Generic regular decompositions for generic zero-dimensional systems

Abstract Two new concepts, generic regular decomposition and regular-decomposition-unstable (RDU) variety for generic zero-dimensional systems, are introduced in this paper and an algorithm is proposed for computing a generic regular decomposition and the associated RDU variety of a given generic ze...
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Autor*in:	Tang, XiaoXian [verfasserIn] Chen, ZhengHong [verfasserIn] Xia, BiCan [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2014

Schlagwörter:	generic zero-dimensional system regular-decomposition-unstable variety parametric triangular decomposition generic regular decomposition

Übergeordnetes Werk:	Enthalten in: Science in China - Heidelberg : Springer, 2001, 57(2014), 9 vom: 08. Jan., Seite 1-14
Übergeordnetes Werk:	volume:57 ; year:2014 ; number:9 ; day:08 ; month:01 ; pages:1-14

Links:	Volltext

DOI / URN:	10.1007/s11432-013-5057-5

Katalog-ID:	SPR019315406

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allfields	10.1007/s11432-013-5057-5 doi (DE-627)SPR019315406 (SPR)s11432-013-5057-5-e DE-627 ger DE-627 rakwb eng 070 004 ASE 54.00 bkl Tang, XiaoXian verfasserin aut Generic regular decompositions for generic zero-dimensional systems 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Two new concepts, generic regular decomposition and regular-decomposition-unstable (RDU) variety for generic zero-dimensional systems, are introduced in this paper and an algorithm is proposed for computing a generic regular decomposition and the associated RDU variety of a given generic zero-dimensional system simultaneously. The solutions of the given system can be expressed by finitely many zero-dimensional regular chains if the parameter value is not on the RDU variety. The so called weakly relatively simplicial decomposition plays a crucial role in the algorithm, which is based on the theories of subresultants. Furthermore, the algorithm can be naturally adopted to compute a non-redundant Wu’s decomposition and the decomposition is stable at any parameter value that is not on the RDU variety. The algorithm has been implemented with Maple 16 and experimented with a number of benchmarks from the literature. Empirical results are also presented to show the good performance of the algorithm. generic zero-dimensional system (dpeaa)DE-He213 regular-decomposition-unstable variety (dpeaa)DE-He213 parametric triangular decomposition (dpeaa)DE-He213 generic regular decomposition (dpeaa)DE-He213 Chen, ZhengHong verfasserin aut Xia, BiCan verfasserin aut Enthalten in Science in China Heidelberg : Springer, 2001 57(2014), 9 vom: 08. Jan., Seite 1-14 (DE-627)385614764 (DE-600)2142898-0 1862-2836 nnns volume:57 year:2014 number:9 day:08 month:01 pages:1-14 https://dx.doi.org/10.1007/s11432-013-5057-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-BBI SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 54.00 ASE AR 57 2014 9 08 01 1-14
spelling	10.1007/s11432-013-5057-5 doi (DE-627)SPR019315406 (SPR)s11432-013-5057-5-e DE-627 ger DE-627 rakwb eng 070 004 ASE 54.00 bkl Tang, XiaoXian verfasserin aut Generic regular decompositions for generic zero-dimensional systems 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Two new concepts, generic regular decomposition and regular-decomposition-unstable (RDU) variety for generic zero-dimensional systems, are introduced in this paper and an algorithm is proposed for computing a generic regular decomposition and the associated RDU variety of a given generic zero-dimensional system simultaneously. The solutions of the given system can be expressed by finitely many zero-dimensional regular chains if the parameter value is not on the RDU variety. The so called weakly relatively simplicial decomposition plays a crucial role in the algorithm, which is based on the theories of subresultants. Furthermore, the algorithm can be naturally adopted to compute a non-redundant Wu’s decomposition and the decomposition is stable at any parameter value that is not on the RDU variety. The algorithm has been implemented with Maple 16 and experimented with a number of benchmarks from the literature. Empirical results are also presented to show the good performance of the algorithm. generic zero-dimensional system (dpeaa)DE-He213 regular-decomposition-unstable variety (dpeaa)DE-He213 parametric triangular decomposition (dpeaa)DE-He213 generic regular decomposition (dpeaa)DE-He213 Chen, ZhengHong verfasserin aut Xia, BiCan verfasserin aut Enthalten in Science in China Heidelberg : Springer, 2001 57(2014), 9 vom: 08. Jan., Seite 1-14 (DE-627)385614764 (DE-600)2142898-0 1862-2836 nnns volume:57 year:2014 number:9 day:08 month:01 pages:1-14 https://dx.doi.org/10.1007/s11432-013-5057-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-BBI SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 54.00 ASE AR 57 2014 9 08 01 1-14
