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Algorithms for Primary Decomposition

Thesis Info

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Author

Idrees, Nazeran

Program

PhD

Institute

Government College University

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2006

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/1029

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725452343

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The primary decomposition methods of Eisenbud, Huneke and Vasconcelos are anal- ysed in detail providing proofs of important theorems and all the corresponding al- gorithms are programmed in the language of Singular. MOreover, we investigated the parallelization of two modular algorithms. In fact, we consider the modular com- putation of Gr ̈obner bases (resp. standard bases) and the modular computation of the associated primes of a zero–dimensional ideal and describe their parallel imple- mentation in Singular. The algorithms of Shimoyama and Yokoyama for primary decomposition of ideals are generalized to submodules of a free module over the polynomial ring in several variables with coefficients in a field. The algorithms are implemented in Singular.
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