{VERSION 5 0 "IBM INTEL NT" "5.0" } {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 Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 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 } {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 "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 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 }{PSTYLE "Maple P lot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and trace have been red efined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "with(stats[fit],leastmediansquare):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "with(plots,pointplot,display):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 24 "numerosmod7:=rand(1..7):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "numerosmod7();" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "gentama\361o s:=rand(15..50):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "gentama \361os();" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#T" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 16 "numerodatos:=10:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 95 "tama\361os:=[]:\nfor i from 1 to numerodatos do\n \+ tama\361os:=[op(tama\361os),gentama\361os()]:\nod:\ntama\361os;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7,\"#C\"#Q\"#V\"#H\"#?\"#N\"#G\"#S\"#Y \"#U" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 213 "tiempos:=[]:\nfor i from 1 \+ to numerodatos do\n randmatrix(tama\361os[i],tama\361os[i],entries=nu merosmod7):\n tinicial:=time():\n Det(%%) mod 7:\n tfinal:=time()-t inicial:\n tiempos:=[op(tiempos),tfinal]:\nod:\ntiempos;\n " }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7,$\"#j!\"$$\"$s\"F&$\"$]#F&$\"#zF&$\" #JF&$\"$T\"F&$\"#ZF&$\"$.#F&$\"$'HF&$\"$=#F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "datos:=[tama\361os,tiempos];" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%&datosG7$7,\"#C\"#Q\"#V\"#H\"#?\"#N\"#G\"#S\"#Y\"#U 7,$\"#j!\"$$\"$s\"F4$\"$]#F4$\"#zF4$\"#JF4$\"$T\"F4$\"#ZF4$\"$.#F4$\"$ 'HF4$\"$=#F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "convert(datos,listlist);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$7,\"#C\"#Q\"#V\"#H\"#?\"#N\"#G\"#S\"#Y\"#U 7,$\"#j!\"$$\"$s\"F2$\"$]#F2$\"#zF2$\"#JF2$\"$T\"F2$\"#ZF2$\"$.#F2$\"$ 'HF2$\"$=#F2" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 123 " Si aplicamos re gresi\363n ahora, obtenemos una relaci\363n lineal entre las variables , que no necesariamente es la que se tiene;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "fit[leastmediansquare[[x,y]]](datos);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"yG,&$!+++veL!#5\"\"\"*&$\"+++]i8!#6F)%\"xGF )F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "funcion1:=-.33587500 00+.1362500000e-1*x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)funcion1G,& $!+++veL!#5\"\"\"*&$\"+++]i8!#6F)%\"xGF)F)" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 148 "plot1:=[]:\nfor j from 1 to numerodatos do\n plot 1:=[op(plot1),[datos[1][j],datos[2][j]]]:\nod:\ngraf1:=pointplot(plot1 ,title=\"DATOS\"):\ndisplay(graf1);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6$-%'POINTSG6,7$$\"#C\"\"!$\"#j!\"$7$$\"#QF)$\"$s \"F,7$$\"#VF)$\"$]#F,7$$\"#HF)$\"#zF,7$$\"#?F)$\"#JF,7$$\"#NF)$\"$T\"F ,7$$\"#GF)$\"#ZF,7$$\"#SF)$\"$.#F,7$$\"#YF)$\"$'HF,7$$\"#UF)$\"$=#F,-% &TITLEG6#Q&DATOS6\"" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 80 " Ya aq u\355 vemos que los datos est\341n lejos de formar una recta del tipo \+ y=a+b*x..." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 195 "plot2:=[]:\n for j from 1 to numerodatos do\n plot2:=[op(plot2),[datos[1][j],subs( x=datos[1][j],funcion1)]]:\nod:\ngraf2:=pointplot(plot2,symbol=cross,c olor=red,title=\"APROXIMACION\"):\ndisplay(graf2);" }}{PARA 13 "" 1 " " {GLPLOT2D 400 300 300 {PLOTDATA 2 "6$-%'POINTSG6.7$$\"#C\"\"!$!)++v) )!#57$$\"#QF)$\"+++v==F,7$$\"#VF)$\"+++++DF,7$$\"#HF)$\"*++]#fF,7$$\"# ?F)$!*++vL'F,7$$\"#NF)$\"++++59F,7$$\"#GF)$\"*++Dc%F,7$$\"#SF)$\"+++D \"4#F,7$$\"#YF)$\"+++v3HF,7$$\"#UF)$\"+++vjBF,-%'COLOURG6&%$RGBG$\"*++ ++\"!\")$F)F)F[o-%'SYMBOLG6#%&CROSSG-%&TITLEG6#Q-APROXIMACION6\"" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "display(\{graf1,graf2\});" } }{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'POINTSG6,7$$ \"#C\"\"!$\"#j!