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Whether you study mathematics as a student or as a professor emeritus, there's something new in Maple 7 for you. " }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 50 "For the High School Student: The RealDoma in option" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "Maple 7's " }{TEXT 264 10 "RealDomain" }{TEXT -1 215 " op tion allows users to work strictly within the domain of real numbers. \+ This is especially useful for students and instructors of introductor y mathematics courses in which complex numbers are not being emphasize d." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 262 35 "By design, Maple is a perfectionist" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "Maple answers the following questi ons in the full generality of complex analysis " }{TEXT 293 10 "by def ault" }{TEXT -1 93 ". However, in introductory math courses, the answe rs will likely confuse the average student." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 273 21 "Question 1: Simplify " }{XPPEDIT 274 0 "sqrt(x^ 2);" "6#-%%sqrtG6#*$%\"xG\"\"#" }}{PARA 0 "" 0 "" {TEXT -1 29 "Student s say, \"I should get |" }{TEXT 275 1 "x" }{TEXT -1 38 "|, right? Wha t's this csgn(x) thing?\"" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "simpli fy( sqrt( x^2 ) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%%csgnG6#%\"x G\"\"\"F'F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 276 21 "Qu estion 2: Simplify " }{XPPEDIT 257 0 "ln(exp(x));" "6#-%#lnG6#-%$expG6 #%\"xG" }}{PARA 0 "" 0 "" {TEXT -1 27 "Students say, \"That's just " } {TEXT 272 1 "x" }{TEXT -1 32 ". Why can't Maple simplify it?\"" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "simplify( log( exp(x) ) );" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%#lnG6#-%$expG6#%\"xG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 277 18 "Question 3: Solve " }{XPPEDIT 257 0 "x^3 +1 = 0;" "6#/,&*$%\"xG\"\"$\"\"\"F(F(\"\"!" }}{PARA 0 "" 0 "" {TEXT -1 27 "Students say, \"That's just " }{TEXT 278 5 "x = -" }{TEXT -1 17 "1. What is this " }{TEXT 271 2 "I " }{TEXT -1 8 "symbol?\"" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "solve( x^3 + 1 = 0, x );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%!\"\",&#\"\"\"\"\"#F&*&^#F%F&-%%sqrtG6#\"\"$ F&F&,&F%F&*&^##F#F'F&F*F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 279 20 "Q uestion 4: What is " }{XPPEDIT 256 0 "ln(-1);" "6#-%#lnG6#,$\"\"\"!\" \"" }{TEXT -1 1 "?" }}{PARA 0 "" 0 "" {TEXT -1 60 "Students say, \"You can't take the log of a negative number.\"" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "ln( -1 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&^#\"\" \"F%%#PiGF%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 280 30 "Question 5: Draw \+ the graph of " }{XPPEDIT 256 0 "x^(1/3);" "6#)%\"xG*&\"\"\"F&\"\"$!\" \"" }}{PARA 0 "" 0 "" {TEXT -1 46 "Students say, \"Where's the rest of the graph?