I would like to know how I can get the primitive polynomials to generate the points of the fields GF(7) and GF(9) using Mathematica. Any help is appreciated.
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Welcome to Mathematica.SE. Your questions could use a bit more details, so that people from other disciplines could help as well. – Sjoerd C. de Vries Aug 14 '15 at 15:14
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Hi, welcome to Mathematica.SE, please consider taking the tour so you learn the basic rules of the site. Here its considered helpful to share your code attempts, hopefully is a well formatted way, so we can quickly see the problem you are facing. Please edit your question and explain further what you need and what have you tried. Include definitions for $GF(n)$. – rhermans Aug 14 '15 at 15:16
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Crossposted (sort-of) at http://math.stackexchange.com/questions/1394575/primitive-polynomial-of-the-field-gf7-and-gf9 – Sjoerd C. de Vries Aug 14 '15 at 15:20
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(1) Find a primitive polynomial. Could use a method from this MSE thread. (2) Generate nonzero field elements from its powers. – Daniel Lichtblau Aug 16 '15 at 18:22
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The FiniteFields package should do what you want, if I understand the question correctly:
Needs["FiniteFields`"];
FieldIrreducible[GF[9], x]
(This was yielded by searching the docs for "galois", by the way. The fifth hit was immediately relevant. Do search the docs before posting, or make it clear why the documented functions don't do what you want.)
Patrick Stevens
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