Solving via modular methods. (English) Zbl 1328.13037

Ibadula, Denis (ed.) et al., Bridging algebra, geometry, and topology. Selected papers based on the presentations at the international conference “Experimental and theoretical methods in algebra, geometry and topology”, Eforie Nord, Romania, June 20–25, 2013. Cham: Springer (ISBN 978-3-319-09185-3/hbk; 978-3-319-09186-0/ebook). Springer Proceedings in Mathematics & Statistics 96, 1-9 (2014).
Summary: 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 H. M. Möller’s algorithm [Appl. Algebra Eng. Commun. Comput. 4, No. 4, 217–230 (1993; Zbl 0793.13013)] of the corresponding ideal in the polynomial ring over the rationals using modular methods, and then apply a solver for univariate polynomials.
For the entire collection see [Zbl 1303.00054].


13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)


Zbl 0793.13013
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