{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 43 "Introduction to Maple\nT. Pajdla, 17 Sep 2011" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "Getting he lp on a topic" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "?introduct ion" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "The simplest problem" }}} {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 arithmetic" }} }{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%*))pRPsJj2FdGY86$*H G&\\iE>10rjU-zUwDI)Q'>*Q@@xT!Ri%)>,%G/.#HM.M'*\\%fVCLDu%HjK<(oxf8&Hi]= KR@jBb.0zkt'yl)y" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "An expression to be reevaluated using its parts ( := )" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 8 "y:= x^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG*$ )%\"xG\"\"#\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 54 "Use Shift-En ter 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 expr ession" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "subs(\{x=2\},x+1) ;\nsubs(\{x=2\},y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 5 "Lists" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "L:=[1,2,3,4];" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG7&\"\"\"\"\"#\"\"$\"\"%" }}} {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#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 5 "A set" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "S:=\{1,a,tree,\"root\"\};" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"SG<&\"\"\"%\"aG%%treeGQ%root6\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Sets sometomes behave like list s" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "S[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"aG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "A simp le list and set manipulation" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "map(x->print([x,x+1]),L):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$ \"\"\"\"\"#" }}{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$%%treeG<#F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$Q%ro ot6\"<#F$" }}}{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(-%&eval bG6#2\"\"#9$F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Call the po cedure" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "g2(2);\ng2(3);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "Apply t he procedure to a list of values" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "map(x->g2(x),L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7 &%&falseGF$%%trueGF%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Select fo r 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 "?LinearAlgebra" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "Matrix" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "A:=Ma trix(2,2,[[a,b],[c,d]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'R TABLEG6%\"*%efb9-%'MATRIXG6#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%\"*_\\cX\"-%'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%\"*!3pb9-%'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 %\"*#*fdX\"-%'MATRIXG6#7$7$,&%\"aG\"\"\"*&\"\"$F.%\"bGF.F.,&*&\"\"#F.F -F.F.*&\"\"%F.F1F.F.7$,&%\"cGF.*&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&%\"b GF&%\"cGF&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "Eigenvalues" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "e:=Eigenvalues(A.B);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"eG-%'RTABLEG6%\"*CkdX\"-%'MATRIXG6 #7$7#,,%\"cG\"\"\"*&\"\"#F0%\"dGF0F0*&F2!\"\"%\"aGF0F0*(\"\"$F0F2F5%\" bGF0F0*&F2F5,6*&\"\"%F0)F/F2F0F0*(\"#;F0F3F0F/F0F0*(F=F0F6F0F/F0F0*(F= F0F9F0F/F0F0*&F@F0)F3F2F0F0*(F@F0F6F0F3F0F0*(\"#CF0F9F0F3F0F0*$)F6F2F0 F0*(\"\"'F0F6F0F9F0F0*&\"\"*F0)F9F2F0F0#F0F2F07#,,F/F0*&F2F0F3F0F0*&F2 F5F6F0F0*(F8F0F2F5F9F0F0*&F2F5F;FOF5&%'VectorG6#%'columnG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "Clear x, y" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "unassign('x','y');" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Expand a product" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 " z:=(x-2)*(x-3);\nexpand(z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG* &,&%\"xG\"\"\"\"\"#!\"\"F(,&F'F(\"\"$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 {PARA 0 "" 0 "" {TEXT -1 82 "Algebraic numbers (= solutions of \+ algebraic equations) can be represented exactly!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "s:=solve(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$F)/F1F-" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "The first out of 5 roots" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "s[1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RootOfG6$,(*$)%#_ZG\"\"&\"\"\"F+F)!\"\"F+F+/%&indexG F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Approximate in floating poi nts with 10 digits" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalf (s[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$$\"+OV%)[w!#5$\"+garCNF& " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Using more digits" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Digits:=50;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'DigitsG\"#]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalf(s[1]);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#^$$\"SPZ>l'**G.t T&3x=B)Hgs%e+OV%)[w!#]$\"SDC3[1URa5e-94ZzJ\\isJgarCNF&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "Back to standard 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 12 " " 1 "" {XPPMATH 20 "6'^$$\"+OV%)[w!#5$\"+garCNF&^$$!+XWK7=F&$\"+,T&R3 \"!\"*$!+yRIn6F.^$F*$!+,T&R3\"F.^$F$$!+garCNF&" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 43 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 145559584 145564952 145569080 145575992 145576424 }{RTABLE M7R0 I6RTABLE_SAVE/145559584X,%)anythingG6"6"[gl!"%!!!#%"#"#%"aG%"cG%"bG%"dG6" } {RTABLE M7R0 I6RTABLE_SAVE/145564952X,%)anythingG6"6"[gl!"%!!!#%"#"#"""""$""#""%6" } {RTABLE M7R0 I6RTABLE_SAVE/145569080X,%)anythingG6"6"[gl!"%!!!#%"#"#,&%"aG"""F)F),&%"cGF)""$ F),&%"bGF)""#F),&%"dGF)""%F)6" } {RTABLE M7R0 I6RTABLE_SAVE/145575992X,%)anythingG6"6"[gl!"%!!!#%"#"#,&%"aG"""%"bG""$,&%"cGF) %"dGF+,&F(""#F*""%,&F-F0F.F16" } {RTABLE M7R0 I6RTABLE_SAVE/145576424X*%)anythingG6"6"[gl!#%!!!"#"#,,%"cG"""%"dG""#%"aG#F)F+% "bG#""$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+6" }