Thanks for the suggestion, Axel.  I downloaded Ghostscript, as well as Xpdf and some other files, but couldn't find a recent GSview for the Mac.  The MacGSview files seemed to be old.  I'll play around with the files and see what luck I have.

I did come across a claim that Mac OS X's app Preview can re-arrange pages in a PDF.  This would solve my problem, but I haven't been able to figure out how to get my version of Preview to do that.  Maybe it's only the more recent one that comes with Leopard that has this capability.

- Dushan

Thanks for the suggestion, Axel.  I downloaded Ghostscript, as well as Xpdf and some other files, but couldn't find a recent GSview for the Mac.  The MacGSview files seemed to be old.  I'll play around with the files and see what luck I have.

I did come across a claim that Mac OS X's app Preview can re-arrange pages in a PDF.  This would solve my problem, but I haven't been able to figure out how to get my version of Preview to do that.  Maybe it's only the more recent one that comes with Leopard that has this capability.

- Dushan

You're probably right about the generic usefulness being doubtful, but I had in mind a situation I had encountered recently, where a simplification had produced a ratio with a huge numerator and large denominator.  Both contained many instances of three radicals.  Substituting symbols for them made it much easier to see what the whole expression really looked like.

- Dushan

You're probably right about the generic usefulness being doubtful, but I had in mind a situation I had encountered recently, where a simplification had produced a ratio with a huge numerator and large denominator.  Both contained many instances of three radicals.  Substituting symbols for them made it much easier to see what the whole expression really looked like.

- Dushan

Your various manipulations have been very instructive; thanks.  In particular, I didn't realize that one could introduce functionality simply by replacing 'Rp' by 'Rp(X,Y)', etc.  This adds all kinds of possibilities.

On the subject of substitutions, an oft-asked question (including by me) is how to get a substitution to act also in the denominator.  One really simple-minded thought that occured to me is to split the expression into numerator and denominator, do the desired substitution in each, then recombine the results.  Are you aware of some potential pitfalls with this strategy?  If it's useful in more than very select cases, a procedure could be made to do it.

Thanks for your comments.

- Dushan

Your various manipulations have been very instructive; thanks.  In particular, I didn't realize that one could introduce functionality simply by replacing 'Rp' by 'Rp(X,Y)', etc.  This adds all kinds of possibilities.

On the subject of substitutions, an oft-asked question (including by me) is how to get a substitution to act also in the denominator.  One really simple-minded thought that occured to me is to split the expression into numerator and denominator, do the desired substitution in each, then recombine the results.  Are you aware of some potential pitfalls with this strategy?  If it's useful in more than very select cases, a procedure could be made to do it.

Thanks for your comments.

- Dushan

I checked again and verified there's no typo.  From the symmetry between 'Rp' and 'Rm' one can see that the second term of your vfX expression can't be right, because it mixes the two.  The original potential can be split up as

    sp1 = ln( Rp*(Rp-Z) ) - ln( Rm*(Rm-Z) )

so since all the operations are linear, the vector field components must also be separatable into independent components, just as you have in the Y component result.  So there's a problem in the X-component's derivation.  I didn't follow all your steps (tho I'll study them), so can't point to the exact source of the error.

- Dushan

I checked again and verified there's no typo.  From the symmetry between 'Rp' and 'Rm' one can see that the second term of your vfX expression can't be right, because it mixes the two.  The original potential can be split up as

    sp1 = ln( Rp*(Rp-Z) ) - ln( Rm*(Rm-Z) )

so since all the operations are linear, the vector field components must also be separatable into independent components, just as you have in the Y component result.  So there's a problem in the X-component's derivation.  I didn't follow all your steps (tho I'll study them), so can't point to the exact source of the error.

- Dushan

I've got several Add-ons:

  1-click Weather,      ColorfulTabs,         Download Panel,

  Download Statusbar, DownThemAll,        Duplicate Tab,

  Firefox Showcase,    Flashblock,            gui:config,

  No Squint,             NoScript,               PopupMaster,

  QuickNote,            Read it Later,         Searchbar Autosizer,

  Site Launcher,        Tabs Open Relative,  User Agent Switcher,

  Weatherbug

I now strongly suspect 'Site Launcher' is the culprit, which I'd forgotten
about.  It will open a site with the key combinations Ctrl-Shft-[a..z].  In
particular Ctrl-Shft-f will open Facebook and Ctrl-Shft-d will open Digg,
whatever that is.

I've never intentionally used it, and have now uninstalled it.  I can't even
recall now why I thought it was a good idea to install it in the first place.

Sorry for the dumb question.

- Dushan

I wholeheartedly agree with the observation that "the error messages are issued to be read by the user, and have to be understandable by any ordinary user".

Labeling error messages as 'helpful' or 'unhelpful' obviously depends on who is doing the labeling.  While a Maple developer would consider them more than 'helpful', a general user, untutored in Maple's inner workings, might find them obscure to the point of uselessness.

Maybe there should be a second level of error message, called 'More detail...', that describes the discrepency between a procedure's expected and actual inputs.  Is something like that already available?

- Dushan

I wholeheartedly agree with the observation that "the error messages are issued to be read by the user, and have to be understandable by any ordinary user".

Labeling error messages as 'helpful' or 'unhelpful' obviously depends on who is doing the labeling.  While a Maple developer would consider them more than 'helpful', a general user, untutored in Maple's inner workings, might find them obscure to the point of uselessness.

Maybe there should be a second level of error message, called 'More detail...', that describes the discrepency between a procedure's expected and actual inputs.  Is something like that already available?

- Dushan

Stephanie,

Thank you, that recommendation made a big difference in getting a result.  Namely, I did get one.  Clearly, the fact that the VectorCalculus package "defines vector fields as functions" is crucial to know, but somehow I missed that info in the documentation I read.  Could you please point me to where that is explained?

Thanks.

- Dushan

Stephanie,

Thank you, that recommendation made a big difference in getting a result.  Namely, I did get one.  Clearly, the fact that the VectorCalculus package "defines vector fields as functions" is crucial to know, but somehow I missed that info in the documentation I read.  Could you please point me to where that is explained?

Thanks.

- Dushan

Okay, I tried it fresh exactly the way you did, and this time it worked!  Now I have to figure out what was done differently.

I must say that so far the VC package has been pretty frustrating, blocking me about 80% of the time with error messages that are too cryptic to help me figure out how to fix the problem.

- Dushan

Okay, I tried it fresh exactly the way you did, and this time it worked!  Now I have to figure out what was done differently.

I must say that so far the VC package has been pretty frustrating, blocking me about 80% of the time with error messages that are too cryptic to help me figure out how to fix the problem.

- Dushan