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New sparse multivariate polynomial factorization algorithms over integers. (English) Zbl 07760776

Dickenstein, Alicia (ed.) et al., Proceedings of the 48th international symposium on symbolic and algebraic computation, ISSAC, Tromsø, Norway, July 24–27, 2023. New York, NY: Association for Computing Machinery (ACM). 315-324 (2023).

MSC: 68W30

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Chèze, Guillaume; Combot, Thierry

Symbolic computations of first integrals for polynomial vector fields. (English) Zbl 1485.34006

Found. Comput. Math. 20, No. 4, 681-752 (2020).

Reviewer: Jaume Giné (Lleida)

MSC: 34A05 34C05 68W30 68W40

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Coxon, Nicholas

Fast Hermite interpolation and evaluation over finite fields of characteristic two. (English) Zbl 1444.68301

J. Symb. Comput. 98, 270-283 (2020).

MSC: 68W30 11T06 11T71 11Y16

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Abelard, Simon; Gaudry, Pierrick; Spaenlehauer, Pierre-Jean

Counting points on genus-3 hyperelliptic curves with explicit real multiplication. (English) Zbl 1532.11079

Scheidler, Renate (ed.) et al., ANTS XIII. Proceedings of the thirteenth algorithmic number theory symposium, University of Wisconsin-Madison, WI, USA, July 16–20, 2018. Berkeley, CA: Mathematical Sciences Publishers (MSP). Open Book Ser. 2, 1-19 (2019).

Reviewer: Juan Tena Ayuso (Valladolid)

MSC: 11G20 11M38 11Y16 14H45

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Monagan, Michael

Linear Hensel lifting for \(\mathbb{F}_p[x,y]\) and \(\mathbb{Z}[x]\) with cubic cost. (English) Zbl 1467.12002

Bradford, Russell (ed.), Proceedings of the 44th international symposium on symbolic and algebraic computation, ISSAC ’19, Beijing, China, July 15–18, 2019. New York, NY: Association for Computing Machinery (ACM). 299-306 (2019).

MSC: 12-08 11Y05 11T06 68W30

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Allem, Luiz E.; Capaverde, Juliane G.; van Hoeij, Mark; Szutkoski, Jonas

Functional decomposition using principal subfields. (English) Zbl 1489.12015

Burr, Michael (ed.), Proceedings of the 42nd international symposium on symbolic and algebraic computation, ISSAC 2017, Kaiserslautern, Germany, July 25–28, 2017. New York, NY: Association for Computing Machinery (ACM). 421-428 (2017).

MSC: 12-08 68W30

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Weimann, Martin

Bivariate factorization using a critical fiber. (English) Zbl 1415.13014

Found. Comput. Math. 17, No. 5, 1219-1263 (2017).

MSC: 13P05 12Y05 14H20 14Q05

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Bostan, A.; Jeannerod, C.-P.; Mouilleron, C.; Schost, É.

On matrices with displacement structure: generalized operators and faster algorithms. (English) Zbl 1371.65025

SIAM J. Matrix Anal. Appl. 38, No. 3, 733-775 (2017).

MSC: 65F05 65Y20

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Bostan, Alin; Chèze, Guillaume; Cluzeau, Thomas; Weil, Jacques-Arthur

Efficient algorithms for computing rational first integrals and Darboux polynomials of planar polynomial vector fields. (English) Zbl 1335.34002

Math. Comput. 85, No. 299, 1393-1425 (2016).

MSC: 34A05 68W30 68W40

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Wu, Wenyuan; Chen, Jingwei; Feng, Yong

Sparse bivariate polynomial factorization. (English) Zbl 1327.12005

Sci. China, Math. 57, No. 10, 2123-2142 (2014).

MSC: 12Y05 68W30 11Y16 12E05 13P05

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Chèze, Guillaume

A recombination algorithm for the decomposition of multivariate rational functions. (English) Zbl 1336.12002

Math. Comput. 82, No. 283, 1793-1812 (2013).

MSC: 12Y05 68W30 12D05

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Berthomieu, Jérémy; Lecerf, Grégoire

Reduction of bivariate polynomials from convex-dense to dense, with application to factorizations. (English) Zbl 1271.12006

Math. Comput. 81, No. 279, 1799-1821 (2012).

Reviewer: Luis David Garcia Puente (Huntsville)

MSC: 12Y05 68W30 11Y16 12D05 13P05

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Chèze, Guillaume

Computation of Darboux polynomials and rational first integrals with bounded degree in polynomial time. (English) Zbl 1215.65040

J. Complexity 27, No. 2, 246-262 (2011).

Reviewer: Rémi Vaillancourt (Ottawa)

MSC: 65D20 33E20 33F05

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Weimann, Martin

A lifting and recombination algorithm for rational factorization of sparse polynomials. (English) Zbl 1236.12001

J. Complexity 26, No. 6, 608-628 (2010).

MSC: 12E05 12Y05 65Y20 68Q25

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Bertone, Cristina; Chèze, Guillaume; Galligo, André

Modular Las Vegas algorithms for polynomial absolute factorization. (English) Zbl 1244.12006

J. Symb. Comput. 45, No. 12, 1280-1295 (2010).

Reviewer: David Sevilla (Linz)

MSC: 12Y05 68W30 13P05

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Lecerf, Grégoire

New recombination algorithms for bivariate polynomial factorization based on Hensel lifting. (English) Zbl 1245.12008

Appl. Algebra Eng. Commun. Comput. 21, No. 2, 151-176 (2010).

