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Solving via modular methods

: Afzal, D.; Kanwal Janjua, F; Pfister, G.; Steidel, S.


Ibadula, D.:
Bridging Algebra, Geometry, and Topology
Cham: Springer International Publishing, 2014 (Springer Proceedings in Mathematics & Statistics 96)
ISBN: 978-3-319-09185-3 (Print)
ISBN: 978-3-319-09186-0 (Online)
Book Article
Fraunhofer ITWM ()

In this chapter we present a parallel modular algorithm to compute all solutions with multiplicities of a given zero-dimensional polynomial system of equations over the rationals. In fact, we compute a triangular decomposition using Möller’s algorithm (Möller, Appl. Algebra Eng. Commun. Comput. 4:217–230, 1993) of the corresponding ideal in the polynomial ring over the rationals using modular methods, and then apply a solver for univariate polynomials.