\"sG%\"tG%#sbG%#saG6#%ipCopyright~(c)~1993 ~Gaston~Gonnet,~Wissenschaftliches~Rechnen,~ETH~Zurich.~All~rights~res erved.G6\"C-@%/9#\"\"$C$@$09&.%'closedG-%&ERRORG6#%Hthe~third~argument ~can~only~be~\"closed\"G>8%%&falseG>FS%%trueG>8&-%#opG6$\"\"\"9%@$4-%$ hasG6$9$FX-%'RETURNG6#FV>8'-FZ6$7$\"\"#FfnFgn>8(-FZ6$7$FfoFfoFgn>8)-%' signumG6#,&FhoFfnFbo!\"\"@&/F]pFbpF^o/F]p\"\"!-F_o6#5FS4-%%typeG6$-%&l imitG6$F]o/FXFbo%)infinityG>8*-%$mapG6$:6#F96%%$rofG%%rof1G%%solsGFBFB C*@$4-F[o6$F]o%'RootOfG-F_o6#F]o>8$-%'indetsG6$F]o-%)specfuncG6$%)anyt hingGFcr@$0-%%nopsG6#FgrFfn-FO6#%?cannot~handle~multiple~RootOfsG>Fgr& Fgr6#Ffn>FS-FZ6$FfnFgr@$4-F\\q6$FS-%(polynomG6$%(numericG%#_ZGFdr>FX-F fq6':6&%\"vGF[rF\\rF9FB6$%)operatorG%&arrowGFB-%%subsG6$/Fgn-Fcr6$FKF] o9'FBFB7#-%'fsolveG6$FSFetFgrFSF]o-FZ6#%\"\"GFBFB--%(readlibG6#%(disco ntGF\\o>8+FV?&8,FdqFVC)>8--%'selectG6$:6#F1FBF\\uFB35/-%*substringG6$F ]o;FfnFfo.Fet/-Fbw6$F]o;FfnFG.%$_NNG/-%#isG6$F]o%(integerGFVFBFB-Fir6$ Fev%'stringG@$0Fhv<\"C0@$2Ffn-Fbs6#FhvC$>Fcv%%FAILG%%nextG>Fhv&FhvFis> 8.7#-%&solveG6$/FevFgrFhv@$0-Fbs6#F]rFfnC$>FcvF^yF_y>8/-F_q6$&FcyFis/F grFbo>80-F_q6$Fcz/FgrFho>81-F_p6#,&FfzFfnF`zFbp@$4-F\\q6$F[[lF`xC$>Fcv F^yF_y@$/F[[lFbpC%>82F`z>F`zFfz>FfzFi[l@&3-F\\q6$F`zF`xFS>F`z,&F`zFfnF fnFfn0F`z,$FbqFbp>F`z-%%ceilG6#F`z@&3-F\\q6$FfzF`xFS>Ffz,&FfzFfnFbpFfn 0FfzFbq>Ffz-%&floorG6#Ffz@$3/-Fbw6$FhvFiwFjw/-F_pFg\\lFbp>F`zFfp@(5/Ff zFbq/F`zFc\\l-F_o6#FT4-F\\q6$F^[lF`xC$>FcvF^yF_y1FfpF^[lF_^lF_y>83-F_p 6#,&FhoFfnFevFbp@(/Fh^lFbpF_y3/Fh^lFfp4FSF_^l4-F\\q6$Fh^lF`x>FcvF^y>84 -F_p6#,&FevFfnFboFbp@(/Ff_lFbpF_y3/Ff_lFfpF`_lF_^l4-F\\q6$Ff_lF`x>FcvF ^y@$3/Fh^lFfn/Ff_lFfnF_^lFcv6#%indetermine~if~the~expression~f~is~cont inuous~in~the~given~rangeGFB" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "iscont(y,x=0..3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "iscont(yi,x=0..3);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "yi;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*PIECEWISEG6$ 7$%\"xG1F'\"\"#7$,&!\"#\"\"\"*$F'F)F-2F)F'" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 13 "subs(x=2,yi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-% *PIECEWISEG6$7$\"\"#1F'F'7$F'2F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "readlib(discont);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# :6$'%\"fG%*algebraicG'%\"xG%%nameG6\"6#%_oCopyright~1992~Gaston~Gonnet ,~Wissenschaftliches~Rechnen,~ETH~ZurichGF+C%>%1_EnvAllSolutionsG%%tru eG>%3_EnvSolveOverRealsGF1-%3discont/duplicatesG6#-%1discont/discontRG 6$9$9%F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "discont(y,x); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "discont(yi,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# <#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "yh:=convert(yi,Heaviside);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#yhG,*%\"xG\"\"\"*&F&F'-%*HeavisideG6#,&F&F'!\"#F'F'! \"\"F)F-*&F)F'F&\"\"#F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 " plot(yh,x=0..3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "discont (yh,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "convert(yh,piecewise);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*PIECEWISEG6$7$%\"xG1F'\"\"#7$,&!\"#\"\"\"*$F'F)F-2F) F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "limit(yi,x=2,left);li mit(yi,x=2,right);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f:=unapply(yi,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG:6# %\"xG6\"6$%)operatorG%&arrowGF(-%*piecewiseG6&19$\"\"#F02F1F0,&!\"#\" \"\"*$F0F1F5F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(2);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "discont(f(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#< #\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "interface(verbose proc=3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "print(discont); " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#:6$'%\"fG%*algebraicG'%\"xG%%nameG 6\"6#%_oCopyright~1992~Gaston~Gonnet,~Wissenschaftliches~Rechnen,~ETH~ ZurichGF+C%>%1_EnvAllSolutionsG%%trueG>%3_EnvSolveOverRealsGF1-%3disco nt/duplicatesG6#-%1discont/discontRG6$9$9%F+F+" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 26 "print(`discont/discontR`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "print(iscont);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 17 "print(piecewise);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 2 }{VIEWOPTS 1 1 0 1 1 1803 }