\"" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "plot( x^(1/3), x = -5..5, y = -1.6..1.6);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7F7$$\"3'********oCR&>!#?$\"3#[*\\Dx0<]7!#= 7$$\"3x******zjuV))F*$\"3%=g8unvz1#F-7$$\"3))*****p!oNt:!#>$\"3,07ePpx 0DF-7$$\"3/+++v*QBE#F6$\"3]#H\"z7$f#GGF-7$$\"3#)*****HJ..k$F6$\"3l-YhU O?9LF-7$$\"3A+++]wE=]F6$\"3#=(4'*=E^)o$F-7$$\"3U+++Dj>uxF6$\"33g&*[D>% zE%F-7$$\"3)********\\7I0\"F-$\"3:xQDN9?AZF-7$$\"3.+++N#)>/;F-$\"3$G([ (3KzNV&F-7$$\"3#*******pRQb@F-$\"37X/()\\Gs&*fF-7$$\"3')*****\\d,]6$F- $\"3_2yB-!*zynF-7$$\"3y******z\">Y2%F-$\"3oi8Q#e(f8uF-7$$\"3a******zC. 6^F-$\"371n@(oE`*zF-7$$\"3U+++!yXu9'F-$\"3X%*pfIv&G])F-7$$\"3E+++N@;=s F-$\"3MnF<]%R.(*)F-7$$\"35+++!\\y))G)F-$\"3/cAJ,qf$R*F-7$$\"3.+++i_QQ5 !#<$\"3s^ZSxZj75Fgp7$$\"3++++!y%3T7Fgp$\"3O]MXk-lu5Fgp7$$\"3))*****f.[ hY\"Fgp$\"3\"ee'eVt.O6Fgp7$$\"31+++#Qx$o;Fgp$\"31wXC=m.'=\"Fgp7$$\"3%* *****RP+V)=Fgp$\"3_*QYF\\T^B\"Fgp7$$\"3#******ppe*z?Fgp$\"3CaoY5C\\w7F gp7$$\"3=+++C\\'QH#Fgp$\"32a*HXSJ)=8Fgp7$$\"3#******H,M^\\#Fgp$\"31yTl \"oFjN\"Fgp7$$\"3=+++0#=bq#Fgp$\"3/H!=IkCMR\"Fgp7$$\"3\"******p?27\"HF gp$\"3Euty#zxyU\"Fgp7$$\"3))******HXaEJFgp$\"3Ot4?&p\\AY\"Fgp7$$\"3*)* ****\\'*RRL$Fgp$\"3-0MU&>#*Q\\\"Fgp7$$\"3%)*****HvJga$Fgp$\"31Il7%o@\\ _\"Fgp7$$\"3;+++8tOcPFgp$\"3)*Q%Rn2&\\a:Fgp7$$\"35+++\\Qk\\RFgp$\"3)4( o$yh62e\"Fgp7$$\"3U+++p0;rTFgp$\"3#*oF:vss4;Fgp7$$\"3;+++lxGpVFgp$\"3m eDwJ5#[j\"Fgp7$$\"39+++!oK0e%Fgp$\"39`CK#3a2m\"Fgp7$$\"33+++<5s#y%Fgp$ \"39vCnx(Q[o\"Fgp7$$\"\"&\"\"!$\"3$opwm%f(*4 " 0 "" {MPLTEXT 1 0 17 "with(RealDomain):" }}{PARA 7 "" 1 "" {TEXT -1 318 "Wa rning, these protected names have been redefined and unprotected: Im, \+ Re, ^, arccos, arccosh, arccot, arccoth, arccsc, arccsch, arcsec, arcs ech, arcsin, arcsinh, arctan, arctanh, cos, cosh, cot, coth, csc, csch , eval, exp, expand, limit, ln, log, sec, sech, signum, simplify, sin, sinh, solve, sqrt, surd, tan, tanh\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 287 21 "Question 1: Simplify " }{XPPEDIT 257 0 "s qrt(x^2);" "6#-%%sqrtG6#*$%\"xG\"\"#" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "simplify( sqrt( x^2 ) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$a bsG6#%\"xG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 288 21 "Question 2: Simpli fy " }{XPPEDIT 256 0 "ln(exp(x));" "6#-%#lnG6#-%$expG6#%\"xG" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "simplify( log( exp(x) ) );" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#%\"xG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 289 18 "Q uestion 3: Solve " }{XPPEDIT 256 0 "x^3+1 = 0;" "6#/,&*$%\"xG\"\"$\"\" \"F(F(\"\"!" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "solve( x^3 + 1 = 0, \+ x );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 290 20 "Question 4: What is " }{XPPEDIT 256 0 "ln(-1);" "6#-% #lnG6#,$\"\"\"!\"\"" }{TEXT -1 1 "?" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "ln( -1 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%*undefinedG" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 291 30 "Question 5: Draw the graph of " } {XPPEDIT 292 0 "x^(1/3);" "6#)%\"xG*&\"\"\"F&\"\"$!