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There is something wrong with the generator of a finite field

asked 2014-09-18 09:46:56 -0500

updated 2015-01-13 11:16:44 -0500

FrédéricC gravatar image

Hi, I am using the sentence" K.<g>=GF(q) " to generate a finite field F_q. When q is a power bigger than 1 of a prime, it is OK. However, when q is a prime, then g turns to be 1. Apparently, 1 is not a generator of a finite field, at least not a generator of the multiplicative group F_{q}^{*}

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answered 2014-09-18 10:10:45 -0500

tmonteil gravatar image

updated 2014-09-18 10:13:13 -0500

Actually 1 is a generator of the kield K if q is prime, since K is the smallest field containing 1.

If you want a generator of the multiplicative group K^*, you can do:

sage: K.multiplicative_generator()
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Asked: 2014-09-18 09:46:56 -0500

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Last updated: Sep 18 '14