### groups of units and finite quotient rings

Dear Sage,
I am not an expert in using the program and I will be grateful if you help me to do the following.
(1) Define the quotient ring R=F_q[u]/(u^2+2)
(2) List the elements of this ring
(3) Define the polynomial ring R[T]
(4) Compute the group of units U(R) of this ring and its cardinality
(2) Factorize T^3+(u+2) in R[T]
(4) Compute the span <t,t-1> in U(R)
You can e-mail me back (eslam60145@yahoo.com)
Thank you in advance.
Best Regards.
Eslam