\"\"" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 41 "plot( x^(1/3), x = -5..5, y = -1.6..1.6);" }} {PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7in7 $$!\"&\"\"!$!3$opwm%f(*4f_PF-$!3Y \\m5p&)3XXmJ\"F-7$$!3#******\\KqP2#F -$!3o_)pm>D_F\"F-7$$!39LL3-TC%)=F-$!3INMQ(>H^B\"F-7$$!3[mmm\"4z)e;F-$! 3GYahz:y$=\"F-7$$!3Mmmmm`'zY\"F-$!3vk9#H`1l8\"F-7$$!3#****\\(=t)eC\"F- $!39^BcYY.w5F-7$$!3!ommmh5$\\5F-$!3]H2*y'Q<;5F-7$$!3S$***\\(=[jL)!#=$! 3F;/a')\\\\6%*Fjq7$$!3)f***\\iXg#G'Fjq$!3cKPAE9sk&)Fjq7$$!3ndmmT&Q(RTF jq$!3W\"=EN,$)GX(Fjq7$$!3Ihm\"HdGe:$Fjq$!3`*GG&fhG3oFjq7$$!3%\\mmTg=>< #Fjq$!3Y%o]'3b,6gFjq7$$!3g***\\7yQ16\"Fjq$!3N6:g`s\"o![Fjq7$$!3vDMLLe* e$\\!#?$!3d])H&>nj-Fis$\"3!e]wQ#3<]7Fjq7$$\"337;/ EvuV))Fis$\"3iN$\"3u`W(y*px0DFjq7$$\"3+l; a)3RBE#Fit$\"3/Lf5g$f#GGFjq7$$\"3xo\"zWU..k$Fit$\"3.WbWwO?9LFjq7$$\"3b smTgxE=]Fit$\"3K'o8gk7&)o$Fjq7$$\"37!o\"HKk>uxFit$\"3a9N7X>%zE%Fjq7$$ \"3womT5D,`5Fjq$\"3e^\\#3X,As%Fjq7$$\"3Gq;zW#)>/;Fjq$\"34%**H>LzNV&Fjq 7$$\"3!=nm\"zRQb@Fjq$\"3A=-PeGs&*fFjq7$$\"3mOLL$e,]6$Fjq$\"3%)\\FG3!*z ynFjq7$$\"3_,+](=>Y2%Fjq$\"3f3+$pe(f8uFjq7$$\"3summ\"zXu9'Fjq$\"3?Ef(f `dG])Fjq7$$\"3#4+++]y))G)Fjq$\"3]Y)*30qf$R*Fjq7$$\"3H++]i_QQ5F-$\"3E&G nvxME,\"F-7$$\"3b++D\"y%3T7F-$\"3kSU\"[E]Y2\"F-7$$\"3+++]P![hY\"F-$\"3 83S(RMPg8\"F-7$$\"3iKLL$Qx$o;F-$\"3AG0c=m.'=\"F-7$$\"3Y+++v.I%)=F-$\"3 u')['H\\T^B\"F-7$$\"3?mm\"zpe*z?F-$\"3owVl5C\\w7F-7$$\"3;,++D\\'QH#F-$ \"3a+;s/9$)=8F-7$$\"3%HL$e9S8&\\#F-$\"3Ms5%>oFjN\"F-7$$\"3s++D1#=bq#F- $\"3;DEBVYU$R\"F-7$$\"3\"HLL$3s?6HF-$\"3Wj`+$zxyU\"F-7$$\"3a***\\7`Wl7 $F-$\"3qVeR&p\\AY\"F-7$$\"3enmmm*RRL$F-$\"3)=Msc>#*Q\\\"F-7$$\"3%zmmTv Jga$F-$\"3^mPH%o@\\_\"F-7$$\"3]MLe9tOcPF-$\"3;\\y&p2&\\a:F-7$$\"31,++] Qk\\RF-$\"3[w-(zh62e\"F-7$$\"3![LL3dg6<%F-$\"303')Qvss4;F-7$$\"3%ymmmw (GpVF-$\"3RE/(>.@[j\"F-7$$\"3C++D\"oK0e%F-$\"3=BNZ#3a2m\"F-7$$\"35,+v= 5s#y%F-$\"3')pz(yxQ[o\"F-7$$\"\"&F*$\"3$opwm%f(*4 " 0 "" {MPLTEXT 1 0 25 "with( OrthogonalSeries );" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#73%$AddG%.ApplyOperatorG%,ChangeBasisG%-CoefficientsG %-ConvertToSumG%%CopyG%'CreateG%'DegreeG%)DerivateG%9DerivativeReprese ntationG%)EvaluateG%(GetInfoG%)MultiplyG%3PolynomialMultiplyG%/ScalarM ultiplyG%5SimplifyCoefficientsG%)TruncateG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 285 9 " Example" }{TEXT -1 85 " : Find the partial differential representation for Jacobi polynomials. In this case, " }{XPPEDIT 18 0 "sigma(x) = x^2-1" "6#/-%&sigmaG6#%\"x G,&*$F'\"\"#\"\"\"F+!\"\"" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 40 "S5 := Create(1/(n+1),JacobiP(n,1,2,x)) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#S5G-%$SumG6$*&,&%\"nG\"\"\"F+F+!\"\"-%(Ja cobiPG6&F*F+\"\"#%\"xGF+/F*;\"\"!%)infinityG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "DerivativeRepresentation(S5,x,root=1) ;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%$SumG6$*,,(*$)%\"nG\"\"#\"\"\"F,*&\" \"&F,F*F,F,\"\"(F,F,,&F*F,\"\"$F,!\"\",&F*F,F+F,F2,&F*F,F,F,F2-%(Jacob iPG6&F*F,F1%\"xGF,/F*;\"\"!