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Is there any way how to work with modules over general rings? Most of the functions work only for modules over PID. For instance span and submoduledo not work if there are zero divisors. Ho does one work with submodules, say over Integers(8), or take the span of vectors over a non PID?

@ndomes Thanks for your answer. But is it possible to iterate on the entire space M? It does not have a list method.

I need to do a for loop on MatrixSpace(MatrixSpace(GF(2), 2), 1, 2) but it turns out to be impossible. Is there anyway to get around it?

Also, as the title says, on what structures is possible to iterate? I would imagine in structures with a natural order, but I am not sure about it.

If $I$ is an ideal of $R$, I would need to use something like

MatrixSpace(I, m, n)

However, the above doesn't work because $I$ is not a ring. How can I get all the matrices with entries from a specific ideal? Or even more generally, matrices with entries from a subset?

The command

MatrixSpace(R,n,m)

gives all the $n\times m$ matrices over R with a module structure. To construct ideals of matrix rings, I would need something like

MatrixSpace(I,n,m)

where $I$ is an ideal of $R$. But the above command would not work as $I$ is not a ring. Any suggestions what to do? Or more generally, how to construct the set of all matrices with entries from a given set?

@kcrisman Could you explain why the very same code does not work is I change the group $g$, say with, AdditiveAbelianGroup([2,2,2])? Thanks

@slelievre Please see the edited question.

@slelievre I fixed all your suggestions. Now I get "free variable 'x' referenced before assignment in enclosing scope". @kcrisman I tried that but I couldn't get the right syntax. Could you please help? It seems that character_table() does not have an attribute for abelian groups. Also, since I am new in sage, I thought it was worth it to try and define a function from scratch. I also having difficulties on using only the additive group of a finite field.

I am trying to calculate the character table of a finite field. The following is my code:

def character_table(q,n):
    k=GF(q^n)
    tr(x)=sum(x^(q^i) for i in [0..n-1])
    ksi = e^(2*pi*I/n)
    chi(x)=ksi^(tr(x))
    for a in k:
        L_a = [chi(a*x) for x in k]
        print L_a

And the TypeError is "free variable 'x' referenced before assignment in enclosing scope". Can somebody help me how to fix the code?

Thanks

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