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Maple needs to be able to do the following: 
RootOf(z^2-3)/RootOf(z^2-2) mod 5  ->  3
Instead we have 
Normal(RootOf(z^2-3)/RootOf(z^2-2)) mod 5;
Error, (in mod/GetAlgExt) only the single algebraic extension case is implemented
I would also like to be able to factor and generally compute with polynomials whose coefficients involve multiple algebraic extensions mod p. These are basic fields, and it is somewhat sad that Maple has no way of computing in them.
algebra

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