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View all copies of this ISBN edition:. Synopsis About this title Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields. About the Author : Gary L. Daniel Panario is a professor of mathematics at Carleton University. Review : " Buy New Learn more about this copy.

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Customers who bought this item also bought. Stock Image. Published by Crc Press, UK New Hardcover Quantity Available: 1. Seller Rating:. New Quantity Available: 1. Majestic Books London, ,, United Kingdom. Mullen, Daniel Panario. New Hardcover Quantity Available: 5. The non-zero elements of a finite field form a cyclic group under multiplication.

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It is necessarily irreducible. The Conway polynomial is chosen to be primitive, so that each of its roots generates the multiplicative group of the associated finite field.

Computational linear algebra over finite fields

The subfields of F p n are fields F p m with m dividing n. The cyclic group formed from the non-zero elements of F p m is a subgroup of the cyclic group of F p n. This necessitates that f m x divide f n x r. This notion of compatibility is called norm-compatibility by some authors.

The Conway polynomial for a finite field is chosen so as to be compatible with the Conway polynomials of each of its subfields. That it is possible to make the choice in this way was proved by Werner Nickel. The Conway polynomial C p , n is defined as the lexicographically minimal monic primitive polynomial of degree n over F p that is compatible with C p , m for all m dividing n. The notion of lexicographical ordering used is the following:.

Since there does not appear to be any natural mathematical criterion that would single out one monic primitive polynomial satisfying the compatibility conditions over all the others, the imposition of lexicographical ordering in the definition of the Conway polynomial should be regarded as a convention.

Algorithms for computing Conway polynomials that are more efficient than brute-force search have been developed by Heath and Loehr. From Wikipedia, the free encyclopedia. GAP 4 Manual.

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The GAP Group. Retrieved 8 February Archived from the original on 20 July Retrieved 9 February