The equations should be explicitly real, so that Re(iQ) should be -Q_i, etc.

But the main issue is whether the Maple numeric pde solver could handle integrodifferential equations - I do not believe so. If not, you should go back and look for fully differential equations for Q_r and Q_i.

Before the label I get:

dismantle(Norm);

NAME(5): Norm #[protected, _syslib]

while, after the label:

dismantle(Norm);

NAME(5): LinearAlgebra:-Norm #[`:-10267`, modulename = LinearAlgebra]

On the other hand:

dismantle(LinearAlgebra:-Norm);

NAME(5): LinearAlgebra:-Norm #[modulename = LinearAlgebra, protected]

I think that the package _UIUtils might be involved here. If this were true, because of its unusual code, I would not be surprised that strange things occur.

What you apparently mean is not an equation, but the so called Theory of everything, which is really a paradigm held by some theoretical physicists.

You just write b_x=b_{xr}+i*b_{xi}, etc. No problem as these equations are linear. But the key point is the number of coordinates. Note that ?pdsolve/numeric state:

PDEsys     - single or set or list of time-dependent partial differential equations in two independent variables

Though you have not written the dependency of the functions, out of the partial derivatives that you are writing it sounds that you may have problems to solve this system numerically with Maple.

You just write b_x=b_{xr}+i*b_{xi}, etc. No problem as these equations are linear. But the key point is the number of coordinates. Note that ?pdsolve/numeric state:

PDEsys     - single or set or list of time-dependent partial differential equations in two independent variables

Though you have not written the dependency of the functions, out of the partial derivatives that you are writing it sounds that you may have problems to solve this system numerically with Maple.

comment the line with #

My technique was more primitive, the text search of an editor. This way, I could identify in the Maple 12 library these names:

  
INTERFACE_ACML 
INTERFACE_ACMLPLOT3D  
INTERFACE_ADML  
INTERFACE_CALLBACK  
INTERFACE_CHAR  
INTERFACE_DEBUG_READLINE  
INTERFACE_DIAG  
INTERFACE_DONE  
INTERFACE_ERROR  
INTERFACE_EXCEL_EXPORT  
INTERFACE_EXCEPT  
INTERFACE_GET  
INTERFACE_HELP  
INTERFACE_INFO  
INTERFACE_INTR  
INTERFACE_JAVA  
INTERFACE_JVM  
INTERFACE_LICENSE  
INTERFACE_LOGO  
INTERFACE_LPRINT  
INTERFACE_MAPLET  
INTERFACE_MAPLETPIPE  
INTERFACE_MAPLET_STATUS  
INTERFACE_PLOT  
INTERFACE_PLOT3D  
INTERFACE_PRINT  
INTERFACE_READLINE  
INTERFACE_REDIRECT  
INTERFACE_RESTART  
INTERFACE_RESULT  
INTERFACE_SECURITY  
INTERFACE_SET  
INTERFACE_START  
INTERFACE_STATUS  
INTERFACE_STOP  
INTERFACE_SYSTEM  
INTERFACE_TEXT  
INTERFACE_WARN  
INTERFACE_WORKSHEET  

What is missing in this list?

In the mean time, until Jacques gets his decent block of time, I have got something useful with the inverse problem: list all the routines that a routine may depend on.

The undocumented routine tools/get_functions_called seems in principle designed for this purpose. It works on the inert representation of the routine (that produced by ToInert), and produces a list like:

`tools/get_functions_called`(sin);
  ["&*", "Im", "JacobiSN", "Re", "arctan", "automap", "complex", 
"cos", "csgn", "evalf", "frac", "has", "identical", "if", "iquo", 
"is", "map", "member", "nops", "op", "select", "selectremove", 
"sin", "sin/normal", "sinh", "specfunc", "sqrt", "subsop", 
"tools/sign", "traperror", "trig/linear_in_Pi", "trunc", "type"]

Note, however, that the code of sin contains a call to NumericTools:-ThrowUndefined:

showstat(sin,8);
sin := proc(x::algebraic)
local res, n, t, pull_out, keep_in, tmp;
       ...
   8     res := NumericTools:-ThrowUndefined(x,('preserve') = 
         ('axes'))
       ...
end proc

but NumericTools:-ThrowUndefined is missing in the above list. So, I have found that tools/get_functions_called does not catch module exports and some other "complex" routine names. I.e., as it stands, it is only partially useful for pursuing an answer to this inverse problem.

One thing that I have been (slowly) looking at are streams, barely mentioned in the documentation, e.g. within ?OpenMaple,VB,streamCallBack, not the most sensible place, in my opinion. And most of the 40 or so that I have identified, are completely undocumented. By black-box testing I have found how a few of them work, but this should be unnecesary. Why Maplesoft does not document this stuff?

I wonder whether those streams are the "communications channels" that you are talking about.    

 

For setting this problem up in Maple you should write it in expanded form, and better split real and imaginary parts as Maple numeric pde solver does not seem to work with complex equations.

For setting this problem up in Maple you should write it in expanded form, and better split real and imaginary parts as Maple numeric pde solver does not seem to work with complex equations.

In this regard, I have been using the late versions of the wxMaxima GUI for Maxima. I would say that it is at a level of functionality like that of Maple V Release 4 worksheet GUI or beyond, more than enough for educational purposes. As it is opensource, multiplatform and (as I have read) it is being developed by just two persons in their spare time, I would find surprising that something similar could not be developed for Maple without much investment.

I will need one or two weeks to process the information contained in Jacques post, as my background is far away from CS and pure math fields. I would be delighted to read replies from the experts in the mean time.

I get:

with(Units:-Standard):
UseSystem(AddSystem(SI,degree[angle])):
sin(Unit(30*arcdeg));

                                 1/2

arcsin(sin(Unit(30*arcdeg)));

                                  Pi
                                 ----
                                  6

I would have expected in this context 30 [arcdeg] or something like that.