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How to show the elements of GF(2^4) as z^k instead of a_0*1+a_1*z+a_2*z^2+a_3*z^3

asked 2 years ago

agregatif2022 gravatar image

Hello, Sage shows elements of GF(2n) as their decomposition in GF(2n) viewed as a vector space over GF(2). But GF(2n) is also a field, whose multiplicative group is cyclic, so elements (except 0) have a natural description as zk with k in [0..(n1)]. How can I make Sage reveal this?

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answered 2 years ago

updated 2 years ago

If F = GF(32), then F.multiplicative_generator() returns a generator g of the cyclic group of units, and for a nonzero element a of F, if it happens to equal g^13, for example, then a._log_repr() returns the string '13'.

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Thank you so much, this is exactly what I was looking for!

agregatif2022 gravatar imageagregatif2022 ( 2 years ago )

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Asked: 2 years ago

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Last updated: Jun 13 '22