Hi all,

I want to define a two sided ideal I=[x*y*x*y-x*y, y*x*y*x-x*y*x] in an unital 
associative free algebra F.<x,y>. (not just in a free algebra) 

I wrote in sage:

F.<x,y>=FreeAlgebra(QQ, implementation='letterplace')
I=F*[x*y*x*y-x*y, y*x*y*x-x*y*x]*F
I()

"But, the error I have faced to is the following:

ArithmaticError: Can only subtract the elements of the same degree."


Also I want to know how can I create a non-commutative infinite dimensional 
quotient algebra F/I.

Is there any way to define such an ideal and this quotient in sage or other 
part of sage like Gap or Singular?

Thanks

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