%)infinityG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 5 "" 0 "" {TEXT 266 16 "Linear Operators" }} {PARA 0 "" 0 "" {TEXT -1 88 "This package assists you in computations \+ involving d'Alembertian terms and annihilators." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "with( LinearOperato rs );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#70%&ApplyG%,DEToOrePolyG%4Fac toredAnnihilatorG%-FactoredGCRDG%;FactoredMinimalAnnihilatorG%4Factore dOrePolyToDEG%9FactoredOrePolyToOrePolyG%4FactoredOrePolyToREG%.Integr ateSolsG%3MinimalAnnihilatorG%,OrePolyToDEG%,OrePolyToREG%,REToOrePoly G%3dAlembertianSolverG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "L :=OrePoly(-x,0,1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG-%(OrePoly G6%,$%\"xG!\"\"\"\"!\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "b:=(4*x^3+1)*ln(x)/(x*sqrt(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%\"bG*(,&*$)%\"xG\"\"$\"\"\"\"\"%F+F+F+-%#lnG6#F)F+F)#!\"$\"\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "dAlembertianSolver(L,b,x,'di fferential');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&-%%sqrtG6#%\"xG\" \"\"-%#lnG6#F(F)!\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 5 "" 0 "" {TEXT 265 25 "Linear Functional Systems" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 32 "with( LinearFunctionalSystems );" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#7-%0AreSameSolutionG%0CanonicalSystemG%-ExtendSeriesG %2HomogeneousSystemG%+IsSolutionG%8MatrixTriangularizationG%3Polynomia lSolutionG%+PropertiesG%1RationalSolutionG%/SeriesSolutionG%5Universal DenominatorG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 515 "sys := [(x +3)*(x + 6)*(x + 1)*(x + 5)*x*y1(x + 1) -\n(x - 1)*(x + 2)*(x + 3)*(x \+ + 6)*(x + 1)*y1(x) -\nx*(x^6 + 11*x^5 + 41*x^4 + 65*x^3 + 50*x^2-36)*y 2(x) +\n6*(x + 2)*(x + 3)*(x + 6)*(x + 1)*x*y4(x),\n(x + 6)*(x + 2)*y2 (x + 1) - x^2*y2(x),\n(x + 6)*(x + 1)*(x + 5)*x*y3(x + 1) +\n(x + 6)*( x + 1)*(x - 1)*y1(x) - x*(x^5 + 7*x^4 + 11*x^3 +\n4*x^2 - 5*x + 6)*y2( x) - y3(x)*(x + 6)*(x + 1)*(x + 5)*x +\n(x + 6)*(x + 1)*x*3*(x + 3)*y4 (x),\n(x + 6)*y4(x + 1) + x^2*y2(x) - (x + 6)*y4(x)];\n\nvars := [y1(x ), y2(x), y3(x), y4(x)];\n\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$sys G7&,**.,&%\"xG\"\"\"\"\"$F*F*,&F)F*\"\"'F*F*,&F)F*F*F*F*,&F)F*\"\"&F*F *F)F*-%#y1G6#F.F*F**.,&F)F*F*!\"\"F*,&F)F*\"\"#F*F*F(F*F,F*F.F*-F26#F) F*F6*(F)F*,.*$)F)F-F*F**&\"#6F*)F)F0F*F**&\"#TF*)F)\"\"%F*F**&\"#lF*)F )F+F*F**&\"#]F*)F)F8F*F*\"#OF6F*-%#y2GF:F*F6*0F-F*F7F*F(F*F,F*F.F*F)F* -%#y4GF:F*F*,&*(F,F*F7F*-FNF3F*F**&FKF*FMF*F6,,*,F,F*F.F*F/F*F)F*-%#y3 GF3F*F***F,F*F.F*F5F*F9F*F**(F)F*,.*$FAF*F**&\"\"(F*FDF*F**&F@F*FHF*F* *&FEF*FKF*F**&F0F*F)F*F6F-F*F*FMF*F6*,-FYF:F*F,F*F.F*F/F*F)F*F6*.F+F*F ,F*F.F*F)F*F(F*FPF*F*,(*&F,F*-FQF3F*F*FUF**&F,F*FPF*F6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%varsG7&-%#y1G6#%\"xG-%#y2GF(-%#y3GF(-%#y4GF(" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "PolynomialSolution(sys, va rs);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&\"\"!F$&%#_cG6#\"\"\"F$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "RationalSolution(sys, vars); " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7&,$*,,&&%#_cG6#\"\"\"\"):Q%)G*&\" )OM;=F*&F(6#\"\"#F*!