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New algorithms for computing primary decomposition of polynomial ideals. (English) Zbl 1229.13003
Fukuda, Komei (ed.) et al., Mathematical software – ICMS 2010. Third international congress on mathematical software, Kobe, Japan, September 13–17, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-15581-9/pbk). Lecture Notes in Computer Science 6327, 233-244 (2010).
Summary: We propose a new algorithm and its variant for computing a primary decomposition of a polynomial ideal. The algorithms are based on the Shimoyama-Yokoyama algorithm [T. Shimoyama and K. Yokoyama, J. Symb. Comput. 22, No. 3, 247–277 (1996; Zbl 0874.13022)] in the sense that all the isolated primary components $$Q _{1},\dots ,Q _{r }$$ of an ideal $$I$$ are first computed from the minimal associated primes of $$I$$. In order to extract the remaining primary components we use $$I:Q$$ where $$Q = Q _{1} \cap \dots \cap Q _{r }$$. Our experiment shows that the new algorithms can efficiently decompose some ideals which are hard to be decomposed by any of known algorithms.
For the entire collection see [Zbl 1196.68008].

##### 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) 13C05 Structure, classification theorems for modules and ideals in commutative rings 68W30 Symbolic computation and algebraic computation
##### Software:
Macaulay2; Risa/Asir; SINGULAR
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