> simplify(M1-N1);
                                       0

For the substitution, you could try something like this,

eval(M1,[s1=sqrt(mu1*epsilon1*kappa^2+v^2+u^2),
         s2=sqrt(mu2*epsilon2*kappa^2+v^2+u^2)]);

acer

p1:=plots:-pointplot(<<1,2,3,4,5>|<1,3,5,7,9>>):
p2:=plots:-pointplot(<<1,2,3,4,5>|<1,4,9,16,25>>):
plots:-display([p1,p2]);

acer

p1:=plots:-pointplot(<<1,2,3,4,5>|<1,3,5,7,9>>):
p2:=plots:-pointplot(<<1,2,3,4,5>|<1,4,9,16,25>>):
plots:-display([p1,p2]);

acer

The expressions assigned to M1 and N1 are not equal.

That's the central problem. Assign M1 and N1 those long expressions without the attempt to subs for s1^2 and s2^2. Then, it is easy to find a set of values for which they are not equal.

> eval(M1-N1,[s1=sqrt(3),s2=sqrt(3),xp=1,mu1=1,mu2=1,
>             epsilon1=1,epsilon2=1,kappa=1,v=1,u=1,w=1,a=1]);

The other problem is trying to substitute s1^2=... and expecting it to replace all instances of s1. Maybe you could consider substituting s1=sqrt(...), etc, using eval instead of subs, and simplify with assumptions on the range/realness of the variables? That might be a means to show the equality, given the the bigger problem were fixed and they were actually equal.

acer

That datatype float[8] rtable (Array, Vector, etc) should be created with enough storage to hold the result.

> restart:
> arrB_GSL := define_external(
>     'gsl_sf_bessel_jl_steed_array','lmax'::integer[4],
>     'x'::float[8],
>     'jl_x_array'::ARRAY(datatype=float[8]),
> 'RETURN'::integer[4],
> LIB="/usr/lib64/libgsl.so"):
>
> jl:=Vector[row](10,datatype=float[8]):
> arrB_GSL(2,3.1,jl);
                                       0
 
> jl;
[0.0134131169139646862, 0.326628473286207754, 0.302678954008171852, 0., 0., 0.,
 
    0., 0., 0., 0.]
 
> jl:=Vector[row](10,datatype=float[8]):
> arrB_GSL(5,3.1,jl);
                                       0
 
> jl;
[0.0134131169139647330, 0.326628473286207810, 0.302678954008171908,
 
    0.161563388017295251, 0.0621415995792689718, 0.0188477075354211120, 0., 0.,
 
    0., 0.]

Axel, your example show code in which that Array would be created with no allocated space.

> steedArr:=Array(datatype=float[8], order=C_order);
steedArr :=
 
    Array({}, datatype = float[8], storage = rectangular, order = C_order)

If there is not enough space in the passed array then the GSL function may attempt to write the data outside the bounds of that array in memory. That would lead to a seg-fault or corruption of other data in Maple's own memory space. (This would certainly happen, if the array had no allocated storage at all, as in the original code posted.)

acer

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

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