\"\"F*,&%\"xGF*F*F1F1,&F3F*F0F*F1,&F3F*\"\"$F*F1,& F3F*\"\"%F*F1#F*\"4gHZY&4G%)o?\"\"!,$*.F3F1,2*&)F3\"\"&F*F.F*\"&dB)*( \"'qN#)F*)F3F8F*F.F*F**(\"(&\\#)GF*)F3F6F*F.F*F**(\"(]y6%F*)F3F0F*F.F* F**(\"+]AdEVF*F3F*F'F*F**(\"+K)QDs#F*F3F*F.F*F1*&\"++yDhMF*F'F*F**&\"+ ?Bhz@F*F.F*F1F*,&F3F*F*F*F1F4F1F5F1F7F1#F*\"7+gx$)ys&o08C\"F;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "sol:=SeriesSolution(sys, var s);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$solGL&,&*&%\"xG\"\"\",(&%#_c G6#F)#!\"\"\"\"'*&#\"%$z'\"#cF)&F,6#\"\"&F)F)*&F2F)&F,6#\"\"%F)F)F)F)- %\"OG6#*$)F(\"\"#F)F),(&F,6#FAF)*&F(F)FCF)F/F " 0 "" {MPLTEXT 1 0 20 "ExtendSeries(sol, 5);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#L&,.*&%\"xG\"\"\",(&%#_cG6#F'#! \"\"\"\"'*&#\"%$z'\"#cF'&F*6#\"\"&F'F'*&F0F'&F*6#\"\"%F'F'F'F'**#F'\" \"#F'F&F',&F&F'F'F-F',(F)#F'\"\"$*&#\"$$\\\"#GF'F3F'F-*&#FCFDF'F7F'F-F 'F'*,#F'F.F'F&F'F=F',&F&F'F \+ " 0 "" {MPLTEXT 1 0 26 "with(RationalNormalForms);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#7'%+AreSimilarG%5IsHypergeometricTermG%6MinimalRepres entationG%5PolynomialNormalFormG%6RationalCanonicalFormG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "F := (n^2-1)*(3*n+1)!/((n+3)!*(2*n+ 7)!);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG**,&*$)%\"nG\"\"#\"\"\" F+F+!\"\"F+-%*factorialG6#,&F)\"\"$F+F+F+-F.6#,&F)F+F1F+F,-F.6#,&F)F* \"\"(F+F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "IsHypergeometr icTerm(F,n,'certificate');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "certificate;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*0,&%\"nG\"\"$\"\"#\"\"\"F),&F&F'\"\"%F)F) F&F),&F&F)F(F)F),&F&F)F)!\"\"F.,&F&F(\"\"*F)F.,&F&F)F+F)!\"##F'F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "(z,r,s,u,v) := RationalCanon icalForm[1](certificate,n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>6'%\"z G%\"rG%\"sG%\"uG%\"vG6'#\"#F\"\"%*&,&%\"nG\"\"\"#\"\"#\"\"$F1F1,&F0F1# F-F4F1F1*&,&F0F1#\"\"*F3F1F1,&F0F1F-F1F1,&F0F1F1!\"\"*&,&F0F1F4F1F1,&F 0F1F3F1F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "MinimalReprese ntation[1](F,n,k);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*,)#\"#F\"\"%% \"nG\"\"\",&F)F*F*!\"\"F*,&F)F*\"\"$F*F,,&F)F*\"\"#F*F,-%(ProductG6$** ,&%\"kGF*#F0F.F*F*,&F6F*#F(F.F*F*,&F6F*#\"\"*F0F*F,,&F6F*F(F*F,/F6;F0F +F*#F*\"'5 " 0 "" {MPLTEXT 1 0 21 "f := y^2 - x*(x^2-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,&*$)%\"yG\"\"#\"\"\"F**&%\"xGF*,&*$)F,F)F*F*F*! 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If no optional parameters were specified, the output could often be unsatisfactory." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "plots[implicitplot]( f, x=-5..5, y=-5..5 );" }}{PARA 13 "" 1 " " {GLPLOT2D 400 300 300 {PLOTDATA 2 "6$-%'CURVESG6]p7$7$$!3a(********* ****f!