Items tagged with noncommutative-product

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I have a expression p:=C*A+A, when i type this to maple, maple display into p:=A*C+A because commutative property of multiplication

but I dont want to do like that. How can I display into p:=C*A+A?

I am trying to simplify noncommutative expressions that use the 'dot' operator: `.`. The following is a minimal example:

a2 . (1/(a2 . (1/a1) . a2)) . a2, which evaluates to:   a2 . (1/(a2 . (1/a1) . a2)) . a2

This should simplify to 'a1', as I am expecting `.` to work like noncommutative multiplication. If there is any way to define this behavior I would appreciate some help. Alternatively, I would also be happy with reworking 'simplify' to work in this scenario. If it helps, I am working with finitely presented groups. If you see the Maple package 'GroupTheory', you'll see that the 'Group' function has this built in. If we input generators and relators it will simplify expressions of the above type, so I know it can be done!

Lastly, I would prefer displaying '1/a1' as 'a1^-1', but that is just for aesthetics.

Here is a minimal document: minimalexample.mw

Dear all

Let q be  a real  different to one and for a fixed positive integer  n  given also 

 

Let x and y satisfies the condition

x*y -q*y*x=1

I will assume that the product is not commutative in all my computation

We would like to write the following function using only y

f(x,y)= x*y^n-q^n*y^n*x

 

all computation done I get f(x,y)=(q^n-1)/(q-1)*y^(n-1)

But how can I get the same result using Maple

Thank you very much for any help

 

 

 

 

 

 

  If I use

 

f:=(a+b)^2;
expand(f);

 

I got 

a^2+2ab+b^2

 

This result holds if ab=ba. Otherwise the result is a^2 + ab + ba + b^2

 

Is there any simpler way to obtain  a^2 + ab + ba + b^2? I looked up http://www.maplesoft.com/support/help/maple/view.aspx?path=dot

but did not find a solution :(

 

Thank you very much!

 

 

 

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