{VERSION 4 0 "IBM INTEL NT" "4.0" } {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 "Hyperlink" -1 17 "" 0 1 0 128 128 1 0 0 1 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 "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 }{CSTYLE "Help Head ing" -1 26 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "Help Normal" -1 30 "Times" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Couri er" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 1 }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 1 }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 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {SECT 0 {PARA 0 "" 0 "" {TEXT 26 9 "Bug fix: " }{TEXT 30 33 "T wo-dimensional plots with coords" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 24 "There are some\027 bugs in " }{MPLTEXT 0 21 12 "changecoords" }{TEXT -1 8 " in the " }{MPLTEXT 0 21 5 "plots" } {TEXT -1 54 " package affecting two-dimensional plots that use the " } {MPLTEXT 0 21 6 "coords" }{TEXT -1 10 " option: " }{MPLTEXT 0 21 11 " contourplot" }{TEXT -1 42 " does not work with this option, and even \+ " }{MPLTEXT 0 21 4 "plot" }{TEXT -1 80 " fails with a coordinate syste m having parameters specified in functional style:" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "contourplot(x-y, x=0..1,y=0..1,coords=pol ar);" }}{PARA 8 "" 1 "" {TEXT -1 67 "Error, (in plot/iplot2d) cannot c onvert to coordinate system polar\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "plot(1, x=0..1, coords=logcosh(2));" }}{PARA 8 "" 1 " " {TEXT -1 72 "Error, (in plot/adaptive) unknown optional argument coo rds = logcosh(2)\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 55 "To remedy these bugs, I have written a replacement for \+ " }{MPLTEXT 0 21 12 "changecoords" }{TEXT -1 48 " for two-dimensional \+ coordinate systems, called " }{MPLTEXT 0 21 14 "changecoords2d" } {TEXT -1 62 ". This function is part of the Maple Advisor Database li brary" }{TEXT -1 37 ". Instead of making a plot with the " }{MPLTEXT 0 21 6 "coords" }{TEXT -1 52 " option, you can first produce the plot \+ without the " }{MPLTEXT 0 21 6 "coords" }{TEXT -1 22 " option and then call " }{MPLTEXT 0 21 14 "changecoords2d" }{TEXT -1 116 " with the pl ot as first argument and the name of the coordinate system as second a rgument. All other options (e.g. " }{MPLTEXT 0 21 7 "scaling" }{TEXT -1 2 ", " }{MPLTEXT 0 21 6 "colour" }{TEXT -1 4 " or " }{MPLTEXT 0 21 4 "axes" }{TEXT -1 56 ") should be part of the first plotting command, not the " }{MPLTEXT 0 21 14 "changecoords2d" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "Note that " } {MPLTEXT 0 21 17 "plot(f(x),x=a..b)" }{TEXT -1 53 " plots the second v ariable in Cartesian coordinates, " }{XPPEDIT 18 0 "y" "6#%\"yG" } {TEXT -1 38 ", as a function of the first variable " }{XPPEDIT 18 0 "x " "6#%\"xG" }{TEXT -1 69 ". In polar coordinates it is more usual to \+ plot the first variable, " }{XPPEDIT 18 0 "r" "6#%\"rG" }{TEXT -1 31 " , as a function of the second, " }{XPPEDIT 18 0 "theta" "6#%&thetaG" } {TEXT -1 19 " (and this is what " }{MPLTEXT 0 21 40 "plot(f(theta), th eta=a..b, coords=polar)" }{TEXT -1 52 " does). However, that could no t be accomplished by " }{MPLTEXT 0 21 38 "changecoords(plot(f(x),x=a.. b), polar)" }{TEXT -1 20 ": it would give you " }{XPPEDIT 18 0 "theta " "6#%&thetaG" }{TEXT -1 18 " as a function of " }{XPPEDIT 18 0 "r" "6 #%\"rG" }{TEXT -1 15 ". Instead of " }{MPLTEXT 0 21 5 "polar" } {TEXT -1 14 ", you can use " }{MPLTEXT 0 21 14 "reverse(polar)" } {TEXT -1 66 ", which interchanges the roles of the two variables and g ives you " }{XPPEDIT 18 0 "r" "6#%\"rG" }{TEXT -1 18 " as a function o f " }{XPPEDIT 18 0 "theta" "6#%&thetaG" }{TEXT -1 1 "." }{TEXT -1 19 " You can also use " }{MPLTEXT 0 21 7 "reverse" }{TEXT -1 42 " with an y of the other coordinate systems." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "changecoords2d(plot(cos(x),x=-Pi/2 .. Pi/2, scaling=c onstrained), reverse(polar));" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "changecoords2d(pointplot([seq([1,7*Pi/10*i],i=0 ..20)], style=line, colour=blue,scaling=constrained), polar);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "changecoords2d(im plicitplot(x=y,x=0..1,y=0..1),logcosh);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "changecoords2d(contourplot(x-y, x=0 ..1, y=0..1, axes=box), logcosh);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "changecoords2d(plot(1, x=0..1), reverse(logco sh(2)));" }{TEXT -1 0 "" }}}}{SECT 0 {PARA 0 "" 0 "" {TEXT 26 10 "See \+ also: " }{HYPERLNK 17 "addcoords" 2 "addcoords" "" }{TEXT -1 2 ", " } {HYPERLNK 17 "changecoords" 2 "changecoords" "" }{TEXT -1 2 ", " } {HYPERLNK 17 "changecoords2d" 2 "changecoords2d" "" }{TEXT -1 2 ", " } {HYPERLNK 17 "contourplot" 2 "contourplot" "" }{TEXT -1 2 ", " } {HYPERLNK 17 "coords" 2 "coords" "" }{TEXT -1 1 "," }{TEXT -1 1 " " } {HYPERLNK 17 "plot(coords)" 2 "plot,coords" "" }{TEXT -1 2 ", " } {HYPERLNK 17 "transform" 2 "plottools,transform" "" }}}{SECT 0 {PARA 0 "" 0 "" {TEXT 26 24 "Maple Advisor Database, " }{TEXT -1 15 " R. Isr ael 1999" }}}}{MARK "0 5 1 0" 47 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }