{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 "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 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 3 }1 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 0 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 "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 94 "gradstep2:= proc(f,pt,h)\n local v;\n v := Df(f,pt);\n [ pt[1] - h*v[1], pt[2] - h*v[2]];\nend;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*gradstep2GR6%%\"fG%#ptG%\"hG6#%\"vG6\"F,C$>8$-% #DfG6$9$9%7$,&&F46#\"\"\"F9*&9&F9&F/F8F9!\"\",&&F46#\"\"#F9*&F;\"\"\"& F/F@F9F=F,F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 344 "findMin: = proc(f,firstguess)\n local i, h, guess, oldht, ht;\n guess := firs tguess;\n oldht := f(op(guess));\n h:=.1;\n for i from 1 to 100 do \n guess := gradstep2(f,guess,h);\n ht := f(op(guess));\n# pri nt(i,guess,ht);\n if ( abs(oldht - ht) < .00001) then\n RET URN(guess);\n fi;\n oldht := ht;\n od;\n RETURN(guess);\n en d:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "Df := proc(f,pt)\n [ D[1](f)(pt[1],pt[2]), D[2](f)(pt[1],pt[2]) ];\nend;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%#DfGR6$%\"fG%#ptG6\"F)F)7$--&%\"DG6#\"\"\"6#9$6$&9% F/&F56#\"\"#--&F.F7F1F3F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f:= (x,y)->x^2+y^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6$ %\"xG%\"yG6\"6$%)operatorG%&arrowGF),&*$)9$\"\"#\"\"\"\"\"\"*$)9%F1F2F 3F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "findMin(f,[1,2]) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+]]UZ:!#7$\"+'4][4$F&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "g:= (x,y)->sin(x*y);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGR6$%\"xG%\"yG6\"6$%)operatorG%&a rrowGF)-%$sinG6#*&9$\"\"\"9%F2F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "findMin(g, [2,3]);" }}{PARA 8 "" 1 "" {TEXT -1 43 "Er ror, (in findMin) cannot evaluate boolean" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 15 "trace(findMin);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# %(findMinG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "findMin(g, [2 ,3]);" }}{PARA 9 "" 1 "" {TEXT -1 36 "\{--> enter findMin, args = g, [ 2, 3]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$\"\"#\"\"$" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%&oldhtG-%$sinG6#\"\"'" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"hG$\"\"\"!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$,&\"\"#\"\"\"-%$cosG6#\"\"'$!\"$!\"\",&\"\"$F(F)$!\"# F/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#htG-%$sinG6#*&,&\"\"#\"\"\"-% $cosG6#\"\"'$!\"$!\"\"F+,&\"\"$F+F,$!\"#F2F+" }}{PARA 9 "" 1 "" {TEXT -1 66 "<-- ERROR in findMin (now at top level) = cannot evaluate boole an\}" }}{PARA 8 "" 1 "" {TEXT -1 43 "Error, (in findMin) cannot evalua te boolean" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "sin((2-.3*cos (6.0))*(3-.2*cos(6.0)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+r!)=b** !#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "trace(findMin);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%(findMinG" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 22 "findMin(g, [2.0,3.0]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+\"yhso\"!\"*$\"+'e.Hz#F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 385 "findMin:= proc(f,firstguess)\n local i, h, gue ss, oldht, ht;\n guess := 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gradstep2(f,guess,h);\n ht := f(op(guess));\n# print (i,guess,ht);\n if ( abs(oldht - ht) < .00001) then\n print (\"took\",i,\"steps. value is\",ht);\n RETURN(guess);\n fi ;\n oldht := ht;\n od;\n print(\"took\",i,\"steps. value is\",h t);\n RETURN(guess);\n en" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "findMin(f,[2,2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&Q%took6\"\"#I Q1steps.~~value~isF$$\"+Jk*fA\"!#9" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# 7$$\"+x+)eZ#!#7F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "findMi n(h,[2,2]);" }}{PARA 8 "" 1 "" {TEXT -1 42 "Error, (in h) integer too \+ large in context" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "trace(f indMin);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%(findMinG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "findMin(h,[2,2]);" }}{PARA 9 "" 1 " " {TEXT -1 36 "\{--> enter findMin, args = h, [2, 2]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$$\"\"#\"\"!F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&oldhtG$\"%[?\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%\"hG$\"\"\"!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$$!%+ ^!\"\"F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#htG$\"+w%[3Q#\"#=" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%&oldhtG$\"+w%[3Q#\"#=" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%&guessG7$$\"+t^;MB\"#:F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#htG$\"+5%\\;g*\"$M#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&oldhtG$\"+5%\\;g*\"$M#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&gue ssG7$$!