{VERSION 3 0 "SUN SPARC SOLARIS" "3.0" } {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 "Hyperlink" -1 17 "" 0 1 0 128 128 1 2 0 1 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 }{CSTYLE " " -1 256 "" 1 12 0 0 0 0 0 2 2 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 1 24 0 0 0 0 0 0 2 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "T imes" 0 14 16 0 0 0 2 2 2 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 "Hea ding 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 16 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "" 2 6 1 {CSTYLE "" -1 -1 "" 0 1 16 0 0 0 0 0 0 0 0 0 2 0 0 }0 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 "Diagnostic" 7 9 1 {CSTYLE "" -1 -1 "" 0 1 64 128 64 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 16 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 72 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Ma ple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 16 0 0 0 0 0 0 0 0 0 0 0 0 } 3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 111 1 240 0 0 1 1 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 0 14 16 0 0 0 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE " R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 0 14 16 0 0 0 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 18 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }2 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {SECT 1 {PARA 258 "" 0 "" {TEXT 257 48 "Chapter 2\n\nThe First Steps: Calculus on Numbers\n" }}{PARA 0 "" 0 "" {TEXT 256 65 "\251 Co pyright 1997, Latin American Maple Center, Petr\363polis, Brasil" }} {PARA 0 "" 0 "" {HYPERLNK 17 "About the Worksheets" 1 "about.mws" "" } }}{SECT 1 {PARA 3 "" 0 "Started" {TEXT -1 19 "2.1 Getting Started" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 19 "2 + 100 / 5^2 * 3 ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "5! / \+ 21 ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"#S\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "2*5; 2^5: 100/4; 100\n \+ /6\n;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#5" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#\"#D" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"#]\"\"$" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "12345\\\n6789;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"**ycM7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "this is a line Maple does not understand" }}{PARA 8 " " 1 "" {TEXT -1 23 "missing operator or `;`" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "Help" {TEXT -1 16 "2.2 Getting Help" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 11 "?plot,polar" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "?dilog" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "?i factor" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "info( ifactor ); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "usage( ifactor );" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "example( ifactor );" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "related( ifactor );" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "I ntegers" {TEXT -1 33 "2.3 Integers and Rational Numbers" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 62 "5 / 81491528324789773434561\n - 101 / 101983469161 38403856439;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##!9uUt**Qc-=H])3*\"MJ? Ly^._Bz*3G8n_$e!)R(4UB*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " number := 4^(4^4);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'numberG\"ft'4 %31!\\OVY*pl%>\"G)Qv`30'['=e=.!pFM!p;)Hu=!o(pat+.k " 0 "" {MPLTEXT 1 0 37 "len gth( number ); # number of digits" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# \"$b\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "123456789 ^ 98765 4321;" }}{PARA 8 "" 1 "" {TEXT -1 23 "Error, object too large" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "number := 10^29 - 10^14 - 1; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'numberG\">**************)****** ********" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "isprime( number ); # check whether the number is prime" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "settime : = time(): # start timing" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "ifactor( number ); # factorize the integer" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*,-%!G6#\"#h\"\"\"-F%6#\"$B#F(-F%6#\"/\\DDo2m(*F(-F%6# \"),n;8F(-F%6#\"% " 0 "" {MPLTEXT 1 0 56 "cp u_time := (time()-settime) * seconds; # computing time" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)cpu_timeG,$%(secondsG$\"%S;!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "nextprime( number ); # determine t he next largest prime" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\">d,+++++*** ************" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "isqrt( numb er ); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"0Qo,mxA;$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "time( assign( factored_number, ifac tor(3!!!) ) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$z'!\"$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "a := 1234: b := 56:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "q := iquo(a,b); # quotient \+ of integer division" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG\"#A" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "r := irem(a,b); # remainder of integer division" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG\"\"#" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "testeq( a = q*b + r ); # \+ check identity" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "igcd(a,b); # greatest common divis or of integers" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "igcdex( a, b, 's', 't' );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "'s' = s, 't' = t, 'a*s + b*t' = a*s + b*t;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6%/%\"sG\"\"\"/%\"tG!