MSC: 12Y05 68W30 11Y16

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Chen, Jing-wei; Feng, Yong; Qin, Xiao-lin; Zhang, Jing-zhong

Exact polynomial factorization by approximate high degree algebraic numbers. (English) Zbl 1356.68272

Kai, Hiroshi (ed.) et al., Proceedings of the 2009 workshop on symbolic-numeric computation, SNC 2009, Kyoto, Japan, August 3–5, 2009. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-60558-664-9). 21-28 (2009).

MSC: 68W30 11Y05 11Y16 65D15 68Q25

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Belabas, Karim; van Hoeij, Mark; Klüners, Jürgen; Steel, Allan

Factoring polynomials over global fields. (English) Zbl 1254.11116

J. Théor. Nombres Bordx. 21, No. 1, 15-39 (2009).

Reviewer: Michael Pohst (Düsseldorf)

MSC: 11Y40 11Y16 11R09

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Elkadi, M.; Galligo, A.; Weimann, M.

Towards toric absolute factorization. (English) Zbl 1180.14056

J. Symb. Comput. 44, No. 9, 1194-1211 (2009).

Reviewer: Anargyros Katsabekis (Karlovassi)

MSC: 14Q99 14M25

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Durvye, Clémence; Lecerf, Grégoire

A concise proof of the Kronecker polynomial system solver from scratch. (English) Zbl 1134.14317

Expo. Math. 26, No. 2, 101-139 (2008).

MSC: 14Q15 13P10 68W30

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Abu Salem, Fatima K.

An efficient sparse adaptation of the polytope method over \(\mathbb F_q\) and a record-high binary bivariate factorisation. (English) Zbl 1134.11045

J. Symb. Comput. 43, No. 5, 311-341 (2008).

MSC: 11Y16 11T06 68W30 65H99

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Lecerf, Grégoire

Improved dense multivariate polynomial factorization algorithms. (English) Zbl 1127.13021

J. Symb. Comput. 42, No. 4, 477-494 (2007).

Reviewer: Didier Henrion (Toulouse)

MSC: 13P05 68W30

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Chèze, Guillaume; Lecerf, Grégoire

Lifting and recombination techniques for absolute factorization. (English) Zbl 1130.12007

J. Complexity 23, No. 3, 380-420 (2007).

Reviewer: Michael Pohst (Berlin)

MSC: 12Y05 68W30 11Y16 12D05 13P05

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Lecerf, Grégoire

Sharp precision in Hensel lifting for bivariate polynomial factorization. (English) Zbl 1125.12003

Math. Comput. 75, No. 254, 921-933 (2006).

MSC: 12Y05 68W30 11Y16 11Y05 13P05

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Gao, Shuhong; Kaltofen, Erich; Lauder, Alan G. B.

Deterministic distinct-degree factorization of polynomials over finite fields. (English) Zbl 1130.11336

J. Symb. Comput. 38, No. 6, 1461-1470 (2004).

MSC: 11T06 11Y16

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Found 25 Documents (Results 1–25)

New sparse multivariate polynomial factorization algorithms over integers. (English) Zbl 07760776

Symbolic computations of first integrals for polynomial vector fields. (English) Zbl 1485.34006

Fast Hermite interpolation and evaluation over finite fields of characteristic two. (English) Zbl 1444.68301

Counting points on genus-3 hyperelliptic curves with explicit real multiplication. (English) Zbl 1532.11079

Linear Hensel lifting for \(\mathbb{F}_p[x,y]\) and \(\mathbb{Z}[x]\) with cubic cost. (English) Zbl 1467.12002

Functional decomposition using principal subfields. (English) Zbl 1489.12015

Bivariate factorization using a critical fiber. (English) Zbl 1415.13014

On matrices with displacement structure: generalized operators and faster algorithms. (English) Zbl 1371.65025

Efficient algorithms for computing rational first integrals and Darboux polynomials of planar polynomial vector fields. (English) Zbl 1335.34002

Sparse bivariate polynomial factorization. (English) Zbl 1327.12005

A recombination algorithm for the decomposition of multivariate rational functions. (English) Zbl 1336.12002

Reduction of bivariate polynomials from convex-dense to dense, with application to factorizations. (English) Zbl 1271.12006

Computation of Darboux polynomials and rational first integrals with bounded degree in polynomial time. (English) Zbl 1215.65040

A lifting and recombination algorithm for rational factorization of sparse polynomials. (English) Zbl 1236.12001

Modular Las Vegas algorithms for polynomial absolute factorization. (English) Zbl 1244.12006

New recombination algorithms for bivariate polynomial factorization based on Hensel lifting. (English) Zbl 1245.12008

Exact polynomial factorization by approximate high degree algebraic numbers. (English) Zbl 1356.68272

Factoring polynomials over global fields. (English) Zbl 1254.11116

Towards toric absolute factorization. (English) Zbl 1180.14056

A concise proof of the Kronecker polynomial system solver from scratch. (English) Zbl 1134.14317

An efficient sparse adaptation of the polytope method over \(\mathbb F_q\) and a record-high binary bivariate factorisation. (English) Zbl 1134.11045

Improved dense multivariate polynomial factorization algorithms. (English) Zbl 1127.13021

Lifting and recombination techniques for absolute factorization. (English) Zbl 1130.12007

Sharp precision in Hensel lifting for bivariate polynomial factorization. (English) Zbl 1125.12003

Deterministic distinct-degree factorization of polynomials over finite fields. (English) Zbl 1130.11336

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