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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Hensel and Newton methods in valuation rings
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by Joachim von zur Gathen PDF
Math. Comp. 42 (1984), 637-661 Request permission

Abstract:

We give a computational description of Hensel’s method for lifting approximate factorizations of polynomials. The general setting of valuation rings provides the framework for this and the other results of the paper. We describe a Newton method for solving algebraic and differential equations. Finally, we discuss a fast algorithm for factoring polynomials via computing short vectors in modules.
References
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Math. Comp. 42 (1984), 637-661
  • MSC: Primary 12J20; Secondary 65P05
  • DOI: https://doi.org/10.1090/S0025-5718-1984-0736459-9
  • MathSciNet review: 736459