The interesting bits may not be in what gets assigned to dsol, but rather what gets assigned to an internal structure that dsol accesses.

Suppose instead that the method being asked about was dverk78. That uses a 7-8 order scheme to create piecewise polynomial interpolants, which each can be used to approximate the solution over a subrange. Now, one might possibly wish to extract those. (The purpose of that is still a little dubious, since plotting by utilizing them may be better done by DEplot. What else would one do with them?) How to find and recognize the data that describes those interpolants, in this next lot, is murky.

restart:
kernelopts(opaquemodules=false):
interface(verboseproc=3):
dsol := dsolve({diff(x(t),t)=sin(t), x(0)=0}, 'numeric', method=dverk78):
T:=eval(`dsolve/numeric/data/modules`[1]);
eval(T:-Data);

For the rosenbrock method, it's perhaps less clear (to me) what one would want to find and extract. But you can mostly examine it in a similar way.

restart:
kernelopts(opaquemodules=false):
interface(verboseproc=3):
dsol := dsolve({diff(x(t),t)=sin(t), x(0)=0}, 'numeric', method=rosenbrock):
T:=eval(`dsolve/numeric/data/modules`[1]);
eval(T:-Data);
op(op(3,eval(T)))["soln_procedure"];

So, what exactly is the data stored inside the local variable _dtbl of that procedure? Can it be extracted easily (without resorting to something like ToInert)?

One can see it printed, inside the debugger. one can also follow its workings, step by step.

> f := op(op(3,eval(T)))["soln_procedure"]:
> stopat(f):
> f(4);
f:
   1*  _xout := _xin;
 
DBG> next
4
f:
   2   _pars := [];
 
DBG> next

acer

These aren't really different techniques. They're just ways of getting various effects, and may be used together or not.

You can save both procedures and modules to library archives ("repositories").

And you can keep distinct procedures' sources in separate text files, or in separate worksheets. The same goes for whole modules.

But you cannot keep the source of different module members (individual exports or locals of the same module) in separate worksheets if you intend to merge them using $include. (You might be able to use `read`, but then you could not use $define.) You can, however, keep those individual module members' sources in separate text files and merge them with those preprocessor directives.

Those directives are thus most useful for managing sources of large modules, if one wants to keep all individual members' sources separate.

You also mentioned wanting to "define" some variable's value in a separate file. For that, $define and $include are great. Also, these serve very well to keep common definitions centrally defined (just like C header files can do).

The stuff about text files being safer against corruption, and better for revision control, still holds I believe. That's not important for everyone, perhaps. And plaintext can be shared/viewed even when Maple is not available. That too, may not be important to everyone.

With the commandline interface, you can load/save sources in batch mode, or do other nifty shell scripty things to them.

acer

These aren't really different techniques. They're just ways of getting various effects, and may be used together or not.

You can save both procedures and modules to library archives ("repositories").

And you can keep distinct procedures' sources in separate text files, or in separate worksheets. The same goes for whole modules.

But you cannot keep the source of different module members (individual exports or locals of the same module) in separate worksheets if you intend to merge them using $include. (You might be able to use `read`, but then you could not use $define.) You can, however, keep those individual module members' sources in separate text files and merge them with those preprocessor directives.

Those directives are thus most useful for managing sources of large modules, if one wants to keep all individual members' sources separate.

You also mentioned wanting to "define" some variable's value in a separate file. For that, $define and $include are great. Also, these serve very well to keep common definitions centrally defined (just like C header files can do).

The stuff about text files being safer against corruption, and better for revision control, still holds I believe. That's not important for everyone, perhaps. And plaintext can be shared/viewed even when Maple is not available. That too, may not be important to everyone.

With the commandline interface, you can load/save sources in batch mode, or do other nifty shell scripty things to them.

acer

Alec's suggestion is about Maple, not Mapleprimes. Start Maple itself. Type in

?zip

and read the Examples section.

The last example on that help-page is this,

> zip(`[]`,[1,2,3] ,[4,5,6]);
 
                           [[1, 4], [2, 5], [3, 6]]

acer

Alec's suggestion is about Maple, not Mapleprimes. Start Maple itself. Type in

?zip

and read the Examples section.

The last example on that help-page is this,

> zip(`[]`,[1,2,3] ,[4,5,6]);
 
                           [[1, 4], [2, 5], [3, 6]]

acer

> one := 1/((x*Dd-x^2*Dcj)*sqrt(x^2-1)):
> two := int(one,x) assuming x>1, Dd>0, Dcj>0, Dcj>Dd:
> three := simplify(%):
> four := subs({x = sqrt(1+Zeta^2)}, three):
> five := simplify(four) assuming Zeta>=0:

> lprint(five);
-(Dcj*arctan((-Dcj+(1+Zeta^2)^(1/2)*Dd)/(-Dd^2+Dcj^2)^(1/2)/Zeta)+arctan(1/
Zeta)*(-Dd^2+Dcj^2)^(1/2))/(-Dd^2+Dcj^2)^(1/2)/Dd

> kernelopts(version);
             Maple 11.02, X86 64 LINUX, Nov 9 2007 Build ID 330022

