Computing Generic Fibers of Polynomial Ideals with FGLM and Hensel Lifting

We describe a version of the FGLM algorithm that can be used to compute generic fibers of positive-dimensional polynomial ideals. It combines the FGLM algorithm with a Hensel lifting strategy. In analogy with Hensel lifting, we show that this algorithm has a complexity quasi-linear in the number of...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:arXiv.org
Hlavní autoři: Berthomieu, Jérémy, Mohr, Rafael
Médium: Paper
Jazyk:angličtina
Vydáno: Ithaca Cornell University Library, arXiv.org 19.09.2024
Témata:
Algorithms
Hoisting
Polynomials
ISSN:2331-8422
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Abstract We describe a version of the FGLM algorithm that can be used to compute generic fibers of positive-dimensional polynomial ideals. It combines the FGLM algorithm with a Hensel lifting strategy. In analogy with Hensel lifting, we show that this algorithm has a complexity quasi-linear in the number of terms of certain \(\mathfrak{m}\)-adic expansions we compute. Some provided experimental data also demonstrates the practical efficacy of our algorithm.
AbstractList We describe a version of the FGLM algorithm that can be used to compute generic fibers of positive-dimensional polynomial ideals. It combines the FGLM algorithm with a Hensel lifting strategy. In analogy with Hensel lifting, we show that this algorithm has a complexity quasi-linear in the number of terms of certain \(\mathfrak{m}\)-adic expansions we compute. Some provided experimental data also demonstrates the practical efficacy of our algorithm.
Author Berthomieu, Jérémy
Mohr, Rafael
Author_xml – sequence: 1
  givenname: Jérémy
  surname: Berthomieu
  fullname: Berthomieu, Jérémy
– sequence: 2
  givenname: Rafael
  surname: Mohr
  fullname: Mohr, Rafael
BookMark eNotjTtPwzAYAC0EEqX0B7BZYk6wP7-SEUUkLQqCoXtlJza4Su0SJzz-PUUw3XK6u0LnIQaL0A0lOS-EIHd6_PIfOXACOWGU8zO0AMZoVnCAS7RKaU8IAalACLZAj1U8HOfJh1fc2GBH3-HaGzsmHB1-icN3iAevB7zprR4S_vTTG66b9gnr0OO1DckOuPXuN3CNLtzJsat_LtG2fthW66x9bjbVfZtpAZCVvKOKE2cMZcbpvtBC9KZzVEDBjFG0tNIapTvFZO-0cZwZpmkvlWGFUJot0e1f9jjG99mmabeP8xhOxx2UAFISwYH9AFnuT_8
ContentType Paper
Copyright 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml – notice: 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
DBID 8FE
8FG
ABJCF
ABUWG
AFKRA
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
HCIFZ
L6V
M7S
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PTHSS
DOI 10.48550/arxiv.2402.03144
DatabaseName ProQuest SciTech Collection
ProQuest Technology Collection
Materials Science & Engineering Collection
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
ProQuest Central Essentials
ProQuest Central
ProQuest Technology Collection
ProQuest One
ProQuest Central
SciTech Premium Collection
ProQuest Engineering Collection
Engineering Database
ProQuest Central Premium
ProQuest One Academic
ProQuest Publicly Available Content Database
ProQuest One Academic Middle East (New)
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Applied & Life Sciences
ProQuest One Academic (retired)
ProQuest One Academic UKI Edition
ProQuest Central China
Engineering Collection
DatabaseTitle Publicly Available Content Database
Engineering Database
Technology Collection
ProQuest One Academic Middle East (New)
ProQuest Central Essentials
ProQuest One Academic Eastern Edition
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
ProQuest Technology Collection
ProQuest SciTech Collection
ProQuest Central China
ProQuest Central
ProQuest One Applied & Life Sciences
ProQuest Engineering Collection
ProQuest One Academic UKI Edition
ProQuest Central Korea
Materials Science & Engineering Collection
ProQuest Central (New)
ProQuest One Academic
ProQuest One Academic (New)
Engineering Collection
DatabaseTitleList Publicly Available Content Database
Database_xml – sequence: 1
  dbid: PIMPY
  name: Publicly Available Content Database
  url: http://search.proquest.com/publiccontent
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Physics
EISSN 2331-8422
Genre Working Paper/Pre-Print
GroupedDBID 8FE
8FG
ABJCF
ABUWG
AFKRA
ALMA_UNASSIGNED_HOLDINGS
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
FRJ
HCIFZ
L6V
M7S
M~E
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PTHSS
ID FETCH-LOGICAL-a522-94c1740fbb13bfad8a55dbcf15283bb719e6eb7ac736dfabf43b3a1d67b3857a3
IEDL.DBID M7S
IngestDate Mon Jun 30 09:15:21 EDT 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed false
IsScholarly false
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-a522-94c1740fbb13bfad8a55dbcf15283bb719e6eb7ac736dfabf43b3a1d67b3857a3
Notes SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
OpenAccessLink https://www.proquest.com/docview/2922660542?pq-origsite=%requestingapplication%
PQID 2922660542
PQPubID 2050157
ParticipantIDs proquest_journals_2922660542
PublicationCentury 2000
PublicationDate 20240919
PublicationDateYYYYMMDD 2024-09-19
PublicationDate_xml – month: 09
  year: 2024
  text: 20240919
  day: 19
PublicationDecade 2020
PublicationPlace Ithaca
PublicationPlace_xml – name: Ithaca
PublicationTitle arXiv.org
PublicationYear 2024
Publisher Cornell University Library, arXiv.org
Publisher_xml – name: Cornell University Library, arXiv.org
SSID ssj0002672553
Score 1.883379
SecondaryResourceType preprint
Snippet We describe a version of the FGLM algorithm that can be used to compute generic fibers of positive-dimensional polynomial ideals. It combines the FGLM...