#=$!3#*************\\hF*7$$!37,+++++]iF*$!3m)*************fF*7$F -7$$!3a:++++++vF*$!3y\")***********\\%F*7$7$$!3![LLLLLLe*F*$!3W)****** *******>F*F37$F97$$!3eKLLLLL$e*F*$\"3wNLLLLL$e\"F*7$7$F@$\"3w,++++++?F *F?7$FE7$$!3/`aaaaaazF*$\"39caaaaaaRF*7$7$$!3o'***********\\iF*$\"3)>+ ++++++'F*FI7$FO7$$!3w(********\\P4'F*$\"35,++++v$4'F*7$7$F0$\"3-,+++++ ]hF*FU7$7$F0F+7$$!3e#Q:YQ:Y)eF*$!3'eh%Q:YQ:hF*7$7$$!3)[************\\& F*F0Fjn7$F`o7$$!3A)*********\\7LF*$!3M)*********\\(o%F*7$7$F<$!3#z**** *********QF*Fdo7$7$F<$\"3#z*************QF*7$$!3k-++++++bF*FR7$Fap7$$! 3w**************fF*Ffn7$Fjo7$$!33NOOOOOO6F*$!3ahjjjjjjGF*7$7$$!3Udmmmm mmT!#>Fw/>wH\"F[s$!2))************ ***F[s7$7$F_s$!2y***************F[s7$$\"39aaaaaa/7F[s$!3'y`aaaaa/)F*7$ 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VIEWG6$;FEFO;FHFK" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" "Curve 12" "Cu rve 13" "Curve 14" "Curve 15" "Curve 16" "Curve 17" "Curve 18" }}}}} {SECT 0 {PARA 4 "" 0 "" {TEXT -1 20 "For the Statistician" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 5 "" 0 "" {TEXT 258 23 "Automatic Curve Fitting " }}{PARA 0 "" 0 "" {TEXT -1 88 "Many new curve fitting techniques hav e been gathered together in one convenient package." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "with(CurveFitting );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7)%(BSplineG%-BSplineCurveG%-Lea stSquaresG%8PolynomialInterpolationG%6RationalInterpolationG%'SplineG% 4ThieleInterpolationG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "da ta := [[.1,2],[1,-1],[3,-3],[5,6], [6,7], [2,-2], [4.5,4], [3.5,.3], [ 3.8, .4]];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%dataG7+7$$\"\"\"!\"\" \"\"#7$F(F)7$\"\"$!\"$7$\"\"&\"\"'7$F1\"\"(7$F*!\"#7$$\"#XF)\"\"%7$$\" #NF)$F-F)7$$\"#QF)$F9F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 " dataPlot := plots[pointplot](data, color=blue, symbol=cross):\ndataPlo t;" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'POINTSG 6+7$$\"\"\"!\"\"$\"\"#\"\"!7$$F(F,$F)F,7$$\"\"$F,$!\"$F,7$$\"\"&F,$\" \"'F,7$F8$\"\"(F,7$F*$!\"#F,7$$\"#XF)$\"\"%F,7$$\"#NF)$F2F)7$$\"#QF)$F DF)-%'SYMBOLG6#%&CROSSG-%'COLOURG6&%$RGBG$F,F,FU$\"*++++\"!\")" 1 2 1 1 10 0 2 6 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "f := LeastSquares(data, x, c urve = a*x^3 + b*x^2 + c*x + d);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"fG,*$\"+d%*4VJ!\"*\"\"\"*&$\"3;7XKE#>(**=!#=F))%\"xG\"\"$F)!\"\"*&$ \"33=ommrOYC!# " 0 "" {MPLTEXT 1 0 60 "fPlot := plot(f, x=0..6):\nplots[di splay]( fPlot, dataPlot );" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CURVESG6$7S7$$\"\"!F)$\"3$******pX*4VJ!#<7$$\"3%**** ***\\#HyI\"!#=$\"35X<\"y<2\\D#F,7$$\"33++]([kdW#F0$\"3oGU_;m>[:F,7$$\" 3++++v;\\DPF0$\"3e$eB,#3?Z#)F07$$\"3W+++D8F,7$$\"39++](Q=\"))**F0$!3Uo9o3XB0 @N\\#F,7$$\"36+++&>q0]\"F,$!3))38*fG!RcE F,7$$\"3'******\\U80j\"F,$!3mgxjkoImFF,7$$\"35+++0ytb@F,$!3u/;2E\">;u#F,7$$\"3'****\\(3wY_AF,$!3>\"Gl.cXmi# F,7$$\"3#)******HOTqBF,$!3KyJg$GU.