@Carl Love 

May be You are right that the author have to define the two terms, but I don't know if it would be right to give a definition of a term "command" in our book while in Maple documentation it is absent.

@Markiyan Hirnyk 

Thanks a lot for your attention to my question! This problem originated exactly in the same situation: we are writing a book devoted to a usage of Maple in learning Higher algebra course. I need to explain Maple routines, to call them 'a function' or 'a command'. In Maple documentation in similar situations sometimes the first one is used, and sometimes the second one. And it's a pity that a clear definition of a command in maple documentation is absent.

My first opinion was similar to Yours: that a Maple command is a more comprehensive concept and a function is a kind of command (a command may be created by a procedure etc). But the fact that different authors have different opinions confused me a bit.

And I fully agree with You that "The Maplesoft  profies' opinion would be interesting" and I think it would be not bad to attract Maple-creators attention to this fact.

PS The especial pleasure was to receive an answer from Ukraine! I have not knew about Your book, but I'll try to find it.   

Thanks a LOT, Mr Alejandro Jakubi! This is the Answer I hoped!  

Thanks a LOT, Mr Alejandro Jakubi! This is the Answer I hoped!  

Thanks for an answer! Certainly, I understand that it's much more faster! That's was just a (trivial) example of a task. Maple really helped to raise students' deep interest to study Abstract Algebra Course!!! So it's a pity indeed that such task can't be solved for tasks of such kind! In any way, Thanks a lot for Your interest to my question!

Thanks for an answer! Certainly, I understand that it's much more faster! That's was just a (trivial) example of a task. Maple really helped to raise students' deep interest to study Abstract Algebra Course!!! So it's a pity indeed that such task can't be solved for tasks of such kind! In any way, Thanks a lot for Your interest to my question!

Thanks for Your answer! The task is following:

To define whether the set of elements M={a+bsqrt(3)|a::integer,b::integer} is a group under addition/multiplication/some abstract operation.

Can such task be solved with the help of Maple? Or I can solve this task only for finite sets (where to define whether an operation is associative, has an identity and so on with a help of Maple is not hard).  

Thanks for Your answer! The task is following:

To define whether the set of elements M={a+bsqrt(3)|a::integer,b::integer} is a group under addition/multiplication/some abstract operation.

Can such task be solved with the help of Maple? Or I can solve this task only for finite sets (where to define whether an operation is associative, has an identity and so on with a help of Maple is not hard).  

Many thanks for Your attention to my question! but it is not the solution. I need an abstract set (infinite). I tried M:={a::integer+b::integer*sqrt(3)} but it fails.

Many thanks for Your attention to my question! but it is not the solution. I need an abstract set (infinite). I tried M:={a::integer+b::integer*sqrt(3)} but it fails.