In Maple 9.52, as well as Maple 11, 'pdsolve' uses separation of variables as default here:

pdsolve(heat, T(y, z));

`&where`(T(y,z) = _F1(y)*_F2(z),[{diff(_F1(y),y) = _c[1]*_F1(y), diff(_F2(z),`$`(z,2)) = (_F2(z)-z^2*_F2(z))*_c[1]-1/z*diff(_F2(z),z)}]); It solves the splitted system in terms of 'Whittaker' functions for Maple 9.5:

pdsolve(heat, T(y, z),build);

T(y,z) = _C1*exp(_c[1]*y)*_C2/z*WhittakerM(1/4*I*_c[1]^(1/2),0,_c[1]^(1/2)*z^2*I)+_C1*exp(_c[1]*y)*_C3/z*WhittakerW(1/4*I*_c[1]^(1/2),0,_c[1]^(1/2)*z^2*I); and in terms of Kummer functions for Maple 11: T(y,z) = _C1*exp(_c[1]*y)*_C2*exp(-1/2*I*_c[1]^(1/2)*z^2)*KummerM(1/2-1/4*I*_c[1]^(1/2),1,_c[1]^(1/2)*z^2*I)+_C1*exp(_c[1]*y)*_C3*exp(-1/2*I*_c[1]^(1/2)*z^2)*KummerU(1/2-1/4*I*_c[1]^(1/2),1,_c[1]^(1/2)*z^2*I); because of a change in the ODE solver, I think. Clearly, in Maple 9.52 the boundary conditions are not used. The same output is produced with the third boundary condition right or wrong. Other forms of solutions can be obtained, eg as sum:

pdsolve(heat, T(y, z),HINT=`+`,build);

T(y,z) = _c[1]*y+_C1-1/16*_c[1]*z^4+1/4*_c[1]*z^2+_C2*ln(z)+_C3; Yet, satisfying the boundary conditions is another issue...

In Maple 9.52, as well as Maple 11, 'pdsolve' uses separation of variables as default here:

pdsolve(heat, T(y, z));

`&where`(T(y,z) = _F1(y)*_F2(z),[{diff(_F1(y),y) = _c[1]*_F1(y), diff(_F2(z),`$`(z,2)) = (_F2(z)-z^2*_F2(z))*_c[1]-1/z*diff(_F2(z),z)}]); It solves the splitted system in terms of 'Whittaker' functions for Maple 9.5:

pdsolve(heat, T(y, z),build);

T(y,z) = _C1*exp(_c[1]*y)*_C2/z*WhittakerM(1/4*I*_c[1]^(1/2),0,_c[1]^(1/2)*z^2*I)+_C1*exp(_c[1]*y)*_C3/z*WhittakerW(1/4*I*_c[1]^(1/2),0,_c[1]^(1/2)*z^2*I); and in terms of Kummer functions for Maple 11: T(y,z) = _C1*exp(_c[1]*y)*_C2*exp(-1/2*I*_c[1]^(1/2)*z^2)*KummerM(1/2-1/4*I*_c[1]^(1/2),1,_c[1]^(1/2)*z^2*I)+_C1*exp(_c[1]*y)*_C3*exp(-1/2*I*_c[1]^(1/2)*z^2)*KummerU(1/2-1/4*I*_c[1]^(1/2),1,_c[1]^(1/2)*z^2*I); because of a change in the ODE solver, I think. Clearly, in Maple 9.52 the boundary conditions are not used. The same output is produced with the third boundary condition right or wrong. Other forms of solutions can be obtained, eg as sum:

pdsolve(heat, T(y, z),HINT=`+`,build);

T(y,z) = _c[1]*y+_C1-1/16*_c[1]*z^4+1/4*_c[1]*z^2+_C2*ln(z)+_C3; Yet, satisfying the boundary conditions is another issue...

In fact, I think that more interesting here and in that blog article, is the "discontinuity engineering" of the primitive/antiderivative function, moving the discontinuities on the complex plane away from the integration path. In that case, starting from the "golf court" obtain the "waterfall".

It is not clear for me, from the final comments in that blog article, whether the difficulty is of implementation (finding "good algorithms") or whether there is no algorithm at all.

But I have heard complaints about this subject from mathematicians using Maple or Mathematica in their courses over ten years ago and they have showed me as an example almost exactly the same integral (instead of 4 and 5 it was 1 and 2).

By the way, I still see the post by jpmay with its math partially upset.

use a Maple like input syntax, have 2D math input/output (using TeX fonts ?), and are stored as ASCII .gcw files with a Mathematica like syntax.

Note, this 2D math input/output regions provides an icon, or a right click menu option,  "Show keyboard syntax" opening a box showing 1D input/output. 1D input is converted on the flight to 2D.

Yes, it seems interesting.

 

 

 

use a Maple like input syntax, have 2D math input/output (using TeX fonts ?), and are stored as ASCII .gcw files with a Mathematica like syntax.

Note, this 2D math input/output regions provides an icon, or a right click menu option,  "Show keyboard syntax" opening a box showing 1D input/output. 1D input is converted on the flight to 2D.

Yes, it seems interesting.

 

 

 

I paste links in source mode. At least for me it works better.

I paste links in source mode. At least for me it works better.

My guess is that it is meant as in Open system

and explicitly forbiden in the licence, for me the Constitution applies in that no inhabitant of this nation can be deprived from his right to do what the law does not forbid.

 

Yes it says: GMP is distributed under the GNU LGPL.

But really it is meant that use of GSL by 'define_external' as above breaks GPL?

 

 

I guess that the bulk of the difficulty would lay in these library routines for algorithmic switching, as they could involve complex numeric issues. Otherwise, I do not see why Maplesoft has not implemented it already.

 

For convenience in maintenance, I prefer to keep the unix utilities ported to win32 and installed  by hand, separated in their own directory within the path. My choice is c:\binw.

 

 

For convenience in maintenance, I prefer to keep the unix utilities ported to win32 and installed  by hand, separated in their own directory within the path. My choice is c:\binw.

 

 

Sounds to me something similar to the way that the GMP library is used.