ASKSAGE: Sage Q&A Forum - Latest question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 07 Mar 2018 08:28:00 -0600Examining the quotients of a module $R\times R$ where $R$ is a finite ring.https://ask.sagemath.org/question/41421/examining-the-quotients-of-a-module-rtimes-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.
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 $(x^3)$.
Obviously the messages are informative enough about what they think is wrong. But this seems like such an elementary task... is there some other class that can handle such a construction?rschwiebWed, 07 Mar 2018 08:28:00 -0600https://ask.sagemath.org/question/41421/