+hIwc?\"$5#F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#htG$\"+IpR4 F\"%%=#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&oldhtG$\"+IpR4F\"%%=#" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$$\"+\"zble'\"%k>F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#htG$\"+!>iL2$\"&H(>" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&oldhtG$\"+!>iL2$\"&H(>" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$$!+Ir0LB\"&bx\"F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#htG$\"+;q;c&*\"'Mw<" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&oldhtG$\"+;q;c&*\"'Mw<" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&gue ssG7$$\"+,D*z/#\"'q)f\"F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#htG$\" +qL0'f#\"(%y)f\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&oldhtG$\"+qL0'f #\"(%y)f\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$$!+IT/Qj\"(/* Q9F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#htG$\"+#p+@4#\")H\"*Q9" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%&oldhtG$\"+#p+@4#\")H\"*Q9" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$$\"+M3V];\"):-&H\"F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#htG$\"+)=&=**H\"*LA]H\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&oldhtG$\"+)=&=**H\"*LA]H\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG7$$!+*[ng3*\"*3?b;\"F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#htG$\"+Ky*)pw\"+q,_l6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&oldhtG$\"+Ky*)pw\"+q,_l6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %&guessG7$$\"+Z;p?U\"+_\"o*[5F&" }}{PARA 9 "" 1 "" {TEXT -1 71 "<-- ER ROR in findMin (now at top level) = integer too large in context\}" }} {PARA 8 "" 1 "" {TEXT -1 42 "Error, (in h) integer too large in contex t" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "findMin(h,[1/2,1/2]); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6&Q%took6\"\"#[Q1steps.~~value~isF$$ \"+/2mih!#8" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+DzEbW!#5F$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Df(h,[2,2]);\ngradstep2(h,[2 ,2],.1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"%?^F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$!%+^!\"\"F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "Df(h,[1/2,1/2]);\ngradstep2(h,[1/2,1/2],.1);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7$#\"\"&\"$c#F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+](o/)\\!#5F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 488 "findMin:= proc(f,firstguess)\n local i, h, guess, o ldht, ht;\n guess := evalf(firstguess); # we want to use approximati ons.\n oldht := f(op(guess));\n h:=.1;\n for i from 1 to 5 do\n \+ guess := gradstep2(f,guess,1/leng(Df(f,guess)));\n ht := f(op(gue ss));\n print(i,guess,ht);\n if ( abs(oldht - ht) < .00001) then\n print(\"took\",i,\"steps. value is\",ht);\n RETURN(gue ss);\n fi;\n oldht := ht;\n od;\n print(\"took\",i,\"steps. \+ value is\",ht);\n RETURN(guess);\n end:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 17 "findMin(h,[2,2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6%\"\"\"7$$\"+>K*GH\"!\"*F%$\"+[l45E!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"#7$$\"+wV'y&e!#5F%$\"+9RJ:&*!#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"$7$$!+OM?87!#5F%$\"+h!\\:Q\"!#=" }}{PARA 11 "" 1 " " {XPPMATH 20 "6%\"\"%7$$\"+uV'y&e!#5F%$\"+#)QJ:&*!#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"&7$$!+NM?87!#5F%$\"+]!\\:Q\"!#=" }}{PARA 11 " " 1 "" {XPPMATH 20 "6&Q%took6\"\"\"'Q1steps.~~value~isF$$\"+]!\\:Q\"!# =" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$!+NM?87!#5F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "if(sin(5) < 3) then\n print (\"yep\");\n fi;" }}{PARA 8 "" 1 "" {TEXT -1 30 "Error, cannot evaluate boolean" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "if(sin(evalf(5)) < 3) then \nprint (\"yep\");\nfi;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q$yep6\"" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 577 "findMin:= proc(f,firstgue ss)\n local i, len, h, guess, oldht, ht;\n guess := evalf(firstguess ); # we want to use approximations.\n oldht := f(op(guess));\n for \+ i from 1 to 100 do\n len := leng(Df(f,guess));\n if ( len > 1) then\n h:=1/len;\n else\n h:=.5;\n fi;\n g uess := gradstep2(f,guess,h);\n ht := f(op(guess));\n# print(i,gue ss,ht);\n if ( abs(oldht - ht) < .00001) then\n print(\"too k\",i,\"steps. value is\",ht);\n RETURN(guess);\n fi;\n \+ oldht := ht;\n od;\n print(\"took\",i,\"steps. value is\",ht);\n \+ RETURN(guess);\n end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f indMin(h,[1,2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&Q%took6\"\"\"$Q1st eps.~~value~isF$$\"+?=*>5*!#:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\" +`h.rH!#5$\"+hdImGF&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }}{MARK "36 0 0" 0 }{VIEWOPTS 1 1 0 2 1 1805 }