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Analyzing the Dual Space of the Saturate...

Li, Xiaoliang...

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Analyzing the Dual Space of the Saturated Ideal of a Regular Set and the Local Multiplicities of its Zeros by Li, Xiaoliang ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	04-08-2023
Summary	In this paper, we are concerned with the problem of counting the multiplicities of a zero-dimensional regular set's zeros. We generalize the squarefree decomposition of univariate polynomials to the so-called pseudo squarefree decomposition of multivariate polynomials, and then propose an algorithm for decomposing a regular set into a finite number of simple sets. From the output of this algorithm, the multiplicities of zeros could be directly read out, and the real solution isolation with multiplicity can also be easily produced. As a main theoretical result of this paper, we analyze the structure of dual space of the saturated ideal generated by a simple set as well as a regular set. Experiments with a preliminary implementation show the efficiency of our method.
ISBN	-
Item Type	Article
File Type	pdf
File Size	29.34 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/1311.6897

Citation

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AMA 11th EditionReferences

Li, Xiaoliang. Analyzing the Dual Space of the Saturated Ideal of a Regular Set and the Local Multiplicities of its Zeros. Australian National University. August 04, 2023. Accessed September 20, 2024. https://online.provdatabase.com/cite/10760

APA 7th EditionReferences

Li, Xiaoliang. (2023). Analyzing the Dual Space of the Saturated Ideal of a Regular Set and the Local Multiplicities of its Zeros. Australian National University. https://online.provdatabase.com/cite/10760

Chicago 17th EditionReferences

Li, Xiaoliang. Analyzing the Dual Space of the Saturated Ideal of a Regular Set and the Local Multiplicities of its Zeros. Australian National University. 2023. https://online.provdatabase.com/cite/10760

HarvardReferences

Li, Xiaoliang. (2023). Analyzing the Dual Space of the Saturated Ideal of a Regular Set and the Local Multiplicities of its Zeros. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/10760. (Accessed 20 September 2024).

Harvard AustraliaReferences

Li, Xiaoliang, 2023, Analyzing the Dual Space of the Saturated Ideal of a Regular Set and the Local Multiplicities of its Zeros, Australian National University, viewed 20 September 2024, <https://online.provdatabase.com/cite/10760>

MLA 9th EditionWorks Cited

Li, Xiaoliang. Analyzing the Dual Space of the Saturated Ideal of a Regular Set and the Local Multiplicities of its Zeros. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/10760.

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