#A/,&*&%\"aGF%F$F%F%*&%\"bGF%F'F%F %\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "1/2345 mod 6;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "`mod` := mods: 1/2345 mod 6;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }}{SECT 1 {PARA 3 "" 0 "Irrationals" {TEXT -1 49 "2.4 Irrational Numbe rs and Floating-Point Numbers" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "25^(1/6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)\"#D#\"\"\"\"\"'\"\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)\"\"&#\"\"\"\"\"$\"\"\"" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 10 "evalf(%%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# $\"+Zf(*4 " 0 "" {MPLTEXT 1 0 24 "convert( \+ %%%, 'float' );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Zf(*4 " 0 "" {MPLTEXT 1 0 11 "25.0^(1/6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Zf(*4 " 0 "" {MPLTEXT 1 0 4 "%^6;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+.+++D!\") " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "90005*0.15;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"(v+N\"!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "evalf( sqrt(2) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# $\"+iN@99!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "Digits;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "Digits := 20: evalf( sqrt(2) );" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#$\"5)[]4tBc8UT\"!#>" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "evalf( Pi, 150 ); " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#$\"at83%f`sJAe]&4Y%Q4ZmI#G8l3[@)z1<@MD[.G')**3iG1k\"yI#fW\\(4#e5 v$*Rpr>%)G]zKQVEYQKz*e`EfTJ!$\\\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Pi := 3.14;" }}{PARA 8 "" 1 "" {TEXT -1 54 "Error, at tempting to assign to `Pi` which is protected" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "electron_rest_mass := 9.109558 * 10^(-31) * kg; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%3electron_rest_massG,$%#kgG$\"5+ +++++!e&4\"*!#]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "protect( 'electron_rest_mass' ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "electron_rest_mass := 5.48593 * 10^(-4) \n * atomic_mass_units;" }} {PARA 8 "" 1 "" {TEXT -1 70 "Error, attempting to assign to `electron_ rest_mass` which is protected" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "unprotect( 'electron_rest_mass' ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "electron_rest_mass := 5.48593 * 10^(-4) \n * atomic_m ass_units;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%3electron_rest_massG,$ %2atomic_mass_unitsG$\"5+++++++$f[&!#B" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "protect( 'electron_rest_mass' ):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 55 "macro( electron_rest_mass = 9.109558 * 10^(- 31) * kg ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "electron_res t_mass;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%#kgG$\"5++++++!e&4\"*!#] " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "protect( 'e' ):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "macro( e = exp(1) ):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "ln(e);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "si n(Pi/10), Zeta(2), limit( erf(x), x=infinity );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%,&*$-%%sqrtG6#\"\"&\"\"\"#\"\"\"\"\"%#!\"\"F,F+,$*$)%#P iG\"\"#F)#F+\"\"'F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Zeta (50) = expand( Zeta(50) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%Zeta G6#\"#],$*$)%#PiGF'\"\"\"#\";-#)*p&=P'G>kd/'R\"TvVBlVD$=9WP__jjLYknad9 xe_G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "Zeta(3); evalf(%); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%%ZetaG6#\"\"$" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#$\"5aG%ffJ!p0-7!#>" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "sin(4) - 2*sin(2)*cos(2); combine(%); evalf(%%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%$sinG6#\"\"%\"\"\"*&-F%6#\"\"#F(-% $cosGF+F(!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"\"\"!#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "(1+sqrt(2))^2-2*(1+sqrt(2))-1; simplify(%); evalf(%%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$),&\"\"\"F'*$-%%sqrtG6#\"\"#\"\"\" F'F,F-F'!\"$F'F(!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "printlevel := 5: \nevalf( sin(1)+ln(2) ); \nprintleve l := 1:" }}{PARA 9 "" 1 "" {TEXT -1 24 "\{--> enter sin, args = 1" }} {PARA 9 "" 1 "" {TEXT -1 41 "<-- exit sin (now at top level) = sin(1) \}" }}{PARA 9 "" 1 "" {TEXT -1 30 "\{--> enter evalf/sin, args = 1" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG$\"\"\"\"\"!" }}{PARA 9 "" 1 "" {TEXT -1 62 "<-- exit evalf/sin (now at top level) = .8414709848078965 0665\}" }}{PARA 9 "" 1 "" {TEXT -1 29 "\{--> enter evalf/ln, args = 2 " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG$\"\"#\"\"!" }}{PARA 9 "" 1 "" {TEXT -1 61 "<-- exit evalf/ln (now at top level) = .69314718055994 530942\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"5h\"=%yOl\"=Y`\"!#>" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "f := x -> arctan( (2*x^2-1) /(2*x^2+1) ): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "g := (x ,y) -> f(x) * f(y):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "g(x,y );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%'arctanG6#*&,&*$)%\"xG\"\"# \"\"\"F,!\"\"\"\"\"F-,&F)F,F/F/!\"\"F/-F%6#*&,&*$)%\"yGF,F-F,F.F/F-,&F 6F,F/F/F1F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "settime := t ime(): # start timing" }}}{EXCHG {PARA 0 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