You're probably better off using some name other than capital Zeta (which is a function, and may be why `simplify` ran into a recusrion limit error when the assumption didn't match the right name). Using zeta instead of Zeta, it seemed ok with or without the assumption.

acer

> one := 1/((x*Dd-x^2*Dcj)*sqrt(x^2-1)):
> two := int(one,x) assuming x>1, Dd>0, Dcj>0, Dcj>Dd:
> three := simplify(%):
> four := subs({x = sqrt(1+Zeta^2)}, three):
> five := simplify(four) assuming Zeta>=0:

> lprint(five);
-(Dcj*arctan((-Dcj+(1+Zeta^2)^(1/2)*Dd)/(-Dd^2+Dcj^2)^(1/2)/Zeta)+arctan(1/
Zeta)*(-Dd^2+Dcj^2)^(1/2))/(-Dd^2+Dcj^2)^(1/2)/Dd

> kernelopts(version);
             Maple 11.02, X86 64 LINUX, Nov 9 2007 Build ID 330022

You're probably better off using some name other than capital Zeta (which is a function, and may be why `simplify` ran into a recusrion limit error when the assumption didn't match the right name). Using zeta instead of Zeta, it seemed ok with or without the assumption.

acer

Most of the Maple math library code has been written over a span of 20+ years. So it doesn't have a truly uniform style. The style of several different authors can be detected in different parts -- a bit like the "fist" of a Morse code sender.

It might be fun to try and guess clumps of library code written by the same author. (Like detecting the supposed author "Q" of parts of the NT.)

The `int/cook` routine(s) are not new, relatively speaking. Are there more bugs in old or new code?

More seriously, it might be nice to have a form of code comment that can survive being saved to a .mla archive, being loaded from archive, and passed to print or eval.

acer

Most of the Maple math library code has been written over a span of 20+ years. So it doesn't have a truly uniform style. The style of several different authors can be detected in different parts -- a bit like the "fist" of a Morse code sender.

It might be fun to try and guess clumps of library code written by the same author. (Like detecting the supposed author "Q" of parts of the NT.)

The `int/cook` routine(s) are not new, relatively speaking. Are there more bugs in old or new code?

More seriously, it might be nice to have a form of code comment that can survive being saved to a .mla archive, being loaded from archive, and passed to print or eval.

acer

It may be possible to contrive alternative names for a snark.

I recall seeing both a French and a German translation of Jabberwocky in The Annotated Alice. The French name was given as le Jaseroque, and the German as der Jammerwoch.

This page indicates that someone thought that Snark remains the same in French, but becomes Schnark in German. (But, what's wrong with Snarque)?

acer

It may be possible to contrive alternative names for a snark.

I recall seeing both a French and a German translation of Jabberwocky in The Annotated Alice. The French name was given as le Jaseroque, and the German as der Jammerwoch.

This page indicates that someone thought that Snark remains the same in French, but becomes Schnark in German. (But, what's wrong with Snarque)?

acer

What you're seeing in E looks like premature evaluation. (Is striving to change p.e. tilting at windmills? I'm not sure.)

Presumably your point is that you want E to be C, without having to set Digits to 20 beforehand. While an uneval (or evaln) argument to a procedure, like sin(Pi) can be prevented from evaluating, the 1/6. inside sin(Pi/6.) is another story.

> pe := proc(x::uneval) lprint(x); x; end proc:

> pe(sin(Pi));
sin(Pi)
                                    sin(Pi)
 
> pe(Pi/6.);
.1666666667*Pi
                                0.1666666667 Pi

acer

What you're seeing in E looks like premature evaluation. (Is striving to change p.e. tilting at windmills? I'm not sure.)

Presumably your point is that you want E to be C, without having to set Digits to 20 beforehand. While an uneval (or evaln) argument to a procedure, like sin(Pi) can be prevented from evaluating, the 1/6. inside sin(Pi/6.) is another story.

> pe := proc(x::uneval) lprint(x); x; end proc:

> pe(sin(Pi));
sin(Pi)
                                    sin(Pi)
 
> pe(Pi/6.);
.1666666667*Pi
                                0.1666666667 Pi

acer

After those changes E will still come out the same.

> unprotect(`*`);
> `*`:=(a,b)->a*b:
> protect(`*`);
> `&/`:=(a,b)->b(a):
> C := sin( Pi/6 ) &/ evalf[20];
                          C := 0.50000000000000000000
 
> C := sin( Pi/6. ) &/ evalf[20];
                          C := 0.50000000009068996821

One might label automatic simplification as one form of p.e.

note. Alec's response was edited while I was composing the above reply, and the first 5 input lines above removed. Sorry, Alec! I suppose that it was realized that automatic simplification cannot be turned off by us mortals.

acer

After those changes E will still come out the same.

> unprotect(`*`);
> `*`:=(a,b)->a*b:
> protect(`*`);
> `&/`:=(a,b)->b(a):
> C := sin( Pi/6 ) &/ evalf[20];
                          C := 0.50000000000000000000
 
> C := sin( Pi/6. ) &/ evalf[20];
                          C := 0.50000000009068996821

One might label automatic simplification as one form of p.e.

note. Alec's response was edited while I was composing the above reply, and the first 5 input lines above removed. Sorry, Alec! I suppose that it was realized that automatic simplification cannot be turned off by us mortals.

acer