@Carl Love

Thank you for your teaching me a lot.
I hadn't noticed how data of Array and Matrix was stored in a computer as the rtable, 
before I read what you kindly wrote to me above.

@Carl Love 

Thank you for your detailed explanation.
As for as long as what you wrote, I could digest it well.

But, on the other hand, there are other things I couldn't understand in the result of the original code of
showstat(`convert/list` :: convert_rtable_to_nested_list);
That is,  its part of 

elif rtable_num_dims(rt) < dim then
   3       return rt[args[3 .. nargs]]
       else
   4       return [seq(procname(rt,dim+1,args[3 .. nargs],i),i = `if`(rtable_num_dims(rt) = 1,rtable_dims(rt),rtable_dims(rt)[dim]))]
       end if

Though I can guess that dim corresponds to your 2, then I can't understand why 2 is alloted to dim.
And, what is "args[3 .. nargs]" there? I understand the grammar of args[3..nargs] in itself, but
I don't understand why and how it is used in the present context. 

And, firstly, I can't understand why "convert_rtable_to_nested_list", which means a property following double collon"::"  in 

`convert/list` in showstat(`convert/list` :: convert_rtable_to_nested_list);

, can be, in turn, a procedure name which is shown in the contents of the result of the code 

 showstat(`convert/list` :: convert_rtable_to_nested_list);

like 

convert_rtable_to_nested_list := proc(rt, dim).

And, then, I can't understand why, for example, 

convert_rtable_to_nested_list(A,3)

does not work to bring some meaningful result other than convert_rtable_to_nested_list(the contents of A,3), though I just alloted the argument of (A, 3) to that procedure.

So, I will appreciate very much if you think further that you will teach me about these things.
But, I might be begging you too much. 
 

@Carl Love 

Thank you for your teaching.
By the way, what is the order attribute you mention.
I will appreciate if you give an example.

@tomleslie 

I sometimes feel that my ability on understanding anything is not so much.
In this case as well, I cannot find any essential distinctions except for comma between numbers.

To me CC and DD looks the same basically.

@acer 

Thank you for teaching me.

@Carl Love 

Sorry, Carl.

I couldn't understand the code of convert/list.
I will appreciate if you write some comments on the code.

Sorry.

@acer 

Thank you for teaching me a lot.
And, thank you for your detailed worksheet.
I could understand that 3 means the hight z, owing to you.

@acer 

Thank you. Owing to you, I could understand what I hadn't understood before.
I have another question.

1 of (3, 2, 1) = HFloat(-.832293673094284814) means 1 of x_1, and 2, which is at the end of (3,2,2), means 2 of x_2. So, I did understand. Then,
what is 3 at the end of (3, 2, 3)? What is 3 at the end of (2, 2, 3) = HFloat(1.)?

As vector has only two dimensions of x_1 and x_2, so I can't understand from where 3 appeared.
I hope you will give me an answer to this question of mine.

@acer 

Thank you.
I could get the output file with the way you kindly taught to me.

@Preben Alsholm 

Thank you for teaching me quite a lot.
As for the principal root, I couldn't understand till you teach it to me.
And, reading your answer, I found it necessary to solve the cubic equation to obtain 1+RootOf(_Z^2 + 3, index = 1).

I had thought only modifying x^3 + 8=0 was necessary to do it, and I couldn't do it.

Thank you for teaching me.

@acer 

Your way of how to use maple to have maple calculate step by step is, I think, one which is applicable widely to various calculation. It will be very helpful to me in using maple hereafter.

Thank you very much

@Kitonum 

Simplifying the double square was very difficult to me.
Your way to solve the problem is very helpful.
Thank you.
 

I tried what you mentioned, but even with parameters not numbers, factoring worked well.

example.mw

So, please append your file.

I think your worksheet might be necessary.

@acer 

Thank you for telling me the difference of the outputs according to the expression to which
the code is directed.