I appreciate your help Professor Grabmeier. I must admit I'm astonished to 
learn that we need tricks to do elementary algebra in a computer algebra system.

------- Original Message -------
On Tuesday, July 18th, 2023 at 8:44 PM, Prof. Dr. Johannes Grabmeier 
<[email protected]> wrote:

> To Ralf's very useful remarks to answer your question let me add the
> following trick, which seems to be very userful for beginners, too: The
> trick is to define (interpreter) variables a, b and c which point to
> objects in the desired distributed domain, which are a, b, c. This
> forces the interpreter not to choose Polynomal Integer , but direktly
> allows to do the desired operation in dmp.
> 
> (7) -> dmp := DMP([a,b,c], Integer)
> 
> 
> (7) DistributedMultivariatePolynomial([a,b,c],Integer)
> Type: Type
> (8) -> a : dmp := a
> 
> 
> (8) a
> Type:
> DistributedMultivariatePolynomial([a,b,c],Integer)
> (9) -> b : dmp := b
> 
> 
> (9) b
> Type:
> DistributedMultivariatePolynomial([a,b,c],Integer)
> (10) -> c : dmp := c
> 
> 
> (10) c
> Type:
> DistributedMultivariatePolynomial([a,b,c],Integer)
> (11) -> (a+b)*c
> 
> 
> (11) a c + b c
> Type:
> DistributedMultivariatePolynomial([a,b,c],Integer)

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