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Mathematics of Computation

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Hensel and Newton methods in valuation rings

Author: Joachim von zur Gathen
Journal: Math. Comp. 42 (1984), 637-661
MSC: Primary 12J20; Secondary 65P05
MathSciNet review: 736459
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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.

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Keywords: Valuation, factorization of polynomials, short vector algorithm, Hensel’s method, Newton’s method, partial differential equations
Article copyright: © Copyright 1984 American Mathematical Society