\\#F,7$$\"37++v3\">)*\\#F,$!3\"G%)o. T-eI#F,7$$\"3:++DEP/BEF,$!3O.'p93N#)4#F,7$$\"3=++](o:;v#F,$!37Jl`44*3& =F,7$$\"3=++v$)[opGF,$!35(=&>m/7)f\"F,7$$\"3%*****\\i%Qq*HF,$!3Me*eA#Q =+8F,7$$\"3&****\\(QIKHJF,$!3_O&ee\\bQl*F07$$\"3#****\\7:xWC$F,$!3127q D2h\\lF07$$\"37++]Zn%)oLF,$!3VS,L&zL&>IF07$$\"3y******4FL(\\$F,$\"3Gos T2h[\")z!#>7$$\"3#)****\\d6.BOF,$\"39FDvr&pzn%F07$$\"3(****\\(o3lWPF,$ \"3g@C+.G*oa)F07$$\"3!*****\\A))ozQF,$\"3)p@43Q+]H\"F,7$$\"3e******Hk- ,SF,$\"3!HP*Qs#R!)p\"F,7$$\"36+++D-eITF,$\"3(GGlr5=P8#F,7$$\"3u***\\(= _(zC%F,$\"3o$>7SA]7`#F,7$$\"3M+++b*=jP%F,$\"3%\\JlBm#fmHF,7$$\"3g***\\ (3/3(\\%F,$\"3O.LH*QA[P$F,7$$\"33++vB4JBYF,$\"353h9dE(yz$F,7$$\"3u**** *\\KCnu%F,$\"3/G2T#f*o0UF,7$$\"3s***\\(=n#f([F,$\"3f=lHC7:CYF,7$$\"3P+ ++!)RO+]F,$\"3TP$Q>j8n,&F,7$$\"30++]_!>w7&F,$\"3%yDVe3F_S&F,7$$\"3O++v )Q?QD&F,$\"3GY!=;11`x&F,7$$\"3G+++5jyp`F,$\"3w]*R^&*Q+5'F,7$$\"3<++]Uj p-bF,$\"3i#*z3FW!=X'F,7$$\"3++++gEd@cF,$\"3#fpv\"fN'eu'F,7$$\"39++v3'> $[dF,$\"3V9$)[mUwNqF,7$$\"37++D6EjpeF,$\"3!)[\"))z\\*H)G(F,7$$\"\"'F)$ \"3?s.m__8IvF,-%'COLOURG6&%$RGBG$\"#5!\"\"F(F(-%'POINTSG6-7$$\"\"\"F_[ l$\"\"#F)7$$Fe[lF)$F_[lF)7$$\"\"$F)$!\"$F)7$$\"\"&F)Fez7$Fez$\"\"(F)7$ Ff[l$!\"#F)7$$\"#XF_[l$\"\"%F)7$$\"#NF_[l$F]\\lF_[l7$$\"#QF_[l$F]]lF_[ l-Fjz6&F\\[lF(F($\"*++++\"!\")-%'SYMBOLG6#%&CROSSG-%+AXESLABELSG6$Q\"x 6\"Q!Fc^l-%%VIEWG6$;F(Fez%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 5 "" 0 "" {TEXT 259 12 "Random Tools" }}{PARA 0 "" 0 "" {TEXT -1 80 "You can now generate random objects of almost a ny data type recognized by Maple." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with( RandomTools );" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#7(%*AddFlavorG%)GenerateG%*GetFlavorG%+GetFlavor sG%*HasFlavorG%-RemoveFlavorG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 37 "Generate a random rational polynomial " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Generate( polynom( rational, x) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,.#!,84L!es\"-&*********\\\"\" \"*&#\",O'*ew)>\",bbbbb&F'%\"xGF'!\"\"*&#\"-(HEpOc\"F&F'*$)F,\"\"#F'F' F-*&#\"+xaG\"e)\"-lmmmm;F'*$)F,\"\"$F'F'F-*&#\",#)*=(e%eF&F')F,\"\"%F' F'*&#\",[oF^A)F7F')F,\"\"&F'F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 91 "Generate a matrix of random complex i ntegers with real and imaginary parts between 2 and 17" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 85 "Matrix( 3, 3, Generate( complex( integer(range =2..17))*identical(x), makeproc=true));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6$\"(oI#G-%'MATRIXG6#7%7%*&^$\"\"(\"#5\"\"\"%\"xGF0*&^ $\"\"$F4F0F1F0*&^$\"#<\"#8F0F1F07%*&^$\"#6\"\"#F0F1F0*&^$\"#7F.F0F1F0* &^$\"#9F.F0F1F07%*&^$F8F.F0F1F0*&^$\"\")\"#;F0F1F0*&^$F@\"#:F0F1F0" }} }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 26 "For the Computer Scientist" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 5 "" 0 "" {TEXT 260 19 "S tring Manipulation" }}{PARA 0 "" 0 "" {TEXT -1 118 "Strings can now be easily split, reversed, concatenated, imploded, case-toggled, trimmed , searched, etc. with the new " }{TEXT 294 11 "StringTools" }{TEXT -1 58 " package. This is of especial use to computer scientists." