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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Computation of Galois groups
over function fields


Authors: Thomas Mattman and John McKay
Journal: Math. Comp. 66 (1997), 823-831
MSC (1991): Primary 12F10, 12Y05
MathSciNet review: 1401943
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Abstract | References | Similar Articles | Additional Information

Abstract: Symmetric function theory provides a basis for computing Galois groups which is largely independent of the coefficient ring. An exact algorithm has been implemented over $\mathbb Q (t_1,t_2,\ldots ,t_m)$ in Maple for degree up to 8. A table of polynomials realizing each transitive permutation group of degree 8 as a Galois group over the rationals is included.


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Additional Information

Thomas Mattman
Affiliation: Mathematics Department, McGill University, Montréal, H3A 2K6, Canada
Email: mattman@math.mcgill.ca

John McKay
Affiliation: Centre Interuniversitaire en Calcul Mathématique Algébrique \ Concordia University \ Montréal, H3G 1M8, Canada
Email: mckay@cs.concordia.ca

DOI: http://dx.doi.org/10.1090/S0025-5718-97-00831-4
PII: S 0025-5718(97)00831-4
Keywords: Galois groups, polynomials, computation
Received by editor(s): June 12, 1995
Received by editor(s) in revised form: December 7, 1995
Additional Notes: Research supported by NSERC and FCAR of Québec.
Article copyright: © Copyright 1997 American Mathematical Society