boundry conditions for this rod setup 

@Rouben Rostamian  
Thanks for pointing this out
I'm not entirely sure what you mean exactly, but got a idea of it 
Yes, i am interested in the details of this setup 

https://www.dropbox.com/scl/fi/cuexecaf3x4wd5vwi28gv/pde-warmet-cilindrische-staaf.png?rlkey=9gob68msfpsdbksuemcxtwtiz&st=t6d7q09s&dl=0

restart:

infolevel[pdsolve] := 3:

assume(k > 0, L > 0):

PDE1D :=
    diff(V(z,t),t)
    =
    k*diff(V(z,t),z$2):

BC1 :=
    -k*D[1](V)(0,t)
    =
    q(t):

BC2 :=
    D[1](V)(L,t)
    =
    0:

IC :=
    V(z,0)
    =
    0:

problem1D := {PDE1D, BC1, BC2, IC}:

sol1D := pdsolve(
    problem1D,
    V(z,t)

This seems the right conditions for this experiment?

BC1 := -k*D[2](T)(r,0,t) = q(t);
BC2 := D[2](T)(r,L,t) = 0;
BC3 := D[1](T)(R,z,t) = 0;
BC4 := D[1](T)(0,z,t) = 0;
IC  := T(r,z,0) = 0;

@Earl 
Hello Earl , the display command ends with : (surpressing outcome),  use  ;  

3_regions_-_proceedure_-velocity_-temperatuur_profielen_7-7-2026.mw
a array plot ...?

Most close to get , so there is more involved ?
most_close_table_to_get_mprimes_7-7-2026.mw
Module code ( start)
3_regions_mprimes-verbeteringen_8-7-2026.mw

 

@dharr 
Thanks, Ctrl J, K  and Ctrl T gives text  and Ctrl M / Ctrl R  seems to me the important key combinations for working in Maple. 
Ctrl .  gives a section , handy too.
Ctrl  Z and Ctrl  X , do and undo. 

Does it depend on the solution family of the ODE that Maple apparently chooses?

Your expectation that the ODE output always uses set notation is probably not always possible.

@acer 

"Just to be clear, that P formula represents a product of terms (and not a sequence)."?

Just to be clear, that P formula represents a product of factors (and not a sequence)

Terms are used in a sum. 
Something went wrong with the message I wrote earlier, and a sentence was left out.
So it is a correction on your earlier sentence.

@acer 
"Just to be clear, that P formula represents a product of terms (and not a sequence)."?

Terms are related to a sum.

@Alfred_F 
Earlier versions of  Maple :  Maple's start-up message, 'Command the brilliance of 1,000 mathematicians'. :-)
 

Thus, from a mathematician’s perspective, this framework is essentially a symbolic ansatz engine expressed in neural-network notation. This also explains why the method ultimately yields explicit analytical formulas, such as Equation (12), rather than a trained predictive model.

In other words, the neural-network architecture serves primarily as a structured language for generating candidate solution families, while the actual determination of the parameters is carried out analytically through algebraic constraints derived from the differential equation. The process therefore resembles symbolic computation and exact-solution techniques far more than modern machine-learning approaches based on optimization and training.

@Alfred_F 
 "It's a shame that it's not as comfortable as in Cabri."  
But Cabri is not Maple and will probably never be  , so this comparison ?

with(plots):
p := [[3,6],[1,0],[4,2],[5,1]]:
X := map2(op,1,p): Y := map2(op,2,p):
display(
    polygonplot(p, color="Honeydew", thickness=2),
    pointplot([seq(seq([i,j], i=min(X)..max(X)), j=min(Y)..max(Y))], symbol=circle),
    pointplot(p, symbol=solidcircle, color="Red"),
    symbolsize=20, scaling=constrained, axes=none
);

Probably shortest code possibly ?, that's why i posted it 

Must be something in  a fraction :  value/0  , is this in de differential equation possible?