### Examining the quotients of a module $R\times R$ where $R$ is a finite ring.

I'm new to Sage, and I've been struggling to get started with (what I thought) should be a basic construction.

I have an $8$-element commutative ring $R$ which is constructed as a quotient of a polynomial ring in two variables. I need to examine all of the quotient of the right $R$ module $R\times R$.

I tried to use `M=R^2`

and got something that looked promising, but when I tried to use the `quotient_module`

method, I kept getting errors. I saw in the docs for that method that quotient_module isn't fully supported, so I started looking at the CombinatorialFreeModule class too.

Can someone recommend an idiomatic way to accomplish the task?

I have been plagued by NotImplemented errors and a myriad of other error messages every step of the way, even when just attempting to find a method to list all elements of my $8$ element ring. All the examples I've seen really look like they stick to basic linear algebra, or free $\mathbb Z$ modules. I just want to do something similar for my small ring of $8$ elements.

N.B. I will work to supply specific error messages and code later today: I'm away from my workstation that has Sage installed right now.

Here's what I've been trying:

```
k # <- (finite field of size 2)
R.<x,y>=PolynomialRing(k)
S = R.quotient([x^2, x*y, y^3])
list(S) # <-- NotImplementedError("object does not support iteration") I noticed it worked for the univariate case though. What's a good way to recover the elements?
M = S^2
v = M.gens()
M.quotient_module([v[0]]) # <- ValueError("unable to compute the row reduced echelon form") TypeError("self must be an integral domain.")
```

Had the same problem with a univariate polynomial ring over $F_2$ mod $(x^3)$.

Is there some other class that can handle such as simple construction?