SourceID proquest
SourceType Aggregation Database
SubjectTerms Algorithms
Hoisting
Polynomials
Title Computing Generic Fibers of Polynomial Ideals with FGLM and Hensel Lifting
URI https://www.proquest.com/docview/2922660542
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3LSgMxFA3aKrjyjY9asnA7beeVzKwEpWMrbRm0i7oqNy8YKDN1phb9e5N0qgvBjcsQCCEJNyf3npyD0K1kEZeeko7UcdExilymvhs5hAOLgFENoZU1m6CTSTSbxWmdcKtqWuU2JtpALQpucuRdL9ZAQWPvwLtbvjnGNcpUV2sLjV3UNCoJrqXuvXznWDxCNWL2N8VMK93VhfIjW3dMSaFjhNuDXyHY3ivJ4X9ndISaKSxleYx2ZH6C9i2fk1en6Gnj1qDvJWyFpTOOE8MNqXChcFosPs1vZFjgodBAscImG4uTx9EYQy7wQJpv6niUKTPAGZom_enDwKltExzQYMqJA65fGT3FmOszBSKCMBSMK9fIuDBG3VgSyShw6hOhgKnAZz64glDmRyEF_xw18iKXFwjLWPU4oZyzUAaSUqBSABBFQIkg9OEStbYrM6-PfjX_WZarv7uv0YGnEYIhX7hxCzVW5bu8QXt8vcqqso2a9_1J-ty2O6pb6XCcvn4BfaGtSQ
linkProvider ProQuest
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1LT8JAEJ4gaPTkOz5Q96DHAn1uezAeVAR5hEQO3MjsK2lCClJE-VH-R3cL1YOJNw6em2yane3s15lvvg_gWrKQS0dJS-q8aBlFLtPfDa2AIwuRUQ2hVWY2QbvdcDCIegX4zGdhDK0yz4lZohZjbmrkVSfSQEFjb8-5m7xaxjXKdFdzC43lsWjJxbv-ZUtvmw86vjeOU3_s3zeslauAhRprWJHHNQivKcZslykUIfq-YFzZRuWEMWpHMpCMIqduIBQy5bnMRVsElLmhT9HVy25ASaMIJ8qYgi_fJR0noBqgu8veaaYUVsXpRzyvmA5GxejEe78yfnaN1Xf_2QbsQamHEzndh4JMDmArY6vy9BCel14U-tYlmWx2zEndMF9SMlakNx4tzKw1jkhTaBicElNrJvWndodgIkhDmiF80o6VWeAI-ut4-2MoJuNEngCRkarxgHLOfOlJSpFKgRioAJXwfBdPoZwHYrj6sNPhTxTO_n58BduNfqc9bDe7rXPYcTQWMjQTOypDcTZ9kxewyeezOJ1eZoeIwHDNMfsC6ykIgA
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Computing+Generic+Fibers+of+Polynomial+Ideals+with+FGLM+and+Hensel+Lifting&rft.jtitle=arXiv.org&rft.au=Berthomieu%2C+J%C3%A9r%C3%A9my&rft.au=Mohr%2C+Rafael&rft.date=2024-09-19&rft.pub=Cornell+University+Library%2C+arXiv.org&rft.eissn=2331-8422&rft_id=info:doi/10.48550%2Farxiv.2402.03144