Robert, what a great honour for Maplesoft to be able to count on you.

Happy retirement! Congratulations!

one problem I can see is that your odes are not specified explicitly in the usual form,

ode1 := diff(H(z),z) = f(H(z),psi(z),z):
ode2 := diff(psi(z),z) = g(H(z),psi(z),z):

where f and g would be some known functions. Instead you have implicit odes. Not sure about Maple's capabilities in this respect. You might try to rewrite your ode system, if possible, in the above form.

I can think of several things you might be meaning, are you looking for a function that is homogeneous of degree 0, i.e. such that for any x, f(x*a,x*b,...)=x*f(a,b...) ?

thanks acer, I have followed every link and read with great interest. I'm still quite far from understanding the subtleties at stake, but little by little certain things become  clearer.

I can see the problems with the overlay. That's a big one, right? At first, I thought that one could extract the colors from the 3D plot and use them to recolor the 2D plot, but that would do nothing to the overlay problem.

Adapting some lines in the Advanced Programming Guide, I got the following,

getShading := proc(curve)
  op(select( type, [ op(curve) ], { list(list(numeric)), specfunc(anything,SHADING) } )) ;
end proc:

getShading(p);
                         SHADING(ZHUE)

but how does one read the information assotiated with SHADING ...

thanks acer, I have followed every link and read with great interest. I'm still quite far from understanding the subtleties at stake, but little by little certain things become  clearer.

I can see the problems with the overlay. That's a big one, right? At first, I thought that one could extract the colors from the 3D plot and use them to recolor the 2D plot, but that would do nothing to the overlay problem.

Adapting some lines in the Advanced Programming Guide, I got the following,

getShading := proc(curve)
  op(select( type, [ op(curve) ], { list(list(numeric)), specfunc(anything,SHADING) } )) ;
end proc:

getShading(p);
                         SHADING(ZHUE)

but how does one read the information assotiated with SHADING ...

I'm afraid I can't offer any specific help here. I opened your worksheet, but you're using stuff I don't know.

As a general recommendation, not useful now but should be in the future, you may want to set up a system of backups and/or version control. This way if a previously fine worksheets suddenly fails, you can go back in time to the working version.

Con you do something like this,

p1:=plot3d(Func, 'color' = whatever, ...
p2:=plot3d(TanPln, 'color' = somethingelse ...

plots:-display([p1,p2]);

@acer 

In Maple 15 with the Standard GUI, if I enter ?% in a worksheet (or if I search for & in an open Help window) then the Help system opens to the `ditto` help-page, sure. But that Help browser's "search" tab on the left shows two matches. One match is for topic `ditto`, and the other match is for topic `value`. So this aspect is already working.

True, but if your settings are set to minimize the "Help Navigator" you wouldn't see it. Hence it would be good to have cross-linking between "ditto" and "value". That would also help with the online search.

Since you mention  wikipedia, isn't one of the best things about it getting lost in the maze of information by clicking on cross-references?

Too many cross references may be counterproductive however. But how about a 2-level referencing

• See Also
• See More

@acer 

In Maple 15 with the Standard GUI, if I enter ?% in a worksheet (or if I search for & in an open Help window) then the Help system opens to the `ditto` help-page, sure. But that Help browser's "search" tab on the left shows two matches. One match is for topic `ditto`, and the other match is for topic `value`. So this aspect is already working.

True, but if your settings are set to minimize the "Help Navigator" you wouldn't see it. Hence it would be good to have cross-linking between "ditto" and "value". That would also help with the online search.

Since you mention  wikipedia, isn't one of the best things about it getting lost in the maze of information by clicking on cross-references?

Too many cross references may be counterproductive however. But how about a 2-level referencing

• See Also
• See More

@acer 

Indeed you're right, the link to both ditto and value(ditto) is quite clear in the GUI's help pages (CTRL+F1). And I wouldn't have missed it.

But, as it happened, I was writing from home, where I do not have Maple, and got my information from the online help pages.

http://www.maplesoft.com/support/help/

I assumed that the content would be the same, as it usually is, I think. A search for "%" returned:

Your search - % - did not match any documents. 
 No pages were found containing "%". 

so I searched for "percentage sign" instead,

http://search.maplesoft.com/search?q=percentage%20sign

and that returns "ditto" but not "value"...

http://www.maplesoft.com/support/help/view.aspx?sid=104987

Hence my impression that the connection between the "ditto" and "value" help pages was absent. Unless I'm mistaken, this shortcoming really refers to the online pages and not to the packaged help pages accessible from the GUI.

@acer 

Indeed you're right, the link to both ditto and value(ditto) is quite clear in the GUI's help pages (CTRL+F1). And I wouldn't have missed it.

But, as it happened, I was writing from home, where I do not have Maple, and got my information from the online help pages.

http://www.maplesoft.com/support/help/

I assumed that the content would be the same, as it usually is, I think. A search for "%" returned:

Your search - % - did not match any documents. 
 No pages were found containing "%". 

so I searched for "percentage sign" instead,

http://search.maplesoft.com/search?q=percentage%20sign

and that returns "ditto" but not "value"...

http://www.maplesoft.com/support/help/view.aspx?sid=104987

Hence my impression that the connection between the "ditto" and "value" help pages was absent. Unless I'm mistaken, this shortcoming really refers to the online pages and not to the packaged help pages accessible from the GUI.

@acer 

I get it. I mean, I understand your point about computing the procedure over and over again. Sorry if I didn't pay enough attention to this point the first time around, I was quite overwhelmed with information and had focused most of my attention on the bits that were easier (for me) to grasp. Thanks to pagan and Joe too, for insisting on this particular coding practice.

As a bonus,

eta(r, u, pars);

is even simpler to write.

thanks for these tips.

P.S. I am indeed the sort of person who writes a procedure without really knowing why!   8-(

@acer 

I get it. I mean, I understand your point about computing the procedure over and over again. Sorry if I didn't pay enough attention to this point the first time around, I was quite overwhelmed with information and had focused most of my attention on the bits that were easier (for me) to grasp. Thanks to pagan and Joe too, for insisting on this particular coding practice.

As a bonus,

eta(r, u, pars);

is even simpler to write.

thanks for these tips.

P.S. I am indeed the sort of person who writes a procedure without really knowing why!   8-(

@pagan 

A recent post by acer has introduced me to the efficiency issues related to producing large plots. I will bear in mind acer's and your remarks in this respect. Thanks!

http://www.mapleprimes.com/posts/123463-ImageTools-For-Complex-argument--Plot

@pagan 

A recent post by acer has introduced me to the efficiency issues related to producing large plots. I will bear in mind acer's and your remarks in this respect. Thanks!

http://www.mapleprimes.com/posts/123463-ImageTools-For-Complex-argument--Plot