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "wit h(StringTools);" }}{PARA 7 "" 1 "" {TEXT -1 58 "Warning, the assigned \+ name Group now has a global binding\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7\\o%'AndMapG%+CapitalizeG%%CharG%-CharacterMapG%&ChompG%-CommonPre fixG%-CommonSuffixG%(CompareG%*CompareCIG%%DropG%(ExplodeG%.FirstFromL eftG%/FirstFromRightG%.FormatMessageG%&GroupG%(ImplodeG%(IsASCIIG%(IsA lphaG%/IsAlphaNumericG%.IsBinaryDigitG%3IsControlCharacterG%(IsDigitG% *IsGraphicG%+IsHexDigitG%-IsIdentifierG%.IsIdentifier1G%(IsLowerG%-IsO ctalDigitG%)IsPrefixG%,IsPrintableG%.IsPunctuationG%(IsSpaceG%)IsSuffi xG%(IsUpperG%%JoinG%)LeftFoldG%,LevenshteinG%9LongestCommonSubSequence G%7LongestCommonSubStringG%*LowerCaseG%$MapG%&OrMapG%$OrdG%'RandomG%)R egMatchG%'RegSubG%'RemoveG%(ReverseG%*RightFoldG%'SearchG%*SearchAllG% 'SelectG%-SelectRemoveG%(SoundexG%&SplitG%(SqueezeG%*SubStringG%+Subst ituteG%.SubstituteAllG%%TakeG%%TrimG%)TrimLeftG%*TrimRightG%*UpperCase G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "LongestCommonSubString ( \"tsaxbaxyz\", \"axcaxy\" );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q$ax y6\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 5 "" 0 "" {TEXT 261 17 "List Manipulation" }}{PARA 0 "" 0 "" {TEXT -1 69 "Sorting, sea rching and manipulating lists is now simple with the new " }{TEXT 295 9 "ListTools" }{TEXT -1 9 " package." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "with(ListTools);" }}{PARA 7 "" 1 "" {TEXT -1 68 "Warning, these names have been rebound: Group, Join, R everse, Split\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#75%,BinaryPlaceG%-B inarySearchG%+CategorizeG%+DotProductG%0FindRepetitionsG%(FlattenG%,Fl attenOnceG%&GroupG%+InterleaveG%%JoinG%-JoinSequenceG%+MakeUniqueG%$Pa dG%,PartialSumsG%(ReverseG%'RotateG%'SortedG%&SplitG%*TransposeG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "myList := [seq( ithprime(i), i=1..100 )];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'myListG7`q\"\"#\" \"$\"\"&\"\"(\"#6\"#8\"#<\"#>\"#B\"#H\"#J\"#P\"#T\"#V\"#Z\"#`\"#f\"#h \"#n\"#r\"#t\"#z\"#$)\"#*)\"#(*\"$,\"\"$.\"\"$2\"\"$4\"\"$8\"\"$F\"\"$ J\"\"$P\"\"$R\"\"$\\\"\"$^\"\"$d\"\"$j\"\"$n\"\"$t\"\"$z\"\"$\"=\"$\"> \"$$>\"$(>\"$*>\"$6#\"$B#\"$F#\"$H#\"$L#\"$R#\"$T#\"$^#\"$d#\"$j#\"$p# \"$r#\"$x#\"$\"G\"$$G\"$$H\"$2$\"$6$\"$8$\"$<$\"$J$\"$P$\"$Z$\"$\\$\"$ `$\"$f$\"$n$\"$t$\"$z$\"$$Q\"$*Q\"$(R\"$,%\"$4%\"$>%\"$@%\"$J%\"$L%\"$ R%\"$V%\"$\\%\"$d%\"$h%\"$j%\"$n%\"$z%\"$([\"$\"\\\"$*\\\"$.&\"$4&\"$@ &\"$B&\"$T&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "BinarySearch ( myList, 89, `<`);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#C" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}}{MARK "4 1 6 3 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 } {RTABLE_HANDLES 2823068 }{RTABLE M7R0 I4RTABLE_SAVE/2823068X,%)anythingG6"6"[gl!"%!!!#*"$"$*&^$""("#5"""%"xGF+*&^$"#6 ""#F+F,F+*&^$"#8F)F+F,F+*&^$""$F6F+F,F+*&^$"#7F)F+F,F+*&^$"")"#;F+F,F+*&^$"#