The problem is as follows:

1- define r := rem(x^3+x+1, x^2+x+1, x, 'q')

2- then once you evaluate this expression, in variables list you may see r as the only variable, whereas q is the quotient variable and it is not provided there.

3- for example if you evaluate q it will give x-1

4- or even you can get the assigned varibles list by anames(user) and it gives both r an q

5- the question is: why q is not shown in variables list