allfields_unstemmed	10.1007/s11432-013-5057-5 doi (DE-627)SPR019315406 (SPR)s11432-013-5057-5-e DE-627 ger DE-627 rakwb eng 070 004 ASE 54.00 bkl Tang, XiaoXian verfasserin aut Generic regular decompositions for generic zero-dimensional systems 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Two new concepts, generic regular decomposition and regular-decomposition-unstable (RDU) variety for generic zero-dimensional systems, are introduced in this paper and an algorithm is proposed for computing a generic regular decomposition and the associated RDU variety of a given generic zero-dimensional system simultaneously. The solutions of the given system can be expressed by finitely many zero-dimensional regular chains if the parameter value is not on the RDU variety. The so called weakly relatively simplicial decomposition plays a crucial role in the algorithm, which is based on the theories of subresultants. Furthermore, the algorithm can be naturally adopted to compute a non-redundant Wu’s decomposition and the decomposition is stable at any parameter value that is not on the RDU variety. The algorithm has been implemented with Maple 16 and experimented with a number of benchmarks from the literature. Empirical results are also presented to show the good performance of the algorithm. generic zero-dimensional system (dpeaa)DE-He213 regular-decomposition-unstable variety (dpeaa)DE-He213 parametric triangular decomposition (dpeaa)DE-He213 generic regular decomposition (dpeaa)DE-He213 Chen, ZhengHong verfasserin aut Xia, BiCan verfasserin aut Enthalten in Science in China Heidelberg : Springer, 2001 57(2014), 9 vom: 08. Jan., Seite 1-14 (DE-627)385614764 (DE-600)2142898-0 1862-2836 nnns volume:57 year:2014 number:9 day:08 month:01 pages:1-14 https://dx.doi.org/10.1007/s11432-013-5057-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-BBI SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 54.00 ASE AR 57 2014 9 08 01 1-14
allfieldsGer	10.1007/s11432-013-5057-5 doi (DE-627)SPR019315406 (SPR)s11432-013-5057-5-e DE-627 ger DE-627 rakwb eng 070 004 ASE 54.00 bkl Tang, XiaoXian verfasserin aut Generic regular decompositions for generic zero-dimensional systems 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Two new concepts, generic regular decomposition and regular-decomposition-unstable (RDU) variety for generic zero-dimensional systems, are introduced in this paper and an algorithm is proposed for computing a generic regular decomposition and the associated RDU variety of a given generic zero-dimensional system simultaneously. The solutions of the given system can be expressed by finitely many zero-dimensional regular chains if the parameter value is not on the RDU variety. The so called weakly relatively simplicial decomposition plays a crucial role in the algorithm, which is based on the theories of subresultants. Furthermore, the algorithm can be naturally adopted to compute a non-redundant Wu’s decomposition and the decomposition is stable at any parameter value that is not on the RDU variety. The algorithm has been implemented with Maple 16 and experimented with a number of benchmarks from the literature. Empirical results are also presented to show the good performance of the algorithm. generic zero-dimensional system (dpeaa)DE-He213 regular-decomposition-unstable variety (dpeaa)DE-He213 parametric triangular decomposition (dpeaa)DE-He213 generic regular decomposition (dpeaa)DE-He213 Chen, ZhengHong verfasserin aut Xia, BiCan verfasserin aut Enthalten in Science in China Heidelberg : Springer, 2001 57(2014), 9 vom: 08. Jan., Seite 1-14 (DE-627)385614764 (DE-600)2142898-0 1862-2836 nnns volume:57 year:2014 number:9 day:08 month:01 pages:1-14 https://dx.doi.org/10.1007/s11432-013-5057-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-BBI SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 54.00 ASE AR 57 2014 9 08 01 1-14
allfieldsSound	10.1007/s11432-013-5057-5 doi (DE-627)SPR019315406 (SPR)s11432-013-5057-5-e DE-627 ger DE-627 rakwb eng 070 004 ASE 54.00 bkl Tang, XiaoXian verfasserin aut Generic regular decompositions for generic zero-dimensional systems 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Two new concepts, generic regular decomposition and regular-decomposition-unstable (RDU) variety for generic zero-dimensional systems, are introduced in this paper and an algorithm is proposed for computing a generic regular decomposition and the associated RDU variety of a given generic zero-dimensional system simultaneously. The solutions of the given system can be expressed by finitely many zero-dimensional regular chains if the parameter value is not on the RDU variety. The so called weakly relatively simplicial decomposition plays a crucial role in the algorithm, which is based on the theories of subresultants. Furthermore, the algorithm can be naturally adopted to compute a non-redundant Wu’s decomposition and the decomposition is stable at any parameter value that is not on the RDU variety. The algorithm has been implemented with Maple 16 and experimented with a number of benchmarks from the literature. Empirical results are also presented to show the good performance of the algorithm. generic zero-dimensional system (dpeaa)DE-He213 regular-decomposition-unstable variety (dpeaa)DE-He213 parametric triangular decomposition (dpeaa)DE-He213 generic regular decomposition (dpeaa)DE-He213 Chen, ZhengHong verfasserin aut Xia, BiCan verfasserin aut Enthalten in Science in China Heidelberg : Springer, 2001 57(2014), 9 vom: 08. Jan., Seite 1-14 (DE-627)385614764 (DE-600)2142898-0 1862-2836 nnns volume:57 year:2014 number:9 day:08 month:01 pages:1-14 https://dx.doi.org/10.1007/s11432-013-5057-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-BBI SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 54.00 ASE AR 57 2014 9 08 01 1-14
language	English
source	Enthalten in Science in China 57(2014), 9 vom: 08. Jan., Seite 1-14 volume:57 year:2014 number:9 day:08 month:01 pages:1-14
