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subfields in finite fields

asked 2010-12-06 08:40:48 +0200

updated 2015-01-13 21:10:24 +0200

FrédéricC gravatar image

Hello! I have another problem with finitefields. I create a field, for example, GF(103^2) and later I use an element from it, which will be also an element of the subfield GF(103), i.e. a=99 is an element of both GF(103) and GF(103^2). But then the program doesn't convert "a" to an element of GF(103)... Do you know a method for this?

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can you update your question with a sample of the code you're using (and what fails to work)?

niles gravatar imageniles ( 2010-12-06 09:01:57 +0200 )edit

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answered 2010-12-06 14:06:29 +0200

Mike Hansen gravatar image

Sage does not try to automatically put elements in the smallest subfield that they belong to. You need to do that explicitly. You can use something like the line g = P(f) below which converts an element f from GF(103^2) to an element g of GF(103) :

sage: R.<a> = GF(103^2)
sage: P.<b> = GF(103)
sage: sage: f = R(99); f
sage: f.parent()
Finite Field in a of size 103^2
sage: g = P(f); g
sage: g.parent()
Finite Field of size 103
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Asked: 2010-12-06 08:40:48 +0200

Seen: 1,032 times

Last updated: Dec 06 '10