{VERSION 6 0 "IBM INTEL NT" "6.0" } {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 }{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 "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 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 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 53 "IRO 2006: Introduction to Maple\nT.Pajdla, 15 Nov 2006" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 " Getting help on a topic" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 " ?introduction" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "The simplest pro blem" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "1+1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Use \+ \":\" to suppress output printing" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "1+1:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Exact ari thmetic" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "200!;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#\"bbl++++++++++++++++++++++++?ZP(*QqB'*yAA#* yhze3q^B1C..E-mo&zbSd7KSK!Rd2CCCvF`[HGuAJT'=HLSDSUm^9iXC#R%*))pRPsJ j2FdGY86$*HG&\\iE>10rjU-zUwDI)Q'>*Q@@xT!Ri%)>,%G/.#HM.M'*\\%fVCLDu%HjK <(oxf8&Hi]=KR@jBb.0zkt'yl)y" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "An expression to be reevaluated using its parts ( := )" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "y:= x^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG*$)%\"xG\"\"#\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 54 "Use Shift-Enter to enter two line in one command cell:" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "x:=1; y;\nx:=2; y;\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "Substitute to an expression" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "subs(\{x=2\},x+1);\nsubs(\{x=2\},y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 5 "Lists" }}}{EXCHG }{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 13 "L:=[1,2,3,4];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG7&\"\"\"\"\"#\"\"$\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Accessing an element of the list" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "L[3];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 5 "A set" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "S:=\{1,a,tree,\"root\"\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"SG<&\"\"\"%\"aGQ%root6\"%%treeG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Sets sometomes behave like lists" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "S[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"aG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "A simple list and \+ set manipulation" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "map(x-> print([x,x+1]),L):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"\"\"\"#" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"$\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"% \"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "map(x->print([x,\{ x\}]),S):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"\"<#F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$%\"aG<#F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# 7$Q%root6\"<#F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$%%treeG<#F$" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "A procedure" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 33 "g2:= proc(x) evalb(x>2) end proc;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#g2Gf*6#%\"xG6\"F(F(-%&evalbG6#2\"\"#9$F(F(F( " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Call the pocedure" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "g2(2);\ng2(3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "Apply the procedure to a list of \+ values" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "map(x->g2(x),L); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&%&falseGF$%%trueGF%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Select for a list with the procedure" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "select(g2,L);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#7$\"\"$\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Loading a package" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(LinearAlgebra):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "Help on \+ LinearAlgebra" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "?LinearAlg ebra" }}}{EXCHG }{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "Matrix" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "A:=Matrix(2,2,[[a,b],[c,d]]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'RTABLEG6%\"*c**=`\"-%'MATRIXG 6#7$7$%\"aG%\"bG7$%\"cG%\"dG%'MatrixG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "A shorcut" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "B: =<<1|2>,<3|4>>;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'RTABLEG6% \"*;kz^\"-%'MATRIXG6#7$7$\"\"\"\"\"#7$\"\"$\"\"%%'MatrixG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "Addition" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "A+B;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\" *_tK_\"-%'MATRIXG6#7$7$,&%\"aG\"\"\"F.F.,&%\"bGF.