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Cannot understand sage polynomial factor notation

asked 2021-12-07 18:54:59 +0200

robbyyt gravatar image

Hello, I am generating a random polynomial over the field GF(2^6), and when I print it, I cannot undertstand the values of certain factors:

The polynomial looks like this: x^9 + (z6^5 + z6^3)*x + z6^4 + z6^2 + z6 What do z6, z6^5 mean? I searched but I was unable to find an answer in the docs.

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answered 2021-12-07 23:35:32 +0200

This arises when constructing the field.

sage: F = GF(64)
sage: F
Finite Field in z6 of size 2^6

The element "z6" is the generator of F over the prime field GF(2): the command F.gen() will return z6, and the documentation returned by F.gen?says 'Return a generator of "self" over its prime field, which is a root of "self.modulus()".' The documentation returned by F.modulus? says 'Return the minimal polynomial of the generator of "self" over the prime finite field.' In this case F.modulus() returns x^6 + x^4 + x^3 + x + 1.

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Thank you very much, I did not see that

robbyyt gravatar imagerobbyyt ( 2021-12-12 22:02:52 +0200 )edit

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Asked: 2021-12-07 18:54:59 +0200

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Last updated: Dec 07 '21