Portal de Periódicos da CAPES

Hensel and Newton methods in valuation rings

1984; American Mathematical Society; Volume: 42; Issue: 166 Linguagem: Inglês

10.1090/s0025-5718-1984-0736459-9

1088-6842

Joachim von zur Gathen,

Complexity and Algorithms in Graphs

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.