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Extension/coercion of finite rings & fields

asked 2013-02-28 09:18:17 -0500

GaryMak gravatar image

updated 2013-02-28 23:06:19 -0500

Hi ...

again harping on my theme of p-adics: here is a characteristic-p toy model of the problem I had here. Will someone please tell me how to do what this code is trying to do?!!

sage: K.<X> = GF(3^2,name='X'); # creates (residue) field which is GF(3)[X]
sage: R = IntegerModRing(3^2)[X];  # extends Z/p^2 by that same X to form quadratic extn - seemingly successfully
sage: print R(X+5); # I try to use X but it still treats it like an "alien" quantity in R ....

thanks!!

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answered 2013-02-28 10:46:35 -0500

fidbc gravatar image

updated 2013-02-28 14:05:52 -0500

Sorry my previous answer was completely wrong.

Perhaps if you use

sage: y=R.gen()

and then

sage: R(y+5)
X+5
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Thank you very much. That certainly solves that problem - I'm now up to the next level of incomprehensibility at least!!

GaryMak gravatar imageGaryMak ( 2013-02-28 23:05:35 -0500 )edit

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Asked: 2013-02-28 09:18:17 -0500

Seen: 206 times

Last updated: Feb 28 '13