sourceStr	Enthalten in Science in China 57(2014), 9 vom: 08. Jan., Seite 1-14 volume:57 year:2014 number:9 day:08 month:01 pages:1-14
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	generic zero-dimensional system regular-decomposition-unstable variety parametric triangular decomposition generic regular decomposition
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isfreeaccess_bool	false
container_title	Science in China
authorswithroles_txt_mv	Tang, XiaoXian @@aut@@ Chen, ZhengHong @@aut@@ Xia, BiCan @@aut@@
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author	Tang, XiaoXian
spellingShingle	Tang, XiaoXian ddc 070 bkl 54.00 misc generic zero-dimensional system misc regular-decomposition-unstable variety misc parametric triangular decomposition misc generic regular decomposition Generic regular decompositions for generic zero-dimensional systems
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topic_title	070 004 ASE 54.00 bkl Generic regular decompositions for generic zero-dimensional systems generic zero-dimensional system (dpeaa)DE-He213 regular-decomposition-unstable variety (dpeaa)DE-He213 parametric triangular decomposition (dpeaa)DE-He213 generic regular decomposition (dpeaa)DE-He213
topic	ddc 070 bkl 54.00 misc generic zero-dimensional system misc regular-decomposition-unstable variety misc parametric triangular decomposition misc generic regular decomposition
topic_unstemmed	ddc 070 bkl 54.00 misc generic zero-dimensional system misc regular-decomposition-unstable variety misc parametric triangular decomposition misc generic regular decomposition
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title	Generic regular decompositions for generic zero-dimensional systems
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title_full	Generic regular decompositions for generic zero-dimensional systems
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title_sort	generic regular decompositions for generic zero-dimensional systems
title_auth	Generic regular decompositions for generic zero-dimensional systems
abstract	Abstract Two new concepts, generic regular decomposition and regular-decomposition-unstable (RDU) variety for generic zero-dimensional systems, are introduced in this paper and an algorithm is proposed for computing a generic regular decomposition and the associated RDU variety of a given generic zero-dimensional system simultaneously. The solutions of the given system can be expressed by finitely many zero-dimensional regular chains if the parameter value is not on the RDU variety. The so called weakly relatively simplicial decomposition plays a crucial role in the algorithm, which is based on the theories of subresultants. Furthermore, the algorithm can be naturally adopted to compute a non-redundant Wu’s decomposition and the decomposition is stable at any parameter value that is not on the RDU variety. The algorithm has been implemented with Maple 16 and experimented with a number of benchmarks from the literature. Empirical results are also presented to show the good performance of the algorithm.
abstractGer	Abstract Two new concepts, generic regular decomposition and regular-decomposition-unstable (RDU) variety for generic zero-dimensional systems, are introduced in this paper and an algorithm is proposed for computing a generic regular decomposition and the associated RDU variety of a given generic zero-dimensional system simultaneously. The solutions of the given system can be expressed by finitely many zero-dimensional regular chains if the parameter value is not on the RDU variety. The so called weakly relatively simplicial decomposition plays a crucial role in the algorithm, which is based on the theories of subresultants. Furthermore, the algorithm can be naturally adopted to compute a non-redundant Wu’s decomposition and the decomposition is stable at any parameter value that is not on the RDU variety. The algorithm has been implemented with Maple 16 and experimented with a number of benchmarks from the literature. Empirical results are also presented to show the good performance of the algorithm.
abstract_unstemmed	Abstract Two new concepts, generic regular decomposition and regular-decomposition-unstable (RDU) variety for generic zero-dimensional systems, are introduced in this paper and an algorithm is proposed for computing a generic regular decomposition and the associated RDU variety of a given generic zero-dimensional system simultaneously. The solutions of the given system can be expressed by finitely many zero-dimensional regular chains if the parameter value is not on the RDU variety. The so called weakly relatively simplicial decomposition plays a crucial role in the algorithm, which is based on the theories of subresultants. Furthermore, the algorithm can be naturally adopted to compute a non-redundant Wu’s decomposition and the decomposition is stable at any parameter value that is not on the RDU variety. The algorithm has been implemented with Maple 16 and experimented with a number of benchmarks from the literature. Empirical results are also presented to show the good performance of the algorithm.
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title_short	Generic regular decompositions for generic zero-dimensional systems
url	https://dx.doi.org/10.1007/s11432-013-5057-5
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