\"$7$$\"#QF)$\"$s\"F,7$$\"#VF)$\"$]#F,7$$\"#HF)$\"#zF,7 $$\"#?F)$\"#JF,7$$\"#NF)$\"$T\"F,7$$\"#GF)$\"#ZF,7$$\"#SF)$\"$.#F,7$$ \"#YF)$\"$'HF,7$$\"#UF)$\"$=#F,-F$6.7$F'$!)++v))!#57$F.$\"+++v==Fin7$F 3$\"+++++DFin7$F8$\"*++]#fFin7$F=$!*++vL'Fin7$FB$\"++++59Fin7$FG$\"*++ Dc%Fin7$FL$\"+++D\"4#Fin7$FQ$\"+++v3HFin7$FV$\"+++vjBFin-%'COLOURG6&%$ RGBG$\"*++++\"!\")$F)F)F\\q-%'SYMBOLG6#%&CROSSG-%&TITLEG6#Q&DATOS6\"" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Cur ve 2" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 85 " Comprobamos que, efecti vamente, la aproximaci\363n y los datos est\341n bastante alejados." } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 130 " Para aproximar mejor, vamos a \+ tomar logaritmos y luego exponenciales, lo que nos permitir\341 aproxi mar por curvas del tipo y=a*x^b:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 140 "logdatos:=datos:\nfor j from 1 to numerodatos do\n \+ logdatos[1][j]:=evalf(log(datos[1][j])):\n logdatos[2][j]:=log(datos[ 2][j]):\nod:\nlogdatos;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7$7,$\"+IQ0 yJ!\"*$\"+ghePOF'$\"+;,?hPF'$\"+IeHnLF'$\"+uAt&*HF'$\"+h![`b$F'$\"+5X? KLF'$\"+a%z))o$F'$\"+'RT'GQF'$\"+='pwt$F'7,$!+`0ikFF'$!+-3EgF'$!+xwgdIF'$!++$\\Xf\"F'$!+DeR<7F '$!+;-EB:F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "fit[leastmed iansquare[[logx,logy]]](logdatos);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# /%%logyG,&$!+\"ym1;\"!\")\"\"\"*&$\"+Fic8F!\"*F)%%logxGF)F)" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 15 " Luego log(y)= " }{XPPEDIT 18 0 "- 11.98543587;" "6#$!+(eV&)>\"!\")" }{TEXT -1 8 "+ log(x^" }{XPPEDIT 18 0 "2.841264511;" "6#$\"+6XETG!\"*" }{TEXT -1 38 ") y por tanto, hacien do exp( ), y=exp(" }{XPPEDIT 18 0 "-11.98543587;" "6#,$$!+(eV&)>\"!\") \"\"\"" }{TEXT -1 4 ")*x^" }{XPPEDIT 18 0 "2.841264511;" "6#$\"+6XETG! \"*" }{TEXT -1 9 ", que es:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "funcion2:=exp(-11.60666781)*(x^2.713566227);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)funcion2G,$*$)%\"xG$\"+Fic8F!\"*\"\"\"$\"+8L<0\"*!#: " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 " Recordamos la distribuci\363 n de nuestros datos:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "dis play(graf1);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6$ -%'POINTSG6,7$$\"#C\"\"!$\"#j!\"$7$$\"#QF)$\"$s\"F,7$$\"#VF)$\"$]#F,7$ $\"#HF)$\"#zF,7$$\"#?F)$\"#JF,7$$\"#NF)$\"$T\"F,7$$\"#GF)$\"#ZF,7$$\"# SF)$\"$.#F,7$$\"#YF)$\"$'HF,7$$\"#UF)$\"$=#F,-%&TITLEG6#Q&DATOS6\"" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 35 " Y dibujamos la nueva aproximaci \363n:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 195 "plot3:=[]:\nfor \+ j from 1 to numerodatos do\n plot3:=[op(plot3),[datos[1][j],subs(x=da tos[1][j],funcion2)]]:\nod:\ngraf3:=pointplot(plot3,symbol=cross,color =red,title=\"APROXIMACION\"):\ndisplay(graf3);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6$-%'POINTSG6.7$$\"#C\"\"!$\"+0%R]1 &!#67$$\"#QF)$\"+*REDw\"!#57$$\"#VF)$\"+=!y\\Y#F27$$\"#HF)$\"+IT^k%)F, 7$$\"#?F)$\"+@&)H)3$F,7$$\"#NF)$\"+0++59F27$$\"#GF)$\"+Zmo&p(F,7$$\"#S F)$\"+i=uD?F27$$\"#YF)$\"+5++gHF27$$\"#UF)$\"+S\\]7BF2-%'COLOURG6&%$RG BG$\"*++++\"!\")$F)F)F\\o-%'SYMBOLG6#%&CROSSG-%&TITLEG6#Q-APROXIMACION 6\"" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1 " }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "display(\{graf1,graf3 \});" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'POINT SG6.7$$\"#C\"\"!$\"+0%R]1&!#67$$\"#QF)$\"+*REDw\"!#57$$\"#VF)$\"+=!y\\ Y#F27$$\"#HF)$\"+IT^k%)F,7$$\"#?F)$\"+@&)H)3$F,7$$\"#NF)$\"+0++59F27$$ \"#GF)$\"+Zmo&p(F,7$$\"#SF)$\"+i=uD?F27$$\"#YF)$\"+5++gHF27$$\"#UF)$\" +S\\]7BF2-%'COLOURG6&%$RGBG$\"*++++\"!\")$F)F)F\\o-%'SYMBOLG6#%&CROSSG -F$6,7$F'$\"#j!\"$7$F.$\"$s\"Ffo7$F4$\"$]#Ffo7$F9$\"#zFfo7$F>$\"#JFfo7 $FC$\"$T\"Ffo7$FH$\"#ZFfo7$FM$\"$.#Ffo7$FR$\"$'HFfo7$FW$\"$=#Ffo-%&TIT LEG6#Q-APROXIMACION6\"" 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 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 " Por tanto, u na aproximaci\363n bastante buena de nuestros datos es " }{XPPEDIT 18 0 "funcion2 := .9105173313e-5*x^2.713566227;" "6#>%)funcion2G,$*$)%\"x G$\"+Fic8F!\"*\"\"\"$\"+8L<0\"*!#:" }{TEXT -1 47 "que es O(x^2.7...), \+ bastante cerca del O(x^3). " }}}}{MARK "34 0 2" 46 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }