Complementary decompositions of monomial ideals and involutive bases

被引:2
作者
Hashemi, Amir [1 ,2 ]
Orth, Matthias [3 ]
Seiler, Werner M. [3 ]
机构
[1] Isfahan Univ Technol, Dept Math Sci, Esfahan 8415683111, Iran
[2] Inst Res Fundamental Sci IPM, Sch Math, Tehran 193955746, Iran
[3] Univ Kassel, Inst Math, D-34109 Kassel, Germany
关键词
Monomial ideals; Combinatorial decompositions; Involutive bases; Quasi-stable ideals; Primary decompositions; COMBINATORIAL DECOMPOSITIONS; ALGORITHM;
D O I
10.1007/s00200-022-00569-0
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
Complementary decompositions of monomial ideals-also known as Stanley decompositions-play an important role in many places in commutative algebra. In this article, we discuss and compare several algorithms for their computation. This includes a classical recursive one, an algorithm already proposed by Janet and a construction proposed by Hironaka in his work on idealistic exponents. We relate Janet's algorithm to the Janet tree of the Janet basis and extend this idea to Janet-like bases to obtain an optimised algorithm. We show that Hironaka's construction terminates, if and only if the monomial ideal is quasi-stable. Furthermore, we show that in this case the algorithm of Janet determines the same decomposition more efficiently. Finally, we briefly discuss how these results can be used for the computation of primary and irreducible decompositions.
引用
收藏
页码:791 / 821
页数:31
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