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Parallelization of modular algorithms. (English) Zbl 1229.13002

The title is a bit of an understatement, the results are also interesting without parallelisation. First, a modular algorithm for the computation of Gröbner bases is given. Its correctness was shown in [E. A. Arnold, “Modular algorithms for computing Gröbner bases”, J. Symb. Comput. 35, No. 4, 403-419 (2003; Zbl 1046.13018)] for the homegeneous case and in [G.-M. Greuel, G. Pfister, A Singular Introduction to Commutative Algebra. Berlin: Springer. (2007; Zbl 1133.13001)] for local orderings; here the case of global orderings is treated. Also, the paper contains a modular algorithm for the computation of associated primes of zero-dimensional ideals.

MSC:

13-04 Software, source code, etc. for problems pertaining to commutative algebra
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
65Y05 Parallel numerical computation
65Y04 Numerical algorithms for computer arithmetic, etc.
68W10 Parallel algorithms in computer science
68W30 Symbolic computation and algebraic computation
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References:

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