\"\"#F.7$,&%\"cGF.\" \"$F.,&%\"dGF.\"\"%F.%'MatrixG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "Multiplication" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "A.B;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*+?j^\"-%'MATRIXG6#7$7$, &%\"aG\"\"\"*&\"\"$F.%\"bGF.F.,&*&\"\"#F.F-F.F.*&\"\"%F.F1F.F.7$,&%\"c GF.*&F0F.%\"dGF.F.,&*&F4F.F9F.F.*&F6F.F;F.F.%'MatrixG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "Determinant" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Determinant(A.B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# ,&*(\"\"#\"\"\"%\"aGF&%\"dGF&!\"\"*(F%F&%\"bGF&%\"cGF&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "Eigenvalues" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "e:=Eigenvalues(A.B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"eG-%'RTABLEG6%\"*/>3a\"-%'MATRIXG6#7$7#,,%\"cG\"\"\"*&\"\"#F0% \"dGF0F0*&F2!\"\"%\"aGF0F0*(\"\"$F0F2F5%\"bGF0F0*&F2F5,6*&\"\"%F0)F/F2 F0F0*(\"#;F0F3F0F/F0F0*(F=F0F6F0F/F0F0*(F=F0F9F0F/F0F0*&F@F0)F3F2F0F0* (F@F0F6F0F3F0F0*(\"#CF0F9F0F3F0F0*$)F6F2F0F0*(\"\"'F0F6F0F9F0F0*&\"\"* F0)F9F2F0F0#F0F2F07#,,F/F0*&F2F0F3F0F0*&F2F5F6F0F0*(F8F0F2F5F9F0F0*&F2 F5F;FOF5&%'VectorG6#%'columnG" }}}{EXCHG }{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "Clear x, y" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " unassign('x','y');" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Expand a pr oduct" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "z:=(x-2)*(x-3);\ne xpand(z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG*&,&%\"xG\"\"\"\"\" #!\"\"F(,&F'F(\"\"$F*F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"xG \"\"#\"\"\"F(*&\"\"&F(F&F(!\"\"\"\"'F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "and simplify (factor) it again" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*& ,&%\"xG\"\"\"\"\"#!\"\"F&,&F%F&\"\"$F(F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "or factor ir explicitely" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\" xG\"\"\"\"\"#!\"\"F&,&F%F&\"\"$F(F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "Equation ( = )" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "eq := x^5-x+1=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqG/,(*$)%\"xG\"\" &\"\"\"F+F)!\"\"F+F+\"\"!" }}}{EXCHG }{EXCHG {PARA 0 "" 0 "" {TEXT -1 82 "Algebraic numbers (= solutions of algebraic equations) can be repr esented exactly!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "s:=solv e(x^5-x+1);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"sG6'-%'RootOfG6$,(* $)%#_ZG\"\"&\"\"\"F.F,!\"\"F.F./%&indexGF.-F'6$F)/F1\"\"#-F'6$F)/F1\" \"$-F'6$F)/F1\"\"%-F'6$F)/F1F-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "The forst out of 5 roots" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "s[1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RootOfG6$,(*$)%#_ZG\"\"& \"\"\"F+F)!\"\"F+F+/%&indexGF+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Approximate in floating points with 10 digits" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 12 "evalf(s[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#^$$\"+OV%)[w!#5$\"+garCNF&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "U sing more digits" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Digits: =50;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'DigitsG\"#]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalf(s[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$$\"SPZ>l'**G.tT&3x=B)Hgs%e+OV%)[w!#]$\"SDC3[1URa5e-94 ZzJ\\isJgarCNF&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "Back to standa rd Digits" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Digits:=10;" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'DigitsG\"#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "All roots" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'^$$\"+OV%)[w!#5$\"+gar CNF&^$$!+XWK7=F&$\"+,T&R3\"!\"*$!+yRIn6F.^$F*$!+,T&R3\"F.^$F$$!+garCNF &" }}}{EXCHG }{EXCHG }}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 153189956 151796416 152327352 151632000 154081904 }{RTABLE M7R0 I6RTABLE_SAVE/153189956X,%)anythingG6"6"[gl!"%!!!#%"#"#%"aG%"cG%"bG%"dGF& } {RTABLE M7R0 I6RTABLE_SAVE/151796416X,%)anythingG6"6"[gl!"%!!!#%"#"#"""""$""#""%F& } {RTABLE M7R0 I6RTABLE_SAVE/152327352X,%)anythingG6"6"[gl!"%!!!#%"#"#,&%"aG"""F)F),&%"cGF)""$ F),&%"bGF)""#F),&%"dGF)""%F)F& } {RTABLE M7R0 I6RTABLE_SAVE/151632000X,%)anythingG6"6"[gl!"%!!!#%"#"#,&%"aG"""%"bG""$,&%"cGF) %"dGF+,&F(""#F*""%,&F-F0F.F1F& } {RTABLE M7R0 I6RTABLE_SAVE/154081904X*%)anythingG6"6"[gl!#%!!!"#"#,,%"cG"""%"dG""#%"aG#F)F+% "bG#""$F+*$,6*$F(F+""%*&F*F)F(F)"#;*&F,F)F(F)F4*&F.F)F(F)F4*$F*F+F6*&F,F)F*F)F6 *&F.F)F*F)"#C*$F,F+F)*&F,F)F.F)""'*$F.F+""*F-F-,,F(F)F*F+F,F-F.F/F1#!""F+F& }