Computing in
Author:
Jacob T. B. Beard
Journal:
Math. Comp. 28 (1974), 11591166
MSC:
Primary 12C05; Secondary 1204
MathSciNet review:
0352058
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Abstract: This paper gives an elementary deterministic algorithm for completely factoring any polynomial over , criteria for the identification of three types of primitive polynomials, an exponential representation for which permits direct rational calculations in as opposed to modular arithmetic over , and a matrix representation for which admits computer computations. The third type of primitive polynomial examined permits the given representation of to display a primitive normal basis over . The techniques developed require only the usual addition and multiplication of square matrices over . Partial tables from computer programs based on certain of these results will appear in later papers.
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 [2]
 J. T. B. BEARD, JR., "Matrix fields over prime fields," Duke Math. J., v. 39, 1972, pp. 313322. MR 0313269 (47:1824)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197403520589
PII:
S 00255718(1974)03520589
Keywords:
Factorization,
arithmetic in finite fields,
irreducibility criterion,
primitive polynomials,
primitive normal bases,
Euler function,
exponent,
linear polynomial,
algebraic closure
Article copyright:
© Copyright 1974 American Mathematical Society
