@emendes 
I didn't write the code myself, but you did, which is a greater achievement..
A good introduktion code book is: Mathematical Computing - An  introduction to programming using Maple 

This is whole new approach for your coding problem

🧠 The Big Idea

The old code treats algebra as:

“a mathematical object that must be analyzed”

The new code treats algebra as:

“a data structure that can be manipulated directly”

And that is what makes it extremely fast.

Those polynomials are a datastructure in Maple 
"That is indeed correct: in Maple, polynomials are stored internally as a data structure (a DAG of operators such as +, *, ^). The terms of a sum are the operands of the + node.
By using convert(expr, list), you read those operands directly – without any mathematical interpretation. That is precisely why the new code is so fast."

generateNonlinearModelsPlusFast := proc(model::list, fullmodel::list, vars::list := [])
local missing, i, n, t;
    n := nops(model);
    missing := [seq(expand(fullmodel[i] - model[i]), i = 1..n)];
    [seq(seq(subsop(i = model[i] + t, model), t = convert(missing[i], list)), i = 1..n)];
end proc:

That's all what is left from your old code :-) , i am sorry
 

This code is aso using the datastructure approach for polynomials , but is less efficient
The first code is a improvement of this code 

#################################################
# NIEUWE ULTRAFAST VERSIE
#################################################

generateNonlinearModelsPlusFast :=

proc(model::list,
     fullmodel::list)

local missing,
      result,
      terms,
      i,
      t;

    missing := map2(

        (a,b) -> expand(b-a),

        model,
        fullmodel

    );

    result := [];

    for i from 1 to nops(model) do

        if type(missing[i], `+`) then

            terms := [op(missing[i])];

        else

            terms := [missing[i]];

        end if;

        for t in terms do

            result := [

                op(result),

                subsop(
                    i = model[i] + t,
                    model
                )

            ];

        end do;

    end do;

    return result;

end proc:

"@Alfred_F The beauty of the result you mentioned in the title is generated by the theoretical fact, not by some animations for a chord on a curve (easy to obtain)."
There are another 50 different proofs for this , if this is the correct number ?:-)

Its like the Phytagorian rule ..

I replaced the KroneckerRules module because it had reached the limits of its simplification capabilities.

This new module to build, uses a tensor-based approach and works structurally.

@Harry Garst 
dimensie_regels_voor_kronecker_en_gewone_matrices_10-5-2026.mw

Using these rules, you can determine which matrix dimensions to use and what the result of the matrix calculation will be of the dimension of the resulting matrix.

@Harry Garst 
I am interested in your code, but of course you’re keeping that to yourself :-)
Upload the existing code to the AI and ask for an educational explanation of the code, or request an explanation of how the code works for a presentation to others.
groet  Jan

matrixcalus_module_8-5-2026_.mw

It turns out that incorporating the entire factor analysis model into the module code is a step too far, and it is recommended to use Maple for this purpose instead.

The module code does contain some educational factor model commands, but they aren't suitable for real statistical work, are they?
Some improvemnents further....

@Harry Garst 
uitleg_vraag_mprimes_7-5-2026.mw

Groet Jan 

More matrix equations (polynome) to solve possible 
matrixcalus_module_7-5-2026.mw

@Harry Garst 

groeten Jan

@Harry Garst 
I tried some examples , much more need to be  tested.
matrixcalus_module_6-5-2026.mw

@Harry Garst 

I've created a MatrixCalculus module and focused on statistics as well. 
Attached a list of the features, but I have no idea if it works with real-world examples.

overzicht_mogelijkeheden_MatricCalculus_module.mw

@Harry Garst 

That doesn't surprise me at all; in Maple, too, there are ongoing developments in the mathematical topics that are implemented in the software.
That will always be the case as new mathematical knowledge is developed for theoretical or practical applications

AI is a great tool for researchers to ask questions.

I’ve also been working on that VEC operator and created a module for it that works structurally the same way as the Kronecker module.
I have no idea what the application is yet, but Kronecker products are also used in it.
Just for curosity. 

Groeten Jan

@Harry Garst 
I can do that for public use, why  not?

 groeten  Jan

How do I evaluate a simplified expression and determine the dimension matrix from module code?

kroneckerproducts_module_with_dimensioncheckDEF_5-5-2026_.mw